Comsol Multiphysics
Comsol Multiphysics
Comsol Multiphysics
Version 4.3b
Contact Information
Visit the Contact Us page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Wordwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: Support Center: www.comsol.com/support Download COMSOL: www.comsol.com/support/download Product Updates: www.comsol.com/support/updates COMSOL Community: www.comsol.com/community Events: www.comsol.com/events COMSOL Video Center: www.comsol.com/video Support Knowledge Base: www.comsol.com/support/knowledgebase Part No. CM010004
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The COMSOL Desktop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Example 1: Structural Analysis of a Wrench . . . . . . . . . . . . . . . . 20 Example 2: The BusbarA Multiphysics Model . . . . . . . . . . . . . 42 Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Parameters, Functions, Variables and Model Couplings. . . . 69 Material Properties and Material Libraries. . . . . . . . . . . . . . . 73 Adding Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Adding Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Parametric Sweeps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Parallel Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Appendix ABuilding a Geometry . . . . . . . . . . . . . . . . . . . . . . 107 Appendix BKeyboard and Mouse Shortcuts . . . . . . . . . . . . . 121 Appendix CLanguage Elements and Reserved Names . . . . 124 Appendix DFile Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Appendix EConnecting with LiveLink Add-Ons. . . . . . . . 142
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Introduction
Computer simulation has become an essential part of science and engineering. Digital analysis of components, in particular, is important when developing new products or optimizing designs. Today a broad spectrum of options for simulation is available; researchers use everything from basic programming languages to various high-level packages implementing advanced methods. Though each of these techniques has its own unique attributes, they all share a common concern: Can you rely on the results? When considering what makes software reliable, its helpful to remember the goal: you want a model that accurately depicts what happens in the real world. A computer simulation environment is simply a translation of real-world physical laws into their virtual form. How much simplification takes place in the translation process helps to determine the accuracy of the resulting model. It would be ideal, then, to have a simulation environment that included the possibility to add any physical effect to your model. That is what COMSOL is all about. Its a flexible platform that allows users to model all relevant physical aspects of their designs. Expert users can go deeper and use their knowledge to develop customized solutions, applicable to their unique circumstances. With this kind of all-inclusive modeling environment, COMSOL gives you the confidence to build the model you want with real-world precision. Certain characteristics of COMSOL become apparent with use. Compatibility stands out among these. COMSOL requires that every type of simulation included in the package has the ability to be combined with any other. This strict requirement mirrors what happens in the real world. For instance in nature electricity is always accompanied by some thermal effect; the two are fully compatible. Enforcing compatibility guarantees consistent multiphysics models and the knowledge that you never have to worry about creating a disconnected model again. Another noticeable trait of the COMSOL platform is adaptability. As your modeling needs change, so does the software. If you find yourself in need of including another physical effect, you can just add it. If one of the inputs to your model requires a formula, you can just enter it. Using tools like parameterized geometry, interactive meshing and custom solver sequences, you can quickly adapt to the ebbs and flows of your requirements. The flexible nature of the COMSOL environment facilitates further analysis by making what-if cases easy to set up and run. You can take your simulation to the production level by optimizing any aspect of your model. Parameter sweeps and target functions can be executed directly in the user interface. From start to finish, COMSOL is a complete problem-solving tool.
Introduction
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MENU BARUse these menus for access to functionality such as file load/save, selections, desktop layout, preferences, and documentation. MODEL BUILDER TOOLBAR
MAIN TOOLBARThe main toolbar has standard buttons for frequently used actions such as load/save, print, and help. It adapts to the active Model Tree node.
MODEL BUILDER WINDOWThe modeling process is controlled through the Model Builder window with a Model Tree together with associated toolbar buttons.
MODEL WIZARD WINDOWGuided steps to set space dimension, physics and study types.
GRAPHICS WINDOWThe Graphics window presents interactive graphics for Geometry, Mesh, and Results. Interactions include rotating, panning, zooming, and selecting. It is the default window for most Results and visualizations.
INFORMATION WINDOWSThe Information windows will display vital model information during the simulation, such as the solution time, solution progress, mesh statistics and solver logs, as well as Results Tables, if any.
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The Desktop on the previous pages is what you see when you first start COMSOL. The COMSOL Desktop provides a complete and integrated environment for physics modeling and simulation. You can customize it to your own needs. The Desktop windows can be resized, moved, docked and detached. Any changes you make to the layout will be saved when you close the session and used again the next time you open COMSOL. As you build your model, additional windows and widgets will be added. (See page 16 for an example of a more developed desktop). Among the possible windows are the following: Settings Window This is the main window for entering all of the specifications of the model, the dimensions of the geometry, the properties of the materials, the boundary conditions and initial conditions, and any other information that the solver will need to carry out the simulation.
Plot Windows These are the windows for graphical output. In addition to the Graphics window, Plot windows are used for Results visualization. Several Plot windows can be used to show multiple results simultaneously. A special case is the Convergence Plot
window, an automatically generated Plot window that displays a graphical indication of the convergence of the solution process while a model is running. Information Windows These are the windows for non-graphical information. They include:
Messages: Various information about events of the current COMSOL
Other Windows
Material Browser: Access the material property libraries. Model Library Update: An update service for downloading new model
points which are currently available for selection. Progress Bar with Cancel Button The Progress Bar with a button for cancelling the current computation, if any, is located in the lower right-hand corner of the COMSOL Desktop window. Dynamic Help The Help window provides context dependent help texts about windows and Model Tree nodes. If you have the Help window open in your desktop (by typing F1 for example) you will get dynamic help (in English only) when you click a node or a window. From the Help window you can search for other topics such as menu items.
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Prefe re n c es
Preferences are settings that affect the modeling environment. Most are persistent between modeling sessions, but some are saved with the model. You access Preferences from the Options menu.
In the Preferences window you can change settings such as graphics rendering, number of displayed digits for Results, or maximum number of CPU cores used for computations. Take a moment to browse your current settings to familiarize yourself with the different options. There are three graphics rendering options available: Open GL, Direct X, and Software Rendering. Direct X is not available on Mac OS X or Linux but is available on Windows if you choose to install the Direct X runtime libraries during installation. If your computer doesnt have a dedicated graphics card, you may have to switch to Software Rendering for slower but fully functional graphics. A list of recommended graphics cards can be found at:
http://www.comsol.com/products/requirements/
If you cannot use the arrow-keys to step up and down the Preferences list, you should change the Rendering selection in the Graphics Preferences.
T h e M o d e l B u i l d e r a n d t h e M o d e l Tre e
The Model Builder is the tool where you define the model: how to solve it, the analysis of results, and the reports. You do that by building a Model Tree. You build the tree by starting with a default Model Tree, adding nodes, and editing the node settings. All of the nodes in the default Model Tree are top-level parent nodes. You can right-click on them to see a list of child nodes, or subnodes, that you can add beneath them. This is the means by which nodes are added to the tree. When you left-click on a child node, then you will see its node settings in the Settings window. It is here that you can edit node settings. It is worth knowing that if you have the Help window open (which is achieved either by clicking Help in the menu bar, or by typing function key F1), then you will also get dynamic help (in English only) when you click on a node.
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R ESULTS N ODES
A Model Tree always has a Root node (initially labeled Untitled.mph), a Global Definitions node and a Results node. The label on the Root node is the name of the multiphysics model file, or MPH file, that this model is saved to on the disk. The Root node has settings for author name, default unit system, and more. The Global Definitions node is where you define parameters, variables, functions, and computations that can be used throughout the Model Tree. They can be used, for example, to define the values and functional dependencies of material properties, forces, geometry, and other relevant features. The Global Definitions node itself has no settings, but its child nodes have plenty of them.
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The Results node is where you access the solution after performing a simulation and where you find tools for processing the data. The Results node initially has five subnodes:
Data Sets: contains a list of
for the Derived Values, or for Results generated by probes that monitor the solution in real-time while the simulation is running.
Export: defines numerical data, images and animations to be exported to
files.
Reports: contains automatically generated or custom reports about the
model in HTML or Microsoft Word format. To these five default subnodes you may also add additional Plot Group subnodes that define graphs to be displayed in the Graphics window or in Plot windows. Some of these may be created automatically, depending on the type of simulations you are performing, but you may add additional figures by right-clicking on the Results node and choosing from the list of plot types.
T HE M ODEL
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S TUDY N ODES
In addition to the three nodes just described, there are two additional top-level node types: Model nodes and Study nodes. These are usually created by the Model Wizard when you create a new model. After using the Model Wizard to specify what type of Physics you are modeling, and what type of Study (e.g. steady-state, time-dependent, frequency-domain, or eigenfrequency analysis) you will carry out, the Wizard automatically creates one node of each type and shows you their contents.
It is also possible to add additional Model and Study nodes as you develop the model. Since there can be multiple Model and Study nodes and it would be confusing if they all had the same name, these types of nodes can be renamed to be descriptive of their individual purposes. If a model has multiple Model nodes, they can be coupled together to form a more sophisticated sequence of simulation steps.
Keyboard Shortcuts
Note that each Study node may carry out a different type of computation, so each one has a separate Compute button. To be more specific, suppose that you build a model that simulates a coil assembly that is made up of two parts, a coil and a coil housing. You could create two Model nodes, one of which modeled the coil and the other of which modeled the coil housing. You would then rename each of the nodes with the name of the object that it modeled. Similarly, you might also create two Study nodes, the first simulating the stationary, or steady-state, behavior of the assembly and the second simulating the frequency response. You could rename these two nodes to Stationary and Frequency Domain. When the model is completed, it could be saved to a file named Coil Assembly.mph. At that point, the Model Tree in the Model Builder would look like the figure to the right. In this figure, the Root node is named Coil Assembly.mph, indicating the file in which the model is saved. The Global Definitions node and the Results node each have their default name. In addition there are two Model nodes and two Study nodes with the names chosen in the previous paragraph.
The COMSOL Desktop
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Parameters are user-defined constant scalars that are usable throughout the Model Tree. (That is to say, they are global in nature.) Important uses are:
Parameterizing geometric dimensions Specifying mesh element sizes Defining parametric sweeps (i.e. simulations that are repeated for a variety
of different values of a parameter). A Parameter Expression can contain numbers, parameters, built-in constants, functions with Parameter Expressions as arguments, and unary and binary operators. For a list of available operators, see Appendix CLanguage Elements and Reserved Names on page 124. Because these expressions are evaluated before a simulation begins, Parameters may not depend on the time variable t. Likewise, they may not depend on spatial variables, like x, y, or z, nor on the dependent variables that your equations are solving for. It is important to know that the names of Parameters are case-sensitive. You define Parameters in the Model Tree under Global Definitions.
Variables
Variables can be defined either in the Global Definitions node or in the Definitions subnode of any Model node. Naturally the choice of where to define the variable depends upon whether you want it to be global (i.e. usable throughout the Model Tree) or locally defined within a single one of the Model nodes. Like a Parameter Expression, a Variable Expression may contain numbers, parameters, built-in constants, and unary and binary operators. However, it may also contain Variables, like t, x, y, or z, functions with Variable Expressions as arguments, and dependent variables that you are solving for as well as their space and time derivatives.
Scope
The scope of a Parameter or Variable is a statement about where it may be used in an expression. As we have said, all Parameters are defined in the Global Definition node of the model tree. This means that they are global in scope and can be used throughout the Model Tree. A Variable may also be defined in the Global Definitions node and have global scope, but they are subject to limitations other than their scope. For example, Variables may not be used in Geometry, Mesh, or Study nodes (with the one exception that a Variable may be used in an expression that determines when the simulation should stop). A Variable that is defined, instead, in the Definitions subnode of a Model node has local scope and is intended for use in that particular Model (but, again, not in Geometry or Mesh nodes). They may be used, for example, to specify material properties in the Materials subnode or to specify boundary conditions or interactions. It is sometimes valuable to limit the scope of the variable to only a certain part of the geometry, such as certain boundaries. For that purpose, provisions are made in the Settings for a Variable definition to apply the definition either to the entire geometry of the Model, or only to certain Domains, Boundaries, Edges, or Points.
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The picture below shows the definition of two Variables, q_pin and R, in which the scope is being limited to just two boundaries identified by numbers 15 and 19.
Similarly they could have been defined only on selected Domains, Edges, or Points. Such Selections can optionally be named and then referenced elsewhere in a model, such as when defining material properties or boundary conditions that will use the Variable. To give a name to the Selection, click on the Create Selection button ( ) to the right of the Selection list. Although Variables defined in the Definitions subnode of a Model node are intended to have local scope, they can still be accessed outside of the Model node in the Model Tree by being sufficiently specific about their identity. This is done by using a dot-notation in which the Variable name is preceded by the name of the Model node in which it is defined and they are joined by a dot. In other words, if the Variable named foo is defined in a Model node named MyModel, then this variable may be accessed outside of the Model node by using MyModel.foo. This can be useful, for example, when you want to use the variable to make plots in the Results node.
B u i l t - i n C o n s t a n t s , Va r i a bl e s a n d F u n c t i o n s
COMSOL comes with many built-in constants, variables and functions. They have reserved names that cannot be redefined by the user. If you use a reserved name for a user-defined variable, parameter, or function, the text where you enter the name will turn orange (a warning) or red (an error) and you will get a tooltip message if you select the text string. Some important examples are:
Mathematical constants such as pi (3.14...) or the imaginary unit i or j Physical constants such as g_const (acceleration of gravity), c_const (speed of light), or R_const (universal gas constant) The time variable t First and second order derivatives of the Dependent variables (the solution)
whose names are derived from the spatial coordinate names and Dependent variable names (which are user-defined variables)
Mathematical functions such as cos, sin, exp, log, log10, and sqrt
See Appendix CLanguage Elements and Reserved Names on page 124 for more information.
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Model Library examples. You can use the step-by-step instructions and the Model MPH-files as a template for your own modeling and applications.
To open the Model Library, select View>Model Library ( ) from the main menu, and then search by model name or browse under a module folder name. Click to highlight any model of interest, and select Open Model and PDF to open both the model and the documentation explaining how to build the model. Alternatively, click the Help button ( ) or select Help>Documentation in COMSOL to search by model name or browse by module. The Model Library is updated on a regular basis by COMSOL. Choose View>Model Library Update ( ) to update the model library. This connects you to COMSOLs Model Update website where you can access the latest models and model updates. This may typically include models that have been added or improved since the latest product release. The MPH-files in the COMSOL Model Library can have two formatsFull MPH-files or Compact MPH-files.
Full MPH-files include all meshes and solutions. In the Model Library these
tooltip with the text Large file and the file size appears when you position the cursor at the models node in the Model Library tree. Compact MPH-files include all settings for the model but have no built meshes and solution data to save file size. You can open these models to study the settings and to mesh and re-solve the models. It is also possible to download the full versionswith meshes and solutionsof most of these models through Model Library Update. In the Model Library such models appear with the icon. If you position the cursor at a compact model in the Model Library window, a No solutions stored message appears. If a full MPH-file is available for download, the corresponding nodes context menu includes a Model Library Update item. The following spread shows an example of a customized Desktop with additional windows.
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MODEL BUILDER WINDOWThe modeling process is controlled through the Model Builder window with a Model Tree together with associated toolbar buttons.
MENU BARUse these menus for access to functionality such as file load/save, selections, desktop layout, preferences, and documentation.
MAIN TOOLBARThe main toolbar has standard buttons for frequently used actions such as load/save, print, and help. It adapts to the active Model Tree node.
MODEL TREEThe Model Tree gives an overview of the model and all the functionality and operations needed for building and solving a model as well as processing the results.
SETTINGS WINDOW Click any node to see its associated settings window displayed next to the Model Builder. MODEL LIBRARY WINDOWEasy access to COMSOL and user model libraries.
PLOT WINDOWThe Plot window visualizes Results quantities, probes, and convergence plots. Several Plot windows can be used to show multiple results simultaneously.
INFORMATION WINDOWSThe Information windows will display vital model information during the simulation such as solution time, solution progress, mesh statistics, and solver logs, as well as Results Tables, if any.
GRAPHICS WINDOWThe Graphics window presents interactive graphics for Geometry, Mesh, and Results. Interactions include rotating, panning, zooming, and selecting. It is the default window for most Results visualizations.
DYNAMIC HELPContinuously updated with online access to the Knowledge Base and Model Gallery. The Help window enables easy browsing with extended search functionality.
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Wor k f l ow a n d S e q u e n c e o f O p e r a t i o n s
In the Model Builder window of this example, every step of the modeling process, from defining global variables to the final report of results, is displayed in the Model Tree.
From top to bottom, the Model Tree defines an orderly sequence of operations. In the following branches of the Model Tree, node order makes a difference and you can change the sequence of operations by moving the nodes up or down the Model Tree:
Geometry Material Physics Mesh
In the Model Definitions branch of the tree, the ordering of the following node types also makes a difference:
Perfectly Matched Layers Infinite Elements
In other branches, the ordering of nodes is not significant with respect to the sequence of operations but some nodes can be reordered for readability. Child nodes to Global Definitions is one such example. You can view the sequence of operations presented as program code statements by saving the model as a Model M-file or as a Model Java-file after having selected Reset History in the File menu. (Note: the model history keeps a complete record of the changes you make to a model as you build it. As such, it includes all your corrections, changes of parameters and boundary conditions, modifications of solver method, etc. Resetting this history removes all of the overridden changes and leaves a clean copy of the most recent form of the model steps.) As you work with the COMSOL Desktop and the Model Builder you will grow to appreciate the organized and streamlined approach. But any description of a user interface is inadequate until you try it for yourself. So, in the next chapters you are invited to work through two examples to familiarize yourself with the software.
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M o d e l W i z a rd
1 To start the software, double-click the COMSOL icon on the desktop which will take you to the Model Wizard. Or when COMSOL is already open, you can start the Model Wizard in one of these three ways:
- Click the New button
- Select File > New from the main menu - Right-click the root node and select Add Model
The Model Wizard, visible to the right of the Model Builder, will guide you through the first steps of setting up a model. The first window lets you select the dimension of the modeling space. 2 In the Select Space Dimension window, the 3D button is selected by default. Click Next .
3 In Add Physics, select Structural Mechanics > Solid Mechanics (solid) . Click Next . With no add-on modules, Solid Mechanics is the only physics user interface available in the Structural Mechanics folder. In the picture to the right, the Structural Mechanics folder is shown as it looks when all add-on modules are available.
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Preset Studies have solver and equation settings adapted to the selected physics: in this example, Solid Mechanics. A Stationary study is used in this casethere is no time-variation of loads or material properties. Any selection from the Custom Studies branch needs manual settings.
Geometr y
This tutorial uses a geometry that was previously created and stored on COMSOLs native CAD format .mphbin. To learn how to build your own geometry, see Appendix ABuilding a Geometry on page 107.
File Locations
The location of the Model Library that contains the model file used in this exercise varies based on the software installation and operating system. On Windows, the file path will be similar to C:\Program Files\COMSOL\COMSOL43b\models\.
1 In the Model Builder window, under Model 1, right-click Geometry 1 select Import .
and
2 In the Import settings window, from the Geometry import list, select COMSOL Multiphysics file.
3 Click Browse and locate the file wrench.mphbin in the Model Library folder of the COMSOL installation folder. Its default location on Windows is
C:\Program Files\COMSOL\COMSOL43b\models\COMSOL_Multiphysics\ Structural_Mechanics\wrench.mphbin
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5 Click the wrench geometry in the Graphics window and experiment with moving it around. As you click and right-click the geometry, it changes color. Click the Zoom In , Zoom Out , Go to Default 3D View , Zoom Extents , and Transparency buttons on the toolbar to see what happens to the geometry:
- To rotate the model, left-click and drag it in the Graphics window. - To move it, right-click and drag. - To zoom in and out, center-click (and hold) and drag.
Also see Appendix BKeyboard and Mouse Shortcuts on page 121 for additional information. The imported model has two parts, or domains, corresponding to the bolt and the wrench. In this exercise, the focus will be on analyzing the stress in the wrench.
Mate rials
The Materials node stores the material properties for all physics and all domains in a Model node. Use the same generic steel material for both the bolt and tool. Here is how to choose it in COMSOL. 1 Open the Material Browser. You open the Material Browser in either of these two ways:
- Right-click Materials
in the Model Builder and select Open Material Browser Material Browser
2 In the Material Browser, under Materials, expand the Built-In folder. Scroll down to find Structural Steel, right-click and select Add Material to Model.
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3 Examine the Material Contents section to see the properties that are available and will be used by the Physics in the simulation (indicated by green check marks).
Also see the busbar tutorial sections Materials on page 49 and Customizing Materials on page 73 to learn more about working with the Material Browser.
Global Definitions
You will now define a global parameter specifying the load applied to the wrench.
Parameters
1 In the Model Builder, right-click Global Definitions Parameters . and choose
2 Go to the Parameters settings window. Under Parameters in the Parameters table (or under the table in the fields), enter these settings:
- In the Name column or field, enter F. - In the Expression column or field, enter 150[N]. The square-bracket
notation is used to associate a physical unit to a numerical value, in this case the unit of force in Newton. The Value column is automatically updated based on the expression entered (when you leave the window or press Return).
- In the Description column or field, enter Applied force.
The sections Global Definitions on page 45 and Parameters, Functions, Variables and Model Couplings on page 69 show you more about working with parameters.
So far you have added the physics and study, imported a geometry, added the material, and defined one parameter. The Model Builder node sequence should now match the figure to the right. The default feature nodes under Solid Mechanics are indicated by a D in the upper left corner of the node icon. The default nodes for Solid Mechanics are: a Linear Elastic Material model, Free boundary conditions that allows all boundaries to move freely with no constraint or load, and Initial Values for specifying initial displacement and velocity values for a nonlinear or transient analysis (not applicable in this case). At any time you can save your model to be able to load it at a later time in exactly the state in which it was saved. 3 From the main menu, select File > Save As, browse to a folder where you have write permissions, and save the file as wrench.mph.
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D o m a i n P hy s i c s a n d B o u n d a r y C o n d i t i o n s
With the geometry and materials defined, you are now ready to set the boundary conditions. 1 In the Model Builder, right-click Solid Mechanics (solid) and select Fixed Constraint . This boundary condition constrains the displacement of each point on a boundary surface to be zero in all directions.
2 In the Graphics window, rotate the geometry by left-clicking and dragging into the position shown. Then left-click the cut-face of the partially modeled bolt (which turns the boundary red) and then right-click to select it (which turns the boundary blue). The Boundary number in the Selection list should be 35.
3 Click the Go to Default 3D View button the geometry to the default view.
4 In the Model Builder, right-click Solid Mechanics (solid) and select Boundary Load. A Boundary Load node is added to the Model Builder sequence.
5 In the Graphics window, click the Zoom Box button on the toolbar and drag the mouse to highlight the area shown in the figure to the right. Release the mouse button.
6 Select the top socket face (Boundary 111) by left-clicking to highlight the boundary in red and right-clicking it to highlight it in blue and add it to the Selection list.
7 In the Boundary Load settings window, under Force, select Total force as the Load type and enter -F in the text field for the z component. The negative sign
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indicates the negative z direction (downward). With these settings, the load of 150 N will be distributed uniformly across the selected surface. Note that to simplify the modeling process, the mechanical contact between the bolt and the wrench is approximated with a material interface boundary condition. Such an internal boundary condition is automatically defined by COMSOL and guarantees continuity in normal stress and displacement across a material interface.
Me sh
The mesh settings determine the resolution of the finite element mesh used to discretize the model. The finite element method divides the model into small elements of geometrically simple shapes, in this case tetrahedrons. In each tetrahedron, a set of polynomial functions is used to approximate the structural displacement fieldhow much the object deforms in each of the three coordinate directions. In this example, because the geometry contains small edges and faces, you will define a slightly finer mesh than the default setting suggests. This will better resolve the variations of the stress field and give a more accurate result. A finer mesh, however, comes at a cost: the computation time as well as memory usage will go up. Choosing a mesh size is always a trade-off between accuracy on the one hand and speed and memory usage on the other hand. 1 In the Model Builder, under Model 1 click Mesh 1 . In the Mesh settings window, under Mesh Settings, select Fine from the Element size list.
3 After a few seconds the mesh is displayed in the Graphics window. Zoom in to the mesh and have a look at the element size distribution.
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Study
In the beginning of setting up the model you selected a Stationary study, which implies that COMSOL will use a stationary solver. For this to be applicable, the assumption is that the load, deformation and stress do not vary in time. The default solver settings will be good for this simulation if your computer has more than 2 GB of in-core memory (RAM). If you should run out of memory, the instructions below will show solver settings that make the solver run a bit slower but use up less memory. To start the solver: 1 Right-click Study 1 and select Compute (or press F8).
If your computers memory is below 2 GB you may at this point get an error message Out of Memory During LU Factorization. LU factorization is one of the numerical methods used by COMSOL for solving the large sparse matrix equation system generated by the finite element method. You can easily solve this example model on a memory-limited machine by allowing the solver to use the hard drive instead of performing all of the computation using RAM. The steps below show how to do this. If your computer has more than 2 GB of RAM you can skip to the end of this section after step 5 below. 1 If you did not already start the computation, you can get access to the solver settings from the Study node. In the Model Builder, right-click Study 1 and choose Show Default Solver .
2 Under Study 1>Solver Configurations, expand the Solver 1 node. 3 Expand the Stationary Solver 1 and left-click Direct . node
A Direct solver is a fast and very robust type of solver that requires little or no manual tuning in order to solve a wide range of physics problems. The drawback is that it may require large amounts of RAM. 4 In the Direct settings window, in the General section, select the Out-of-core check box. Leave the default In-core memory (RAM) setting of 512 MB. This setting ensures that if your computer runs low of RAM during computation, the solver will start using the hard drive as a complement to RAM. Allowing the solver to use the hard drive instead of just RAM will slow the computation down somewhat. 5 Right-click Study 1 and select Compute (or press F8). After a few seconds of computation time, the default plot is displayed in the Graphics window. You can find other useful information about the computation in the Messages and Log windows; click the Messages and Log tabs under the Graphics window to see the kind of information available to you. These windows can also be opened from the main View menu.
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2 In the settings window under Expression, from the Unit list select MPa (or enter MPa in the field).
If you wish to study the stress more accurately, expand the Quality section. From the Recover list select Within domains. This setting will recover information about the stress level from a collection of elements rather than from each element individually. It is not active by default since it makes visualizations slower. The Within domain setting will treat each domain separately and the stress recovery will not cross material interfaces.
3 Click the Plot button in the toolbar of the settings window for the Surface plot and then the Zoom Extents button on the Graphics toolbar. The plot is regenerated with the updated unit and shows the von Mises stress distribution in the bolt and wrench under an applied vertical load. (This plot does not use the Recover option described earlier.)
For a typical steel used for tools like a wrench, the yield stress is about 600 MPa, which means that we are getting close to plastic deformation for our 150 N load (which corresponds to about 34 pounds force). You may also be interested in a safety margin of, say, a factor of three. To quickly assess which parts of the wrench are at risk of plastic deformation, you can plot an inequality expression such as solid.mises>200[MPa]. 1 Right-click the Results node and add a 3D Plot Group and select Surface . . 2 Right-click the 3D Plot Group 2 node
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3 In the Surface settings window click the Replace Expression button and select Solid Mechanics>Stress>von Mises Stress (solid.mises). When you know the variable name beforehand, you can also directly enter solid.mises in the Expression field. Now edit this expression to: solid.mises>200[MPa]. This is a boolean expression that evaluates to either 1, for true, or 0, for false. In areas where the expression evaluates to 1, the safety margin is exceeded. (You also here use the Recover feature described earlier.) 4 Click the Plot button . 5 In the Model Builder, click 3D Plot Group 2. Press F2 and in the Rename 3D Plot Group dialog box, enter Safety Margin. Click OK. The resulting plot shows that the stress in the bolt is high, but the focus of this exercise is on the wrench. If you wished to comfortably certify the wrench for a 150 N load with a factor-of-three safety margin, you would need to change the handle design somewhat, such as making it wider.
You may have noticed that the manufacturer, for various reasons, has chosen an asymmetric design of the wrench. Because of that, the stress field may be different if the wrench is flipped around. Try now, on your own, to apply the same force in the other direction and visualize the maximum von Mises stress to see if there is any difference.
E VALUATING
THE
M AXIMUM
VON
M ISES S TRESS
1 To study the maximum von Mises stress in the wrench, in the Results section of the Model Tree, right-click the Derived Values node and select Maximum>Volume Maximum. 2 In the Volume Maximum settings window under Selection choose Manual and select the wrench domain 1 by left-clicking on the wrench in the Graphics window and then right-clicking. We will only consider values in the wrench domain and neglect those in the bolt. 3 In the Expression text field enter the function ppr(solid.mises). The function ppr() corresponds to the Recover setting in the earlier note on page 34 for Surface plots. The Recover setting with the ppr function is used to increase the quality of the stress field results. It uses a polynomial-preserving recovery (ppr) algorithm, which is a higher-order interpolation of the solution on a patch of mesh elements around each mesh vertex. It is not active by default since it makes Results evaluations slower. 4 Under Expression, select or enter MPa as the Unit. 5 In the toolbar for Volume Maximum, click Evaluate to evaluate the maximum stress. The result will be displayed in a Table window and will be approximately 363 MPa. To see where the maximum value is attained, you can use a Max/Min Volume plot. 6 Right-click the Results node and add a 3D Plot Group . 7 Right-click the 3D Plot Group 3 node Volume . and select More Plots>Max/Min
8 In the Max/Min Volume settings window, in the Expression text field, enter the function ppr(solid.mises).
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9 In the settings window under Expression, from the Unit list select MPa (or enter MPa in the field). 1 0 Click the Plot button . This type of plot simultaneously shows the location of the max and min values and also their coordinate location in the table below.
P ARAMETERIZING
THE
M ESH
We will now define a parametric sweep for successively refining the mesh size while solving and then finally plot the maximum von Mises stress vs. mesh size. First, lets define the parameters that will be used for controlling the mesh density. 1 In the Model Builder, click Parameters under Global Definitions . 2 Go to the Parameters settings window. Under Parameters in the Parameters table (or under the table in the fields), enter these settings:
- In the Name column or field, enter hd. This parameter will be used in the
4 Now, enter another parameter with Name h0, Expression 0.01, and Description Starting element size. This parameter will be used to define the element size at the start of the parametric sweep. 5 In the Model Builder, under Model 1 click Mesh 1 . In the Mesh settings window, under Mesh Settings, select User-controlled mesh from the Sequence type list. 6 Under Mesh 1, click the Size node . 7 In the Size settings window under Element Size, click the Custom button. Under Element Size Parameters, enter:
- h0/hd in the Maximum element size field. - h0/(4*hd) in the Minimum element size field. - 1.3 in the Maximum element growth rate field. - 0.1 in the Resolution of curvature field. - 0.2 in the Resolution of narrow regions field.
P ARAMETRIC S WEEP
AND
S OLVER S ETTINGS
As a next step, add a parametric sweep for the parameter hd. 1 In the Model Builder, right-click Study 1 and select Parametric Sweep . A Parametric Sweep node is added to the Model Builder sequence. 2 In the Parametric Sweep settings window, under the table, click the Add button . From the Parameter names list in the table, select hd.
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3 Enter a range of Parameter values to sweep for. Click the Range button and enter the values in the Range dialog box. In the Start field, enter 1. In the Step field, enter 1, and in the Stop field, enter 6. Click Replace. The Parameter value list will now display range(1,1,6). The settings above make sure that as the sweep progresses, the value of the parameter hd increases and the maximum and minimum element sizes decrease. See page 96 for more information on defining parametric sweeps. For the highest value of hd, the number of DOFs will exceed one million. Therefore, we will switch to a more memory efficient iterative solver. 4 Under Study 1>Solver Configurations>Solver 1, expand the Stationary Solver 1 node, right-click Stationary Solver 1 , and select Iterative. The Iterative solver option typically reduces memory usage but can require physics-specific tailoring of the solver settings for efficient computations. 5 Under General in the settings window for Iterative, set Preconditioning to Right. (This is an optional low-level solver option which in this case will avoid a warning message that otherwise will appear. However, this setting does not affect the resulting solution. Preconditioning is a mathematical transformation used to prepare the finite element equation system for using the Iterative solver.) 6 Right-click the Iterative 1 node and select Multigrid. The Multigrid iterative solver uses a hierarchy of meshes of different densities and different finite element shape function orders. 7 Click the Study 1 node and select Compute , either in the Settings window or by right-clicking the node. The computation time will be a few minutes (depending on the computer hardware) and memory usage will be about 4GB.
R ESULTS A NALYSIS
As a final step, analyze the results from the parametric sweep by displaying the maximum von Mises stress in a Table.
1 In the Model Builder under Results>Derived values, select the Volume Maximum node. The solutions from the parametric sweep are stored in a new Data set named Solution 2. Now change the Volume Maximum settings accordingly: 2 In the settings window for Volume Maximum, change the Data set to Solution 2. 3 From the Evaluate toolbar button at the top of the Volume Maximum settings window, select to evaluate in a New Table. This evaluation may take a minute or so. 4 To plot the results in the Table, click the Graph Plot button at the top of the Table window. Generating this plot may take a minute or so. It is more interesting to plot the maximum value vs. the number of DOFs. This is possible by using a built-in variable numberofdofs. 5 Right-click the Derived Values node and select Global Evaluation. 6 In the settings window for Global Evaluation, change the Data set to Solution 2. 7 In the Expressions field, enter numberofdofs. 8 From the Evaluate toolbar button at the top of the Global Evaluation settings window, select to evaluate in a Table 2 (to display the DOF values for each parameter next to the previously evaluated data). This convergence analysis shows that the computed value of the maximum von Mises stress in the wrench handle will increase from the original 367 MPa, for a mesh with about 50,000 DOFs, to 370 MPa for a mesh with about 1,100,000 DOFs. It also shows that 300,000 DOFs essentially gives the same accuracy as 1,100,000 DOFs; see the table below.
DEGREES OF FREEDOM COMPUTED MAX VON MISES STRESS (MPA)
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The goal of your simulation is to precisely calculate how much the busbar heats up. Once you have captured the basic multiphysics phenomena, you will have the chance to investigate thermal expansion yielding structural stresses and strains in the busbar and the effects of cooling by an air stream. The Joule heating effect is described by conservation laws for electric current and energy. Once solved for, the two conservation laws give the temperature and electric field, respectively. All surfaces, except the bolt contact surfaces, are cooled by natural convection in the air surrounding the busbar. You can assume that the exposed parts of the bolt do not contribute to cooling or heating of the device. The electric potential at the upper-right vertical bolt surface is 20 mV and the potential at the two horizontal surfaces of the lower bolts is 0 V.
busbar using a parameter and then solve for a range of parameter values. The result is a plot of the average temperature as a function of the width.
In the section Parallel Computing on page 104 you learn how to solve the
M o d e l W i z a rd
1 Open the Model Wizard. To open the Model Wizard, double-click the COMSOL icon on the desktop. Or when COMSOL is already open, choose between one of these three ways to open the Model Wizard:
- Click the New button
- Select File > New from the main menu - Right-click the root node and select Add Model
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2 When the Model Wizard opens, select a space dimension; the default is 3D. Click the Next button .
3 In the Add Physics window, expand the Heat Transfer > Electromagnetic Heating folder, then right-click Joule Heating and choose Add Selected. Click the Next button . You can also double-click or click the Add Selected button to add physics. Another way to open the Add Physics window is to right-click the Model node and select Add Physics . Note that you may have fewer items in your physics list depending on the add-on modules installed. The figure on the right is shown for the case where all add-on modules are installed.
4 In the Select Study Type window, click to select the Stationary study type. Click the Finish button . Preset Studies are studies that have solver and equation settings adapted to the selected physics; in this example, Joule heating. Any selection from the Custom Studies branch needs manual fine-tuning. Note also here that you may have fewer study types in your study list depending on the installed add-on modules.
Global Definitions
To save time, its recommended that you load the geometry from a file. In that case, you can skip to Geometry on page 46. If you, on the other hand, want to draw the geometry yourself, the Global Definitions branch is where you define the parameters. First complete the steps 1 to 3 below to define the parameter list for the model and then skip to the section Appendix A Building a Geometry on page 107. You may then return to this section and use this busbar.mph file.
2xrad_1
The Global Definitions node in the Model Builder stores Parameters, Variables, and tbb Functions with a global scope. The Model Builder tree can hold several models simultaneously, and the Definitions with a global scope are made available for all models. In this particular example, there is only one Model node in which the parameters are used, so if you wish to limit the scope to this single model you
Example 2: The BusbarA Multiphysics Model
wbb
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could define, for example, Variables and Functions in the Definitions subnode available directly under the corresponding Model node. However, no Parameters can be defined here because COMSOL Parameters are always global. Since you will run a geometric parameter study later in this example, define the geometry using parameters from the start. In this step, enter parameters for the length for the lower part of the busbar, L, the radius of the titanium bolts, rad_1, the thickness of the busbar, tbb, and the width of the device, wbb. You will also add the parameters that control the mesh, mh, a heat transfer coefficient for cooling by natural convection, htc, and a value for the voltage across the busbar, Vtot. 1 Right-click Global Definitions and choose Parameters table, click the first row under Name and enter L. . In the Parameters
2 Click the first row under Expression and enter the value of L, 9[cm]. You can enter the unit inside the square brackets. 3 Continue adding the other parameters: L, rad_1, tbb, wbb, mh, htc, and Vtot according to the Parameters list. It is a good idea to enter descriptions for variables in case you want to share the model with others and for your own future reference.
4 Click the Save button and name the model busbar.mph. Then go to Appendix ABuilding a Geometry on page 107.
Geometr y
This section describes how the model geometry can be opened from the Model Library. The physics, study, parameters, and geometry are included with the model file you are about to open.
2 In the Model Library tree under COMSOL Multiphysics > Multiphysics, select busbar_geom. To open the model file you can:
- Double-click the name - Right-click and select an option
tree The geometry in this model file is parameterized. In the next few steps, we will experiment with different values for the width parameter, wbb.
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click the
In the Parameters settings window, click in the wbb parameters Expression column and enter 10[cm] to change the value of the width wbb. 4 In the Model Builder, click the Form Union node and then the Build All button to rerun the geometry sequence.
5 In the Graphics toolbar click the Zoom Extents button busbar in the Graphics window.
wbb=5cm
wbb=10cm
on the toolbar.
7 Return to the Parameters table and change the value of wbb back to 5[cm]. 8 In the Model Builder, click the Form Union node and then click the Build All button to rerun the geometry sequence. 9 On the Graphics toolbar, click the Zoom Extents button . 1 0 If you built the geometry yourself you are already using the busbar.mph file, but if you opened the Model Library file, from the main menu, select File > Save As and rename the model busbar.mph. After creating or opening the geometry file, it is time to define the materials.
Mate rials
The Materials node stores the material properties for all physics and geometrical domains in a Model node. The busbar is made of copper and the bolts are made of titanium. Both these materials are available from the Built-In material database.
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The Materials node will show a red in the lower-right corner if you try to solve without first defining a material (you are about to define that in the next few steps). 2 In the Material Browser, expand the Built-In materials folder and locate Copper. Right-click Copper and select Add Material to Model. A Copper node is added to the Model Builder. 3 Click the Material Browser tab.
4 In the Material Browser, scroll to Titanium beta-21S in the Built-In material folder list. Right-click and select Add Material to Model.
to get an overview of
, click Copper.
The Material Contents section has useful feedback about the models material property usage. Properties that are both required by the physics and available from the material are marked with a green check mark . Properties required by the physics but missing in the material are marked with a warning sign . A property that is available but not used in the model is unmarked. The Coefficient of thermal expansion in the table above is not used, but will be needed later when heat-induced stresses and strains are added to the model.
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Because the copper material is added first, by default all parts have copper material assigned. In the next step you will assign titanium properties to the bolts, which overrides the copper material assignment for those parts. 8 In the Model Builder, click Titanium beta-21S.
9 Select All Domains from the selection list and then click Domain 1 in the list. Now remove Domain 1 from the selection list. To remove a domain from the selection list (or any geometric entity such as boundaries, edges, or points), you can use either of these two methods:
- Click Domain 1 in the selection list found in the Material settings window,
then click the Remove from Selection button remove it from the selection list.
- In the Graphics window, click domain 1 to select it, and then right-click to
1 0 In the Material settings window, be sure to inspect the Material Contents section for the titanium material. All the properties used by the physics should have a green check mark . Close the Material Browser.
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Physics
Next you will inspect the physics domain settings and set the boundary conditions for the heat transfer problem and the conduction of electric current. 1 In the Model Builder, expand the Joule Heating node to examine the default physics nodes. The D in the upper left corner of a nodes icon ( ) means it is a default node. The equations that COMSOL solves are displayed in the Equation section of the settings window. The default equation form is inherited from the study added in the Model Wizard. For the Joule Heating node, COMSOL displays the equations solved for the temperature and electric potential. To always display the section in its expanded view, click the Expand Sections button ( ) on the Model Builder toolbar and select Equations. Selecting this option expands all the Equation sections on physics settings windows.
The domain level Joule Heating Model 1 node has the settings for heat conduction and current conduction. The contributions of the Joule Heating Model 1 node to the equation system are underlined in the Equation section. The heating effect for Joule heating is set in the Electromagnetic Heat Source 1 node. The Electric Insulation 1 node corresponds to the conservation of electric current, and the Thermal Insulation 1 node contains the default boundary condition for the heat transfer problem. The Initial Values 1 node contains initial guesses for the nonlinear solver for stationary problems and initial conditions for time-dependent problems. 2 Right-click the Joule Heating node . In the second section of the context menuthe boundary sectionselect Heat Transfer>Heat Flux.
Boundary section
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3 In the Heat Flux settings window, select All boundaries from the Selection list. Assume that the circular bolt boundaries are neither heated nor cooled by the surroundings. In the next step you will remove the selection of these boundaries from the heat flux selection list, which leaves them with the default insulating boundary condition for the Heat Transfer interfaces. 4 Rotate the busbar to view the back. Click one of the circular titanium bolt surfaces to highlight it in green. Right-click anywhere in the Graphics window to remove this boundary selection from the Selection list. Repeat this step to remove the other two circular bolt surfaces from the selection list. Boundaries 8, 15, and 43 are removed.
Cross-check: Boundaries 8, 15, and 43 are removed from the Selection list.
15 43
5 In the Heat Flux settings window under Heat Flux, click the Inward heat flux button. Enter htc in the Heat transfer coefficient field, h. This parameter was either entered in the Parameter table in Global Definitions on page 45 or imported with the geometry. Continue by setting the boundary conditions for the electric current according to the following steps: 6 In the Model Builder, right-click the Joule Heating node . In the second section of the context menuthe boundary sectionselect Electric Currents > Electric Potential. An Electric Potential node is added to the Model Builder.
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7 Click the circular face of the upper titanium bolt to highlight it and right-click anywhere to add it (boundary 43) to the Selection list.
43
8 In the Electric Potential settings window, enter Vtot in the Electric potential field. The last step is to set surfaces of the two remaining bolts to ground. 9 In the Model Builder, right-click the Joule Heating node . In the boundary section of the context menu, select Electric Currents > Ground. A Ground node is added to the Model Builder. The node sequence under Joule Heating should now match this figure.
1 0 In the Graphics window, click one of the remaining bolts to highlight it. Right-click anywhere to add it to the Selection list. Repeat this step to add the last bolt. Boundaries 8 and 15 are added to the selection list for the Ground boundary condition.
15
Me sh
The simplest way to mesh is to create an unstructured tetrahedral mesh, which is perfect for the busbar. Alternatively, you can create several meshing sequences as shown in Adding Meshes on page 75. A physics-controlled mesh is created by default. In most cases, it is possible to skip to the Study branch and just solve the model. For this exercise, the settings are investigated in order to parameterize the mesh settings.
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1 In the Model Builder, click the Mesh 1 node . In the Mesh settings window, select User-controlled mesh from the Sequence type list. 2 Under Mesh 1, click the Size node . The asterisk (*) that displays in the upper-right corner of the icon indicates that the node is being edited. 3 In the Size settings window under Element Size, click the Custom button. Under Element Size Parameters, enter:
- mh in the Maximum element size field. Notice that mh is 6 mmthe
value entered earlier as a global parameter. By using the parameter mh, element sizes are limited to this value.
- mh-mh/3 in the Minimum element
size field. The Minimum element size is slightly smaller than the maximum size.
- 0.2 in the Resolution of curvature
field. The Resolution of curvature determines the number of elements on curved boundaries: a lower value gives a finer mesh. The Maximum element growth rate determines how fast the elements should grow from small to large over a domain. The larger this value is, the larger the growth rate. A value of 1 does not give any growth. The Resolution of narrow regions works in a manner similar to the Resolution of curvature.
Study
1 To run a simulation, in the Model Builder, right-click Study 1 and choose Compute . Or press F8. The Study node automatically defines a solution sequence for the simulation based on the selected physics and the study type. The simulation only takes a few seconds to solve.
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Results
The default plot displays the temperature in the busbar. The temperature difference in the device is less than 10 K due to the high thermal conductivity of copper and titanium. The temperature variations are largest on the top bolt, which conducts double the amount of current compared to the two lower bolts. The temperature is substantially higher than the ambient temperature of 293 K. 1 Click and drag the image in the Graphics window to rotate and view the back of the busbar. 2 On the Graphics toolbar, click the Go to Default 3D View button . You can now manually set the color table range to visualize the temperature difference in the copper part.
3 In the Model Builder, expand the Results > Temperature node Surface 1 node .
4 In the Surface settings window, click Range to expand the section. Select the Manual color range check box and enter 323 in the Maximum field (replace the default).
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5 Click the Plot button on the Surface settings window. On the Graphics toolbar, click the Zoom Extents button to view the updated plot.
6 Click and drag in the Graphics window to rotate the busbar and view the back.
The temperature distribution is laterally symmetric with a vertical mirror plane running between the two lower titanium bolts and cutting through the center of the upper bolt. In this case, the model does not require much computing power and you can model the whole geometry. For more complex models, you can consider using symmetries to reduce the computational requirements. Now let us generate a Surface plot that shows the current density in the device.
1 In the Model Builder, right-click Results and add a 3D Plot Group . Right-click 3D Plot Group 2 and add a Surface node .
2 In the Surface settings window under Expression, click the Replace Expression button . Select Joule Heating (Electric Currents) > Currents and charge > Current density norm (jh.normJ).
jh.normJ is the variable for the magnitude, or absolute value, of the current density vector. You can also enter jh.normJ in the Expression field when you know the variable name.
The plot that displays in the Graphics window is almost uniform in color due to the high current density at the contact edges with the bolts. The next step is to manually change the color table range to visualize the current density distribution. 4 On the Surface settings window under Range, select the Manual color range check box. Enter 1e6 in the Maximum field and replace the default.
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The resulting plot shows how the current takes the shortest path in the 90-degree bend in the busbar. Notice that the edges of the busbar outside of the bolts are hardly utilized for current conduction.
6 Click and drag the busbar in the Graphics window to view the back. Continue rotating the image to see the high current density around the contact surfaces of each of the bolts.
Make sure to save the model. This version of the model, busbar.mph, is reused and renamed during the next set of tutorials. When you are done, click the Go to Default 3D View button toolbar and create a model thumbnail image. on the Graphics
FROM
P LOTS
With any solution, you can create an image to display in COMSOL when browsing for model files. After generating a plot, select File>Save Model Thumbnail from the main menu. There are two other ways to create images from a plot. One is to click the Image Snapshot button in the Graphics toolbar to directly create an image. You can also add an Image node to an Export node, for creating image files, by right-clicking the plot group of interest and then selecting Add Image to Export. This completes the Busbar example. The next sections are designed to improve your understanding of the steps implemented so far, and to extend your simulation to include additional effects like thermal expansion and fluid flow. These additional topics begin on the following pages:
Parameters, Functions, Variables and Model Couplings on page 69
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Material Properties and Material Libraries on page 73 Adding Meshes on page 75 Adding Physics on page 77 Parametric Sweeps on page 96 Parallel Computing on page 104 Appendix ABuilding a Geometry on page 107
Advanced Topics
Par a m e t e r s , F u n c t i o n s , Va r i a bl e s a n d M o d e l C o u p l i n g s
This section explores working with Parameters, Functions, Variables and Model Couplings. Global Definitions and Model Definitions contain functionality that help you to prepare model inputs and model couplings and to organize simulations. You have already used the functionality for adding Parameters to organize model inputs in Global Definitions on page 45. Functions, available as both Global Definitions and Model Definitions, contain a set of predefined functions templates that can be useful when setting up multiphysics simulations. For example, the Step function template can create a smooth step function for defining different types of spatial or temporal transitions. To illustrate using functions, assume that you want to add a time dependent study to the busbar model by applying an electric potential across the busbar that goes from 0 V to 20 mV in 0.5 seconds. For this purpose, you could use a step function to be multiplied with the parameter Vtot. Add a function that goes smoothly from 0 to 1 in 0.5 seconds to find out how functions can be defined and verified.
D EFINING F UNCTIONS
For this section, you can continue working with the same model file created in the previous section. Locate and open the file busbar.mph if it is not already open on the COMSOL Desktop.
Advanced Topics
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2 In the Step settings window, enter 0.25 in the Location field to set the location of the middle of the step, where it has the value of 0.5.
3 Click Smoothing to expand the section and enter 0.5 in Size of the transition zone field to set the width of the smoothing interval. Keep the default Number of continuous derivatives at 2. 4 Click the Plot button in the Step settings window.
70 | Advanced Topics
If your plot matches the one below, this confirms that you have defined the function correctly.
You can also add comments and rename the function to make it more descriptive. 5 Right-click the Step 1 node in the Model Builder and select Properties .
Advanced Topics
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For the purpose of this exercise, assume that you want to introduce a second model to represent an electric device connected to the busbar through the titanium bolts. A first step would be to rename Model 1 to specify that it represents the busbar. 1 Right-click the Model 1 node and select Rename (or press F2). 2 In the Rename Model window, enter Busbar. Click OK and save the model.
72 | Advanced Topics
To learn more about working with definitions, in the Model Builder click the Definitions or Global Definitions node and press F1 to open the Help window . This window displays help about the selected item in the COMSOL Desktop and provides links to the documentation. It could take up to a minute for the window to load the first time it is activated, but the next time it will load quickly.
C USTOMIZING M ATERIALS
Let us keep working on the busbar. 1 In the Model Builder, under Materials, click Copper .
Advanced Topics
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2 In the Material settings window, the Materials Properties section contains a list of all the definable properties. Expand the Solid Mechanics > Linear Elastic Material section. Right-click Bulk Modulus and Shear Modulus and select Add to Material. This lets you define the bulk modulus and shear modulus for the copper in your model. 3 Locate the Material Contents section. Bulk modulus and Shear modulus rows are now available in the table. The warning sign indicates the values are not yet defined. To define the values, click the Value column. In the Bulk modulus row, enter 140e9 and in the Shear modulus row, enter 46e9.
By adding these material properties, you have changed the Copper material. You cannot save this in the read-only Solid Mechanics material library, however, you can save it to your own material library. 4 In the Model Builder, right-click Copper and select Add Material to User Defined Library .
74 | Advanced Topics
Addin g M eshes
A model can contain different meshing sequences to generate meshes with different settings. These sequences can then be accessed by the study steps. In the study, you can select which mesh you would like to use in a particular simulation. In the busbar model, a second mesh node is now added to create a mesh that is refined in the areas around the bolts and the bend.
A DDING
M ESH
1 In order to keep this model in a separate file for later use, from the main menu, select File > Save as and rename the model busbar_I.mph. 2 To add a second mesh node, right-click the Busbar (mod1) node and select Mesh . By adding another Mesh node, it creates a Meshes parent node that contains both Mesh 1 and Mesh 2.
3 Click the Mesh 2 node. In the Mesh settings window under Mesh Settings, select User-controlled mesh as the Sequence type. A Size and Free Tetrahedral node are added under Mesh 2.
Advanced Topics
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The asterisk in the upper-right corner of a node icon indicates that the node is being edited. 5 In the Size settings window under Element Size, click the Custom button. 6 Under Element Size Parameters, enter:
- mh/2 in the Maximum element size field, where mh is 6 mmthe
76 | Advanced Topics
Compare Mesh 1 and Mesh 2 by clicking the Mesh nodes. The mesh is updated in the Graphics window. An alternative for using many different meshes is to run a parametric sweep of the parameter for the maximum mesh size, mh, that was defined in the section Global Definitions on page 45.
Mesh 1
Mesh 2
A dd i n g P hy s i c s
COMSOL's distinguishing characteristics of adaptability and compatibility are prominently displayed when you add physics to an existing model. In this section, you will understand the ease with which this seemingly difficult task is performed. By following these directions, you can add structural mechanics and fluid flow to the busbar model.
S TRUCTURAL M ECHANICS
After completing the busbar Joule heating simulation, we know that there is a temperature rise in the busbar. What kind of mechanical stress is induced by thermal expansion? To answer this question, let us expand the model to include the physics associated with structural mechanics.
Advanced Topics
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To complete these steps, either the Structural Mechanics Module or the MEMS Module (which enhances the standard Solid Mechanics interface) is required. If you want to add cooling by fluid flow, or dont have the Structural Mechanics Module or MEMS Module, read this section and then go to Cool by Adding Fluid Flow on page 83. 1 Open the model busbar.mph that was created earlier. From the main menu, select File>Save as and rename the model busbar_II.mph. 2 In the Model Builder, right-click the Busbar node and select Add Physics 3 In the Model Wizard under Structural Mechanics, select Solid Mechanics . To add this interface, you can double-click it, right-click and select Add Selected, or click the Add Selected button . 4 Click the Finish button and save the file. You do not need to add any studies. .
When adding additional physics, you need to make sure that materials included in the Materials node have all the required properties for the selected physics. In this example, you already know that all properties are available for copper and titanium. You can start by adding the effect of thermal expansion to the structural analysis.
78 | Advanced Topics
5 In the Model Builder under Solid Mechanics, right-click the Linear Elastic Material 1 node and from the domain level select Thermal Expansion . A Thermal Expansion node is added to the Model Builder.
6 In the Thermal Expansion settings window under Model Inputs, select Temperature (jh/jhm1) from the Temperature list. This is the temperature field from the Joule Heating interface (jh/jhm1) and couples the Joule heating effect to the thermal expansion of the busbar. With the Structural Mechanics Module, the Thermal Stress predefined multiphysics interface is also available to define thermal stresses and strains. Next, constrain the busbar at the position of the titanium bolts. 7 In the Model Builder, right-click Solid Mechanics and from the boundary level, select Fixed Constraint . A node with the same name is added to the Model Builder. 8 Click the Fixed Constraint node. In the Graphics window, rotate the busbar to view the back. Click the circular surface of one of the bolts to highlight it and right-click to add this surface to the Selection list.
Advanced Topics
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9 Repeat this procedure for the remaining bolts to add boundaries 8, 15, and 43.
Next we update the Study to take the added effects into account.
S OLVING
FOR JOULE
H EATING
AND
T HERMAL E XPANSION
The Joule heating effect is independent of the stresses and strains in the busbar, assuming small deformations and ignoring the effects of electric contact pressure. This means that you can run the simulation using the temperature as input to the structural analysis. In other words, the extended multiphysics problem is weakly coupled. As such, you can solve it in two separate study steps to save computation timeone for Joule heating and a second one for structural analysis. 1 In the Model Builder, right-click Study 1 and select Study Steps>Stationary to add a second stationary study step.
When adding study steps you need to manually connect the correct physics with the correct study step. We shall start by removing the structural analysis from the first step. 2 Under Study 1, click the Step 1: Stationary node .
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3 In the Stationary settings window, locate the Physics and Variables Selection. 4 In the Solid Mechanics (solid) row under Solve for, click to change the check mark to an to remove Solid Mechanics from Study 1.
Now repeat these steps to remove Joule heating from the second study step. 5 Under Study 1, click Step 2: Stationary 2 .
6 Under Physics and Variables Selection, in the Joule Heating (jh) row under Solve for, click to change the check mark to an to remove Joule Heating from Step 2. 7 Right-click the Study 1 node and select Compute (or press F8) to solve the problem.
Save the file busbar_II.mph, which now includes the Solid Mechanics interface and the additional study step.
R ESULTING D EFORMATION
Now add a displacement to the plot.
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2 In the Surface settings window in the Expression section, click the Replace Expression button . From the context menu, select Solid Mechanics>Displacement>Total Displacement. You can also enter solid.disp in the Expression field. 3 Click Range to expand the section. Click to clear the Manual color range check box.
The local displacement due to thermal expansion is displayed by COMSOL as a surface plot. Next well add information about the busbar deformation. 4 In the Model Builder, under Results>3D Plot Group 2, right-click the Surface 1 node and add a Deformation . The plot automatically updates in the Graphics window.
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The deformations shown in the figure are highly amplified to make visible the very small distortions that actually take place.
5 Save the busbar_II.mph file, which now includes a Surface plot with a Deformation. You can also plot the von Mises and principal stresses to assess the structural integrity of the busbar and the bolts.
C OOL
BY
After analyzing the heat generated in the busbar and possibly the induced thermal stresses, you might want to investigate ways of cooling it by letting air flow over its surfaces. These steps do not require any additional modules. When you have the CFD Module or the Heat Transfer Module, the Conjugate Heat Transfer multiphysics interface is available. This automatically defines coupled heat transfer in solids and fluids including laminar or turbulent flow. Adding fluid flow to the Joule heating model forms a new multiphysics coupling. To simulate the flow domain, you need to create an air box around the busbar. You can do this manually by altering the geometry from your first model or by opening a Model Library file. In this case, you will open a model with the box already created.
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Having loaded the geometry, you will now learn how to simulate air flow according to this figure:
Air outlet
Air inlet
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3 In the Parameters settings window, click the empty row just below the Vtot row. In the Name column, enter Vin. Enter 1e-1[m/s] in the Expression column and a description of your choice in the Description column. 4 Select File>Save As and save the model with a new name, busbar_box_I.mph.
A DDING A IR
The next step is to add the material properties of air. 1 Select View>Material Browser. 2 In the Material Browser, expand the Built-In tree. Right-click Air and select Add Material to Model. Click the Material Browser tab and close it. 3 In the Model Builder under Materials, click the Air node.
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4 In the Graphics window, click the air box (Domain 1) to highlight it (in red) and right-click to add it to the Selection list (which changes the color to blue).
2 In the Add Physics tree under Fluid Flow>Single-Phase Flow double-click Laminar Flow to add it to the Selected physics section. You do not need to add any more studies. Click the Finish button .
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3 On the Graphics toolbar, click the Select Boundaries button Wireframe rendering button to look inside the box.
Now that you have added fluid flow to the model, you need to couple the heat transfer part of the Joule Heating interface to the fluid flow. 4 In the Model Builder, right-click Joule Heating . In the first section of the context menu, the domain level, select Heat Transfer>Heat Transfer in Fluids.
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5 In the Graphics window select the air box (Domain 1) and right-click to add it to the Selection list. Now couple the fluid flow and the heat transfer phenomena.
6 In the Heat Transfer in Fluids settings window under Model Inputs, select Velocity field (spf/ fp1) from the Velocity field list. This identifies the flow field from the Laminar Flow interface and couples it to heat transfer. Now define the boundary conditions by specifying the inlet and outlet for the heat transfer in the fluid domain. 7 In the Model Builder, right-click Joule Heating . In the second section of the context menu, the boundary section, select Heat Transfer>Temperature. A Temperature node is added to the Model Builder
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8 In the Graphics window, click the inlet boundary, Boundary 2, and right-click to add it to the Selection list. This sets the inlet temperature to 293.15 K, the default setting. Click the Transparency button in the Graphics toolbar to turn off transparency, since we do not need this anymore. Click the Wireframe Rendering button in the Graphics toolbar. The graphics should look like the image on the right. Continue by defining the outlet. 9 In the Model Builder, right-click Joule Heating . At the boundary level, select Heat Transfer>Outflow. An Outflow node is added to the Model Builder.
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1 0 In the Graphics window, click the outlet boundary, Boundary 5, and right-click to add it to the Selection list.
The settings for the busbar, the bolts and the Electric Potential 1 and Ground 1 boundaries have retained the correct selection, even though you added the box geometry for the air domain. To confirm this, click the Electric Potential 1 and the Ground 1 nodes in the Model Builder to verify that they have the correct boundary selection.
Lets continue with the flow settings. You need to indicate that fluid flow only takes place in the fluid domain and then set the inlet, outlet, and symmetry conditions.
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1 In the Model Builder, click the Laminar Flow node . In the Laminar Flow settings window, click the Clear Selection button .
2 In the Graphics window, click the air box (Domain 1) and right-click to add it to the Selection. It is good practice to verify that the Air material under the Materials node has all the properties that this multiphysics combination requires. In the Model Builder under Materials, click Air. In the Material settings window under Material Contents, verify that there are no missing properties, which are marked with a warning sign . The section Materials on page 49 has more information. Lets continue with the boundaries. 3 In the Model Builder, right-click Laminar Flow and at the boundary level select Inlet. An Inlet node is added to the Model Builder.
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4 In the Graphics window, select the inlet (Boundary 2) and right-click to add it to the Selection list.
5 In the Inlet settings window under Velocity in the U0 field, enter Vin to set the Normal inflow velocity.
6 Right-click Laminar Flow and at the boundary level select Outlet . In the Graphics window, select the outlet (Boundary 5) and right-click to add it to the Selection list. The last step is to add symmetry boundaries. You can assume that the flow just outside of the faces of the channel is similar to the flow just inside these faces. This is correctly expressed by the symmetry condition. 7 Right-click Laminar Flow and select Symmetry. A Symmetry node is added to the sequence.
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8 In the Graphics window, click one of the blue faces in the figure below (Boundaries 1, 3, 4, or 48) and right-click each one to add all to the Selection list. Save the busbar_box_I.mph file, which now includes the Air material and Laminar Flow interface settings.
When you know the boundaries, you can click the Paste button and enter the information. In this example, enter 1,3,4,48 in the Paste selection window. Click OK and the boundaries are automatically added to the Selection list.
C OARSENING
THE
M ESH
To get a quick solution, we will change the mesh slightly and make it coarser. The current mesh settings would take a relatively long time to solve, and you can always refine it later. 1 In the Model Builder, expand the Mesh 1 node and click the Size node .
2 In the Size settings window under Element Size, click the Predefined button and ensure that Normal is selected.
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You can assume that the flow velocity is large enough to neglect the influence of the temperature increase in the flow field. It follows that you can solve for the flow field first and then solve for the temperature using the results from the flow field as input. This is implemented with a study sequence.
S OLVING
FOR
F LUID F LOW
AND JOULE
H EATING
When the flow field is solved before the temperature field it yields a weakly coupled multiphysics problem. The study sequence described in this section automatically solves such a weak coupling. 1 In the Model Builder, right-click Study 1 and select Study Steps>Stationary to add a second stationary study step to the Model Builder.
Next, the correct physics needs to be connected with the correct study step. Start by removing Joule heating from the first step.
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3 In the Stationary settings window locate the Physics and Variables Selection section. In the Joule Heating (jh) row, click to change the check mark to an in the Solve for column, removing Joule Heating (jh) from Study 1. 4 Repeat the step. Under Study 1 click Step 2: Stationary 1 . Under Physics and Variables Selection, in the Laminar Flow (spf) row click in the Solve for column to change the check mark to an .
5 Right-click the Study 1 node and select Compute (or press F8) to automatically create a new solver sequence that solves the two problems in sequence.
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6 After the solution is complete, click the Transparency button toolbar to visualize the temperature field inside the box.
on the Graphics
The Temperature Surface plot that displays in the Graphics window shows the temperature in the busbar and in the surrounding box. You can also see that the temperature field is not smooth due to the relatively coarse mesh. A good strategy to get a smoother solution would be to refine the mesh to estimate the accuracy. 7 Save the busbar_box_I.mph file up to this point so you can return to this file if you want. The next steps use the original busbar.mph file.
Par am et ri c Swe ep s
S WEEPING
G EOMETRIC P ARAMETER
It is often useful to generate multiple instances of a design with the objective of meeting specific constraints. In the previous busbar example, a design goal might be to lower the operating temperature, or to decrease the current density. We will demonstrate the former. Since the current density depends on the geometry of the busbar, varying the width, wbb, should change the current density and, in turn,
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have some impact on the operating temperature. Let us run a parametric sweep on wbb to study this change.
A DDING
P ARAMETRIC S WEEP
1 Open the model file busbar.mph. In the Model Builder, right-click Study 1 and select Parametric Sweep . A Parametric Sweep node is added to the Model Builder sequence.
2 In the Parametric Sweep settings window, under the table, click the Add button . From the Parameter names list in the table, select wbb.
The Sweep type, available above the Parameter names, is used to control parametric sweeps with multiple parameters. You select between sweeping for All combinations of the given parameters or a subset of Specified combinations.
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3 Enter a range of Parameter values to sweep the width of the busbar from 5 cm to 10 cm with 1 cm increments. There are different ways to enter this information:
- Copy and paste or enter range(0.05,0.01,0.1) into the Parameter value
list field.
- Click the Range
button and enter the values in the Range dialog box. In the Start field, enter 5e-2. In the Step field, enter 1e-2, and in the Stop field, enter 1e-1. Click Replace.
Next, define an Average Model Coupling, which can later be used to calculate the average temperature in the busbar. 4 Under Model 1, right-click Definitions Average . and select Model Couplings>
5 In the Average settings window select All domains from the Selection list. This creates an operator called aveop1.
The aveop1 is now available to calculate the average of any quantity defined on those domains. A little later this is used to calculate the average temperature, but it can also be used to calculate average electric potential, current density, and so forth. 6 Right-click Study 1 and select Compute to run the sweep. 7 Select File>Save As to save the model with a new name, busbar_III.mph.
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2 In the Surface settings window, click Range to expand the section. Select the Manual color range check box. Enter 309.35 in the Maximum field (replace the default) to plot wbb at 10 cm.
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3 The Temperature (jh) 1 plot is updated in the Graphics window for wbb=0.1[m] (10[cm]).
Compare the wider busbar plot to the temperature for wbb=0.05[m] (5[cm]). 1 In the Model Builder, click the first Temperature (jh) node .
2 In the 3D Plot Group settings window, select Solution 2 from the Data set list. This data set contains the results from the parametric sweep. 3 In the Parameters value list, select 0.05 (which represents wbb=5 cm). Click the Plot button . Click the Zoom Extents button on the Graphics toolbar.
The Temperature (jh) plot is updated for wbb=0.05[m] (5[cm]). Note that you may have updated the color range for this plot already and then your plot may look different compared to the one below. If not, follow the steps below.
Like the wider busbar, the plot may be quite uniform in color, so change the maximum color range. 1 Under the first Temperature (jh) node, click the Surface node . 2 In the Surface settings window, click Range to expand the section (if it is not already expanded). Select the Manual color range check box.
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3 Enter 323 in the Maximum field (replace the default) to plot wbb at 5 cm. The Temperature (jh) plot is updated in the Graphics window for wbb=0.05[m] (5[cm]).
Click the first and second Temperature plot nodes to compare the plots in the Graphics window. The plots show that the maximum temperature decreases from 331 K to 318 K as the width of the busbar increases from 5 cm to 10 cm.
2 In the 1D Plot Group settings window, select Solution 2 from the Data set list.
node.
4 Under y-Axis Data, click the first row in the Expressions column and enter aveop1(T). This operator is the one we defined on page 98 for later use. You use a similar syntax to calculate the average of other quantities.
5 Click to expand the Legends section. Select the Expression check box. This adds a legend at the top right corner of the graph.
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6 Click the Plot button and save the busbar_III.mph model with these additional plots that use the parametric sweep results.
In the plot, the average temperature also decreases as the width increases. This indicates that the goal of a lower operating temperature would be fulfilled by using a wider busbar. The subject of parametric sweeps raises the question of parallel computing; it would be efficient if all parameters were solved simultaneously.
Par a l l e l C o m p u t i n g
COMSOL supports most forms of parallel computing including shared memory parallelism for multicore processors and high performance computing (HPC) clusters and clouds. Any COMSOL license will be multicore enabled. For cluster or cloud computing, a Floating Network License is needed. You can use clusters or clouds either for Cluster Sweep or for Cluster Computing. If you have a Floating Network License, these two options are available from the Study node by right-clicking. However, you first need to enable Advanced Study
C LUSTER S WEEP
Cluster Sweep is used for solving several models in parallel where each model has a different set of Parameters. This can be seen as a generalization of Parametric Sweep. Right-click the Study node to add a Cluster Sweep node. The Study Settings for Cluster Sweep is similar to that of Parametric Sweep, but additional settings are required for the cluster or cloud being used. The below picture shows how the top of the settings window for Cluster Sweep would look like for the same sweep as defined in Parametric Sweeps on page 96.
C LUSTER C OMPUTING
You can also utilize a cluster or cloud to solve a single large model using distributed memory. For maximum performance, the COMSOL cluster implementation can utilize shared-memory multicore processing on each node in combination with the Message Passing Interface (MPI) based distributed memory
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model. This brings a major performance boost by making the most out of the computational power available. Right-click the Study node to add a Cluster Computing node. The Cluster Computing settings window, shown below, helps to manage the simulation with settings for the cluster or cloud.
You choose the type of cluster job you want to do from the Cluster type list. COMSOL supports Windows Computer Cluster Server (WCCS) 2003, Windows HPC Server (HPCS) 2008, Open Grid Scheduler/ Grid Engine (OGS/GE), or Not distributed. To learn more about running COMSOL in parallel, see the COMSOL Multiphysics Reference Manual.
on the Work Plane settings toolbar. Continue by editing the axis and grid settings in Work Plane 1.
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Note that the values you type will be automatically adjusted slightly after you enter it to adapt to the screen aspect ratio. Under Grid:
- Select the Manual Spacing check
box.
- In the x spacing and y spacing fields, enter 5e-3.
on the
You can use interactive drawing to create a geometry using the drawing toolbar buttons while pointing and clicking in the Graphics window. You can also
to add geometry
Click the Plane Geometry node under a Work Plane node to open the interactive drawing toolbar.
In the next sequence of steps we create a profile of the busbar. 5 In the Model Builder under Work Plane 1, right-click Plane Geometry select Rectangle . In the Rectangle settings window under Size, enter:
- L+2*tbb in the Width field. - 0.1 in the Height field .
and
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6 Create a second rectangle. Under Work Plane 1, right-click Plane Geometry and select Rectangle Under Size, enter:.
- L+tbb in the Width field - 0.1-tbb in the Height field.
Use the Boolean Difference operation to subtract the second rectangle from the first one. 7 Under Work Plane 1, right-click Plane Geometry and select Boolean Operations>Difference . In the Graphics window, click r1 and right-click to add r1 to the Objects to add list in the Difference settings window. To help select the geometry you can display geometry labels in the Graphics window. In the Model Builder under Geometry 1>WorkPlane 1>Plane Geometry, click the View 2 node. Go to the View settings window and select the Show geometry labels check box. 8 Click the Difference node. In the Difference settings window, click the Activate selection button to the right of the Objects to subtract list. Then select the smaller rectangle (left-click multiple times to cycle through overlapping geometry objects) and right-click to add r2 to the list. Click Build Selected . Another way to select r2 in the Graphics window is to use the Selection List window. Select View>Selection List and in the Selection List settings window,
click to highlight r2 (solid). Then right-click r2 (solid) in the list to add it to the Object to subtract list. After building the selected geometry, you should have a backward-facing, L-shaped profile. Continue by rounding the corners of the L-shaped profile.
Select point 3 to add it to the Vertices to fillet list. There are different ways to add the points:
- In the Graphics window, click point 3 (in the inner right corner), and
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1 0 Enter tbb in the Radius field. Click Build Selected This takes care of the inner corner. 1 1 For the outer corner, right-click Plane Geometry and select Fillet . 1 2 In the Graphics window, click point 6, the outer corner, and right-click to add it to the Vertices to fillet list. 1 3 Enter 2*tbb in the Radius field. Click Build Selected .
Next you extrude the work plane to create the 3D busbar geometry. 1 In the Model Builder, right-click Work Plane 1 and select Extrude . In the Extrude settings window, enter wbb in the Distances from Plane table (replace the default) to extrude to the width of the profile.
The table allows you to enter several values in order to create sandwich structures with different layer materials. In this case, only one extruded layer is needed.
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2 Click Build Selected and then click the Zoom Extents button on the Graphics toolbar. Click the Save button and name the model busbar.mph (if you have not already done so).
Next, create the titanium bolts by extruding two circles drawn in two work planes. 3 In the Model Builder, right-click Geometry 1 and add a Work Plane . A Work Plane 2 node is added. In the Work Plane settings window, under Work Plane, select Face parallel as the Plane type.
4 In the Graphics window, click face 8 (highlighted in the figure). Once this surface is highlighted in red, right-click anywhere in the Graphics window to add it to the Planar face list in the Work Plane settings window. Face number 8 is now highlighted in blue and the work plane is positioned on top of face number 8.
Face 8
5 Click the Show Work Plane button to draw the first circle representing the position of the first bolt. Click the Zoom Extents button on the Graphics toolbar.
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6 Under Work Plane 2, right-click Plane Geometry and select Circle . In the Circle settings window:
- Under Size and Shape in the Radius field, enter rad_1. - Under Position, the xw and yw
Continue creating the bolt by adding an extrude operation. 1 In the Model Builder, right-click Work Plane 2 and select Extrude . In the Extrude settings window, in the first row of the Distances from Plane table, enter -2*tbb to extrude the circle.
2 Click the Build Selected button to create the cylindrical part of the titanium bolt that runs through the busbar.
Draw the two remaining bolts. 3 Right-click Geometry 1 and select Work Plane . A Work Plane 3 node is added. In the Work Plane settings window, for Work Plane 3, select Face parallel as the Plane type. 4 In the Graphics window, click Face 4 (shown in the figure). When this surface is highlighted red, right-click anywhere in the Graphics window to add it to the Planar face list in the Work Plane settings window.
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5 Click the Show Work Plane button on the Work Plane settings window and the Zoom Extents button on the Graphics toolbar to get a better view of the geometry. To parameterize the position of the two remaining bolts, add the circles that form the cross sections of the bolts. 6 Under Work Plane 3, right-click Plane Geometry In the Circle settings window:
- Under Size and Shape, enter rad_1
Copy the circle that you just created to generate the third bolt in the busbar. 7 Under Work Plane 3, right-click Plane Geometry and select Transforms>Copy . 8 In the Graphics window, click the circle c1 to highlight it. Right-click anywhere in the Graphics window and add the circle to the Input object list in the Copy settings window. 9 In the Copy settings window under Displacement, enter wbb/2 in the yw field.
Your geometry, as shown in the workplane, should match this figure so far. Continue by extruding the circles.
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1 1 In the Model Builder, right-click Work Plane 3 and select Extrude . In the Extrude settings window, in the first row of the Distances from Plane table, enter -2*tbb (replace the default). Click Build All . The geometry and its corresponding geometry sequence should match the figures below. Click the Save button and name the model busbar.mph.
To continue with the busbar tutorial, return to the section Materials on page 49.
F1 Ctrl+F1
F1 Command+F1
Display help for the selected node or window Open the COMSOL Documentation front page in an external window Rename the selected node, file, or folder Disable selected nodes Enable selected nodes Update the Data Sets Solutions with respect to any new Global Definitions and Definitions without re-solving the model Build the selected node in the geometry and mesh branches, or compute to the selected node in the solver sequence Build the geometry, build the mesh, compute the entire solver sequence, update results data, or update the plot Delete selected nodes Collapse a branch in the Model Tree Expand a branch in the Model Tree Move to the node above in the Model Tree Move to the node below in the Model Tree Move to the previously selected node in the Model Tree Move to the next selected node in the Model Tree
F2 F3 F4 F5
F2 F3 F4 F5
F7
F7
F8
F8
Del Left arrow (Windows); Shift + left arrow (Linux) Right arrow (Windows); Shift + right arrow (Linux) Up arrow Down arrow Alt+left arrow Alt+right arrow
Del Left arrow Right arrow Up arrow Down arrow Ctrl+left arrow Ctrl+right arrow
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SHORTCUT (MAC)
ACTION
Ctrl+A
Command+A
Select all domains, boundaries, edges, or points; select all cells in a table Deselect all domains, boundaries, edges, or points Copy text in fields New model Open file Print Save file Paste copied text Undo the last operation Redo the last undone operation Move a definitions node, geometry node, physics node (except default nodes), material node, mesh node, study step node, or results node up one step Move a definitions node, geometry node, physics node (except default nodes), material node, mesh node, study step node, or results node down one step Switch focus to the next window on the desktop New Physics Builder Switch focus to the previous window on the desktop Switch focus to the Model Builder window Switch focus to the settings window Switch focus to the previous section in the settings window Switch focus to the next section in the settings window
Ctrl+D Ctrl+C Ctrl+N Ctrl+O Ctrl+P Ctrl+S Ctrl+V Ctrl+Z Ctrl+Y Ctrl+up arrow
Command+D Command+C Command+N Command+O Command+P Command+S Command+V Command+Z Ctrl+Shift+Z Command+up arrow
Ctrl+down arrow
Command+down arrow
Ctrl+Tab Ctrl+Shift+N Ctrl+Shift+Tab Ctrl+Alt+left arrow Ctrl+Alt+right arrow Ctrl+Alt+up arrow Ctrl+Alt+down arrow
Ctrl+Tab Command+Shift+N Ctrl+Shift+Tab Command+Alt+left arrow Command+Alt+right arrow Command+Alt+up arrow Command+Alt+down arrow
SHORTCUT (MAC)
ACTION
Ctrl+F10 Ctrl+Space
Open the context menu Open list of predefined quantities for insertion in Expression fields for plotting and results evaluation Rotate the scene around the axes parallel to the screen X- and Y-axes with the origin at the scene rotation point. Move the visible frame on the image plane in any direction. The scene is zoomed in/out around the mouse position where the action started. Tilt and pan the camera by rotating about the X- and Y axes in the image plane. Move the camera in the plane parallel to the image plane. Move the camera into and away from the object (dolly in/out). Rotate the camera around the axis.
Left-click and hold down the mouse button while dragging the mouse. Right-click and hold down the mouse button while dragging the mouse. Middle-click and hold down the mouse button while dragging the mouse. Press Ctrl and left-click. While holding down both buttons, drag the mouse. Press Ctrl and right-click. While holding down both buttons, drag the mouse. Press Ctrl and middle-click. While holding down both buttons, drag the mouse. Press Ctrl+Alt and left-click. While holding down both buttons, drag the mouse. Press Alt and left-click. While holding down both buttons, drag the mouse. Press Alt and right-click. While holding down both buttons, drag the mouse. Press Alt and middle-click. While holding down both buttons, drag the mouse.
Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse. Same as for Windows, only available for two-button mouse.
Rotate the camera about its axis between the camera and the scene rotation point (roll direction). Move the scene in the plane orthogonal to the axis between the camera and the scene rotation point. Move the camera along the axis between the camera and the scene rotation point.
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These language elements are built-in or user-defined. Operators cannot be user-defined. Expressions are always user-defined.
C o n s t a n t s a n d Par a m e t e r s
There are three different types of Constants: Built-in Mathematical and Numerical Constants, Built-in Physical Constants, and Parameters. Parameters are User-defined Constants which can vary over parameter sweeps. Constants are scalar valued. The tables below list the Built-in Mathematical and Numerical Constants as well as Built-in Physical Constants. Constants and Parameters can have units.
B UILT - IN M ATHEMATICAL
DESCRIPTION
AND
N UMERICAL C ONSTANTS
NAME VALUE
Floating point relative accuracy for double floating point numbers, also known as machine epsilon The imaginary unit Infinity,
eps
2-52 (~2.220410-16)
i, j inf, Inf
i, sqrt(-1) A value larger than what can be handled with floating point representation An undefined or unrepresentable value such as the result of 0/0 or inf/inf 3.141592653589793
Not-a-number
NaN, nan
pi
Acceleration of gravity Avogadro constant Boltzmann constant Characteristic impedance of vacuum (impedance of free space) Electron mass Elementary charge Faraday constant Fine-structure constant Gravitational constant Molar volume of ideal gas (at 273.15 K and 1 atm) Neutron mass Permeability of vacuum (magnetic constant) Permittivity of vacuum (electric constant)
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DESCRIPTION
NAME
VALUE
Plancks constant Plancks constant over 2 pi Proton mass Speed of light in vacuum Stefan-Boltzmann constant Universal gas constant Wien displacement law constant
P ARAMETERS
Parameters are user-defined constant scalars in the Global Definitions branch in the Model Tree. Example uses are:
parameterizing geometric dimensions, parameterizing mesh element sizes, defining parameters to be used in parametric sweeps.
A Parameter can be defined as an expression in terms of numbers, Parameters, built-in constants, and functions of parameters and built-in constants. Parameters should be assigned a unit, using [], unless they are dimensionless.
Var i abl e s
There are two types of Variables: built-in and user-defined. Variables can be scalars or fields. Variables can have units. Note: There is a group of user-defined variables of special interest. Spatial coordinate variables and dependent variables. These variables have default names based on the space dimension of the geometry and the Physics interface respectively. As a result of the names chosen for these variables, a list of built-in variables will be created by COMSOL: the first and second order derivatives with respect to space and time.
B UILT - IN VARIABLES
NAME DESCRIPTION TYPE
Time Frequency Eigenvalue Phase angle Number of degrees of freedom Mesh element size (length of the longest edge of the element) Mesh type index for the mesh element; this is the number of edges in the element. Mesh element number Volume scale factor variable; this is the determinant of the Jacobian matrix for the mapping from local (element) coordinates to global coordinates. A mesh quality measure between 0 (poor quality) and 1 (perfect quality)
qual
Field
x, y, z r, phi, z u, T, etc.
Example: T is the name for the temperature in a 2D, time-dependent heat transfer model, x and y are the spatial coordinate names. In this case, the following built-in variables will be generated: T, Tx, Ty, Txx, Txy, Tyx, Tyy, Tt, Txt, Tyt, Txxt, Txyt, Tyxt, Tyyt, Ttt, Txtt, Tytt, Txxtt, Txytt, Tyxtt, and Tyytt. Here, Tx corresponds to the partial derivative of the temperature T with respect to x, and Ttt corresponds to the second-order time derivative of T, and so on. If the spatial coordinate variables have other namesfor example, psi and chithen Txy would be Tpsichi, and Txt would be Tpsit. (The time variable t is built-in; the user cannot change its name.)
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Functio n s
There are two types of Functions: Built-in and User-defined. Functions can be scalar valued or field valued depending on the input argument(s). Some Functions can have units for both input and output arguments.
abs acos acosh acot acoth acsc acsch arg asec asech asin asinh atan atan2 atanh besselj bessely besseli besselk ceil conj cos cosh cot coth
Absolute value Inverse cosine (in radians) Inverse hyperbolic cosine Inverse cotangent (in radians) Inverse hyperbolic cotangent Inverse cosecant (in radians) Inverse hyperbolic cosecant Phase angle (in radians) Inverse secant (in radians) Inverse hyperbolic secant Inverse sine (in radians) Inverse hyperbolic sine Inverse tangent (in radians) Four-quadrant inverse tangent (in radians) Inverse hyperbolic tangent Bessel function of the first kind Bessel function of the second kind Modified Bessel function of the first kind Modified Bessel function of the second kind Nearest following integer Complex conjugate Cosine Hyperbolic cosine Cotangent Hyperbolic cotangent
abs(x) acos(x) acosh(x) acot(x) acoth(x) acsc(x) acsch(x) arg(x) asec(x) asech(x) asin(x) asinh(x) atan(x) atan2(y,x) atanh(x) besselj(a,x) bessely(a,x) besseli(a,x) besselk(a,x) ceil(x) conj(x) cos(x) cosh(x) cot(x) coth(x)
NAME
DESCRIPTION
SYNTAX EXAMPLE
csc csch erf exp floor gamma imag log log10 log2 max min mod psi range real round sec sech sign sin sinh sqrt tan tanh
Cosecant Hyperbolic cosecant Error function Exponential Nearest previous integer Gamma function Imaginary part Natural logarithm Base-10 logarithm Base-2 logarithm Maximum of two arguments Minimum of two arguments Modulo operator Psi function and its derivatives Create a range of numbers Real part Round to closest integer Secant Hyperbolic secant Signum function Sine Hyperbolic sine Square root Tangent Hyperbolic tangent
csc(x) csch(x) erf(x) exp(x) floor(x) gamma(x) imag(u) log(x) log10(x) log2(x) max(a,b) min(a,b) mod(a,b) psi(x,k) range(a,step,b) real(u) round(x) sec(x) sech(x) sign(u) sin(x) sinh(x) sqrt(x) tan(x) tanh(x)
The following functions are only available when solving and not when evaluating parameters and variables in the user interface: acosh, acoth, acsch, asech, asinh, atanh, besselj, bessely, besseli, besselk, erf, gamma, and psi.
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the list of reserved names. For more information see the COMSOL Multiphysics Reference Manual.
NAME NAME NAME NAME
adj at ballavg ballint bdf centroid circavg circint circumcenter d depends dest diskavg diskint
down dtang error fsens if integrate isdefined isinf islinear isnan jacdepends lindev linper linpoint
linsol lintotal lintotalavg lintotalpeak lintotalrms linzero mean nojac pd ppr pprint prev reacf realdot
scope.ati sens shapeorder side sphavg sphint subst test timeavg timeint try_catch up var with
Analytic
The function name is its identifier, for example an1. The function is a mathematical expression of its arguments. Example: Given the arguments x and y, its definition is sin(x)*cos(y). The function has an arbitrary number of arguments. The function name is its identifier, for example elev1. Used to import geospatial elevation data from digital elevation models and map the elevation data to a function of x and y. A DEM file contains elevation data for a portion of the Earths surface. The resulting function behaves essentially like a grid-based interpolation function. The function name is its identifier, for example gp1. The Gaussian pulse function defines a bell-shaped curve according to the expression 1 y x = -------------e 2
x x0 ----------------------2 2
2
The name of the function with comma-separated arguments within parenthesis. For example: an1(x,y)
Elevation
The name of the function with comma-separated arguments within parenthesis. For example: elev1(x,y)
Gaussian Pulse
The name of the function with a single argument within parenthesis. For example: gp1(x)
It is defined by the mean parameter, x0, and the standard deviation, . The function has one argument.
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TEMPLATE NAME
SYNTAX EXAMPLE
Image
The function name is its identifier, for example im1. Used to import an image (in BMP, JPEG, PNG, or GIF format) and map the images RGB data to a scalar (single channel) function output value. By default the functions output uses the mapping (R+G+B)/ 3. The function name is its identifier, for example int1. An interpolation function is defined by a table or file containing the values of the function in discrete points. The file formats are the following: spreadsheet, grid, or sectionwise. The function has one to three arguments. The function name is its identifier, for example pw1. A piecewise function is created by splicing together several functions, each defined on one interval. Define the argument, extrapolation and smoothing methods, and the functions and their intervals. This function has one argument with different definitions on different intervals, which must not overlap or have any holes between them. The function name is its identifier, for example rm1. A ramp function is a linear increase with a user-defined slope that begins at some specified time. The function has one argument. It can also be smoothed.
The name of the function with comma-separated arguments within parenthesis. For example: im1(x,y)
Interpolation
The name of the function with comma-separated arguments within parenthesis. For example: int1(x,y,z)
Piecewise
The name of the function with a single argument within parenthesis. For example: pw1(x)
Ramp
The name of the function with a single argument within parenthesis. For example: rm1(x)
TEMPLATE NAME
SYNTAX EXAMPLE
Random
The function name is its identifier, for example rn1. A random function generates white noise with uniform or normal distribution and has one or more arguments to simulate white noise. The function has arbitrary number of arguments. The function name is its identifier, for example rect1. A rectangle function is 1 in an interval and 0 everywhere else. The function has one argument. The function name is its identifier, for example step1. A step function is a sharp transition from 0 to some other value (amplitude) at some location. The function has one argument. It can also be smoothed. The function name is its identifier, for example tri1. A triangle function is a linear increase and linear decline within an interval and 0 everywhere else. The function has one argument. It can also be smoothed. The function name is its identifier, for example wv1. A waveform function is a periodic function with one of several characteristic shapes: sawtooth, sine, square, or triangle. The function has one argument. It can also be smoothed.
The name of the function with comma-separated arguments within parenthesis. For example: rn1(x,y) The arguments x and y are used as a random seeds for the random function. The name of the function with a single argument within parenthesis. For example: rect1(x) The name of the function with a single argument within parenthesis. For example: step1(x)
Rectangle
Step
Triangle
The name of the function with a single argument within parenthesis. For example: tri1(x)
Waveform
The name of the function with a single argument within parenthesis. For example: wv1(x)
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TEMPLATE NAME
SYNTAX EXAMPLE
An external function defines an interface to one or more functions written in the C language (which can be a wrapper function interfacing source code written in for example Fortran). Such an external function can be used, for example, to interface a user-created shared library. Note that the extension of a shared library file depends on the platform: .dll (Windows), .so (Linux), or .dylib (Mac OS X). A MATLAB function interfaces one or more functions written in the MATLAB language. Such functions can be used as any other function defined in COMSOL provided LiveLink for MATLAB and MATLAB are installed. (MATLAB functions are evaluated by MATLAB at runtime.)
The name of the function and the appropriate number of arguments within parenthesis. For example: myextfunc(a,b)
The name of the function and the appropriate number of arguments within parenthesis. For example: mymatlabfunc(a,b)
PRECEDENCE LEVEL
SYMBOL
DESCRIPTION
1 2 3 4 5 6 7 8 9 10 11
Grouping, Lists, Scope Power Unary: Logical Not, Minus, Plus Unit Multiplication, Division Binary: Addition, Subtraction Comparisons: Less-Than, Less-Than or Equal, More-Than, More-Than or Equal Comparisons: Equal, Not Equal Logical And Logical Or Element Separator in Lists
Ex pres sions
P ARAMETERS
A Parameter Expression can contain: Numbers, Parameters, Constants, Functions of Parameter Expressions, Unary and Binary Operators. Parameters can have units.
VARIABLES
A Variable Expression can contain: Numbers, Parameters, Constants, Variables, Functions of Variable Expressions, Unary and Binary Operators. Variables can have units.
F UNCTIONS
A Function definition can contain: input arguments, Numbers, Parameters, Constants, Functions of Parameter Expressions including input arguments, Unary and Binary Operators.
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C O M S O L F i l e Fo r m a t s
The COMSOL Model file type, with the extension .mph, is the default file type containing the entire Model Tree. The file contains both binary and text data. The mesh and solution data are stored as binary data, while all other information is stored as plain text. The COMSOL binary and text file types, with the extension .mphbin and .mphtxt, respectively, contain either geometry objects or mesh objects which can be imported directly to the Geometry or Mesh branches in the Model Tree. The Physics Builder file type, with the extension .mphphb, contains one or more physics user interfaces that you can access from the Model Wizard. See the Physics Builder Manual, for more information. See Supported External File Formats for more information about all the other formats supported by COMSOL.
FILE TYPE EXTENSION READ WRITE
S u p p o r t e d E x t e r n a l F i l e For m a t s
CAD
The CAD Import Module allows for import of a range of industry-standard CAD file types. Additional file types are available through the bidirectional functionality of the LiveLink products for CAD as well as with the File Import for CATIA V5 add-on.
The DXF (2D), VRML (3D), and STL (3D) file types are available for import with COMSOL Multiphysics and dont require any add-on products.
FILE TYPE EXTENSION READ WRITE
AutoCAD (3D only)1 Autodesk Inventor2 Creo Parametric2 Pro/ENGINEER2 Solid Edge3 SolidWorks2 SpaceClaim4 DXF (2D only) Parasolid ACIS Step
2 2
.dwg .ipt, .iam .prt, .asm .prt, .asm .par, .asm .sldprt, .sldasm .scdoc .dxf, .x_t, .xmt_txt, .x_b, .xmt_bin .sat, .sab, .asat, .asab .step, .stp .iges, .igs
Yes6 Yes Yes Yes Yes6 Yes Yes6 Yes Yes Yes Yes Yes Yes Yes Yes
Yes6 Yes6 Yes6 Yes6 Yes6 Yes6 Yes6 Yes Yes Yes No No No No Yes
Requires LiveLink for AutoCAD 2Requires one of the LiveLink products for AutoCAD, Creo Parametric, Inventor, Pro/ ENGINEER, Solid Edge, SolidWorks, or SpaceClaim; or the CAD Import Module 3Requires LiveLink for Solid Edge 4 Requires LiveLink for SpaceClaim 5 Requires the CAD Import Module (or one of the LiveLink products for AutoCAD, Creo Parametric, Inventor, Pro/ENGINEER, Solid Edge, SolidWorks, or SpaceClaim) and the File Import for CATIA V5 6 From/To file via linked CAD package 7 Limited functionality for a single geometric domain only
ECAD
The ECAD Import Module allows for import of 2D layout files with automatic conversion to 3D CAD models. The Touchstone file type is used for exporting S-parameters, impedance, and admittance values from simultaneous port and
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frequency sweeps. The SPICE Circuit Netlist file type is converted at import to a series of lumped circuit element nodes under an Electrical Circuit node.
FILE TYPE EXTENSION READ WRITE
NETEX-G1 ODB++(X)1 GDS1 Touchstone SPICE Circuit Netlist2 1Requires the ECAD Import Module 2
No No No Yes No
M ATERIAL D ATABASES
The Chemical Reaction Engineering Module can read CHEMKIN files to simulate complex chemical reactions in the gas phase. The Plasma Module can read LXCAT files for sets of electron impact collision cross-sections.
FILE TYPE EXTENSION READ WRITE
CHEMKIN
1 1
No n/a No
Requires Chemical Reaction Engineering Module Any extension is allowed, these are the most common extensions
M ESH
The NASTRAN Bulk Data file types are used to import a volumetric mesh. The VRML and STL file types are used to import a triangular surface mesh, and cannot be used for creating a volumetric mesh. If imported as a Geometry, then VRML and STL files can be used as a basis for creating a volumetric mesh for a single geometric domain.
FILE TYPE EXTENSION READ WRITE
No No Yes
I MAGES
AND
M OVIES
Results visualization can be exported to a number of common image file types, see the table below. Images can also be read and used as interpolation functions for physics modeling. Animations can be exported to one of the Animated GIF, Adobe Flash, and AVI file types.
FILE TYPE EXTENSION READ WRITE
JPEG PNG BMP TIFF GIF EPS (1D graphs only) Animated GIF Adobe AVI1
1
.jpg, .jpeg .png .bmp .tif, .tiff .gif .eps .gif .swf .avi
Flash
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P ROGRAMMING L ANGUAGES
AND
S PREADSHEET
Model Java-Files are editable script files, with the extension .java, that contain sequences of COMSOL Multiphysics commands as Java code. Edit the files in a text editor to add additional commands. You can compile these Java files into Java Class files, with the extension .class, and run them as separate applications. Model M-files are editable script files, similar to the Model Java-files, for use with MATLAB. Model M-files, which have the extension .m, contain a sequence of COMSOL Multiphysics commands as a MATLAB M-file. Run the Model M-files in MATLAB like any other M-file scripts. Also edit the files in a text editor to include additional COMSOL Multiphysics commands or general MATLAB commands. Running files in the Model M-file format requires the COMSOL LiveLink for MATLAB.
FILE TYPE EXTENSION READ WRITE
MATLAB: MATLAB:
Java: Model Java File Java: Model Class File C: Function Excel2
1Requires LiveLink for MATLAB 2 Requires LiveLink for Excel, available for Windows only 3
N UMERICAL
AND I NTERPOLATION
D ATA FORMATS
The Grid, Sectionwise, and Spreadsheet file types can be read for defining Interpolation functions. The Sectionwise and Spreadsheet file types can furthermore be read and used for defining Interpolation curves and written for exporting Results. In addition, Tables can be copy-pasted on spreadsheet format. Parameters and Variables can be imported and exported to the Plain text, Comma-separated values, or Data file types. The Continuous and Discrete color table text file types are used for user-defined color tables for Results visualization. Digital Elevation Model (DEM) files can be read and used as a Parametric Surface for defining a Geometry.
FILE TYPE EXTENSION READ WRITE
Copy and paste spreadsheet format Excel spreadsheet1 Table Grid Sectionwise Spreadsheet Parameters Variables Continuous and Discrete color table DEM
n/a .xlsx .txt, .csv, .dat .txt .txt, .csv, .dat .txt, .csv, .dat .txt, .csv, .dat .txt, .csv, .dat .txt .dem
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
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LiveLink
for MATLAB
LiveLink
for AutoCad
LiveLink
for Creo Parametric
LiveLink
for Inventor - Bidirectional Mode - One Window Mode
No Yes No No
No No No No
LiveLink
for Pro/ENGINEER
LiveLink
for Solid Edge
LiveLink
for SolidWorks - Bidirectional Mode - One Window Mode
No Yes No
No No No
Yes No Yes
LiveLink
for SpaceClaim
1 When
you open a COMSOL model from Excel, a COMSOL model window starts and a link is established automatically. The COMSOL model window is an output window that displays geometry, mesh, and results.
2 A COMSOL model that includes a table reference to an Excel spreadsheet automatically starts an Excel process in the background when the model is run in COMSOL Desktop. 3 You can start a COMSOL Server from a MATLAB session using the "system" command and then connect to it using "mphstart" in the MATLAB command prompt.
COMSOL Product
4 The
"COMSOL 4.3b with MATLAB" desktop shortcut starts a COMSOL Server and MATLAB, then connects them automatically. When you run a COMSOL model in the COMSOL Desktop that includes a MATLAB function (Global Definitions>Functions), a MATLAB engine and connection is started automatically. You can connect a MATLAB session to a running COMSOL Server using the COMSOL command "mphstart" in the MATLAB command prompt.
5
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