New Features in Version 4.1

This section is addressed to users of previous versions of QuickField. It contains brief description of new options and capabilities. Since all these features are described later in more details, you can skip this section, if you are new to QuickField.

Command Line

Now you can run QuickField in unattended mode, specifying the list of problems in command line to be solved one by one. You can use Windows system features to schedule problems to be solved at specified time, e.g., at night. To learn more about this feature, see Scheduling QuickField.

Problem Tree

The problem tree, as you normally see it to the left of QuickField window, now incorporates data label trees. You can directly edit material properties and boundary conditions in this view. Furthermore, when you select a label in the problem tree, it becomes highlighted in the model view, and vice versa; giving you the ability to check correspondences between geometric objects and material data assigned to them.

When several problems are loaded at the same time, you can choose to solve all of them, or any subset of them, at once.

Changing problem’s coordinate system (Cartesian or polar) or length units now is immediately reflected in the Model and Postprocessor views.

Creation of a new problem is now done through a wizard, allowing you to choose correct problem parameters (the kind of analysis, class of symmetry, coordinates, length units, etc.) while the problem is created.

Model Editor

•	The ‘Smart Grid’ mode changes grid size according to your zooming actions.

•	Creating new vertices and edges with mouse is now more convenient and safe.

•	You can select geometric objects by their labels.

Postprocessor

•	Now draws field pictures faster.

•	New postprocessor window inherits previous window’s setting, including the contour.

•	The state of the window can be saved to a file for restoring in latter sessions (just as it was in version 3.4).

•	You can switch between color and gray-scale pictures to prepare reports for color or monochrome printers.

•	Docking window for local values:

•	highlights the quantity shown with the color map;

•	allows in-place editing of point’s of interest coordinates (Cartesian or polar);

•	has its own context menu, providing fast access to several controls in Field Picture dialog.

•	Docking legend window:

•	allows to manipulate the fill range;

•	provides selection of curves shown in X-Y plot;

•	has its own context menu;

•	can be copied to Clipboard.

•	Force and torque integrals can now be calculated for stress analysis problem.

•	Tables can be saved as text files.

•	A special table containing field quantities calculated in nodes of rectangular grid can be saved to file in text or binary format.


What is QuickField?

Welcome to QuickField Finite Elements Analysis System. QuickField is an interactive environment for electromagnetic, thermal and stress analysis. Standard analysis types include:

Linear and nonlinear magnetostatics.

Time-harmonic magnetics (involving eddy current analysis).

Electrostatics.

Distribution of electric currents.

Linear and nonlinear heat transfer and diffusion.

Linear stress analysis.

Coupled problems.

During a 15-minute session, you can describe the problem (geometry, material properties, sources and other conditions), obtain solution with high accuracy and analyze field details looking through full color picture. With QuickField, complicated field problems can be solved on a PC with very moderate resources.


Basic organization of QuickField

In QuickField, you work with several types of documents: problems, geometry models, material libraries and so on. Each document is opened into a separate window within the main application window of QuickField. You can open any number of documents at once. When switching between windows, you switch from one document to another. Only one document and one window are active at a time, so you can edit the active document. Editing actions are listed in the menu residing on the top of main window of QuickField. Menu contents are different for different document types. You can also use context-specific menus, which are available by right-button mouse click on specific items in document window.

The QuickField documents are:

Problem corresponds to specific physical problem solved by QuickField. This document stores the general problem parameters, such as the type of analysis (“Electrostatics”, “Magnetostatics”, “Heat transfer” and etc.) or the model type (planar or axisymmetric). Click [image] for details.

Geometric Model is a complete description of the geometry, the part labels and the mesh of your model. Several problems may share the same model (this is particularly useful for coupling analysis). Click [image] for details.

Property Description, or Data, documents are specific to types of analysis (Electrostatics data, Stress Analysis data, etc.) These documents store the values of material properties, loadings and boundary conditions for different part labels. Data documents can be used as material libraries for many different problems. Click [image] for details.

For the problem to be solved and analyzed, it must reference the model and data documents. For convenience, the problem can reference two data documents at once: one document containing properties for commonly used materials (material library), and another document containing data specific for the problem or group of problems.

Between sessions, QuickField documents are stored in disk files, separate file for each document. During the session, you can create new documents or open existing ones.

Using this very flexible architecture, QuickField helps you build and analyze your design problems very quickly. In analyzing a problem, the typical sequence of phases that you go through with QuickField is depicted in the flowchart below:


Window management tips

QuickField is a Multiple Documents Interface (MDI) application, so you can work with several QuickField documents (problem descriptions, geometry models, data sets, etc.) at once. Dealing with specific documents will be discussed later in dedicated chapters, and now let’s discuss general principles of creating new documents, opening existing ones, switching between them and so on.

To create a new, empty QuickField document, you can:

•	Launch QuickField from your Start menu, and then click New in the QuickField’s File menu or use correspondent icon on QuickField toolbar. The dialog box appears asking you, which kind of QuickField document you want to create; or

•	Click right mouse button on your desktop (screen region not occupied by any application), and choose the kind of document in the context menu (thus creating the document on the desktop); or

•	Use Windows Explorer to select specific directory where you want new document to be created, and click New in the main menu or context menu of Explorer.

To open an existing QuickField document, you can:

•	Double-click it in Windows Explorer or any file management utility; or

•	While QuickField is running, click Open in the QuickField’s File menu or click Open tool on QuickField’s toolbar; or

•	Drag the document’s icon from Explorer to any part of the QuickField window.

To close the document, click Close in the File menu, or click Close icon on the document’s window frame. If the document has been changed since last save, you will be asked to save the changes to file.

To switch between windows within QuickField, press CTRL+TAB or click on any visible part of the window you want to switch to.

Once the document is open, its window can be minimized to an icon, maximized to the full size of QuickField window, or brought to ‘normal’ size, which you can change by dragging the window’s corners. This is particularly useful when you want to see several documents at once. Also you can automatically arrange all non-minimized windows side-by-side by clicking Tile Horizontally or Tile Vertically in the Window menu.


Magnetostatic analysis overview
Magnetostatic analysis

Magnetic analysis is used to design or analyze variety of devices such as solenoids, electric motors, magnetic shields, permanent magnets, magnetic disk drives, and so forth. Generally the quantities of interest in magnetostatic analysis are magnetic flux density, field intensity, forces, torques, inductance, and flux linkage.

QuickField can perform linear and nonlinear magnetostatic analysis for 2-D and axisymmetric models. The program is based on a vector potential formulation. Following options are available for magnetic analysis:

Material properties: air, orthotropic materials with constant permeability, ferromagnets, current carrying conductors, and permanent magnets. B-H curves for ferromagnets can easily be defined through a curve editor.

Loading sources: current density, uniform external field and permanent magnets.

Boundary conditions: Prescribed potential values (Dirichlet condition), prescribed values for tangential flux density (Neumann condition), constant potential constraint for zero normal flux conditions on the surface of superconductor.

Postprocessing results: magnetic potential, flux density, field intensity, forces, torques, magnetic energy, flux linkage, self and mutual inductances.

Special features: A postprocessing calculator is available for evaluating user-defined integrals on given curves and surfaces. The magnetic forces can be used for stress analysis on any existing part (magneto-structural coupling).

Related Topics

Magnetostatic formulations in Theoretical Description


Time-harmonic electromagnetic analysis overview
Time-harmonic electromagnetic analysis

Time-harmonic electromagnetic analysis is used to analyze magnetic field caused by alternating currents and, vise versa, electric currents induced by alternating magnetic field (eddy currents). This kind of analysis is useful for designing inductor devices, solenoids, electric motors, and so forth. Generally the quantities of interest in harmonic magnetic analysis are electric current (and its source and induced component), voltage, generated Joule heat, magnetic flux density, field intensity, forces, torques, impedance and inductance.

Following options are available for harmonic magnetic analysis:

Material properties: air, orthotropic materials with constant permeability, current-carrying conductors with known current or voltage.

Loading sources: voltage, total current, current density or uniform external field.

Boundary conditions: Prescribed potential values (Dirichlet condition), prescribed values for tangential flux density (Neumann condition), constant potential constraint for zero normal flux conditions on the surface of superconductor.

Postprocessing results: magnetic potential, current density, voltage, flux density, field intensity, forces, torques, Joule heat, magnetic energy, impedances, self and mutual inductances.

Special features: A postprocessing calculator is available for evaluating user-defined integrals on given curves and surfaces. The magnetic forces can be used for stress analysis on any existing part (magneto-structural coupling); and power losses can be used as heat sources for thermal analysis (electro-thermal coupling).

Related Topics

Time-harmonic magnetics in Theoretical Description


Electrostatic analysis overview
Electrostatic analysis

Electrostatic analysis is used to design or analyze variety of capacitive systems such as fuses, transmission lines and so forth. Generally the quantities of interest in electrostatic analysis are voltages, electric fields, capacitances, and electric forces.

QuickField can perform linear electrostatic analysis for 2-D and axisymmetric models. The program is based on Poisson's equation. Following options are available for electrostatic analysis:

Material properties: air, orthotropic materials with constant permittivity.

Loading sources: Voltages, and electric charge density.

Boundary conditions: Prescribed potential values (Voltages), prescribed values for normal derivatives (surface charges), and prescribed constraints for constant potential boundaries with given total charges.

Postprocessing results: voltages, electric fields, gradients of electric field, flux densities (electric displacements), surface charges, self and mutual capacitances, forces, torques, and electric energy.

Special features: A postprocessing calculator is available for evaluating user-defined integrals on given curves and surfaces. Floating conductors with unknown voltages and given charges can be modeled. The electrostatic forces can be used for stresses on any existing part (electro-structural coupling).

Related Topics

Electrostatic formulations in Theoretical Description


Current flow analysis overview
Current flow analysis

Current flow analysis is used to analyze variety of conductive systems. Generally the quantities of interest in current flow analysis are voltages, current densities, electric power losses (Joule heat).

QuickField can perform linear current flow analysis for 2-D and axisymmetric models. The program is based on Poisson's equation. Following options are available for current flow analysis:

Material properties: orthotropic materials with constant resistivity.

Loading sources: Voltages, electric current density.

Boundary conditions: Prescribed potential values (voltages), prescribed values for normal derivatives (surface current densities), and prescribed constraints for constant potential boundaries.

Postprocessing results: voltages, current densities, electric fields, electric current through a surface, and power losses.

Special features: A postprocessing calculator is available for evaluating user-defined integrals on given curves and surfaces. The electric power losses can be used as heat sources for thermal analysis (electro-thermal coupling).

Related Topics

Current flow formulations in Theoretical Description


Thermal analysis overview
Thermal analysis

Thermal analysis plays an important role in design of many different mechanical and electrical systems. Generally the quantities of interest in thermal analysis are temperature distribution, thermal gradients, and heat losses.

QuickField can perform linear and nonlinear thermal analysis for 2-D and axisymmetric models. The program is based on heat conduction equation with convection and radiation boundary conditions. Following options are available for thermal analysis:

Material properties: orthotropic materials with constant thermal conductivity, isotropic temperature dependent conductivities.

Loading sources: constant and temperature dependent volume heat densities, convective and radiative sources, Joule heat sources imported from current flow analysis.

Boundary conditions: Prescribed temperatures, boundary heat flows, convection, radiation, and prescribed constraints for constant temperature boundaries.

Postprocessing results: temperatures, thermal gradients, heat flux densities, and total heat losses or gains on a given part.

Special features: A postprocessing calculator is available for evaluating user-defined integrals on given curves and surfaces. Plate models with varying thickness can be used for thermal analysis. The temperatures can be used for thermal stress analysis (thermo-structural coupling).

Related Topics

Heat transfer in Theoretical Description


Stress analysis overview
Stress analysis

Stress analysis plays an important role in design of many different mechanical and electrical components. Generally the quantities of interest in stress analysis are displacements, strains and different components of stresses.

QuickField can perform linear stress analysis for 2-D plane stress, plane strain, and axisymmetric models. The program is based on Navier equations of elasticity. Following options are available for stress analysis:

Material properties: isotropic and orthotropic materials.

Loading sources: concentrated loads, body forces, pressure, thermal strains, and imported electric or magnetic forces from electrostatic or magnetostatic analysis.

Boundary conditions: prescribed displacements, elastic spring supports.

Postprocessing results: displacements, stress components, principal stresses, von Mises stress, Tresca, Mohr-Coulomb, Drucker-Prager, and Hill criteria.

Related Topics

Stress analysis in Theoretical Description


Property description documents
Structure of problem database

A special database is built for each problem solved with QuickField. The core of the database is the problem description, which is stored in file with the extension .pbm. The problem description contains the basics of the problem: its subject, the plane, the precision class, etc., and also references to all other files, which constitute the problem database. These files are the model file, with standard extension .mod, and physical data (property description) files, with extension .dms, .dhe, .des, .dcf, .dht, or .dsa, depending on the subject of the problem.

The problem description may refer to one or two files of physical data. Both files have the same format, and differ only in purpose. Usually, the first data file contains specific data related to the problem, as the second file is a library of standard material properties and boundary conditions, which are common for a whole class of problems.

Depending on the problem type, you may share a single model file or a single data file between several similar problems.

While solving the problem, QuickField creates one more file—the file of results with the .res extension. This file always has the same name as the problem description file, and is stored in the same folder.

•	To create a new, empty problem description, click New in the File menu and then select QuickField problem in the list that appears. Then enter the name and path of the new problem, and select new problem’s parameters: kind of analysis, plane, precision, length units, etc.

•	To open an existing document, click Open in the File menu, or use drag and drop features of Windows.

Related Topics

The problem editor


The problem editor

In problem view, you can edit problem description options, as well as material properties, field sources and boundary conditions. The tree shows the names of files, referenced by the problem. Data and library data tree branches contains label lists, assigned to blocks, edges and vertices.

0	Icons displayed by the labels mean:

	Block label with specified material properties
	Edge label with specified boundary condition
	Vertex label with specified boundary condition or source
	Label referenced in models not yet given the properties
	Empty block label excluded from consideration
	Label with default boundary condition and zero source
•	To start editing the model, or another problem referenced as coupling link, double-click its name in the tree, or click Edit File in the context menu, or click correspondent item in Edit menu.

•	To solve the problem, click Solve Problem in the Edit menu or context (right mouse button) menu.

•	To analyze the results, click View Results in the Edit menu or context menu.

How to…

Change problem properties

Create a label

Edit label properties

Rename a label

Delete a label

Duplicate a label

Move label to other location

Related Topics

The problem database

Editing problem properties


Selecting the name and the folder for the new problem

Problem file name

Type the name for the new problem. The extension will be added automatically.

Create in folder

Type the folder path, or click Browse to search for the folder.


Editing problem description properties

Problem type

Select the type of analysis, which your problem belongs to.

Model class

Select the geometry class of your model: plane or axisymmetric.

Precision

Select the precision you need. Note that higher precision leads to longer solution time.

Formulation

Select the formulation of planar stress analysis problem. Refer to Theoretical description for details.

Frequency

Type the value of frequency for the time-harmonic magnetics problem. Note the difference between frequency f and angular frequency ω: ω = 2πf.

Files

Edit the file names of your model and data files. You may use long file names. If the name is given without the full path, it is assumed with respect to the problem description file. You can also click Browse to select file in any folder on your hard disk or the network.

Open

Instantly loads selected file into the new QuickField window.


Establishing coupling links

To add a data link:

1	Select the type of the data in the Data Type pull-down list box;

2	Type a name of the source problem in the Problem text box, or click Browse button to make the selection in the list of existing problems;

3	And, click Add button to add the link to the list of data sources.

To change a data link:

1	Select the link of choice in the Data Sources list box;

2	Change the source problem name as necessary;

3	And, click Update button to update the link in the list of data sources.

To delete a link:

1	Select the link of choice in the Data Sources list box;

2	And, click Delete button to delete the link from the list of data sources, or use the Delete All button to delete all data links at once.

Related Topics

Coupled problems in Theoretical Description


Choosing length units and coordinate system
Choosing length units

QuickField allows you to use various units for coordinates when creating model's geometry. You can use microns, millimeters, centimeters, meters, kilometers, inches, feet, or miles.

Chosen units are associated with each particular problem, which gives you freedom to use different units for different problems. Usually units of length are chosen before creating the model geometry. It is possible to change units of length later, but it does not affect physical dimensions of the model. So, if you create your geometry as a square with 1 m side and then switch to centimeters, you will get a square measured 100 cm by 100 cm, which is the same as it was before. To actually change size of the model you should rather use Scaling option of the Move Selected command of the Model Editor.

The choice of length units does not affect units for other physical parameters, which always use standard SI units. The only physical quantity that is measured in chosen units of length, is the displacement vector in stress analysis problems.

Cartesian vs. polar coordinates

Problem geometry as well as material properties and boundary conditions can be defined in Cartesian or polar coordinate systems. There are several places in QuickField where you can make choice between Cartesian and polar coordinate systems. Using Coordinates tab in Problem Properties dialog, you can define the default coordinate system associated with a problem. Definition of orthotropic material properties, some loads and boundary conditions depends on the choice of the coordinate system. You can choose Cartesian or polar coordinate system for each element of data individually and independently from the default coordinate system associated with the problem. This choice is available in the dialog boxes of the Data Editor.


Solving the problem

To solve a problem, several conditions have to be met: the problem type, plane, required precision and other parameters have to be specified in the problem description. The model document must contain complete model with mesh and labels. Each label referred by the model is to be defined in the problem's property description documents.

To obtain the problem solution, click Solve Problem in the Edit menu or context (right mouse button) menu of the Problem editor. You may skip this action and directly proceed to the analysis results by clicking Analyze Results in the Edit or context menu. If the problem has not been solved yet, or its results are out of date, the solver will be invoked automatically.

You can also solve several problems one after another in unattended mode. Click Batch Solve in the Edit menu, and then select the problems you want to be solved in the list of all open problems. Unlike the previously described solving mode, when you can continue editing models, data and analyzing the results, in batch mode all the QuickField windows are suspended.

See also Scheduling QuickField for solving at specified time.

While the solver is running, special bar indicator lets you see the progress of the solution process. Linear problems are solved by using a powerful preconditioned conjugate gradients method. The preconditioning based on the geometric decomposition technique guaranties a very high speed and close to linear dependence between number of nodes and the resulting solution time. Nonlinear problems are solved using the Newton-Raphson method. The Jacobian matrix arising at each step of the Newton-Raphson method is inverted the same way as it is done for linear problems.


Achieving maximum performance

The algorithm used in QuickField solver does not require the whole data of the problem to fit into RAM of your computer. The solver can effectively handle linear algebraic systems with matrices several times bigger than the amount of available physical memory. Data that don’t fit into memory are stored on the hard disk, and highly optimized access mechanism is used to retrieve these data when needed. The size of the problem you can solve on your computer is only limited by the amount of free disk space. Disk space consumption is very low compared to other FEA packages, only about 1.3 MB per ten thousand degrees of freedom.

Although size of the problem is not limited by the amount of available RAM, having additional memory may improve performance. Obviously the performance is at the highest when all the data can be stored in memory and relatively slow disk access is not used during solution. The following table gives you some rough estimation on how big a problem can be to fit completely into memory of your computer.

	Amount of RAM
	4 MB	8 MB	16 MB
All classes of problems except Stress Analysis	29000 nodes	53000 nodes	100000 nodes
Stress Analysis problems	12500 nodes	24000 nodes	46000 nodes

Again, above numbers do not mean that you cannot solve larger problems. Yes, you can, and it will still be much faster than the majority of other FEA packages.


Scheduling QuickField
Scheduling QuickField for solving problems at a certain time

You can use QuickField command-line switch /Solve to run QuickField in unattended mode for solving a set of problems. For example, you can issue the following command from your Command Prompt (DOS Prompt in Windows 95 terminology):

>"C:\Program Files\QuickField\QField.exe" /Solve "C:\My Problems\Magn*.pbm"

Please note the use of double quotation marks around the pathnames with spaces. The list of arguments may contain several items, with optional wildcards (*) in it.

There are several ways to schedule an application to run at specified time with specific set of parameters. The most convenient seems to be the Task Scheduler supplied with Microsoft Internet Explorer 4.0. (If you have not installed the Task Scheduler, you can click Product Updates in Help menu of the Internet Explorer, and follow instructions on the screen to install it).

To schedule QuickField:

1	Double-click My Computer on the desktop, open the Scheduled Tasks folder and double-click the Add Scheduled Task icon. The Scheduled Task Wizard appears.

2	Follow the wizard’s instructions to run QuickField once at specified time, and choose to open advanced properties of the task before clicking Finish on the last wizard’s page.

3	After the wizard completes, the task properties dialog will appear. In its Run box, add the /Solve switch and the list of problems you wish to be solved.

If you have no Task Scheduler, you still can schedule QuickField. In Windows NT, you can use the at command, or the System Agent that comes with Microsoft Plus! for Windows 95. See Windows Help for details how to use these utilities.


Solving in batch mode

In the Problems to Solve list, check or uncheck the problems you want to solve at once, and then click Solve. Unlike normal solving procedure, the batch mode suspends all the QuickField editor windows.


Property description documents

Property description is a kind of QuickField document containing material properties, field sources and boundary conditions for specific problem or group of problems. The document consists of labels divided into three groups:

•	block labels describe material properties and loads for subregions of the model;

•	edge labels assign specific boundary conditions to your model’s boundaries;

•	vertex labels describe singular sources or constraints applied to points of your model.

Property description documents are specific to types of analysis. Each document occupies separate QuickField window and is stored in a separate disk file. File extensions are also specific to disciplines:

Kind of analysis	File extension
Magnetostatics	.dms
Time-harmonic magnetics	.dhe
Electrostatics	.des
Current flow	.dcf
Heat transfer	.dht
Stress analysis	.dsa
Normally, you edit these properties in Problem Editor view, but you can open separate window for property description, if, for example, you want to enter data to the material library.

•	To create a new property description, click New in the File menu and then select appropriate type of document in the list that appears.

•	To open existing document, click Open in the File menu, or use drag and drop features of Windows, or, while working with problem description, double-click the name of associated property description file.

Related Topics

Editing material properties


Editing material properties
Editing material properties and boundary conditions

In property description view, you assign material properties, field sources and boundary conditions to labeled geometrical objects. The tree shows labels assigned to blocks, edges and vertices.

Icons displayed by the labels mean:

	Block label with specified material properties
	Edge label with specified boundary condition
	Vertex label with specified boundary condition or source
	Label referenced in models not yet given the properties
	Empty block label excluded from consideration
	Label with default boundary condition and zero source
How to…

Create a label

Edit label properties

Rename a label

Delete a label

Duplicate a label

Move label to other location

Related Topics

What is property description

Assigning labels to geometrical objects in Model Editor


Creating new label
Create a new label

1	In the Insert menu, click Block Label or Edge Label or Node Label, or go to correspondent group of labels in the tree and click New Label in the context (right mouse button) menu.

2	New label will appear in the list prompting you to give it the name you want.

3	Just type the label’s name you wish and press ENTER.

Shortcut: INS


Editing label properties
Edit label properties

•	In the list, double-click the label you want to edit.

•	Or, select the label with right mouse button and click Properties in the context menu.

•	Or, select the label and click Properties in the Edit menu.

Shortcut: ALT+ENTER


Renaming label
Rename label

•	In the list, select the label and then click it again after a pause (to avoid double-click effect).

•	Or, select the label with right mouse button and click Rename in the context menu.

•	Or, select the label and click Rename in the Edit menu.


Deleting label
Delete label

•	In the list, select the label with right mouse button and click Delete in the context menu.

•	Or, select the label and click Delete in the Edit menu.

Shortcut: DEL


Copying label
Copy label

Labels can be copied within single property description document or between documents of the same type.

1	In the list, select the label you want to copy with right mouse button and click Copy in the context menu.

2	Switch to destination window and click Paste in the Edit menu or context menu.

Or,

1	Drag the label to destination position with the mouse.

Shortcut: CTRL+INS, SHIFT+INS


Moving label
Move (Cut and Paste) label

1	In the list, select the label you want to move with right mouse button and click Cut in the context menu.

2	Switch to destination window and click Paste in the Edit menu or context menu.

Or,

1	Drag the label to destination position with the mouse holding down the SHIFT key.

Shortcut: SHIFT+DEL, SHIFT+INS


Electric Permittivity

Enter components of permittivity tensor here, or leave None or blank to specify that the block with the corresponding label is excluded. To define two different components, first check the Anisotropic box. Choose Relative or Absolute to specify absolute values of permittivity or relative to permittivity of vacuum.

Electric Charge Density

Enter the value of distributed charge density here.

Coordinates

Have sense for anisotropic dielectrics or compound (laminated) materials modeled as anisotropic. Specify Cartesian or Polar according to the class of symmetry of anisotropy.

Related Topics

Formulations

Field sources


Voltage

To specify Dirichlet boundary condition (known voltage), check this box and enter value of voltage. It may be specified as linear function of Cartesian coordinates.

Surface Charge

To specify a Neumann boundary condition (surface charge), check the box and enter charge value.

Floating Conductor

Check this box to specify the edge (group of edges), as a floating conductorvoltage is equal but not a priori known.

Related Topics

Formulations

Field sources

Boundary conditions


Voltage

To specify Dirichlet boundary condition (known voltage), check this box and enter the value of voltage.

Electric Charge

To specify concentrated charge, check the box and enter the charge value.

Related Topics

Formulations

Field sources

Boundary conditions


Permeability

Enter components of permeability tensor here, or leave None or blank to specify that the block with the corresponding label is excluded. To define two different components, first check the Anisotropic box. Choose Relative or Absolute to specify absolute values of permeability or relative to permeability of vacuum. With nonlinear materials, you need to define the magnetization curve, instead of magnetic permeability. Check the Nonlinear box to get into the B-H curve editor. If a B-H curve had already been defined, you would see a B-H Curve button that can be clicked to get into the curve editor.

Current Density

Enter the value of distributed current density here.

Coercive Force of Magnet

Enter the magnitude and direction in degrees for the coercive force. To specify linear or circular magnetization, select Cartesian or Polar coordinates respectively.

Coordinates

Have sense for permanent magnets and anisotropic magnetics (also compound or laminated materials modeled as anisotropic). Specify Cartesian or Polar according to the class of symmetry of anisotropy and/or magnetization.

Related Topics

Formulations

Field sources


Magnetic Potential

To specify Dirichlet boundary condition (known magnetic potential), check this box and enter the value of potential. It may be specified as linear function of Cartesian coordinates.

Tangential Field

To specify Neumann boundary condition (surface current), check the box and enter the surface current density value.

Zero Normal Flux

Check this box to specify the edge (group of edges) as a boundary not penetrated by magnetic fieldmagnetic potential (flux function in axisymmetric case) is equal but not a priori known.

Related Topics

Formulations

Field sources

Boundary conditions


Magnetic Potential

To specify Dirichlet boundary condition (known potential), check this box and enter the value of potential.

Linear Current

To specify concentrated current, check the box and enter current value.

Related Topics

Formulations

Field sources

Boundary conditions


Permeability

Enter components of permeability tensor here, or leave None or blank to specify that the block with the corresponding label is excluded. To define two different components, first check the Anisotropic box. Choose Relative or Absolute to specify absolute values of permeability or relative to permeability of vacuum.

Conductivity

Enter the value of conductivity here or leave zero for non conductive material.

Field Source

Specify the kind of source (current density or total current for areas with negligible skin effect, and total current or voltage for real conductors) and magnitude and phase of the source.

Coordinates

Have sense for anisotropic magnetics or compound (laminated) materials modeled as anisotropic. Specify Cartesian or Polar according to the class of symmetry of anisotropy.

Related Topics

Formulations

Field sources


Magnetic Potential

To specify Dirichlet boundary condition (known magnetic potential), check this box and enter magnitude of potential and its phase. Magnitude may be specified as a linear function of Cartesian coordinates.

Tangential Field

To specify Neumann boundary condition (surface current), check the box and enter surface current density magnitude and phase.

Zero Normal Flux

Check this box to specify the edge (group of edges) as a boundary not penetrated by magnetic fieldmagnetic potential (flux function in axisymmetric case) is equal but not a priori known.

Related Topics

Formulations

Field sources

Boundary conditions


Magnetic Potential

To specify Dirichlet boundary condition (known potential), check this box and enter the magnitude of potential and its phase.

Linear Current

To specify concentrated current, check the box and enter magnitude and potential of the current.

Related Topics

Formulations

Field sources

Boundary conditions


Electric Resistivity

Enter components of resistivity tensor here, or leave None or blank to specify that the block with the corresponding label is excluded. To define two different components, first check the Anisotropic box.

Coordinates

Have sense for anisotropic conductors or compound (laminated) conductors modeled as anisotropic. Specify Cartesian or Polar according to the class of symmetry of anisotropy.

Related Topics

Formulations

Field sources


Voltage

To specify Dirichlet boundary condition (known voltage), check this box and enter value of voltage. It may be specified as linear function of Cartesian coordinates.

Normal Current Density

To specify Neumann boundary condition, check the box and enter current density value.

Superconductor

Check this box to specify the edge (group of edges) as a superconductorvoltage is equal but not a priori known.

Related Topics

Formulations

Field sources

Boundary conditions


Voltage

To specify Dirichlet boundary condition (known voltage), check this box and enter value of voltage.

External Current

To specify source of external current, check the box and enter current value.

Related Topics

Formulations

Field sources

Boundary conditions


Thermal Conductivity

Enter components of conductivity tensor here, or leave None or blank to specify that the block with the corresponding label is excluded. To define two different components, first check the Anisotropic box. With nonlinear materials, you need to define the dependency curve instead of component values. Check the Nonlinear box to get into the curve editor. If the curve had already been defined, you would see a button that can be clicked to get into the curve editor.

Volume Power of Heat Source

Enter the value or check Function of Temperature to enter the dependency curve. If the curve had already been defined, you would see a button that can be clicked to get into the curve editor.

Coordinates

Have sense for anisotropic linear materials or compound (laminated) materials modeled as anisotropic. Specify Cartesian or Polar according to the class of symmetry of anisotropy.

Related Topics

Formulations

Field sources


Temperature

To specify boundary condition of the first kind (known temperature), check this box and enter value of temperature. It may be specified as linear function of Cartesian coordinates.

Heat Flux

To specify boundary condition of the second kind (heat flux), check the box and enter flux value.

Convection

To specify convection boundary condition, check the box and enter values of film coefficient and temperature of contacting medium.

Radiation

To specify radiation boundary condition, check the box and enter values of emissivity coefficient and ambient radiation temperature.

Equal Temperature

Check this box to specify the edge (group of edges) as having equal, but not a priori known temperature.

Related Topics

Formulations

Field sources

Boundary conditions


Temperature

To specify known temperature, check this box and enter its value.

Heat Source

To specify concentrated heat source, check the box and enter source value.

Related Topics

Formulations

Field sources

Boundary conditions


On this page, enter components of elasticity tensor: Young’s moduli, Poisson’s ratios and shear modulus. Leave None or blank in any Young’s moduli box to specify that the block with the corresponding label is excluded. With isotropic material, only two components of a tensor are independent. To define orthotropic properties, first check the Anisotropic box.

Coordinates

Have sense for anisotropic materials or compound (sliced) materials modeled as orthotropic. Specify Cartesian or Polar according to the class of symmetry of anisotropy.

Related Topics

Displacement, Strain and Stress


Thermal Strain

Enter coefficients of thermal expansion here. To define variant coefficients in different directions, first check the Anisotropic box. Normally, you specify also the temperature difference between strained and strainless states. With coupled problems, where the temperature of strained state is obtained from thermal analysis, you should specify the temperature of unstrained state.

Body Force

Enter components of body force density here. Both components can be issued as linear function of coordinates.

Coordinates

Specify Cartesian or Polar according to the class of symmetry of anisotropy of thermal expansion or body force.

Related Topics

Thermal strain

External forces


Allowable stresses are only used in postprocessing stage to calculate the Mohr-Coulomb, Drucker-Prager, and Hill criteria. You don't need to define allowable stresses, if these criteria are of no interest to you. To define different components, first check the Anisotropic box.

Coordinates

Have sense for orthotropic materials. Specify Cartesian or Polar according to the class of symmetry of anisotropy.

Related Topics

Calculated physical quantities


Fixed Displacement

Specifies constraints along one or both coordinate axes. To apply fixed displacement along an axis, check the appropriate box and then enter a value of displacement as linear function of Cartesian coordinates.

Normal Pressure

The loading may be specified as linear function of coordinates.

Surface Force

Specify surface force density vector components.

Coordinates

Specify Cartesian or Polar according to the class of symmetry of applied boundary condition(s).

Related Topics

Restriction conditions

External forces


Rigid Constraint

To describe rigid constraint along some axis, check the appropriate box, and then enter the value of fixed displacement.

External Force

Specify concentrated force components here.

Elastic Support

Enter predetermined displacement and the support elasticity in one or both coordinate directions here.

Related Topics

Restriction conditions

External forces


Editing the curves

Curve functions, which describe some field dependent parameters, are implemented as tables containing two columns: an argument and a function, e.g., magnetic field intensity and flux density or temperature and thermal conductivity. Editing the table is supported with graphical presentation of the dependency, which is interpolated with cubic spline between the entered points. The solver uses the same curve as you see on your screen.

To add the new point to the dependency, type in two values and press ENTER key or click Add button. If the argument of a new point coincides with the argument of existing one, new point replaces the old one.

To remove the point, select it in the table or in the graph and click Delete button or press the DEL key.

You may control the scaling of the graph with use of Zoom In or Zoom Out buttons or selecting rectangular area in the graph.

To exit from editing the curve, click Close button or press ESC. Note that subsequent canceling of label data editing with ESC key or the Cancel button will discard all changes in the curve editing.


Theoretical description

QuickField solves 2D boundary value problems for elliptic partial differential equation for either scalar or one-component vector potential. It also solves 2D solid stress analysis problems (plane stress, plane strain, axisymmetric stress). There are three main classes of 2D problems: plane, plane-parallel and axisymmetric. Plane problems usually arise when describing heat transfer processes in thin plates. They are solved in planar rectangular coordinate system. Plane-parallel problems use right-handed Cartesian coordinate system xyz. It is assumed that neither geometric shape and properties of material nor field sources vary in z-direction. The problem is described, solved and the results are analyzed in xy-plane, which we will call the plane of model. Axisymmetric problems are formulated in cylindrical coordinate system zrθ. The order of axes is chosen for conformity with the plane-parallel case. Physical properties and field sources are assumed to not depend on the angle coordinate. All operations with the model are done in zr-plane (more precise in a half plane r ≥ 0). Z-axis is assumed to be horizontal and directed to the right, r-axis is directed up.

The geometric configuration of the problem is defined as a set of curved polygonal subregions in the plane of model. Each region corresponds to a domain with a particular set of physical properties. We will use term blocks for polygonal subregions, term edges for line segments and circular arcs that constitute their boundaries and term vertices for ends of edges and for isolated points. Those edges that separate whole problem region from other part of the plane, where no field is calculated, constitutes the outward boundary of the region. Other edges constitute inner boundaries.


Magnetostatic formulations

QuickField can solve both linear and nonlinear magnetic problems. Magnetic field may be induced by the concentrated or distributed currents, permanent magnets or external magnetic fields.

The magnetic problem is formulated as the Poisson's equation for vector magnetic potential A (B = curl A, B—magnetic flux density vector). The flux density is assumed to lie in the plane of model (xy or zr), while the vector of electric current density j and the vector potential A are orthogonal to it. Only jz and Az in planar or jθ and Aθ in axisymmetric case are not equal to zero. We will denote them simply j and A. The equation for planar case is

and for axisymmetric case is

where components of magnetic permeability tensor μx and μy (μz and μr), components of coercive force vector Hcx and Hcy (Hcz and Hcr), and current density j are constants within each block of the model.

Note. Isotropic (μx = μy or μz = μr) but field dependent permeability is assumed in nonlinear case. Magnetization characteristic of material is described by the B-H curve.


Field sources in magnetostatics

The field sources can be specified in blocks, at the edges or at the individual vertices of the model. Possible field sources include space, surface and linear electric currents and permanent magnets. The coercive force is chosen to be primary characteristic for the permanent magnets.

A point source in the xy-plane describes a linear current in out-of-plane direction. In axisymmetric case the point source represents the current in a thin ring around the axis of symmetry. Edge-bound source in the plane of model represents a surface current in three-dimensional world. It is specified by the Neumann boundary conditions for the edge. The space current is described by the electric current density associated with the block. Current density in a coil can be obtained from the equation

where n is a number of turns, I is a total current, and S is a cross-sectional area of the coil.


Boundary conditions in magnetostatics

The following boundary conditions can be specified at outward and inner boundaries of the region.

Dirichlet condition specifies a known value of vector magnetic potential A0 at the vertex or at the edge of the model. This boundary condition defines normal component of the flux density vector. It is often used to specify vanishing value of this component, for example at the axis of symmetry or at the distant boundary. QuickField also supports the Dirichlet condition with a function of coordinates, it has the form

 for planar problems;

 for axisymmetric problems.

Parameters a, b and c are constants for each edge, but can vary from one piece of the boundary to another. This approach allows you to model an uniform external field by specifying non zero normal component of the flux density at arbitrary straight boundary segment.

Let  be an elevation angle of the segment relative to the horizontal axis (x in planar or z in axisymmetric case). Then in both plane and axisymmetric cases the normal flux density is

.

Here we assume right-hand direction of positive normal vector.

Choice of constant terms a for different edges has to satisfy the continuity conditions for function A0 at all edges' junction points.

Note. For problem to be defined correctly the Dirichlet condition has to be specified at least at one point. If the region consists of two or more disjoint subregions, the Dirichlet conditions have to be specified at least at one point of the each part. Zero Dirichlet condition is defaulted at the axis of rotation for the axisymmetric problems.

Neumann condition has the following form

 at outward boundaries,

 at inner boundaries,

where Ht is a tangent component of magnetic field intensity, "+" and "–" superscripts denote quantities to the left and to the right side of the boundary and  is a linear density of the surface current. If  value is zero, the boundary condition is called homogeneous. This kind of boundary condition is often used at an outward boundary of the region that is formed by the plane of magnetic antisymmetry of the problem (opposite sources in symmetrical geometry). The homogeneous Neumann condition is the natural one, it is assumed by default at all outward boundary parts where no explicit boundary condition is specified.

Note. Zero Dirichlet condition is defaulted at the axis of rotation for the axisymmetric problems.

If the surface electric current is to be specified at the plane of problem symmetry and this plane forms the outward boundary of the region, the current density has to be halved.

Zero flux boundary condition is used to describe superconducting materials that are not penetrated by the magnetic field. Vector magnetic potential is a constant within such superconducting body (rA = const in axisymmetric case), therefore superconductor's interior can be excluded from the consideration and the constant potential condition can be associated with its surface.

Note. If the surface of a superconductor has common points with any Dirichlet edge, the whole surface has to be described by the Dirichlet condition with an appropriate potential value.


Permanent magnets

Since the coercive force is considered in QuickField to be the piecewise constant function, its contribution to the equation is equivalent to surface currents which flow along the surface of the permanent magnet in direction orthogonal to the model plane. The density of such effective current is equal to jump of the tangent component of the coercive force across the magnet boundary. For example, rectangular magnet with the coercive force Hc directed along x-axis can be replaced by two oppositely directed currents at its upper and lower surfaces. The current density at the upper edge is numerically equal to Hc, and –Hc at the lower edge.

Therefore, the permanent magnet can be specified by either coercive force or Neumann boundary conditions at its edges. You can choose more convenient and obvious way in each particular case.

Permanent magnets with nonlinear magnetic properties need some special consideration. Magnetic permeability is assumed to be defined by the following equation

.

It must be pointed out that B dependence is different from the analogous curve for the same material but without permanent magnetism. If the real characteristic for the magnet is not available for you, it is possible to use row material curve as an approximation. If you use such approximation and magnetic field value inside magnet is much smaller than its coercive force, it is recommended to replace the coercive force by the following effective value

,

where Br is remanent induction.


Calculated physical quantities in magnetostatics

For magnetostatic problems the QuickField postprocessor calculates the following set of local and integral physical quantities.

Local quantities:

•	Vector magnetic potential A (flux function rA in axisymmetric case);

•	Vector of the magnetic flux density B = curl A

—for planar case;

—for axisymmetric case;

•	Vector of magnetic field intensity

where μ is the magnetic permeability tensor.

Integral quantities:

•	Total magnetostatic force acting on bodies contained in a particular volume

,

where integral is evaluated over the boundary of the volume, and n denotes the vector of the outward unit normal.

•	Total torque of magnetic forces acting on bodies contained in a particular volume

where r is a radius vector of the point of integration. The torque vector is parallel to z-axis in the planar case, and is identically equal to zero in the axisymmetric one. The torque is considered relative to the origin of the coordinate system. The torque relative to any other arbitrary point can be obtained by adding extra term of F × ro, where F is the total force and ro is the radius vector of the point.

•	Magnetic field energy

—linear case;

—nonlinear case.

•	Flux linkage per one turn of the coil

—for planar case;

—for axisymmetric case;

the integral has to be evaluated over the cross section of the coil, and S is the area of the cross section.

For planar problems all integral quantities are considered per unit length in z-direction.

The domain of integration is specified in the plane of the model as a closed contour consisting of line segments and circular arcs.


Inductance calculation

To get self inductance of a coil, leave the current on in this coil only and make sure that all other currents are turned off. After solving the problem go to the Postprocessor and obtain flux linkage for the contour coinciding with the cross section of the coil. Once you’ve done that, the inductance of the coil can be obtained from the following equation:

,

where n is a number of turns in the coil,  is a flux linkage, j is a current per one turn of the coil.

Mutual inductance between two coils can be obtained in a similar way. The only difference from the previous case is that electric current has to be turned on in one coil, and the flux linkage has to be evaluated over the cross section of another.

In plane-parallel case every coil has to be represented by at least two conductors with equal but opposite currents. In some cases both conductors are modeled, in other cases only one of two conductors is included in the model and the rest is replaced by the boundary condition A = 0 at the plane of symmetry. If the magnetic system is symmetric, the inductance can be obtained based on the flux linkage for one of the conductors only. The result has to be then multiplied by a factor of two to account for the second conductor. If the model is not symmetric, then the total inductance can be obtained by adding up the analogous terms for each conductor. Note that the current should be turned on in all conductors corresponding to one coil.

In plane-parallel case the inductance is calculated per unit length in z-direction.


Time-harmonic magnetic field

Time-harmonic electromagnetic analysis is the study of electric and magnetic fields arising from the application of an alternating (AC) current source, or an imposed alternating external field.

Variation of the field with respect to time is assumed to be sinusoidal. All field components and electric currents vary with time like

,

where zo is a peak value of z, φz — its phase angle, and ω — the angular frequency.

Complex representation of harmonic time dependency facilitates multiple phase analysis based on one complex solution. Real and imaginary parts of a complex quantity

,

have phase angles shifted by 90 degrees, and their linear combination may be used to represent any arbitrary phase angle.

Depending on the phase shift between two oscillating components of a vector, the vector can rotate clockwise or counterclockwise, or oscillate along certain direction. Generally, the end of such a vector draws an ellipse. The semimajor axis of the ellipse corresponds to the peak value of the vector. The ratio between minor and major axes of the ellipse defines the coefficient of polarization. The coefficient of polarization is assumed to be positive for the counterclockwise and negative for the clockwise rotation. Zero coefficient corresponds to the linear polarization.

Total current in a conductor can be considered as a combination of a source current produced by the external voltage and an eddy current induced by the oscillating magnetic field

The problem is formulated as a partial differential equation for the complex amplitude of vector magnetic potential A (B = curl A, B—magnetic flux density vector). The flux density is assumed to lie in the plane of model (xy or zr), while the vector of electric current density j and the vector potential A are orthogonal to it. Only jz and Az in planar or jθ and Aθ in axisymmetric case are not equal to zero. We will denote them simply j and A. The equation for planar case is

;

and for axisymmetric case is

.

where electric conductivity g and components of magnetic permeability tensor μx and μy (μz and μr) are constants within each block of the model. Source current density jo is assumed to be constant within each model block in planar case and vary as 1/r in axisymmetric case.

The described formulation ignores displacement current density term ∂D/∂t in the Ampere’s Law. Typically the displacement current density is not significant until the operating frequency approaches the MHz range.

Note. Permanent magnets and nonlinear magnetic properties cannot be simulated in a time-harmonic analysis. Since the entire field must vary sinusoidally, this would prevent permanent magnets or effects of saturation from being simulated using the harmonic analysis. Permanent magnets supply a constant flux to the system. Saturation of the material indicates that as the field intensity increases, the flux density in the material would not be able to follow the same sinusoidal behavior.


Field sources in time-harmonic magnetics

The field sources can be specified in the blocks, at the edges or at the individual vertices of the model. Possible field sources include space, surface and linear electric currents and voltages applied to conductive areas.

A point source in the xy-plane corresponds to a linear current in out-of-plane direction. In axisymmetric case the point source represents the current in a thin ring around the axis of symmetry. Edge-bound source in the plane of model represents a surface current in three-dimensional world. It is specified by the Neumann boundary conditions for the edge.

There are several ways to specify space-distributed electric current. In a massive conductor, you can specify either a total current or a voltage applied to the conductor. In planar problems, voltage drop is specified per unit depth of the model, and in axisymmetric case voltage is assumed per one turn around the axis of symmetry. Nonzero voltage applied to a conductor in axisymmetric problem means that the conductor has a radial cut, and the voltage is applied to sides of the cut. In practice this option could be used to describe known voltage applied to massive spiral wiring, in which case the total voltage drop for the coil should be divided by number of turns in the coil.

Note. The meanings of zero total current and zero voltage applied to a conductor are very different. Zero voltage means that the conductor’s ends are short circuit, and zero value of the total current means open ends of the conductor.

Field source could also be specified in non-conductive areas. This option is useful to specify current in coils made of thin wire, where skin effect is insignificant. You can specify either a total current or a current density, whichever is easier to calculate in a specific case. Current density in a coil can be obtained from the equation

,

where n is a number of turns, I is a total current, and S is a cross-sectional area of the coil.

Note. In order to properly model thin wire coils, the source current density jo in non-conductive areas is assumed to be uniform in both plane and axisymmetric cases. Its behavior is different for massive conductors, where source current density varies as 1/r in axisymmetric case.


Boundary conditions in time-harmonic magnetics

The following boundary conditions can be specified at outward and inner boundaries of the region.

Dirichlet condition specifies a known value of vector magnetic potential A0 at the vertex or at the edge of the model. This boundary condition defines normal component of the flux density vector. It is often used to specify vanishing value of this component, for example at the axis of symmetry or at the distant boundary. QuickField also supports the Dirichlet condition with a function of coordinates, it has the form

—for planar problems;

—for axisymmetric problems.

Parameters a, b and c are constants for each edge, but can vary from one piece of the boundary to another. This approach allows you to model an uniform external field by specifying non zero normal component of the flux density at arbitrary straight boundary segment.

Let α be an elevation angle of the segment relative to the horizontal axis (x in planar or z in axisymmetric case). Then in both plane and axisymmetric cases the normal flux density is

.

Here we assume right-hand direction of positive normal vector.

Choice of constant terms a for different edges has to satisfy the continuity conditions for function A0 at all edges' junction points.

Neumann condition has the following form

—at outward boundaries,

—at inner boundaries,

where Ht is a tangent component of magnetic field intensity, "+" and "–" superscripts denote quantities to the left and to the right side of the boundary and  is a linear density of the surface current. If  value is zero, the boundary condition is called homogeneous. This kind of boundary condition is often used at an outward boundary of the region that is formed by the plane of magnetic antisymmetry of the problem (opposite sources in symmetrical geometry). The homogeneous Neumann condition is the natural one, it is assumed by default at all outward boundary parts where no explicit boundary condition is specified.

Note. Zero Dirichlet condition is defaulted at the axis of rotation for the axisymmetric problems.

If the surface electric current is to be specified at the plane of problem symmetry and this plane forms the outward boundary of the region, the current density has to be halved.

Zero flux boundary condition is used to describe superconducting materials that are not penetrated by the magnetic field. Vector magnetic potential is a constant within such superconducting body (rA = const in axisymmetric case), therefore superconductor's interior can be excluded from the consideration and the constant potential condition can be associated with its surface.

Note. If the surface of a superconductor has common points with any Dirichlet edge, the whole surface has to be described by the Dirichlet condition with an appropriate potential value.


Calculated physical quantities in time-harmonic magnetics

The following local and integral physical quantities are calculated in the process of harmonic magnetic field analysis.

Local quantities:

•	Complex amplitude of vector magnetic potential A (flux function rA in axisymmetric case);

•	Complex amplitude of voltage U applied to the conductor;

•	Complex amplitude of total current density j = j0 + jeddy, source current density j0 and eddy current density jeddy  = iωgA;

•	Complex vector of the magnetic flux density B = curl A

 for planar case;

 for axisymmetric case;

•	Complex vector of magnetic field intensity

where μ is the magnetic permeability tensor.

•	Time average and peak Joule heat density

•	Time average and peak magnetic field energy density

•	Time average Poynting vector (local power flow)

•	Time average Lorentz force density vector

•	Magnetic permeability μ (its largest component in anisotropic media);

•	Electric conductivity g.

Integral quantities:

•	Complex magnitude of electric current through a particular surface

and its source and eddy components I0 and Ie.

•	Time average and peak Joule heat in a volume

•	Time average and peak magnetic field energy

•	Time average and peak power flow through the given surface (Poynting vector flow)

•	Time average and oscillating part of Maxwell force acting on bodies contained in a particular volume

where integral is evaluated over the boundary of the volume, and n denotes the vector of the outward unit normal.

•	Time average and peak Maxwell force torque acting on bodies contained in a particular volume

where r is a radius vector of the point of integration.

•	Time average and oscillating part of Lorentz force acting on conductors contained in a particular volume

•	Time average and peak Lorentz force torque acting on bodies contained in a particular volume

where r is a radius vector of the point of integration.

The torque vector is parallel to z-axis in the planar case, and is identically equal to zero in the axisymmetric one. The torque is considered relative to the origin of the coordinate system. The torque relative to any other arbitrary point can be obtained by adding extra term of F × ro, where F is the total force and ro is the radius vector of the point.

Note. Magnetic field produces forces acting on the current carrying conductors and on the ferromagnetic bodies. The force acting on conductors is known as Lorentz force, while the Maxwell force incorporates both components. If the second (ferromagnetic) component is negligible or is not considered, we recommend calculating the electromagnetic force as Lorentz force. Its precision is less sensitive to the contour path, and you can simply select conductors via block selection to calculate the force. With Maxwell force, this method leads to very rough results, and you are recommended to avoid coinciding of your contour parts and material boundaries, as described in Calculating integrals.

The domain of integration is specified in the plane of the model as a closed contour consisting of line segments and circular arcs.


Impedance calculation

Impedance in time-harmonic electromagnetic analysis is a complex coefficient between complex values of current and voltage, V = ZI. Its real part represents active resistance of the conductor, calculated with the skin effect taken into account. The imaginary part of the impedance is the inductance multiplied by the angular frequency ω.

As values of voltage and current in any conductor are easily accessible in the postprocessor, you can determine the impedance by dividing voltage by current using complex arithmetic. Let V and I be peak values of voltage and current, and φV and φI be phases of those quantities. Then the active resistance could be calculated as

and the inductance as

To get mutual inductance between two conductors, you can specify nonzero total current in one of them, make the ends of the other open (applying zero total current), and measure the voltage induced in the second conductor by the current in the first one.

Note. As in planar case voltage is applied and measured per unit length, the impedance is also calculated per unit length in z-direction.


Electrostatic formulations

Electrostatic problems are described by the Poisson's equation for scalar electric potential U (E = –gradU, E—electric field intensity vector). The equation for planar case is

,

and for axisymmetric case is

,

where components of electric permittivity tensor εx, εy or εz, εr and electric charge density ρ are constants within each block of the model.


Field sources in electrostatics

QuickField provides possibility to specify electric charges located in the blocks, at the edges or at the individual vertices of the model. The electric charge specified at a point of the xy-plane corresponds to a charged string, which is perpendicular to the plane of the model, and is described by the linear charge density. In axisymmetric case the vertex charge represents a charged circle around the axis of symmetry or a point charge located on the axis. To incorporate both these cases a total charge value is associated with the vertex. For the charged circle the total charge is connected with its linear density by the relationship q = 2πr⋅ρ. Edge-bound charge in the plane of model represents a surface-bound charge in three-dimensional world. It is described by surface charge density and is specified by the Neumann boundary condition for the edge. The charge density associated with a block is equivalent to the space charge.


Boundary conditions in electrostatics

The following boundary conditions can be specified at outward and inner boundaries of the region.

Dirichlet condition specifies a known value of electric potential U0 at the vertex or at the edge of the model (for example on a capacitor plate). This kind of boundary condition is also useful at an outward boundary of the region that is formed by the plane of electric antisymmetry of the problem (opposite charges in symmetrical geometry). U0 value at the edge can be specified as a linear function of coordinates. The function parameters can vary from one edge to another, but have to be adjusted to avoid discontinuities at edges' junction points.

Note. For problem to be defined correctly the Dirichlet condition has to be specified at least at one point. If the region consists of two or more disjoint subregions, the Dirichlet conditions have to be specified at least at one point of every part.

Neumann condition is defined by the following equations:

 at outward boundaries,

 at inner boundaries,

where Dn is a normal component of electric induction, "+" and "–" superscripts denote quantities to the left and to the right side of the boundary, σ is a surface charge density. If σ value is zero, the boundary condition is called homogeneous. It indicates vanishing of the normal component of electric field intensity vector. This kind of boundary condition is used at an outward boundary of the region that is formed by the symmetry plane of the problem. The homogeneous Neumann condition is the natural one, it is defaulted at all outward boundary parts where no explicit boundary condition is specified.

If the surface-bound charge is to be specified at the plane of problem symmetry and this plane is the outward boundary of the region, the surface charge density has to be halved.

Constant potential boundary condition is used to describe surface of an isolated “floating” conductor that has constant but unknown potential value.

Note. The edge described as possessing constant potential should not have common points with any Dirichlet edge. In that case the constant potential edge has to be described by a Dirichlet condition with appropriate potential value.


Calculated physical quantities in electrostatics

For electrostatic problems the QuickField postprocessor calculates the following set of local and integral physical quantities.

Local quantities:

•	Scalar electric potential U;

•	Vector of electric field intensity E = –gradU

 for planar case;

 for axisymmetric case;

•	Tensor of the gradient of electric field intensity G = gradE

—for planar case;

—for axisymmetric case;

and also its principal components G1 and G2.

•	Vector of electric induction D = εE, where ε is electric permittivity tensor.

Integral quantities:

•	Total electric charge in a particular volume

,

where integral is evaluated over the boundary of the volume, and n denotes the vector of the outward unit normal.

•	Total electrostatic force acting on bodies contained in a particular volume

•	Total torque of electrostatic forces acting on bodies contained in a particular volume

where r is a radius vector of the point of integration. The torque vector is parallel to z-axis in the planar case, and is identically equal to zero in the axisymmetric one. The torque is considered relative to the origin of the coordinate system. The torque relative to any other arbitrary point can be obtained by adding extra term of F × ro, where F is the total force and ro is the radius vector of the point.

•	Energy of electric field

.

For planar problems all integral quantities are considered per unit length in z-direction.

The domain of integration is specified in the plane of the model as a closed contour consisting of line segments and circular arcs.


Capacitance calculation

There are several ways to calculate capacitance using QuickField. The easiest one of them is based on measuring an electric potential produced by a known charge. To get capacitance of a conductor, put constant potential boundary condition on its surface, specify an arbitrary non zero electric charge in one of the vertices on the surface of the conductor (in fact, the charge will be distributed over the conductor’s surface), and turn off all other field sources in the model. Once the problem is solved, go to the Postprocessor and take the value of electric potential somewhere on the surface of the conductor. The capacitance of the conductor can be obtained from the equation

where q is the electric charge and U is the potential of the conductor.

To calculate mutual capacitance between two conductors put a charge on one conductor and measure electric potential on another. Constant potential boundary condition has to be applied to the surfaces of both conductors.


Formulations in current flow analysis

QuickField is able to calculate the distribution of electric current in systems of conductors. The problems of current distribution are described by the Poisson's equation for scalar electric potential U.

The equation for planar case is

and for axisymmetric case is

where components of electric resistivity tensor ρx, ρy or ρz, ρr are constant within each model block.

The electric current density j can be obtained from the equation


Field sources in current flow analysis

With the problems of current flow, the field sources are external currents supplied to the boundary of a conductor. QuickField provides possibility to specify external current density at the edges or at the individual vertices of the model. The current density specified at a point of the xy-plane corresponds to a knife-edge current collector, which is perpendicular to the plane of the model, and is described by the linear current density. In axisymmetric case the vertex source represents a circular collector around the axis of symmetry or a point collector located on the axis. To incorporate both these cases, a total current value is associated with the vertex. For the circular knife-edge collector the total current value is connected with its linear density by the relationship I = 2πr⋅σ. Edge-bound current density in the plane of model represents a surface-bound external current density in three-dimensional world. It is specified by the Neumann boundary condition for the edge.


Boundary conditions in current flow analysis

The following boundary conditions can be specified at outward and inner boundaries of the region.

Dirichlet condition specifies a known value of electric potential U0 at the vertex or at the edge of the model. U0 value at the edge can be specified as a linear function of coordinates. The function parameters can vary from one edge to another, but have to be adjusted to avoid discontinuities at edges' junction points.

Note. For problem to be defined correctly the Dirichlet condition has to be specified at least at one point. If the region consists of two or more disjoint subregions, the Dirichlet conditions have to be specified at least at one point of every part.

Neumann condition is defined by the following equations:

 at outward boundaries,

 at inner boundaries,

where jn is a normal component of the current density vector, "+" and "–" superscripts denote quantities to the left and to the right side of the boundary, and j at right hand side is a density of the external current. If j value is zero, the boundary condition is called homogeneous. This kind of boundary condition is used at an outward boundary of the region that is formed by the symmetry plane of the problem. The homogeneous Neumann condition is the natural one, it is defaulted at all outward boundary parts where no explicit boundary condition is specified.

If the surface-bound current density is to be specified at the plane of problem symmetry and this plane is the outward boundary of the region, the surface current density has to be halved.

Constant potential boundary condition is used to describe surface of a conductor having much greater conductivity than the surrounding medium. This conductor is assumed to have constant but unknown potential value.

Note. The edge described as possessing constant potential should not have common points with any Dirichlet edge. In that case the constant potential edge has to be described by the Dirichlet condition with an appropriate potential value.


Calculated physical quantities in current flow analysis

For problems of current flow, the QuickField postprocessor calculates the following set of local and integral physical quantities.

Local quantities:

•	Scalar electric potential U;

•	Vector of electric field intensity E = –gradU

 for planar case;

 for axisymmetric case;

•	Vector of current density

where ρ is electric resistivity tensor.

Integral quantities:

•	Electric current through a given surface

where n denotes the vector of the unit normal.

•	Joule heat produced in a volume

For planar problems all integral quantities are considered per unit length in z direction.

The domain of integration is specified in the plane of the model as a closed contour consisting of line segments and circular arcs.


Heat transfer formulations

With QuickField you can analyze linear and nonlinear temperature fields.

Heat-transfer equation for linear problems is:

—planar case;

—axisymmetric case;

for nonlinear problems:

—planar case;

—axisymmetric case;

where:

T	—	temperature;

λx(y,z,r)	—	components of heat conductivity tensor;

λT	—	heat conductivity as a function of temperature approximated by cubic spline (anisotropy is not supported in nonlinear case);

q	—	volume power of heat sources, in linear case—constant, in nonlinear case—function of temperature approximated by cubic spline.

In linear case all the parameters are constants within each block of the model.

The heat transfer problems for thin plates are very analogous to the plane-parallel problems and we will not discuss them especially.


Heat sources

QuickField provides possibility to specify the heat sources located in the blocks, at the edges or at the individual vertices of the model. The heat source specified at a point of the xy-plane corresponds to a linear string-like heater, which is perpendicular to the plane of the model, and is described by the generated power per unit length. In axisymmetric case the vertex heat source represents a heating circle around the axis of symmetry or a point heater located on the axis. To incorporate both these cases a total generated power value is associated with the vertex. For the heating circle the total power is connected with its linear density by the relationship q  2πr⋅ql. Edge-bound heat source in the plane of model represents a surface heat source in three-dimensional world. It is described by power per unit area and is specified by the heat flux boundary condition for the edge. The volume power density associated with a block corresponds to the volume heat source.


Boundary conditions in heat transfer

The following boundary conditions can be specified at outward and inner boundaries of the region.

Known temperature boundary condition specifies a known value of temperature T0 at the vertex or at the edge of the model (for example on a liquid-cooled surface). T0 value at the edge can be specified as a linear function of coordinates. The function parameters can vary from one edge to another, but have to be adjusted to avoid discontinuities at edges' junction points.

This boundary condition sometimes is called the boundary condition of the first kind.

Heat flux boundary condition is defined by the following equations:

—at outward boundaries,

—at inner boundaries,

where Fn is a normal component of heat flux density, "+" and "–" superscripts denote quantities to the left and to the right side of the boundary. For inner boundary qs, denotes the generated power per unit area, for outward boundary it specifies the known value of the heat flux density across the boundary. If qs, value is zero, the boundary condition is called homogeneous. The homogeneous condition at the outward boundary indicates vanishing of the heat flux across the surface. This type of boundary condition is the natural one, it is defaulted at all outward boundary parts where no explicit boundary condition is specified. This kind of boundary condition is used at an outward boundary of the region, which is formed by the symmetry plane of the problem.

If the surface heat source is to be specified at the plane of problem symmetry and this plane constitutes the outward boundary of the region, the surface power has to be halved.

This boundary condition sometimes is called the boundary condition of the second kind.

Convection boundary condition can be specified at outward boundary of the region. It describes convective heat transfer and is defined by the following equation:

where α is a film coefficient, and T0—temperature of contacting fluid medium. Parameters  and T0 may differ from part to part of the boundary.

This boundary condition sometimes is called the boundary condition of the third kind.

Radiation boundary condition can be specified at outward boundary of the region. It describes radiative heat transfer and is defined by the following equation:

where kSB is a Stephan-Boltsman constant, β is an emissivity coefficient, and T0—ambient radiation temperature. Parameters β and T0 may differ from part to part of the boundary.

Note. For heat transfer problem to be defined correctly the known temperature boundary condition, or the convection, or the radiation has to be specified at least at some parts of the boundary.

Constant temperature boundary condition may be used to describe bodies with very high heat conductivity. You can exclude interior of these bodies from the consideration and describe their surface as the constant temperature boundary.

Note. The edge described as possessing constant temperature cannot have common points with any edge where the temperature is specified explicitly. In that case the constant temperature edge has to be described by the boundary condition of the first kind with an appropriate temperature value.


Calculated physical quantities in heat transfer

For heat transfer problems the QuickField postprocessor calculates the following set of local and integral physical quantities.

Local quantities:

•	Temperature T;

•	Vector of the heat flux density F  –λ grad T

 for planar case;

 for axisymmetric case;

The postprocessor can calculate the heat flux through an arbitrary closed or unclosed surface

where n denotes the unit vector of normal to the surface. The surface is specified by a contour consisting of line segments and circular arcs in the plane of the model.


Stress analysis formulations
Stress Analysis

Within QuickField package, the plane stress, the plane strain and the axisymmetric stress models are available with both isotropic and orthotropic materials. The plane stress model is suitable for analyzing structures that are thin in the out-of-plane direction, e.g., thin plates subject to in-plate loading. Out-of-plane direct stress and shear stresses are assumed to be negligible. The plane strain model is formulated by assuming that out-of-plane strains are negligible. This model is suitable for structures that are thick in the out-of-plane direction.

Displacement, Strain and Stress

The displacement field is assumed to be completely defined by the two components of the displacement vector δ in each point:

—for plane problems;

—for axisymmetric problems.

Only three components of strain and stress tensors are independent in both plane stress and plane strain cases. The strain-displacement relationship is defined as:

.

The corresponding stress components:

.

The axisymmetric problem formulation also includes the out-of-plane direct strain εθ, caused by the radial deformation. The strain-displacement relationship is defined as:

.

The corresponding stress components:

.

The equilibrium equations for the plane problems are:

and for the axisymmetric problems are:

where ƒx, ƒy and ƒz, ƒr are components of the volume force vector.

For linear elasticity, the stresses are related to the strains using relationship of the form

,

where D is a matrix of elastic constants, and ε0 is the initial thermal strain. The specific form of the matrix depends on a particular problem formulation.

For plane stress and isotropic material:

.

For plane stress and orthotropic material:

.

For plane strain and isotropic material:

.

For plane strain and orthotropic material:

.

For axisymmetric problem and isotropic material:

;

For axisymmetric problem and orthotropic material:

.

In all these equations E denotes Young's modulus of the isotropic material; Ex, Ey, Ez, Er, and Eθ are the Young's moduli of the orthotropic material along the corresponding axes; ν is a Poisson's ratio for isotropic material; νyx, νzx, νzy, νrz, νθz, νθr are the Poisson's ratios for orthotropic material; Gxy and Gzr are the shear moduli.


Thermal strain

Temperature strain is determined by the coefficients of thermal expansion and difference of temperatures between strained and strainless states. Components of the thermal strain for plane stress and isotropic material are defined by the following equation:

;

plane stress, orthotropic material:

;

plane strain, isotropic material:

;

plane strain, orthotropic material:

;

axisymmetric problem, isotropic material:

;

axisymmetric problem, orthotropic material:

,

where α is a coefficient of thermal expansion for isotropic material; α x, αy, αz, αr, αθ are the coefficients of thermal expansion along the corresponding axes for orthotropic material; ΔT is the temperature difference between strained and strainless states.


External forces

QuickField provides way to specify concentrated loads, surface and body forces. The concentrated loads are defined at vertices as two components of the corresponding vector. The surface forces at the edges of the model are specified by the vector components or by the normal pressure. The body forces are defined by their components within blocks of the model. Each component of the body force vector can be specified as a linear function of the coordinates. This feature can be used, for example, to model centrifugal forces. The normal pressure also can be linear function that is useful for hydrostatic pressure.

Note. The concentrated load is specified by the force per thickness unit for plane problems and by the total force value for axisymmetric ones. In the last case the force can be applied to the point at the axis of symmetry or distributed along the circle around the axis.

Any surface force which is directed along the normal to the surface can be described as a pressure. The pressure is considered positive if it is directed inside region at its outward boundary or from right to left at the inner boundary. Left and right are referred relative to the edge intrinsic direction, which is always counterclockwise for arcs and is determined for line segments by the order of picking vertices when the edge is created.


Restriction conditions

Rigid constraint condition along one or both axes can be specified at any vertex or along any edge of the model. Prescribed displacement at restrained edge can be specified as a linear function of the coordinates.

Elastic support condition describes a vertex subject to springy force which is proportional to difference between actual and predetermined displacement. The elastic support condition is characterized by the predetermined displacement and the support elasticity.

Note. For problem to be defined correctly the constraint or elastic support conditions have to be specified in such a way to exclude rigid body shifts and rotations of the model or its parts without increasing the potential energy. Two translational and one rotational degrees of freedom have to be restricted for plane problem, in axisymmetric case only shift in z-direction has to be excluded.


Calculated physical quantities in stress analysis

For the stress analysis problems the QuickField postprocessor calculates the following set of local and integral physical quantities.

Local quantities:

•	The absolute value of displacement

•	Maximum and minimum principal stresses in the plane of model σ1 and σ2;

•	Normal and tangential stresses along coordinate axes σx, σy and τxy (σz, σr and τrz in axisymmetric case);

•	Normal stress in out-of-plane direction (σz—for xy-plane, σθ—for rz-plane). For the plane stress problems this component vanishes by the definition;

•	Von Mises criterion (stored energy of deformation):

;

where σ1, σ2 and σ3 denote the principal stresses in descending order.

•	Tresca criterion (maximum shear):

•	Mohr-Coulomb criterion:

where

,

σ+ and σ– denote tensile and compressive allowable stress.

•	Drucker-Prager criterion:

,

where

;

.

•	Hill failure index for orthotropic materials:

,

where σ1, σ2 and τ12 are computed stresses in the material directions and,

;

;

,

where

are tensile, compressive and shear allowable stresses.

Integral quantities:

•	Total force acting on a particular volume

where σ is the stress tensor.

The integral is evaluated over the boundary of the volume, and n denotes the vector of the outward unit normal.

•	Total torque of the forces acting on a particular volume

where r is a radius vector of the point of integration.

The torque vector is parallel to z-axis in the planar case, and is identically equal to zero in the axisymmetric one. The torque is considered relative to the origin of the coordinate system. The torque relative to any other arbitrary point can be obtained by adding extra term of F × ro, where F is the total force and ro is the radius vector of the point.


Coupled problems

QuickField is capable of importing loads (distributed sources) calculated in some problem into the problem of another type. Following coupling types are supported:

•	Heat transfer caused by Joule heat generated in the current flow or time-harmonic electromagnetic problem.

•	Thermal stresses based on a calculated temperature distribution.

•	Stress analysis of the system loaded by magnetic forces.

•	Stresses in electrostatic system.

In addition to imported loads, you can define any other loads and boundary conditions, similar to non-coupled problem.

You can combine several coupling types in one problem. E.g., after calculating distribution of currents, electrostatic and magnetic fields as separate problems based on the same model file, you can calculate temperature distribution from Joule heat and then find stresses caused by temperature and magnetic and electrostatic forces at once. However, such problems are rather rare.

Further we will call the problem, from which the data are being loaded, the source problem, and the problem, which imports the data, the target problem.

There are several rules to follow with coupled problems:

•	Both source and target problem must share a single model file.

•	Both problems must use the same formulation (plane or axisymmetric).

•	Source problem must be up-to-date when solving the target problem.

Note. In spite of the requirement that both coupled problems must use the same model file, the geometrical region for the problems need not coincide, i.e., some subregions those are in use in one problem, could be excluded from consideration in the other one.

Importing Joule Heat to Heat Transfer Problem

While importing data from current flow problem to heat transfer one, heat sources due to Joule law are assumed in all subregions included into consideration in both source and target problems. In time-harmonic electromagnetic problems Joule heat is generated in all conductors.

Importing temperature distribution to stress analysis problem

While calculating thermal stresses, initial strains are assumed in all subregions, which are included into consideration in both problems and possess nonzero value of thermal expansion coefficient (or at least one of its components in anisotropic case).

Importing magnetic forces to stress analysis problem

While importing magnetic force to stress analysis problem:

•	Body force is assumed in all subregions included into consideration in both source and target problems, if those subregions have nonlinear magnetic properties and/or current density is defined (Lorentz force).

•	Surface force is assumed at the boundaries separating subregions with different magnetic properties, boundaries with surface current, or outward boundaries in sense of magnetic problem. The surface force is also generated in the cases, when only one subregion, say, to the left of the boundary is active in sense of magnetic problem, and only the subregion to the right of it is active in stress analysis problem.

Importing electrostatic forces to stress analysis problem

While importing electrostatic force to stress analysis problem:

•	Body force is assumed for all subregions included into consideration in both source and target problems and carrying distributed charge density.

•	Surface force is assumed at the boundaries separating subregions with different permittivity, boundaries with surface charge, or outward boundaries in sense of electrostatic problem. The surface force is also generated in the cases, when only one subregion, say, to the left of the boundary is active in sense of electrostatic problem, and only the subregion to the right of it is active in stress analysis problem.


block

Polygonal subregion of the geometric model, possibly multiply-connected. Blocks are surrounded by edges, which are created while describing a model. Each block may have a label for assigning a particular set of physical properties.


edge

Line segment or circular arc that constitutes subregion boundaries of the geometric model. Edge may have a label to specify particular boundary condition, constraint and/or field source on it.


vertex

Ends of edges or isolated points in the geometric model. Vertex may have a label to specify particular boundary condition, constraint and/or field source in the corresponding point.


label

String literal of up to 16 characters. Labels link together geometric objects in your model (blocks, edges and vertices) and numerical data describing entities in real world, which these objects stand for: material properties, loads and boundary conditions.


spacing
mesh spacing value

Defines approximate distance between mesh nodes in the neighborhood of the model vertex.


No Help topic is associated with this item.


Solve Problem

Solves the currently selected problem


Batch Solve

Solves any of currently open problems


Analyze Results

Opens the Postprocessor window for the problem. If the problem has not been solved yet, asks to start solver.


Edit File

Opens the file referenced by the problem for editing.


Insert Label

Inserts new, empty label of a given type.


Insert Mode

Switches the model view into insert mode allowing creation of new vertices and edges.


Selection Mode

Switches the model view into selection mode allowing selection of existing objects.


Select All

Selects all objects in the active window.


Unselect All

Deselects all selected objects in the active window.


Move Selection

Moves selected objects to a new location preserving the model topology.


Grid Settings

Changes grid settings and visibility.


Add Vertices

Allows to type coordinates of new vertices from keyboard.


Build Mesh

Builds the mesh in blocks.


Remove Mesh

Removes the mesh from blocks.


About QuickField

Displays QuickField version and copyright information.


Exits QuickField, prompting you to save any unsaved changes.


Arc Angle

Specifies the style of newly created edges: line segments or arcs. You can either choose between predefined angles or type a value. Zero means line segment.


Arc Angle

Specifies the style of new contour elements: line segments or arcs. You can either choose between predefined angles or type a value. Zero means line segment.


Export Field

Saves field values on specified rectangular grid to file in text or binary format.


Displays or hides the toolbar.


Displays or hides the Model toolbar.


Displays or hides the Postprocessor toolbar.


Geometric models

Geometric model is a type of QuickField document describing the problem geometry. It contains specific geometric objects and establishes the correspondence between the objects and material properties, field sources and boundary conditions.

Vertex, edge, and block are three basic types of geometric objects, which constitute the model in QuickField.

Vertex is a point on the plane with coordinates defined by the user or calculated automatically as intersection of the edges. For each vertex you can define the mesh spacing value and the label. The mesh spacing value defines approximate distance between mesh nodes in the neighborhood of the vertex. The label is used, for example, to describe a line source or load.

Edge is a line segment or a circular arc connecting two vertices. It can't intersect any other edge of the region. If an edge being created contains an existing vertex, two adjacent edges are created. New vertices are automatically created in all points where new edge intersects the existing ones and all intersected edges are split by these vertices. Edges can be labeled, for example, to specify the boundary conditions.

Block is a continuous subregion with its boundary consisting of edges and possibly isolated vertices. A block may contain holes, which can be formed by chains of edges or by isolated vertices. Each block has to be labeled to describe material properties. Labels of the blocks are also used to define distributed field sources. Unlabeled block is not included in calculation of field even it is covered by the mesh. The mesh is created block by block automatically or according to the mesh spacing value defined for particular vertices.

The Label is a string of up to 16 characters length, which establishes the correspondence between geometrical parts of the model and physical values assigned to them. Any printable characters including letters, digits, punctuation marks, space character are permitted, except for asterisk () and question mark (?) characters. The label cannot begin with space character; trailing spaces are ignored. Labels are case-sensitive.

The Mesh Spacing value defines an approximate element size around a vertex. The mesh spacing parameter is associated with the vertex and measured in the current units of length. By setting mesh spacing values in some vertices you can control the mesh density and therefore the accuracy of the solution.

Related Topics

Editing the model


Editing the model

The model view gives you the possibility to describe the geometric shape of your problem—its geometric model.

Model development consists of three stages:

Geometry description and manipulation;

Definition of properties, field sources and boundary conditions;

Mesh generation.

Related Topics

What is the geometric model

Tuning the picture in Model view

Importing models from CAD systems


Geometry description

To describe model geometry, you define vertices and edges, which form boundaries of all subregions having different physical properties. You can create vertices and edges; move, copy and delete any geometric object. To perform editing actions upon several objects at once, you can use selection mechanism.

How to…

Create new vertex

Create new edge

Select objects

Duplicate or move objects

Delete objects

Edit objects’ properties


To create new vertices:

1	In the Edit menu or context (right mouse button) menu, click Insert Mode to switch the view into insert mode.

2	Make sure that current coordinate grid settings fit coordinates of vertices you want to create.

3	Just use mouse or DIRECTION keys to move the cursor to point where you want new vertex to appear and click left mouse button or press ENTER.

4	Please don’t forget to switch the insert mode off after finishing insertion—otherwise you can easily insert unwanted objects!

Or:

1	In the Edit menu, click Add Vertices.

2	Enter new vertex coordinates and click Add. Repeat if you need more vertices.

3	Click Close.

Shortcut: INS


To create new edges:

1	In the Edit menu or context (right mouse button) menu, click Insert Mode to switch the view into insert mode.

2	Use pull-down list box in the Model toolbar to choose new edge type (line segment or arc) and the arc angle—you may use predefined angles listed or type different value; zero angle corresponds to line segment.

3	Drag mouse with left button pressed, or use SHIFT+DIRECTION keys to drag the cursor from starting to ending point of the edge. You can use existing vertices as well as create new vertices while creating edges. If snap to grid feature is active, new vertices can be created only on grid nodes.

4	Please don’t forget to switch the insert mode off after finishing insertion—otherwise you can easily insert unwanted objects!

Shortcut: INS


To select geometric objects:

1	Make sure that insert mode is off.

2	Click objects you want to select with SHIFT or CTRL key pressed, or click and drag diagonally to select several connected objects at once. In latter case, only those objects are selected that entirely fit in the selection rectangle.

You also may use Select All and Unselect All commands in the Edit or context menu. Note that you can select objects of different types (blocks, edges or vertices) at once.

Also, when you select some label in the problem view, all the geometric object having that label become selected.

Shortcut: INS


Copying and moving geometric objects

Repeated geometry elements can be easily created by means of copying any set of objects to new location. To make a copy:

1	Select any number of objects (blocks, edges and vertices) you want to copy.

2	In the Edit menu or context menu, click Duplicate Selection. The dialog box appears, asking for copying parameters.

3	Select transformation, enter its parameters and click OK. The new objects will appear on screen and the program will be waiting for your confirmation, so you could be sure that you entered the parameters correctly.

4	Click Yes to confirm copying. New objects will be ‘implanted’ into the model, and selection will move to the last copy.

The copy operation effects all explicitly set properties of the selected objects, including labels and spacing values. Only the mesh is not copied.

Caution. Use copy operation with care, because improperly set transformation parameters may cause creating new objects in the wrong places. Such improper objects may interfere with the existing objects and generate a lot of useless intersection points, which will be hard to remove later.

You can also move selected objects to other location with the restriction that region topology will not change, and no new intersection or coinciding will arise. To move selected objects, click Move Selection in the Edit menu or context menu. The dialog box that appears is very similar to copying dialog box.

Related Topics

Geometric transformations

Objects selection


Geometric transformations

Geometric transformations available with move and copy operations are:

Displacement	parallel displacement is applied to selected objects for specified displacement vector. With copy operation, several copies can be asked for, it means that copying operation will be performed several times, each time being applied to the previous result. Parameters needed are displacement vector components.

Rotation	selected objects are rotated around the specified point for the specified angle. With copy operation, several copies can be asked for, it means that copying operation will be performed several times, each time being applied to the previous result. Parameters needed are center of rotation coordinates and angle measured in degrees.

Symmetry	selected objects are mirrored; symmetry line is specified by coordinates of any point on it and the angle between the horizontal axis and the symmetry line. Positive value of an angle means counter-clockwise direction. This transformation is available for copy operation only.

Scaling	selected objects are dilated (constricted) by means of homothetic transformation. Parameters needed are center of homothety and scaling factor. This transformation is available for move operation only.

Related Topics

Copying and moving geometric objects


To delete geometric objects:

1	Select objects you want to delete.

2	In the Edit menu or context menu, click Delete Selection.

If the selection contains vertices only and the vertex being removed connects exactly two edges, which can be treated as single edge when eliminating that vertex, those are joined together. Otherwise confirmation will be asked to delete all the connected edges.

Shortcut: DEL


To edit objects’ properties:

1	Select objects.

2	In the Edit menu or context menu, click Properties.

Shortcut: ALT+ENTER, mouse double-click


Importing models from CAD systems

You can import model geometry or its fragments from the DXF file produced by any major CAD system. To do so, click Import DXF in the File menu and then type or select required file name. The visible region is automatically extended if needed to assure visibility of all imported geometric objects. If the model is not empty when reading the DXF file, it is recommended to save the current model’s state before the operation. This will give you a chance to return to the initial stage if the imported objects incidentally overlap the existing part of model.


Assigning labels to objects

The correspondence between geometrical objects and their physical properties, such as material properties, boundary conditions, or field sources is established by the use of labels. To assign labels to objects:

1	Select objects.

2	In the Edit menu or context menu, click Properties.

3	Type the label and click OK.

If you select objects of different type at once, you can set labels to selected objects of each kind (blocks, or edges, or vertices) separately on different pages of Property dialog.

Shortcut: ALT+ENTER, mouse double-click


Meshing technology

After creating the geometry of the model or its parts, you can proceed with building the finite element mesh. You can easily build a non-uniform mesh for a highly complex geometry. You may choose a fine mesh in some regions and very coarse in others, since the geometric decomposition technique would produce a smooth transition from large to small element sizes. Generally, the mesh has to be fine where the field changes most rapidly (high gradient), and also where you need high precision.

If the geometry is rather simple, or a draft precision for preliminary design analysis is satisfactory, it is suggested to use the fully automatic mode to create the mesh. With this option, once you built your geometry you would simply click Build Mesh and a suitable mesh is automatically created without any information on the mesh size.

You also have the option to pick the mesh density if you choose to do so. The mesh density is controlled by spacing values in vertices. The spacing value defines approximate distance between mesh nodes around that vertex. You never need to define the spacing in all the model's vertices. To obtain uniform mesh you can set the spacing in any one vertex. This value is spread among all other vertices automatically. If you need the non-uniform mesh, define spacing values only in those vertices where you need finest and roughest mesh. The spacing values are automatically interpolated to other vertices to smooth the mesh density distribution. The group selection mechanism allows assigning the value to several vertices at once.

After defining spacing values, you can proceed with the mesh building. The mesh is built block by block. You may choose to build the mesh in one block or in selected blocks or in entire region at once.

Changing the density of a pre-built mesh (e.g. if solution results show that you need more precision somewhere in the region) obey some rules:

•	When you change the spacing value in some vertex, the mesh is removed automatically in those blocks, which are connected to that vertex.

•	The mesh that is not removed, freezes spacing values along its boundary from recalculation as if those values were defined manually; so if you need major changes in the mesh density, first remove the mesh in the whole region.

Related Topics

How to set mesh spacing

How to build the mesh

How to remove the mesh


Mesh spacing
To set mesh spacing:

1	Select vertices, edges or blocks, in neighborhood of which you need to specify the same spacing value.

2	In the Edit menu or context menu, click Properties.

3	Type the spacing value and click OK.

If you choose to specify mesh spacing while selecting blocks or edges, the spacing value is actually assigned to all the vertices located on those edges or block boundaries.

Shortcut: ALT+ENTER, mouse double-click


Mesh building
To build the mesh:

•	In the Edit menu or context (right mouse button) menu, click Build Mesh and then click appropriate option from submenu that appears.

•	Or, select Build Mesh button on the toolbar. In this case the domain for building mesh is selected in following order:

•	In selected blocks, if any;

•	In labeled blocks, if any;

•	In all blocks in the region.


Mesh removing
To remove the mesh:

•	In the Edit menu or context (right mouse button) menu, click Remove Mesh. Then click appropriate option from submenu.

•	Or, select Remove Mesh button on the toolbar. In this case the mesh is removed from selected blocks, if any, or from all meshed blocks.


Tuning the picture in Model view

There are several options you can change to adjust the picture to best suit the task you are currently performing:

Scaling the picture (zoom)

Visibility of model details

Background grid

You also can open several windows for the same model and set different scaling factor and details visibility in each of them. To do so, click New Window in the Window menu.


Zooming the model
To magnify the picture:

1	Click Zoom In button in the model toolbar

2	Select the rectangle (click and drag diagonally), which then will occupy the whole window.

To see more of the model:

•	Click Zoom Out button in the model toolbar.

•	Or, click Zoom to Fit to see the whole model.


Model discretization visibility

There are four switches Mesh, Domain, Breaking, and Spacing, which control the discretization visibility level. These are accessible in the View menu. When all these switches are off, region is displayed without discretization. This mode is useful for region geometry description and label setting. If the Spacing mode is switched on, all explicitly set spacing values are shown as circles with the appropriate radii.

When Breaking switch is on, the size of the elements along the edges is shown as tic marks on the edges. It is convenient to use both Spacing and Breaking when specifying the mesh spacing values. Mesh lets you see the complete triangular mesh. Turn it on to check the mesh building process. Domain without Mesh displays the domains due to geometric decomposition process.


Using background grid
Background grid

Using the grid makes the process of creating model vertices and edges easier and helps to check the model. To change the grid, click Grid Settings in the Edit menu or context (right mouse button) menu.

Snap to Grid switches grid attraction on and off. Attraction means that mouse clicks create new vertices only at grid nodes making model description more fast and safe.

Show Grid switches on and off grid visibility.

Edit Spacing to change the grid density. To apply different horizontal and vertical spacing, first check the Anisotropic box.

Selecting Scale with Zoom will subsequently change the grid spacing according to your zoom operations.

Editing Origin gives you the ability to create vertices at even distances from certain point, which coordinates you enter here.


Block properties

Label allows you to view or set the label for selected blocks. You can either choose from existing block labels or type a new label string.

Spacing shows the mesh spacing value defined for the vertices belonging to block boundary.

•	To specify the same value for all these vertices, click Manual and type the value.

•	To revert all vertices to automatic spacing calculation, click Automatic.

Note that spacing value you set will apply to all vertices involved in the selection set, including selected blocks boundaries, ends of selected edges and vertices selected by themselves.

Related Topics

How to set mesh spacing

How to build the mesh

Assigning labels to objects


Edge properties

Label allows you to view or set the label for selected edges. You can either choose from existing edge labels or type a new label string.

Spacing shows the mesh spacing value defined for the vertices at selected edges’ ends.

•	To specify the same value for all these vertices, click Manual and type the value.

•	To revert all vertices to automatic spacing calculation, click Automatic.

Note that spacing value you set will apply to all vertices involved in the selection set, including selected blocks boundaries, ends of selected edges and vertices selected by themselves.

Related Topics

How to set mesh spacing

How to build the mesh

Assigning labels to objects


Vertex properties

Label allows you to view or set the label for selected vertices. You can either choose from existing vertex labels or type a new label string.

Spacing shows the mesh spacing value defined for the selected vertices.

•	To specify the same value for all vertices, click Manual and type the value.

•	To revert all vertices to automatic spacing calculation, click Automatic.

Note that spacing value you set will apply to all vertices involved in the selection set, including selected blocks boundaries, ends of selected edges and vertices selected by themselves.

Related Topics

How to set mesh spacing

How to build the mesh

Assigning labels to objects


Properties summary

Shows the statistics for your model.


Analyzing solution

To analyze the problem solution, choose View Results in Edit menu or context menu of the problem window.

The QuickField postprocessor provides various ways of results’ presentation:

field pictures,

local field values,

integral quantities,

X-Y plots,

tables.


Working with field pictures

When you choose to analyze the solution, QuickField opens a new document window showing the picture of calculated field. In this window, you can:

Choose Field Picture to select desired method of field presentation and scaling factors for the quantities;

Scale (or zoom) the picture;

Display local field data at specific points;

Create or edit a contour;

Calculate integral quantities;

Draw X-Y plots;

Display tables.

The picture can be saved to Window Clipboard or file.

The field picture is provided with the legend.

QuickField can display several different field pictures for the same problem. To open a new window, choose New Window in Window menu.

Related Topics

Formulae


Field picture in magnetostatics

Magnetic Field Lines option switches visibility of flux lines. Use Scale to change the density of field lines.

Vectors display magnitude and direction of magnetic field as a family of arrows.

Color Map displays distribution of chosen quantity.

While editing any scaling parameter, you can use Suggest to get the default value of the parameter, calculated with respect to visible part of the region.


Field picture in electrostatics

Equilines of Potential option switches visibility of field lines. Use Scale to change the lines’ density.

Vectors display magnitude and direction of electric field as a family of arrows.

Color Map displays distribution of chosen quantity.

While editing any scaling parameter, you can use Suggest to get the default value of the parameter, calculated with respect to visible part of the region.


Field picture in heat transfer

Isotherms option switches visibility of field lines. Use Scale to change the lines’ density.

Vectors display magnitude and direction of heat flux as a family of arrows.

Color Map displays distribution of chosen quantity.

While editing any scaling parameter, you can use Suggest to get the default value of the parameter, calculated with respect to visible part of the region.


Field picture in current flow

Equilines of Potential option switches visibility of field lines. Use Scale to change the lines’ density.

Vectors display magnitude and direction of electric field as a family of arrows.

Color Map displays distribution of chosen quantity.

While editing any scaling parameter, you can use Suggest to get the default value of the parameter, calculated with respect to visible part of the region.


Field picture in time-harmonic magnetics

Field Lines option switches visibility of flux lines at specified phase. Optionally, you can see second family of lines at phase shifted by quarter of period. Use Scale to change the density of field lines.

Vectors display magnitude and direction of magnetic field, strength, or Poynting vector as a family of arrows.

Color Map displays distribution of chosen quantity. You can choose between momentary values (at phase specified), root-mean-square (RMS) values, or peak values.

While editing any scaling parameter, you can use Suggest to get the default value of the parameter, calculated with respect to visible part of the region.


Field picture in stress analysis

Deformed Boundary and Shape indicated by means of deformed and original rectangular grid. Use Scale to adjust the picture.

Vectors of Displacement display magnitude and direction of deformation as a family of arrows.

Tensors of stress or strain display a pair of eigenvectors reflecting the direction of principal axes, magnitudes and signs of principal stresses (blue color denotes tension, red color—compression).

Color Map displays distribution of chosen quantity.

While editing any scaling parameter, you can use Suggest to get the default value of the parameter, calculated with respect to visible part of the region.

Change Cell size to adjust the grid used to display deformed shape, vector and tensor plots.


field lines

Those are isotherms for temperature fields, lines of equal potential in electrostatics and flux lines for magnetostatic problems.

To manipulate the picture, change the distance between neighboring lines. This distance is measured in units of chosen quantity.


vectors
vector plot

Family of line segments showing magnitude and direction of the vector quantity. Vectors are drawn in the nodes of the regular rectangular grid.

You can change the grid cell size and the scaling factor for a desired vector quantity.


color map

Shows distribution of a chosen scalar quantity. The color map is accompanied by the legend showing the correspondence between colors and numerical values.

You can adjust the color scale by changing the range limits for the chosen quantity.


contour

A directed curved line consisting of line segments and arcs (including the edges of the model). Contours are used to display X-Y plots or tables, and to calculate integrals.

Rules applied to the contours:

•	Contour may not intersect itself.

•	Open and closed contours are discerned.

•	Multiply connected contours have sense only for calculating integral quantities.

Contour is shown in the window as a set of directed lines or color-filled interior (closed counter-clockwise-directed contours).


Zooming the field picture
To magnify the picture:

1	Click Zoom In button in the postprocessor toolbar

2	Select the rectangle (click and drag diagonally), which then will occupy the whole window.

To see more of the model:

•	Choose Zoom Out button in the postprocessor toolbar.

•	Or, choose Zoom to Fit to see the whole model.


Examining local field data

To obtain local field data, choose Local Values in View menu or context (right mouse button) menu in field picture window. Then you can click points where you need to know the values of the field quantities.

Local values are shown in a window, which also provides additional functionality:

•	To enter coordinates of the point of interest from keyboard, select any of coordinates with mouse and then click it again (after a period, to avoid the double-click effect). You can edit either Cartesian or polar coordinates.

•	Double-clicking the item, you can change the quantity, whose distribution is shown as color map in the field view.

•	Values of physical quantities can be copied to clipboard for printing numerical results, or to pass them to other application program, e.g., a spreadsheet program to produce a report. Click Copy to Clipboard in the context (right mouse button) menu. To see or copy exactly those field quantities you need, you can expand or collapse branches in the tree.

•	Context (right mouse button) menu also allows fast access to several other controls otherwise accessible in the Field Picture dialog.

Related Topics

Formulae


Editing contours

QuickField allows editing contours in field picture windows. The following operations change the current contour state:

Adding lines	attaches a line segment or an arc to the contour. The arc is specified by its degree measure (zero means line segment) and two end points. Any arbitrary line may initiate the contour, but only adjacent lines are accepted later. The line cannot be added to the closed contour. There are two ways to add lines to contour:
Choose Pick Elements from Contour menu or context menu and then drag mouse with left button pressed.
Or, choose Add Lines from Contour menu or context menu and enter end points coordinates from keyboard.

Adding edges	appends the contour with an edge of the model. The contour may be initiated by any arbitrary edge, but only adjacent edges are accepted later. The edge cannot be added to the closed contour, or if the ending point of the contour does not currently coincide with model’s vertex.
To add edges, choose Pick Elements from Contour menu or context menu and then pick series of adjacent edges with mouse.

Adding blocks	considers the current closed contour as a border of the plane region and updates that region by adding (or subtracting) a block of the model in the sense of set theory.
To add blocks, choose Pick Elements from Contour menu or context menu and then pick blocks with mouse.

Close contour	closes an open contour by connecting its open ends with a straight line or an arc, depending on current degree measure in the postprocessing toolbar.

Change direction	alters the contour direction.

Clear	deletes the entire contour.

Delete last	deletes the last element (line or edge) in the contour. Not applicable to multiply connected contours.

The direction of the contour is significant in the following cases:

•	For volume integrals, the domain of integration lies to the left of the contour.

•	For surface integrals, the positive normal vector points to the right relative to the contour direction.

•	The starting point of the contour corresponds to zero point at the x-axis of the X-Y plot.

•	If the plotted or the integrated function has different values to the left and to the right of the contour, the right-hand value is used.


X-Y plots

You can analyze field distribution along contours. To open new X-Y plot window, choose X-Y plot in View menu or context (right mouse button) menu in field picture window, in which the contour is already defined.

In X-Y plot view, you can:

•	Select the set of shown quantities. Choose X-Y Plot Curves from View or context menu.

•	Zoom the plot in or out.

•	View the correspondence between quantities and curves (the legend).

•	Copy the picture to clipboard or file.

•	Open new X-Y plot window for the same contour.

Related Topics

Formulae


Selecting shown quantities
Selecting quantities

Single X-Y plot can show several quantities having the same unit of measurement at once. According to this, all quantities are combined into groups. To select quantities, choose the group among Groups of Quantities, and then Add quantities of your choice among the Available Quantities.

You can also edit Minimum and Maximum values of Y axis of the plot. Use Suggest to calculate the range limits for selected set of quantities.

To manipulate X-Y plot appearance, switch on or off markers and gridlines visibility.

Related Topics

Formulae


Calculating integrals

To calculate integrals, choose Integral Values in View menu or context (right mouse button) menu in field picture window, in which the contour is already defined.

QuickField calculates line, surface and volume integrals. In plane-parallel problem, a contour defines cylindrical (in generalized sense) surface of infinite depth, or volume of that cylinder for volume integral. Therefore, in plane-parallel formulation surface and volume integrals are calculated per unit depth. In axisymmetric problem, a contour defines toroidal surface, or toroid for volume integral.

Positive direction of a contour is counter-clockwise. The direction of the contour is accounted as follows:

•	For volume integrals the domain of integration lies to the left of the contour.

•	For surface integrals the positive normal vector points to the right relative to the contour direction.

•	If the plotted or the integrated function has different values to the left and to the right of the contour, the right-hand value is used.

Force, torque and electric charge integrals represent real physical quantities only when the contour is closed. However, these integrals are calculated for the unclosed contours too, for particular interest.

When the electrostatic or magnetic force, torque, electric charge, electric current or heat flux are to be calculated, the domain of integration may be chosen by many different ways. The only requirement for the surface of integration is to contain all the necessary bodies, but to avoid any extra bodies or field sources. It is important to understand that the accuracy will be the best if you choose the integration surface as far as possible from the places with strong inhomogeneity of field, e.g., field sources or boundaries of conducting or ferromagnetic bodies.

When calculating the flux linkage the domain of integration must exactly fit the cross section of the coil.

Related Topics

Integral formulae


Postprocessor tables
Tables

QuickField can display the field data at discrete points, distributed along the currently selected contour, in table view. To open new table window, choose Table in View menu or context (right mouse button) menu in field picture window, in which the contour is already defined.

In table view, you can:

•	Select the list of shown quantities (table columns). Choose Columns in View or context menu.

•	Select how the points are distributed along the contour (table rows). Choose Rows in View or context menu.

•	Insert additional rows at specified distance from the beginning of the contour. Choose Insert in Edit or context menu.

•	Copy the set of rows or the whole table to Windows clipboard. In latter case (when all of the rows are selected), column headers are also copied. To copy the header only, click the right mouse button within the header and choose Copy Header from the context menu.

•	Save the table to a file on disk. Click Save As in the File menu and select the name for the file.


Exporting field
Exporting field values

To work with the field data in other applications, QuickField can save various field quantities of the whole model or any of its rectangular sub-regions into a file .

To save the field:

1	In any postprocessor window, click Export Field in the File menu. The Field Export wizard appears.

2	In the Available Quantities list, choose the quantities you want to be written to the file.

3	Edit the dimensions of the output region and the density of the grid, in the nodes of which field values will be exported.

4	You may want to include the number of rows, columns and quantities, to make it easier for the target application to understand the file. In case of binary file, these values are written as 32-bit integers. When done, click Next.

5	Choose the name and folder for the file, or click Browse to find the location.

6	The file can be stored either in text or in binary format. The latter takes less disk space, but can be unreadable on computers based on other than Intel platform.

7	Column Titles and Values Format controls help you tune the appearance of the file.

8	Click Finish to save the file.


Color Legend
Color map legend

The legend shows the correspondence between colors in the field picture and their numerical values. In the legend window, you can manipulate the range of the color plot:

•	Click within the color bar and move mouse with left button held down to narrow (zoom in) the range.

•	Double-click within the color bar to return the range to its default.

The legend can be copied to clipboard as picture. Before that you may want to change from color plot to gray scale for monochrome printing. These command are available in the context (right mouse button) menu.


X-Y Legend
X-Y plot legend

The legend shows the notation for curves in X-Y plot. In the legend window, you can select quantities to show their distribution.

The legend can be copied to clipboard as picture. Before that you may want to change from color plot to gray scale for monochrome printing. These command are available in the context (right mouse button) menu.


Nonlinear permanent magnet (magnetostatic analysis example)
Magn1: Nonlinear permanent magnet

A permanent magnet and a steel keeper in the air.

Problem type:

A nonlinear plane-parallel problem of magnetostatics.

Geometry:

All dimensions are in centimeters.

The permanent magnets are made of ALNICO, coercive force is 147218 A/m. The polarizations of the magnets are along vertical axis opposite to each other. The demagnetization curve for ALNICO:

H (A/m)	–147218	–119400	–99470	–79580	–53710	–19890	0.0
B (T)	0.0	0.24	0.4	0.5	0.6	0.71	0.77
The B-H curve for the steel:

H (A/m)	400	600	800	1000	1400	2000	3000	4000	6000
B (T)	0.73	0.92	1.05	1.15	1.28	1.42	1.52	1.58	1.60
Comparison of results

Maximum flux density in Y-direction:

ANSYS	0.42
COSMOS/M	0.404
QuickField	0.417
See the Magn1.pbm problem in the Examples folder.


Solenoid actuator (magnetostatic analysis example)
Magn2: Solenoid actuator

A solenoid actuator consists of a coil enclosed in a ferromagnetic core with a plunger. Calculate the magnetic field and a force applied to the plunger.

Problem type:

A nonlinear axisymmetric problem of magnetics.

Geometry:

All dimensions are in centimeters.

Given:

Relative permeability of air and coil μ = 1;
Current density in the coil j = 1,000,000 A/m²;
The B-H curve for the core and the plunger:

H (A/m)	460	640	720	890	1280	1900	3400	6000
B (T)	0.80	0.95	1.00	1.10	1.25	1.40	1.55	1.65
Problem:

Obtain the magnetic field in the solenoid and a force applied to the plunger.

Solution:

This magnetic system is almost closed, therefore outward boundary of the model can be put relatively close to the solenoid core. A thicker layer of the outside air is included into the model region at the plunger side, since the magnetic field in this area cannot be neglected.

Mesh density is chosen by default, but to improve the mesh distribution, three additional vertices are added to the model. We put one of these vertices at the coil inner surface next to the plunger corner, and two others next to the corner of the core at the both sides of the plunger.

A contour for the force calculation encloses the plunger. It is put in the middle of the air gap between the plunger and the core. While defining the contour of integration, use a strong zoom-in mode to avoid sticking the contour to existing edges.

The calculated force applied to the plunger F = 374.1 N.

See the Magn2.pbm problem in the Examples folder.

Comparison of results

Maximum flux density in Z-direction in the plunger:

	Bz (T)
Reference	0.933
QuickField	1.0183
Reference

D. F. Ostergaard, "Magnetics for static fields", ANSYS revision 4.3, Tutorials, 1987.


Ferromagnetic C-magnet (magnetostatic analysis example)
Magn3: Ferromagnetic C-magnet

A permanent C-magnet in the air. The example demonstrates how to model curved permanent magnet using the equivalent surface currents.

Problem Type:

Plane problem of magnetics.

Geometry of the magnet:

Given:

Relative permeability of the air μ = 1;
Relative permeability of the magnet μ = 1000;
Coercive force of the magnet Hc = 10000 A/m.

The polarization of the magnet is along its curvature.

Solution:

To avoid the influence of the boundaries while modeling the unbounded problem, we'll enclose the magnet in a rectangular region of air and specify zero Dirichlet boundary condition on its sides.

Magnetization of straight parts of the magnet is specified in terms of coercive force vector. Effective surface currents simulate magnetization in the middle curved part of the magnet.

See the Magn3.pbm problem in the Examples folder.


Electric motor (magnetostatic analysis example)
Magn4: Electric motor

A brushless DC motor with permanent magnets and three phase coil excitation.

Problem Type:

A nonlinear plane-parallel problem of magnetostatics.

Geometry:

Axial length of the motor is 40 mm.

The four magnets are made of Samarium-Cobalt with relative permeability of 1.154 and coercive force of 550000 A/m. The current densities for the coil slots are as follows: 1,300,000 A/m² on R+, –1,300,000 A/m² on R–, 1,300,000 A/m² on S+, –1,300,000 A/m² on S–, and zero on T+ and T–. The inner and outer frames are made of Cobalt-Nickel-Copper-Iron alloy.

The B-H curve for the Cobalt-Nickel-Copper-Iron alloy:

H  (A/m)	20	60	80	95	105	120
B  (T)	0.19	0.65	0.87	1.04	1.18	1.24
H  (A/m)	140	160	180	200	240	2500
B  (T)	1.272	1.3	1.32	1.34	1.36	1.45
The B-H curve for the steel:

H  (A/m)	400	600	800	1000	1400	2000	3000	4000	6000
B  (T)	0.73	0.92	1.05	1.15	1.28	1.42	1.52	1.58	1.60
See the Magn4.pbm problem in the Examples folder.


Slot embedded conductor (time-harmonic magnetics example)
HMagn1: Slot embedded conductor

Problem Type:

A plane problem of time-harmonic magnetic field.

Geometry:

A solid copper conductor embedded in the slot of an electric machine carries a current I at a frequency f.

Given:

Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper σ = 58,005,000 S/m;
Current in the conductor I = 1 A;
Frequency f = 45 Hz.

Problem:

Determine current distribution within the conductor and complex impedance of the conductor.

Solution:

We assume that the steel slot is infinitely permeable and may be replaced with a Neumann boundary condition. We also assume that the flux is contained within the slot, so we can put a Dirichlet boundary condition along the top of the slot. See HMagn1.pbm problem in the Examples folder for the complete model.

The complex impedance per unit length of the conductor can be obtained from the equation

where V is a voltage drop per unit length. This voltage drop on the conductor can be obtained in Local Values mode of the postprocessing window, clicking an arbitrary point within the conductor.

Comparison of Results

	Re Z (Ohm/m)	Im Z (Ohm/m)
Reference	0.00017555	0.00047113
QuickField	0.00017550	0.00047111
Reference

A. Konrad, “Integrodifferential Finite Element Formulation of Two-Dimensional Steady-State Skin Effect Problems”, IEEE Trans. Magnetics, Vol MAG-18, No. 1, January 1982.


Symmetric double line of conductors (time-harmonic magnetics example)
HMagn2: Symmetric double line of conductors

Problem Type:

A plane problem of time-harmonic magnetic field.

Geometry:

Two copper square cross-section conductors with equal but opposite currents are contained inside rectangular ferromagnetic coating. All dimensions are in millimeters.

Given:

Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper σ = 56,000,000 S/m;
Magnetic permeability of coating μ = 100;
Conductivity of coating σ = 1,000,000 S/m;
Current in the conductors I = 1 A;
Frequency f = 100 Hz.

Problem:

Determine current distribution within the conductors and the coating, complex impedance of the line, and power losses in the coating.

Solution:

We assume that the flux is contained within the coating, so we can put a Dirichlet boundary condition on the outer surface of the coating. See HMagn2.pbm problem in the Examples folder for the complete model.

The complex impedance per unit length of the line can be obtained from the equation

where V1 and V2 are voltage drops per unit length in each conductor. These voltage drops are equal with opposite signs due to the symmetry of the model. To obtain a voltage drop, switch to Local Values mode in postprocessing window, and then pick an arbitrary point within a conductor.

The impedance of the line Z = 0.000493 + i 0.000732 Ohm/m.

To obtain power losses in the coating:

1	In the postprocessing mode, choose Pick Elements and pick the coating block to create the contour.

2	Choose Integral Values and select Joule heat from the list of integral quantities and choose Calculate.

The power losses in the coating P = 0.0000437 W/m.


Microstrip transmission line (electrostatic analysis example)
Elec1: Microstrip transmission line

A shielded microstrip transmission line consists of a substrate, a microstrip, and a shield.

Problem Type:

Plane-parallel problem of electrostatics.

Geometry:

The transmission line is directed along z-axis, its cross section is shown on the sketch. The rectangle ABCD is a section of the shield, the line EF represents a conductor strip.

Given:

Relative permittivity of air ε = 1;
Relative permittivity of substrate ε = 10.

Problem:

Determine the capacitance of a transmission line.

Solution:

There are several different approaches to calculate the capacitance of the line:

•	To apply some distinct potentials to the shield and the strip and to calculate the charge that arises on the strip;

•	To apply zero potential to the shield and to describe the strip as having constant but unknown potential and carrying the charge, and then to measure the potential that arises on the strip.

Both these approaches make use of the equation for capacitance:

.

Other possible approaches are based on calculation of stored energy of electric field. When the voltage is known:

,

and when the charge is known:

Experiment with this example shows that energy-based approaches give little bit less accuracy than approaches based on charge and voltage only. The first approach needs to get the charge as a value of integral along some contour, and the second one uses only a local value of potential, this approach is the simplest and in many cases the most reliable.

The first and third approaches are illustrated in the Elec1_1.pbm problem in the Examples folder, and the Elec1_2.pbm explains the second and the fourth approaches.

Results:

Theoretical result:	C = 178.1 pF/m.
Approach 1:	C = 177.83 pF/m (99.8%).
Approach 2:	C = 178.47 pF/m (100.2%).
Approach 3:	C = 177.33 pF/m (99.6%).
Approach 4:	C = 179.61 pF/m (100.8%).


Two conductor transmission line (electrostatic analysis example)
Elec2: Two conductor transmission line

Problem Type:

A plane problem of electrostatics.

Geometry:

The problem's region is bounded by ground from the bottom side and extended to infinity on other three sides.

Given:

Relative permittivity of air ε = 1;
Relative permittivity of dielectric ε = 2.

Problem:

Determine self and mutual capacitance of conductors.

Solution:

To avoid the influence of outer boundaries, we'll define the region as a rectangle large enough to neglect side effects. To calculate the capacitance matrix we set the voltage U = 1 V on one conductor and U = 0 on the another one.

Self capacitance: ;

Mutual capacitance: ;

where charge Q1 and Q2 are evaluated on rectangular contours around conductor 1 and 2 away from their edges. We chose the contours for the C11 and C12 calculation to be rectangles 6 ≤ x ≤ 0, 0 ≤ y ≤ 4 and 0 ≤ x ≤ 6, 0 ≤ y ≤ 4 respectively.

Comparison of Results

	C11 (F/m)	C12 (F/m)
Reference	9.231011	8.501012
QuickField	9.43 1011	8.571012
Reference

A. Khebir, A. B. Kouki, and R. Mittra, "An Absorbing Boundary Condition for Quasi-TEM Analysis of Microwave Transmission Lines via the Finite Element Method", Journal of Electromagnetic Waves and Applications, 1990.

See the Elec2.pbm problem in the Examples folder.


Slot of an electric machine (heat transfer example)
Heat1: Slot of an electric machine

Temperature field in the stator tooth zone of power synchronous electric machine.

Problem Type:

The plane-parallel problem of heat transfer with convection.

Geometry:

All dimensions are in millimeters. Stator outer diameter is 690 mm. Domain is a 10-degree segment of stator transverse section. Two armature bars laying in the slot release ohmic loss. Cooling is provided by convection to the axial cooling duct and both surfaces of the core.

Given:

Specific copper loss: 360000 W/m³;
Heat conductivity of steel: 25 J/K·m;
Heat conductivity of copper: 380 J/K·m;
Heat conductivity of insulation: 0.15 J/K·m;
Heat conductivity of wedge: 0.25 J/K·m;

Inner stator surface:

Convection coefficient: 250 W/K·m²;
Temperature of contacting air: 40°C.

Outer stator surface:

Convection coefficient: 70 W/K·m²;
Temperature of contacting air: 20°C.

Cooling duct:

Convection coefficient: 150 W/K·m²;
Temperature of contacting air: 40°C.

See the Heat1.pbm problem in the Examples folder.


Cylinder with temperature dependent conductivity (heat transfer example)
Heat2: Cylinder with temperature dependent conductivity

A very long cylinder (infinite length) is maintained at temperature Ti along its internal surface and To along its external surface. The thermal conductivity of the cylinder is known to vary with temperature according to the linear function λ(T) = C0 + C1·T.

Problem Type:

An axisymmetric problem of nonlinear heat transfer.

Geometry:

Given:

Ri = 5 mm, Ro = 10 mm;
Ti = 100°C, To = 0°C;
C0 = 50 W/K·m, C1 = 0.5 W/K·m.

Problem:

Determine the temperature distribution in the cylinder.

Solution:

The axial length of the model is arbitrarily chosen to be 5 mm.

Comparison of Results

Radius	QuickField	Theory
0.6	79.2	79.2
0.7	59.5	59.6
0.8	40.2	40.2
0.9	20.7	20.8
See the Heat2.pbm problem in the Examples folder.


Perforated plate (stress analysis example)
Stres1: Perforated plate

A thin rectangular sheet with a central hole subject to tensile loading.

Problem Type:

Plane problem of stress analysis (plane stress formulation).

Geometry of the plate:

Length: 240 mm;
Width: 180 mm;
Radius of central opening: 30 mm;
Thickness: 5 mm.

Given:

Young's modulus E = 207000 N/mm²;
Poisson's ratio ν = 0.3.

The uniform tensile loading (40 N/mm²) is applied to the bottom edge of the structure.

Problem:

Determine the concentration factor due to presence of the central opening.

Solution:

Due to mirror symmetry one quarter of the structure is presented, and internal boundaries are restrained in X and Y directions respectively.

The concentration factor may be obtained from the loading stress (40 N/mm²) and the maximum computed stress (146 N/mm²) as

k = 146 / 40 = 3.65.

See the Stres1.pbm problem in the Examples folder.


Stress distribution in a long solenoid (magneto-structural coupling example)
Coupl1: Stress distribution in a long solenoid

A very long, thick solenoid has a uniform distribution of circumferential current. The magnetic flux density and stress distribution in the solenoid has to be calculated.

Problem Type:

An axisymmetric problem of magneto-structural coupling.

Geometry:

Given:

Dimensions Ri = 1 cm, Ro = 2 cm;
Relative permeability of air and coil μ = 1;
Current density j = 1e5 A/m²;
Young's modulus E = 1.075e11 N/m²;
Poisson's ratio ν = 0.33.

Problem:

Calculate the magnetic flux density and stress distribution.

Solution:

Since none of physical quantities varies along z-axis, a thin slice of the solenoid could be modeled. The axial length of the model is arbitrarily chosen to be 0.2 cm. Radial component of the flux density is set equal to zero at the outward surface of the solenoid. Axial displacement is set equal to zero at the side edges of the model to reflect the infinite length of the solenoid.

Comparison of Results

Magnetic flux density and circumferential stress at r = 1.3 cm:

	Bz T	σθ N/m²
Reference	8.796e-3	97.407
QuickField	8.798e-3	96.71
Reference

F. A. Moon, "Magneto-Solid Mechanics", John Wiley & Sons, N.Y., 1984, Chapter 4.

See the Coupl1MS.pbm and Coupl1SA.pbm problems in the Examples folder for magnetic and structural parts of this problem respectively.


Cylinder subject to temperature and pressure (thermo-structural coupling example)
Coupl2: Cylinder subject to temperature and pressure

A very long, thick-walled cylinder is subjected to an internal pressure and a steady state temperature distribution with Ti and To temperatures at inner and outer surfaces respectively. Calculate the stress distribution in the cylinder.

Problem Type:

An axisymmetric problem of thermal-structural coupling.

Geometry:

Given:

Dimensions Ri = 1 cm, Ro = 2 cm;
Inner surface temperature Ti = 100°C;
Outer surface temperature To = 0°C;
Coefficient of thermal expansion α = 1e-6 1/K;
Internal pressure P = 1e6 N/m²;
Young's modulus E = 3e11 N/m²;
Poisson's ratio ν = 0.3.

Problem:

Calculate the stress distribution.

Solution:

Since none of physical quantities varies along z-axis, a thin slice of the cylinder can be modeled. The axial length of the model is arbitrarily chosen to be 0.2 cm. Axial displacement is set equal to zero at the side edges of the model to reflect the infinite length of the cylinder.

Comparison of Results

Radial and circumferential stress at r  1.2875 cm:

	σr N/m²	σθ N/m²
Theory	3.9834e6	5.9247e6
QuickField	3.959e6	5.924e6
Reference

S. P. Timoshenko and Goodier, "Theory of Elasticity", McGraw-Hill Book Co., N.Y., 1961, pp. 448-449.

See the Coupl2HT.pbm and Coupl2SA.pbm problems in the Examples folder for the corresponding heat transfer and structural parts of this problem.


Temperature distribution in an electric wire (electro-thermal coupling example)
Coupl3: Temperature distribution in an electric wire

Calculate the temperature distribution in a long current carrying wire.

Problem Type:

An axisymmetric problem of electro-thermal coupling.

Geometry:

Given:

Wire diameter d = 10 mm;
Resistance R = 3e-4 Ω/m;
Electric current I = 1000 A;
Thermal conductivity λ = 20 W/K·m;
Convection coefficient α = 800 W/K·m²;
Ambient temperature To = 20°C.

Problem:

Calculate the temperature distribution in the wire.

Solution:

We arbitrary chose a 10 mm piece of wire to be represented by the model. For data input we need the wire radius r = 5 mm, and the resistivity of material:

,

and voltage drop for our 10 mm piece of the wire:

.

For the current flow problem we specify two different voltages at two sections of the wire, and a zero current condition at its surface. For heat transfer problem we specify zero flux conditions at the sections of the wire and a convection boundary condition at its surface.

Comparison of Results

Center line temperature:

	T °C
Theory	33.13
QuickField	33.14
Reference

W. Rohsenow and H. Y. Choi, "Heat, Mass, and Momentum Transfer", Prentice-Hall, N.J., 1963.

See the Coupl3CF.pbm and Coupl3HT.pbm problems in the Examples folder for the corresponding current flow and heat transfer parts of this problem.


Tokamak solenoid (magneto-structural coupling example)
Coupl4: Tokamak solenoid

The central solenoid of the ohmic heating system for a tokamak fusion device.

Problem Type:

An axisymmetric problem of magneto-structural coupling.

Geometry:

The solenoid consists of 80 superconducting coils fixed in common plastic structure. Due to mirror symmetry one half of the structure is modeled.

Given:

Data for magnetic analysis:

Current density in coils j = 3e8 A/m²;
Magnetic permittivity of plastic, coils and liquid helium inside coils μ = 1.

Data for stress analysis:

Copper of coils:

Young's modulus E = 7.74e10 N/m²;
Poisson's ratio ν = 0.335;
Maximum allowable stress: 2.2e8 N/m².

Plastic structure:

Young's modulus E = 2e11 N/m²;
Poisson's ratio ν = 0.35;
Maximum allowable stress: 1e9 N/m².

In the Examples folder the Coupl4MS.pbm is the problem of calculating the magnetic field generated by the solenoid, and Coupl4SA.pbm analyzes stresses and deformations in coils and plastic structure due to Lorentz forces acting on the coils.


Your Examples folder contains Magn1 problem, nonlinear permanent magnet. Here we’ll provide you with step-by-step instructions how to create and solve just the same problem from scratch. We'll forget the solution made in Magn1.pbm, and start a new problem, Magnet.pbm.

To create a new problem:

1	Click New in the File menu; the dialog box appears, asking for the kind of QuickField document you wish to create.

2	Click QuickField Problem, and then click OK. Then, new dialog box asks for the file name and location for the new problem.

3	In the Problem file name box, type Magnet.

4	In the Create in folder area, change the folder, if needed.

5	Click Next.

  Continue


To assign the problem with appropriate features:

1	In the Problem Type area, click Magnetostatics.

2	Click Plane-parallel.

3	We'll agree with suggested model and data file names (Magnet.mod and Magnet.dms.) Click Next.

To select convenient length measurement units (millimeters):

1	Click Millimeters.

2	Click Finish to accept the new problem.

3	QuickField now opens the new problem window for Magnet.pbm. On the File menu, click Save to store the problem description in the file.

To start editing the model:

1	On the Edit menu, click Geometry Model, or double-click Magnet.mod item in the tree, or click Edit File from context menu clicking right mouse button on that item.

2	Confirm creating new model.

The model window now opens. For convenience, you can maximize the window.

  Continue


Creating geometry elements

First, we should make a decision concerning dimensions of the problem's region. Since the given problem is physically unbounded, the magnetic system must be surrounded with a layer of air thick enough to neglect the influence of the boundary. We suppose that three times the width of the air gap between the magnet and the steel keeper will be a satisfactory thickness of the air layer around the magnet, so the rectangle 100x100 mm will fit our region's geometry.

The first step with the new model in Model Editor is to adjust window dimensions fitting the problem's region. Since the problem has vertical axis of symmetry, it is convenient to set zero of x-axis at the axis of symmetry. So the region fits the square (–50 ≤ x ≤ 50, 0 ≤ y ≤ 100). To make this rectangle occupying most of the window:

1	On the toolbar, click Zoom In.

2	Move mouse pointer to (–50, 0), checking the coordinates in lower right corner of the QuickField application window. You need not position mouse exactly at this point but somewhere to the bottom left not far the point.

3	Click the left mouse button and drag to (50, 100).

4	The window reflects your zoom operation. Click Zoom In once again co close zooming mode.

To simplify object creation, we’ll use Snap to Grid feature.

We notice that all sketch element sizes are multipliers of 10 mm in both horizontal and vertical directions. To set 10 mm grid:

1	On Edit or context menu, click Grid Settings, a dialog box appears.

2	In the Horizontal box, type 10. Since Anisotropic box is unchecked, the same value appears in Vertical box.

3	Grid origin at (0, 0) is okay, so we need not change anything else. Click OK to close the dialog.

  Continue


Now we can proceed with defining the geometry itself. To create edges constituting the model boundaries:

1	Press INS (or Insert Mode on Edit menu, or Insert Vertices/Edges on context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Click the left mouse button at (–20, 20) and drag to (20, 20) to create the edge AB. The edge appears on the screen immediately as you release the mouse button.

3	Repeat 2 at (–20, 30 : 20, 30) for CF, (–20, 40 : –10, 40) for GH, (10, 40 : 20, 40) for IJ, (-20, 20 : -20, 40) for AG, (-10, 30 : -10, 40) for DH and so on. There is no matter, in which order you create edges, direction of edges also does not matter. If the point you want to click is out of window, use scroll bars to scroll the picture. Don't worry about making mistakes—you can remove erroneous vertices and edges later. Don’t forget to create edges OPRQ surrounding the model.

4	Press INS again to cancel Insert mode and return to Pick mode.

If you have created excess points or edges, you can remove them now:

1	Hold CTRL key and pick excess objects with mouse to select them. If you have selected the object you did not want to, pick it again to unselect it. Release CTRL.

2	Press DEL (or Delete Selection on Edit menu or context menu). Deleted objects immediately disappear.

  Continue


We are done with the model's geometry. Now we can assign labels to geometrical objects to describe material properties, sources and boundary conditions.

The problem contains four materials having different properties: the air, the steel and two pieces of permanent magnet, which differ in direction of magnetization vector. To be clear, we can use the labels Air, Steel, ALNICO Up and ALNICO Dn to label appropriate blocks. To assign these labels to blocks:

1	Double-click within the CDHG rectangle. The block becomes selected and the Selection Properties dialog appears.

2	In Label box, type ALNICO Dn.

3	Click OK to close the dialog.

4	Repeat the last actions to label the CDJI rectangle as ALNICO Up, and the OPRQ as Air.

5	Pick inside the ABFC rectangle, then press and hold CTRL key and pick inside the KLNM rectangle to select two blocks at once.

6	Click right mouse button within selected area to bring up the context menu without changing the selection.

7	On the context menu, click Properties and assign the Steel label to both blocks.

8	Click OK to close the dialog.

Edge labels are used to define specific boundary conditions on inner and outer boundaries of the region. In our case, we need to specify zero Dirichlet boundary condition for the outer boundary (rectangle OPRQ). To assign labels to edges:

1	Pick consecutively four edges, which constitute the rectangle OPRQ, holding the CTRL key. Those edges become highlighted that indicates the selection. If you have selected excess edge, vertex or block, pick it once more to unselect it.

2	Click right mouse button within selection to bring up the context menu without changing the selection.

3	On the context menu, click Properties and assign the Zero label to selected edges.

4	Click OK to close the dialog.

Now we have finished with assigning labels to geometrical objects.

  Continue


We can proceed with building a mesh of finite elements. To define the mesh density, we need to define mesh spacing parameters in several vertices of the model. We suppose that the field is most non-homogeneous around the magnets, so the mesh there must be maximum dense. Therefore, we'll assign the spacing value of 5 mm to the vertices G, H, I and J and the value of 12 mm to the vertices O, P, R and Q to build the mesh of approximately 200 nodes. To define spacing values:

1	Select vertices G, H, I and J and click Properties on the context menu.

2	Click Manual spacing and type 5.

3	Click OK to close the dialog.

4	Repeat these actions to assign 12 mm spacing to vertices O, P, R and Q.

5	On the Edit menu, click Build Mesh, and then In All Blocks to build the meshes for all blocks at once.

Now the model is ready. To save model in a file, click Save from the File menu.

  Continue


To edit material properties and boundary conditions:

You probably noticed that the block and edge labels appeared in the problem view while you have entered them in the model. Icons are supplied with question mark icon, which means that the labels are referenced by the model, but the data for them are not yet defined. Now we’ll proceed with assigning data to labels.

To define the data for block label Air:

1	Double-click the Air item or click Properties in its context menu. A dialog box appears, prompting to enter material properties and distributed source for block label Air.

2	Type 1 in any text box for components of magnetic permeability tensor.

3	Click OK.

  Continue


Now we'll learn how to describe nonlinear magnetic properties by means of editing the B-H curve. To start editing for block label Steel:

1	Double-click the Steel item or click Properties in its context menu. The property editing dialog box appears.

2	Select the Nonlinear box. This causes starting the B-H Curve Editor.

With the Curve Editor, you can simply enter the values from the table, point by point, checking the curve in the graph to the left of the table. The point (0; 0) is always presented in the table, which cannot be edited nor deleted. Since the cursor is already in the box for new B value, you can start entering new points. To create the first point (B = 0.73 T, H = 400 A/m, see the table below):

1	Type 0.73 and press ENTER. The cursor will move to the box for H value.

2	Type 400 and press ENTER. The new point will be added to the table and immediately displayed in the graph. The cursor will return back to the box for B value.

3	Repeat these actions for other points of the table. Points may be entered in any order.

H (A/m)	400	600	800	1000	1400
B (T)	0.73	0.92	1.05	1.15	1.28
H (A/m)	2000	3000	4000	6000
B (T)	1.42	1.52	1.58	1.60
In case of mistyping, the erroneous point would in general produce a noticeable anomaly in the displayed curve. You can select this point in the graph or in the table and then delete it or correct its coordinates.

When you are done with entering points, and the curve looks like classic B-H curve, click the Close button to finish curve editing and return to property editing dialog. Since we do not want to change any more values, click OK button to finish editing data for label Steel.

  Continue


Describing data for the permanent magnet is a bit more complicated. In addition to demagnetization curve, the direction of resistant magnetization should be specified by means of the vector of coercive force. Now we'll define the demagnetization curve for label ALNICO Up:

1	Double-click ALNICO Up item or click Properties in its context menu. The property editing dialog box appears.

2	Type 1 in any text box for components of magnetic permeability tensor. This is void action, the only purpose of which is to specify that the data for the label is not empty, so that other text boxes will become available.

3	In the Magnitude text box for coercive force, type 147218.

4	In the Direction box, type 90. Direction is counted counter-clockwise from the horizontal axis.

5	Click the Nonlinear box. This starts the B-H Curve Editor.

Note that the predefined point is now at (-147218, 0). It is exactly the first point from the table below. Now we can continue with adding all other points from the table. When this job is done, click the Close button to finish curve editing and return to property editing dialog. Then click OK button to finish editing data for label ALNICO Up.

H (A/m)	–147218	–119400	–99470	–79580
B (T)	0.0	0.24	0.4	0.5
H (A/m)	–53710	–19890	0.0
B (T)	0.6	0.71	0.77
  Continue


To define data for label ALNICO Dn, we need not repeat all this actions. We can simply copy the data from ALNICO Up, and change the direction of the coercive force. To do this:

1	Select ALNICO Up in the tree.

2	On the Edit menu or context menu, click Copy. Open the menu again and click Paste. The copy of ALNICO Up named ALNICO Up (2) appears in the tree.

3	Select ALNICO Up (2) in the tree.

4	On the Edit menu or context menu, click Rename. Change the name to ALNICO Dn and press ENTER.

5	Double-click ALNICO Dn item or click Properties in its context menu. The property editing dialog box appears.

6	In the Direction box, change 90 to -90 to change the direction of coercive force to the opposite one.

7	Click OK.

  Continue


Now we'll continue with edge labels' data. We'll define the label Zero as homogeneous Dirichlet boundary condition (A = 0). To define the data for edge label Zero:

1	Select its name in the Edge Labels branch and double-click it or click Properties in its context menu. The property editing dialog box appears, allowing to assign to edge label any of possible boundary conditions.

2	Select the Magnetic Potential box. Zero value of pre-defined potential will be suggested.

3	Click OK.

All the data needed to solve the problem is now defined.

At last, we can solve the problem and analyze the solution. To do this in one step:

1	On the Edit menu or context menu, click Analyze Results. You will be suggested to solve the problem first, as the results are absent. You should also agree to save the data to the data description file.

2	Click OK.

  Done


Your Examples folder contains Magn4 problem, electric motor. Here we’ll provide you with step-by-step instructions how to create and solve just the same problem from scratch. We'll forget the solution made in Magn4.pbm, and start a new problem, Motor.pbm.

To create a new problem:

1	Click New in the File menu; the dialog box appears, asking for the kind of QuickField document you wish to create.

2	Select QuickField Problem and click OK. Then, new dialog box asks for the file name and location of the new problem.

3	In the Problem file name box, type Motor.

4	In the Create in folder area, change the folder, if needed.

5	Click Next.

  Continue


To assign the problem with appropriate features:

1	In the Problem Type area, click Magnetostatics.

2	Click Plane-parallel.

3	We'll agree with suggested model and data file names (Motor.mod and Motor.dms.) Click Next.

To select convenient length measurement units (millimeters):

1	Click Millimeters.

2	Click Finish to accept the new problem.

3	QuickField now opens the new problem window for Magnet.pbm. On the File menu, click Save to store the problem description in the file.

To start editing the model:

1	In the Edit menu, click Geometry Model, or double-click Motor.mod item in the tree, or click Edit File from context menu clicking right mouse button on that item.

2	Confirm creating new model.

The model window now opens. For convenience, you can maximize the window.

  Continue


Creating geometry elements

First, we should make a decision concerning dimensions of the problem's region. We choose a region large enough to contain the outer rim of the motor, so the rectangle 50x50 mm will fit our region's geometry.

The first step with the new model in Model Editor is to adjust window dimensions fitting the problem's region. Due to the model’s geometry, it is convenient to use the coordinate system with the origin at the center of the motor. So the region fits the square (–25 ≤ x ≤ 25, –25 ≤ y ≤ 25). To make this rectangle occupying most of the window:

1	Click Zoom In toolbar button.

2	Move mouse pointer to (–25, 25), checking the coordinates in lower right corner of the QuickField application window. You need not position mouse exactly at this point but somewhere to the bottom left not far the point.

3	Click the left mouse button and drag to (25, 25).

4	The window reflects your zoom operation. Click Zoom In once again co close zooming mode.

With this model, we’ll use 0.5 mm grid to create the most of geometry elements and we’ll use keyboard input to create precise elements that do not fit in 0.5 mm grid. To use Snap to Grid feature:

1	From Edit or context menu, click Grid Settings, a dialog box appears.

2	In Horizontal, type 0.5. Since Anisotropic box is unchecked, the same value appears in Vertical box.

3	Grid origin at (0, 0) is okay, so click OK to close the dialog.

  Continue


Now we can proceed with defining the geometry itself. Due to existing pattern in the model’s geometry, we’ll first create a few parts and then use a series of move and copy commands to generate a complete model. Let’s start with the coils and steel parts on the stator. Our first goal is to create 1/24 part of the coil structure.

We’ll first create edges AB and CD as horizontal line segments, and then rotate them by 7.5 degrees to their normal position. To create these edges we’ll need few auxiliary geometric objects, which will be deleted once we find required intersection points.

First we’ll create line segment from point (0, 0.375) to point (17, 0.375) and two 180° arcs with radii 12.5 and 14 mm:

1	Use Zoom In to set window dimensions to approximately (0, -20 : 40, 20). This is done for ability to control creation of new points visually.

2	In the Edit menu, click Add Vertices. The dialog box appears, allowing you to create new vertices entering their coordinates from keyboard.

3	Type 0 for x and 0.375 for y, then press ENTER to create a vertex.

4	Repeat the last step for the vertex with coordinates (17, 0.375).

5	Click Close to close the dialog box.

  Continue


Now we create horizontal line segment:

1	Press INS (or Insert Mode from Edit menu, or Insert Vertices/Edges from context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Click the left mouse button at first point (0, 0.375) and drag mouse to the second point (17, 0.375).

To create two arcs:

1	In New Edge Angle box on the toolbar, select Half arc (180°).

2	Drag from (0, –14) to (0, 14). New arc appears in the window.

3	Now drag from (0, –12.5) to (0, 12.5).

4	Press INS again to cancel Insert mode and return to Pick mode.

If you have created excess points or edges, you can remove them now:

1	Hold down the CTRL key and pick excess objects with mouse to select them. If you have selected the object you did not want to, pick it again to unselect it. Release CTRL.

2	Press DEL (or Delete Selection from Edit menu or context menu). Deleted objects immediately disappear.

  Continue


The intersection of the arcs with the line segment produced points A and B. Now we can delete extra line segments to the left of A and to the right of B:

1	Pick the vertex with coordinates (0, 0.375). The vertex will be highlighted.

2	Hold down the CTRL key and pick vertex with coordinates (17, 0.375). It will be added to selection.

3	Press DEL (or Delete Selection from Edit menu or context menu).

We have created the edge AB, now we can create CD using Copy command:

1	Pick a short line segment between arcs.

2	On the Edit menu or context menu, click Duplicate Selection, a dialog box appears.

3	Click Symmetry and then OK. By default the object is reflected with respect to the horizontal axis. At this point you can see a preview of the edge being created. To complete the creation process, click Yes button in the confirmation dialog box. Notice that the newly created edge remains selected, so there is no need to select it again in order to copy or move it.

  Continue


Now, when the edges AB and CD are created, we can rotate them to their final position:

1	On the Edit menu or context menu, click Select All, then Move Selection on the same menu. A dialog box appears.

2	Click Rotation, type 7.5 in the Angle text box, and then click OK. The whole group of edges will be rotated counter-clockwise by 7.5 degrees around the center point (0, 0).

We can now create the vertex E as a mirror image of the vertex A relative to X-axis.

1	Pick the vertex A.

2	On the Edit menu or context menu, click Duplicate Selection, a dialog box appears.

3	Click Symmetry and then OK. By default the vertex is reflected with respect to the X-axis. To confirm creation of new vertex, click Yes in the dialog box.

Next step is to create edges FG and GH. We will again build two arcs and one line segment to get points F, G and H as a result of intersection. Now we create the arcs:

1	Press INS (or Insert Mode from Edit menu, or Insert Vertices/Edges from context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Drag from (0, –17.5) to (0, 17.5). New arc appears in the window.

3	Now drag from (0, –20.5) to (0, 20.5).

To create a line segment:

1	On the Edit menu, click Add Vertices. The dialog box appears.

2	Type 13 for x and 0.75 for y, then press ENTER to create a vertex.

3	Repeat the last step for the vertex with coordinates (22, 0.75).

4	Click Close to close the dialog box.

5	Change Half arc (180°) to Straight Line (0°) as New Edge Angle.

6	Click the left mouse button at first point (13, 0.75) and drag mouse to the second point (22, 0.75).

7	Press INS again to cancel Insert mode and return to Pick mode.

  Continue


We have created edges FG and GH. To create edges IJ and JK we will first create a copy of the line segment FH using symmetry relative to X-axis, and then will rotate this copy by 15 degrees to obtain the line segment IK.

1	Pick edges FG and GH.

2	On the Edit menu or context menu, click Duplicate Selection, a dialog box appears.

3	Click Symmetry and then OK. By default the object is reflected relative to the X-axis. Confirm creation of new edges by clicking Yes button in the dialog box.

4	Click Duplicate Selection again. This time click Rotation, then type 15 for the Angle, then click OK. Confirm creation of new edges by clicking Yes button in the dialog box.

Lets now clean up our stator fragment by deleting all auxiliary elements. Finally we have to get a picture similar to the one shown. The most convenient way to delete an edge that contains an auxiliary vertex is to delete that vertex.

1	On the Edit menu or context menu, click Unselect All.

2	Hold down the CTRL key and pick vertices you want to delete. You can use rectangular selection (clicking and dragging diagonally) to select adjacent group of vertices.

3	Press DEL (or Delete Selection from Edit menu or context menu). Deleted objects immediately disappear.

This way you can delete all extra vertices and edges except the edge AC. To delete this last edge:

1	Click Zoom In on the toolbar. Select the region to zoom-in containing the edge AC.

2	Pick the edge AC.

3	Press DEL.

4	Click Zoom to Fit on the toolbar to see the whole model.

  Continue


Once we have finished with the fragment of the coil structure, we could create all the coils using the copy operation with rotation. But we will delay this process to keep more room for building the geometry of the rotor. Now we will start creating a magnet of the rotor.

1	On the Edit menu, click Add Vertices to create vertices with coordinates: (6.25, 5), (5, 6.25), (–5, 6.25).

2	Click Zoom to Fit on the toolbar to see the whole model.

Now we create edges AB, BC and two intermediate vertical edges which will eventually become CD and BE:

1	Press INS (or click Insert Mode on Edit menu, or Insert Vertices/Edges on context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Drag from (6.25, 5) to (5, 6.25), from (5, 6.25) to (–5, 6.25) , from (5, 6.25) to (5, 12), from (–5, 6.25) to (–5, 12).

To build the arc ED we will first create a bigger arc of the same radius:

1	Change Straight Line (0°) to Half arc (180°) as New Edge Angle.

2	Drag from (12, 0) to (–12, 0).

3	Press INS again to cancel Insert mode and return to Pick mode.

Now we can get rid of the extra edges, two arcs and two line segments. Finally we have to get a picture similar to the one shown here.

1	Hold down the CTRL key and pick vertices you want to delete.

2	Press DEL (or Delete Selection from Edit menu or context menu).

We are done with the first magnet and can now create the other three.

1	Click and drag diagonally to select all elements of the rotor fragment.

2	On the Edit menu or context menu, click Duplicate Selection, a dialog box appears.

3	Click Rotation and put 90 for Angle and 3 for Copies. Click OK. Confirm creation of new elements by clicking Yes.

  Continue


Let’s do the similar operation with the coil slots:

1	Click and drag diagonally to select all elements of the stator fragment. Remember that selected become only those model elements, which fit in the rectangle wholly.

2	On the Edit menu or context menu, click Duplicate Selection, a dialog box appears.

3	Click Rotation and put 15 for Angle and 23 for Copies. Click OK. Confirm creation of new elements by clicking Yes.

To complete the model geometry we have to create three circles with radii 5, 23 and 25 mm.

1	Press INS (or Insert Mode from Edit menu, or Insert Vertices/Edges from context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Drag from (5, 0) to (–5, 0) and then back from (–5, 0) to (5, 0), from (23, 0) to (–23, 0) and back, from (25, 0) to (–25, 0) and back.

3	Press INS again to cancel Insert mode and return to Pick mode.

We are now done with the model's geometry.

  Continue


Now we can assign labels to geometrical objects to describe material properties, sources and boundary conditions.

The problem contains five materials: the air, the steel, the frame’s Cobalt-Nickel-Copper-Iron alloy, Samarium-Cobalt magnets and coils. We’ll use the labels Air, Steel, Cobalt Alloy, and Magnet. Since the components of coercive force for each magnet would change, it is easier to define the permanent magnets by equivalent surface currents applied to the side edges of each magnet. In our case this approach is not exact, since it ignores coercive force in a thin curved part of each magnet. But explicit experiment shows that two approaches give very close results, so we can use the more convenient one.

Coils are loaded through a three-phase set up, with each phase having into and out of plane directions. We will use labels: Coil R+, Coil R–, Coil S+, Coil S–, Coil T+, and Coil T–.

To assign labels to blocks:

1	Double-click inside the steel section. The whole steel block surrounding all the 24 coil slots becomes selected and the Properties dialog box appears.

2	In Label area, type Steel and click OK.

3	Select the two air regions (the air gap between the rotor and stator and the air inside the inner frame), and label them as Air. Remember that simple clicking the object clears the previous selection, while clicking with the CTRL held down appends current object to the selection.

4	Next, select the inner and outer frames and type in the corresponding label Cobalt Alloy.

5	Select all the coil blocks that belong to R+ group. If you have selected an excess block, pick it once more to unselect it.

6	Label selected blocks as Coil R+.

7	Repeat the above process to label the rest of the coil slots according to the model’s figure as Coil R–, Coil  S+, Coil S–, Coil T+, Coil T–.

8	Next, assign Magnet label to all the four permanent magnet pieces.

  Continue


Edge labels are used to define surface currents on the edges of the magnets as well as specific boundary condition of zero Dirichlet boundary condition (zero normal flux, A = 0) at the very outer boundary of the frame. We need to assign the proper surface currents to create two radialy inward and two radialy outward directions for coercivities of the magnets. To assign labels to edges:

1	Select the two outer semicircular edges on the outer frame.

2	Press ALT+ENTER, the Properties dialog box appears.

3	In Label area, type A = 0 and press ENTER.

4	To label magnet edges, select the two side magnets’ edges in the first quadrant and two in the third quadrant, and label them as Magnet Left.

5	Repeat the above process to label the magnets’ edges in second and fourth quadrants as Magnet Right.

Now we are finished with assigning labels to geometrical objects.

We can proceed with building a mesh of finite elements. We’ll use the fully automatic mode to create the mesh. With this option we don’t need to specify the mesh density at any point, QuickField’s sophisticated mesher determines a suitable mesh automatically.

•	On the Edit menu, click Build Mesh and then In All Blocks to build the meshes for all blocks at once.

Now the model is ready. To save model in a file, click Save from the File menu.

  Continue


To edit material properties and boundary conditions:

You probably noticed that the block and edge labels appeared in the problem view while you have entered them in the model. Icons are supplied with question mark icon, which means that the labels are referenced by the model, but the data for them are not yet defined. Now we’ll proceed with assigning data to labels.

To define the data for block label Air:

1	Double-click the Air item or click Properties in its context menu. A dialog box appears, prompting to enter material properties and distributed source for block label Air.

2	Type 1 in any text box for components of magnetic permeability tensor.

3	Click OK.

Analogous to the above steps define the relative permeability and current density of all the coils Coil R+, Coil R–, Coil  S+, Coil S–, Coil T+, Coil T–. The current densities for the coil slots are as follows: 1,300,000 A/m² on R+, –1,300,000 A/m² on R–, 1,300,000 A/m² on S+, –1,300,000 A/m² on S–, and zero on T+ and T–.

Next define the relative permeability of the Magnet, relative permeability of Samarium-Cobalt is 1.154. Since we chose to define the coercivity of the magnet through equivalent current sheets at the edges, don’t enter any value for the coercive force of the magnet.

  Continue


Now we'll learn how to describe nonlinear magnetic properties by means of editing the B-H curve. To start editing for block label Steel:

1	Double-click the Steel item or click Properties in its context menu. The property editing dialog box appears.

2	Select the Nonlinear box. This causes starting the B-H Curve Editor.

With the Curve Editor, you can simply enter the values from the table, point by point, checking the curve in the graph to the left of the table. The point (0; 0) is always presented in the table, which cannot be edited nor deleted. Since the cursor is already in the box for new B value, you can start entering new points. To create the first point (B = 0.73 T, H = 400 A/m, see the table below):

1	Type 0.73 and press ENTER. The cursor will move to the box for H value.

2	Type 400 and press ENTER. The new point will be added to the table and immediately displayed in the graph. The cursor will return back to the box for B value.

3	Repeat these actions for other points of the table. Points may be entered in any order.

H (A/m)	400	600	800	1000	1400
B (T)	0.73	0.92	1.05	1.15	1.28
H (A/m)	2000	3000	4000	6000
B (T)	1.42	1.52	1.58	1.60
In case of mistyping, the erroneous point would in general produce a noticeable anomaly in the displayed curve. You can select this point in the graph or in the table and then delete it or correct its coordinates.

When you are done with entering points, and the curve looks like classic B-H curve, click the Close button to finish curve editing and return to property editing dialog. Since we do not want to change any more values, click OK button to finish editing data for label Steel.

Repeat the above steps to define the corresponding B-H curve for the Cobalt Alloy label:

H  (A/m)	20	60	80	95	105	120
B  (T)	0.19	0.65	0.87	1.04	1.18	1.24
H  (A/m)	140	160	180	200	240	2500
B  (T)	1.272	1.3	1.32	1.34	1.36	1.45
  Continue


Now we'll continue with edge labels' data. We'll define the label A = 0 as a homogeneous Dirichlet boundary condition (A = 0). To define the data for edge label A = 0:

1	Select its name in the Edge Labels branch and double-click it or click Properties in its context menu. The property editing dialog box appears, which allows assigning to edge label any of possible boundary conditions.

2	Select the Magnetic Potential box. Zero value of pre-defined potential will be suggested.

3	Click OK.

Next, we'll define the surface current for the edge labels Magnet Left and Magnet Right. To define the data for edge label Magnet Left:

1	Double-click it or click Properties in its context menu. The property editing dialog box appears.

2	Select the Tangential Field box and type 550000.

3	Click OK.

4	Repeat the above process, for the edge label Magnet Right (tangential field value would be –550000).

All the data needed to solve the problem is now defined.

  Continue


At last, we can solve the problem and analyze the solution. To do this in one step:

1	Click within the problem description tree (on the left side of QuickField window) to activate the view.

2	On the Edit menu or context menu, click Analyze Results. You will be suggested to solve the problem first, as the results are absent. You should also agree to save the data to the data description file.

3	Click OK.

Once the problem is solved, the Postprocessor starts automatically and the resulting flux lines through the motor are displayed. There are many options and capabilities for analyzing the results in the Postprocessor. We will only show the steps needed to determine the torque on the rotor. To do this, first we have to define a closed contour in the air gap surrounding the rotor and then ask for the torque value. The necessary steps are as follows:

1	On the Contour menu, click Add Lines, a dialog box appears allowing manual typing new contour element’s parameters.

2	In Arc Angle area, click Half arc (180°) (we’ll create a circular contour by connecting two 180 degree arcs in the middle of the air gap).

3	Type the coordinates of the first point (x = 12.25, y = 0) and press ENTER.

4	Change x to –12.25, and press ENTER again, a semicircular path appears.

5	Press ESC to close the dialog.

6	On the Contour menu or context menu, click Close Contour.

The postprocessor will connect starting and ending points of the contour (currently consisting of a single arc), using the arc angle shown in Arc Angle box in the toolbar. The area surrounded by the contour becomes highlighted to show that the contour is closed and has positive direction.

To calculate the torque:

1	On the View menu, click Integral Values, or click correspondent button on the toolbar, an Integral Calculator dialog box appears.

2	In the list of Integral Quantities, double-click Mechanical torque. The value of torque immediately appears: 2.19 Nm/m. To get full torque of a real electric motor this value has to be multiplied by the axial length of the motor. For the 40 mm long motor it yields 8.7610-3 Nm.

3	Click Close to go back to the postprocessor window.

  Continue


Frequently, the torque has to be calculated for different positions of the rotor, QuickField can easily facilitate such a parametric analysis. In the next steps, we’ll show how easy it is to move the rotor assembly to the new position and then run analysis and calculate the torque again. The necessary steps are as follows:

1	In the Problem Description tree, double-click the Motor.mod item to bring up the model window.

2	Select all the blocks on the rotor assembly, meaning the four magnets and the inner frame.

3	Using Move Selection on the Edit menu, rotate all the selected blocks by 45 degrees. Note that the mesh moves with the blocks and only the mesh in the air gap between the rotor and the stator is destroyed.

4	On the Edit menu, click Build Mesh and then In Nonmeshed Blocks, then click OK to mesh the air gap region only.

Now, we can solve the problem again and analyze the solution:

1	In the Problem Description tree, click Solve Problem on the Edit menu or context menu. You will be prompted to save the changed model to the file.

2	Click OK.

Once the problem is solved, the Postprocessor starts automatically and the resulting flux lines for the new configuration of the motor are displayed. Now you can follow exactly the same steps that were explained earlier to calculate the torque. The new value of the torque is 0.52 Nm/m.

  Done


Your Examples folder contains Elec1 problem, microstrip transmission line. Here we’ll provide you with step-by-step instructions how to create and solve just the same problem from scratch. We'll forget the solution made in Elec1_2.pbm, and start a new problem, Strip.pbm.

To create a new problem:

1	On the File menu, click New; the dialog box appears asking for the kind of QuickField document you wish to create.

2	Click QuickField Problem, and then click OK. Then, new dialog box asks for the file name and location for the new problem.

3	In the Problem file name box, type Strip.

4	In the Create in folder area, change the folder, if needed.

5	Click Next.

  Continue


To assign the problem with appropriate features:

1	In the Problem Type area, click Electrostatics.

2	Click Plane-parallel.

3	We'll agree with suggested model and data file names (Strip.mod and Strip.des.) Click Next.

To select convenient length measurement units (centimeters):

1	Click Centimeters.

2	Click Finish to accept the new problem.

3	QuickField now opens the new problem window for Strip.pbm. On the File menu, click Save to store the problem description in the file.

To start editing the model:

1	On the Edit menu, click Geometry Model, or double-click the Strip.mod item in the tree, or click Edit File from context menu clicking right mouse button on that item.

2	Confirm creating new model.

The model window now opens. For convenience, you can maximize the window.

  Continue


Creating geometry elements

First, we should make a decision concerning dimensions of the problem's region. Since the problem has vertical axis of symmetry, it is convenient to set zero of x-axis at the axis of symmetry.

The first step with the new model in Model Editor is to adjust window dimensions fitting the problem's region. Since the problem has vertical axis of symmetry, it is convenient to set zero of x-axis at the axis of symmetry. So the region fits the square (–5 ≤ x ≤ 5, 0 ≤ y ≤ 10). To make this rectangle occupying most of the window:

1	On the toolbar, click Zoom In.

2	Move mouse pointer to (–5, 0), checking the coordinates in lower right corner of the QuickField application window. You need not position mouse exactly at this point but somewhere to the bottom left not far the point.

3	Click the left mouse button and drag to (5, 10).

4	The window reflects your zoom operation. Click Zoom In once again co close zooming mode.

To simplify object creation, we’ll use Snap to Grid feature.

We notice that all sketch element sizes are multipliers of 0.5 cm in both horizontal and vertical directions. To set up the 0.5 cm grid:

1	On Edit or context menu, click Grid Settings, a dialog box appears.

2	In the Horizontal box, type 0.5. Since Anisotropic box is unchecked, the same value appears in Vertical box.

3	Grid origin at (0, 0) is okay, so we need not change anything else. Click OK to close the dialog.

  Continue


Now we can proceed with defining the geometry itself. To create edges constituting the model boundaries:

1	Press INS (or Insert Mode on Edit menu, or Insert Vertices/Edges on context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Click the left mouse button at (–0.5, 1) and drag to (0.5, 1) to create the edge EF. The edge appears on the screen immediately as you release the mouse button.

3	Repeat 2 at (–5, 0 : 5, 0) for AB, (5, 0 : 5, 10) for BC, (5, 10 : –5, 10) for CD, (-5, 10 : -5, 0) for DA. There is no matter, in which order you create edges, direction of edges also does not matter. If the point you want to click is out of window, use scroll bars to scroll the picture. Don't worry about making mistakes—you can remove erroneous vertices and edges later.

4	Press INS again to cancel Insert mode and return to Pick mode.

If you have created excess points or edges, you can remove them now:

1	Hold CTRL key and pick excess objects with mouse to select them. If you have selected the object you did not want to, pick it again to unselect it. Release CTRL.

2	Press DEL (or Delete Selection on Edit menu or context menu). Deleted objects immediately disappear.

We need some additional constructing to create edges separating substrate from the air. The easy way to create them is to copy the edge AB shifting it 1 cm up. To make a copy:

1	Click the AB edge with right mouse button. The edge is selected and the context menu appears.

2	In the menu, click Duplicate Selection, a dialog box with the parameters for copy operation appears.

3	Click Displacement.

4	In δy box, type 1.

5	Click OK, and then confirm the operation by clicking Yes.

The copy of the line segment AB crosses vertices E and F and produces two new edges separated by these vertices.

  Continue


We are done with the model's geometry. Now we can assign labels to geometrical objects to describe material properties, sources and boundary conditions.

The model contains two blocks having different material properties: the air and the substrate. To be clear, we can use the word Air to label the upper block and Substrate for the lower one. To assign these labels to blocks:

1	Double-click the upper block. It becomes selected and the Selection Properties dialog appears.

2	In Label box, type Air.

3	Click OK to close the dialog.

4	Repeat these actions to label the lower block as Substrate.

Edge labels are used to define specific boundary conditions on inner and outer boundaries of the region. In our case, we need to specify boundary conditions for the shield (rectangle ABCD) and for the strip (line EF). To assign labels to edges:

1	Double-click the EF edge and label it as Strip.

2	Pick consecutively six edges, which constitute the rectangle ABCD, holding down the CTRL key. Those edges become highlighted that indicates the selection. If you have selected excess edge, vertex or block, pick it once more to unselect it. Do not forget to unselect the EF edge.

3	Click right mouse button within selection to bring up the context menu without changing the selection.

4	On the context menu, click Properties and assign the Shield label to selected edges.

5	Click OK to close the dialog.

We also need to assign vertex label to any vertex contacting the strip, to specify that the strip is charged. No matter which vertex you choose, the charge will be distributed through the entire conductor. To assign the label to a vertex:

1	Double-click a vertex, E or F, a dialog box appears.

2	In Label box, type Charge.

3	Click OK to close the dialog.

Now we have finished with assigning labels to geometrical objects.

  Continue


We can proceed with building a mesh of finite elements. To define the mesh density, we need to define mesh spacing parameters in several vertices of the model. We suppose that the electric field is most non-homogeneous near the ends of the strip, so the mesh there must be very fine. Therefore, we'll assign the spacing value of 0.5 cm to the vertices E and F and the value of 1 cm to the vertices A, B, C and D to build the mesh of approximately 200 nodes. To define spacing values:

1	Select vertices A, B, C and D and click Properties on the context menu.

2	Click Manual spacing and type 1.

3	Click OK to close the dialog.

4	Repeat these actions to assign 0.5 cm spacing to vertices E and F.

5	On the Edit menu, click Build Mesh, and then In All Blocks to build the meshes for all blocks at once.

Now the model is ready. To save model in a file, click Save from the File menu.

  Continue


To edit material properties and boundary conditions:

You probably noticed that the block and edge labels appeared in the problem view while you have entered them in the model. Icons are supplied with question mark icon, which means that the labels are referenced by the model, but the data for them are not yet defined. Now we’ll proceed with assigning data to labels.

To define the data for block label Air:

1	Double-click the Air item or click Properties in its context menu. A dialog box appears, prompting to enter material properties and distributed source for block label Air.

2	Type 1 in any text box for components of electric permittivity tensor.

3	Click OK.

Repeat last actions for the label Substrate. The value of relative permittivity of substrate is 10.

  Continue


Now we'll continue with edge labels' data. To define the data for edge label Shield:

1	Select its name in the Edge Labels branch and double-click it or click Properties in its context menu. The property editing dialog box appears, allowing assigning to edge label any of possible boundary conditions.

2	Click Voltage. Zero value of pre-defined potential will be suggested.

3	Click OK.

To define the data for edge label Strip:

1	Double-click its name.

2	Click Floating Conductor.

3	Click OK.

We need to define the vertex label Charge to assign the charge to the strip. To determine the capacitance, the exact value of the charge does not matter. We'll choose a value of 1.

To define the data for vertex label Charge:

1	Double-click its name in the Vertex Labels branch and click Open. A dialog box appears, allowing to specify the charge, or to assign the Dirichlet boundary condition.

2	Click Electric Charge and type 1.

3	Click OK.

All the data needed to solve the problem is now defined.

  Continue


At last, we can solve the problem and analyze the solution. To do this in one step:

1	On the Edit menu or context menu, click Analyze Results. You will be suggested to solve the problem first, as the results are absent.

2	Click OK.

After finishing, the Postprocessor starts automatically. There are many possibilities to analyze the field in the Postprocessor. We will show only those steps needed to determine the capacitance:

•	Click at the point (0.0, 1.0) (exactly; the convenient way is to use Zoom In feature.)

The window to the left of the picture expands its tree and shows the values at the point. The potential of the strip is 4.717e9 Volts. The capacitance is

Note that, with plane-parallel problems, we specify the sources as specific values per unit depth (e.g., the charge of the strip), and the result is specific capacitance per unit depth, measured in F/m.

If you now look through the model provided with Elec1_2.pbm, Elec1.mod, you will find some hints for obtaining finer mesh near the vertices E and F—the points of singularity.

Since the Model Editor cannot squeeze the mesh spacing inside the edge, but only from one end to another, two extra vertices have been added in central points of edges AB and EF. The first of these vertices allows the Model Editor to adjust automatically the spacing around it, since the strip is very close to this point. The second vertex is aimed to specify manual spacing value for it, which helps to decrease the total number of nodes in the mesh, without loss of precision.

  Done


Your Examples folder contains Coupl1 set of problems illustrating stress distribution in a long solenoid. Here we’ll provide you with step-by-step instructions how to create and solve just the same problems from scratch. We'll forget the solution made in Coupl1MS.pbm and Coupl1SA.pbm, and start a new problem, SolMag.pbm. We use a suffix `Mag’ to underline that this will represent the magnetic part of our problem.

To create a new problem:

1	On the File menu, click New; the dialog box appears asking for the kind of QuickField document you wish to create.

2	Click QuickField Problem, and then click OK. Then, new dialog box asks for the file name and location for the new problem.

3	In the Problem file name box, type SolMag.

4	In the Create in folder area, change the folder, if needed.

5	Click Next.

  Continue


To assign the problem with appropriate features:

1	In the Problem Type area, click Magnetostatics.

2	Click Axisymmetric.

3	We'll agree with suggested data file name (SolMag.dms), but change the model file name to Sol.mod to stress out the fact, that the model file will be shared between magnetic and stress analysis problems. In Geomerty, change SolMag.mod to Sol.mod.

4	Click Next.

To select convenient length measurement units (centimeters):

1	Click Centimeters.

2	Click Finish to accept the new problem.

QuickField now opens the new problem window for SolMag.pbm. On the File menu, click Save to store the problem description in the file.

To start editing the model:

1	On the Edit menu, click Geometry Model, or double-click the Sol.mod item in the tree, or click Edit File from context menu clicking right mouse button on that item.

2	Confirm creating new model.

The model window now opens. For convenience, you can maximize the window.

  Continue


Creating geometry elements

First, we should make a decision concerning dimensions of the problem's region. Since the problem has vertical axis of symmetry, it is convenient to set zero of x-axis at the axis of symmetry.

The first step with the new model in Model Editor is to adjust window dimensions fitting the problem's region. Since none of the physical quantities varies along z-axis, we'll model a thin slice of the solenoid. We'll choose the axial length of this slice to be 0.2 cm, from –0.1 to 0.1 along z-axis. The whole model fits in the square (–1 ≤ z ≤ 1, 0 ≤ r ≤ 2). To make this rectangle occupying most of the window:

1	On the toolbar, click Zoom In.

2	Move mouse pointer to (–1, 0), checking the coordinates in lower right corner of the QuickField application window. You need not position mouse exactly at this point but somewhere to the bottom left not far the point.

3	Click the left mouse button and drag to (1, 2).

4	The window reflects your zoom operation. Click Zoom In once again co close zooming mode.

To simplify object creation, we’ll use Snap to Grid feature.

To set up the 0.1 cm grid:

1	On Edit or context menu, click Grid Settings, a dialog box appears.

2	In the Horizontal box, type 0.1. Since Anisotropic box is unchecked, the same value appears in Vertical box.

3	Grid origin at (0, 0) is okay, so we need not change anything else. Click OK to close the dialog.

  Continue


Now we can proceed with defining the geometry itself. To create edges constituting the model boundaries:

1	Press INS (or Insert Mode on Edit menu, or Insert Vertices/Edges on context menu, or corresponding button on the toolbar) to switch Model Editor to Insert mode.

2	Click the left mouse button at (–0.5, 1) and drag to (0.5, 1) to create the edge EF. The edge appears on the screen immediately as you release the mouse button.

3	Repeat 2 at (–0.5, 1 : 0.5, 1), (–0.5, 2 : 0.5, 2), (–0.5, 0 : –0.5, 2), (0.5, 0 : 0.5, 2). There is no matter, in which order you create edges, direction of edges also does not matter. If the point you want to click is out of window, use scroll bars to scroll the picture. Don't worry about making mistakes—you can remove erroneous vertices and edges later.

4	Press INS again to cancel Insert mode and return to Pick mode.

If you have created excess points or edges, you can remove them now:

1	Hold CTRL key and pick excess objects with mouse to select them. If you have selected the object you did not want to, pick it again to unselect it. Release CTRL.

2	Press DEL (or Delete Selection on Edit menu or context menu). Deleted objects immediately disappear.

  Continue


We are done with the model's geometry. Now we can assign labels to geometrical objects to describe material properties, sources and boundary conditions.

The bottom rectangle represents the air inside the solenoid, so we'll assign the label Air to it. The top rectangle represents the slice of the solenoid coil itself, so we'll label it Coil. To assign these labels to blocks:

1	Double-click the upper block. It becomes selected and the Selection Properties dialog appears.

2	In Label box, type Air.

3	Click OK to close the dialog.

4	Repeat these actions to label the lower block as Coil.

  Continue


Edge labels are used to define the boundary conditions. For magnetic problem we need to specify only a zero flux condition at outward surface of the solenoid, but to make the model suitable for the stress analysis too, we'll also assign labels to the side edges of the coil. To assign labels to edges:

1	Double-click the top edge and label it as Outer.

2	Pick consecutively two side edges of the top rectangle holding down the CTRL key. Those edges become highlighted that indicates the selection. If you have selected excess edge, vertex or block, pick it once more to unselect it. Do not forget to unselect the top edge.

3	Click right mouse button within selection to bring up the context menu without changing the selection.

4	On the context menu, click Properties and assign the No axial disp label to selected edges.

5	Click OK to close the dialog.

Now we have finished with assigning labels to geometrical objects.

  Continue


We can proceed with building a mesh of finite elements. For simplicity we will use a homogeneous mesh with element size approximately equal to 0.06 cm. To build the mesh:

1	Double-click any vertex in the model. It becomes selected and the Selection Properties dialog appears.

2	Click Manual spacing and type 0.06.

3	Click OK to close the dialog.

4	On the Edit menu, click Build Mesh, and then In All Blocks to build the meshes for all blocks at once.

Now the model is ready. To save model in a file, click Save from the File menu.

  Continue


To edit material properties and boundary conditions:

You probably noticed that the block and edge labels appeared in the problem view while you have entered them in the model. Icons are supplied with question mark icon, which means that the labels are referenced by the model, but the data for them are not yet defined. Now we’ll proceed with assigning data to labels.

To define the data for block label Air:

1	Double-click the Air item or click Properties in its context menu. A dialog box appears, prompting to enter material properties and distributed source for block label Air.

2	Type 1 in any text box for components of magnetic permeability tensor.

3	Click OK.

To define the data for block label Coil:

1	Double-click the Coil item or click Properties in its context menu. The property editing dialog box appears.

2	Type 1 in any text box for components of magnetic permeability tensor.

3	Type 1e6 in the Current Density text box.

4	Click OK.

  Continue


Now we'll continue with edge labels' data. We'll specify a zero flux condition (Bn = 0) for the Outer label. To define the data for the edge label Outer:

1	Select its name in the Edge Labels branch and double-click it or click Properties in its context menu. The property editing dialog box appears, allowing assigning to edge label any of possible boundary conditions.

2	Click Zero Normal Flux.

3	Click OK.

To define a natural boundary condition for the edge label No axial displ:

1	Double-click its name.

2	Click OK, the dialog box by default represents the natural boundary condition. In the tree, this fact is underlined by the `0’ mark upon the icon.

All the data needed to solve the problem is now defined. To save the data in a file, click Save on the File menu.

  Continue


We can now solve the problem and analyze the magnetic field. To do this in one step:

1	On the Edit menu or context menu, click Analyze Results. You will be suggested to solve the problem first, as the results are absent. You should also agree to save the data to the data description file.

2	Click OK.

After finishing, the Postprocessor starts automatically.

  Continue


Once we got the results for the magnetic part of our problem, we can proceed with the stress analysis. To perform the stress analysis we will need a new problem description:

1	On the File menu, click New; the dialog box appears asking for the kind of QuickField document you wish to create.

2	Click QuickField Problem, and then click OK. Then, new dialog box asks for the file name and location for the new problem.

3	In the Problem file name box, type SolStress.

4	In the Create in folder area, change the folder, if needed.

5	Click Next.

  Continue


To assign the problem with appropriate features:

1	In the Problem Type area, click Stress Analysis.

2	Click Axisymmetric.

3	We'll agree with suggested data file name (SolStress.dsa), but change the model file name to Sol.mod. In Geomerty, change SolStress.mod to Sol.mod.

4	Click Next.

To select convenient length measurement units (centimeters):

1	Click Centimeters.

2	Click Finish to accept the new problem.

QuickField now opens the new problem window for SolStress.pbm.

To specify the problem coupling:

1	On the Edit menu, click Properties, a dialog box appears.

2	Click the Links tab.

3	In Data Type area, select Magnetic forces option.

4	Click Browse, and double-click a SolMag.pbm file. If you would not see it in the list, then you forgot to save it to disk. In this case, click OK to close the dialog, activate the SolMag problem and click Save on the File menu. Then return to the previous point again.

5	Click Add, a new line will appear in Data Sources.

6	Click OK to accept changed problem properties.

7	On the File menu, click Save to store the problem description in the file.

  Continue


Next our step is to define material properties and boundary conditions for the structural problem.

To define the data for block label Air:

1	Double-click the Air item or click Properties in its context menu.

2	A dialog box appears, prompting to enter material properties and loads. The block labeled Air has to be excluded from stress calculation. Since the boxes for the Young's moduli already contain word None, the all we need to do is to click OK button. Exclamation sign upon the icon in the tree indicates that blocks possessing this label do not participate in the analysis.

To define the data for block label Coil:

1	Double-click the Coil item or click Properties in its context menu. The property editing dialog box appears.

2	Type 1.075e11 in any one of three text boxes for Young's moduli.

3	Type 0.33 in any one of three text boxes for Poisson's ratios.

4	Click OK.

  Continue


Now we'll continue with edge labels' data. To define the data for the edge label No axial displ:

1	Select its name in the Edge Labels branch and double-click it or click Properties in its context menu. The property editing dialog box appears, allowing assigning to edge label any of possible boundary conditions.

2	Click the Z check box inside Prescribed Displacement rectangle. The value of displacement component is zero by default.

3	Click OK.

To define a natural boundary condition for the edge label Outer:

1	Double-click its name.

2	Click OK, the dialog box by default represents the natural boundary condition. In the tree, this fact is underlined by the `0’ mark upon the icon.

All the data needed to solve the structural problem are now defined. To save the data in a file, click Save on the File menu.

  Continue


Now we can solve the problem and analyze stresses in the coil. To do this in one step:

1	On the Edit menu or context menu, click Analyze Results. You will be suggested to solve the problem first, as the results are absent. You should also agree to save the data to the data description file.

2	Click OK.

After finishing, the Postprocessor starts automatically. One of many possible actions is to examine the local data in particular points. Simply click the points to see the field data in the window to the left of the field picture.

  Done


This file is used by the Dialog Box Help Editor. It provides a topic that is used to alias topic IDs that should display no Help.  Include this file in the FILES section of the Help Project (.hpj) file.


Contact information

To learn more about Student’s QuickField and more powerful products, available from Tera Analysis,

please contact Student's QuickField support team at:

Tera Analysis Europe

Web: www.tor.ru/quickfield

E-mail: support@tor.spb.su

Tel:	+7 812 316 1965

Fax:	+7 812 110 1334

or visit homepage of Tera Analysis Co.:

Web: www.tera-analysis.com


Additional examples

Our WWW site www.tor.ru/quickfield/advanced contains a wide range of examples solved with Professional QuickField. Your Student’s edition is fully capable of analyzing very large problems from Professional QuickField.