trinitas - solid mechanics · the trinitas program is an integrated graphical environment for...

TRINITAS

a Finite Element stand-alone tool for

Conceptual design, Optimization and

General finite element analysis

Introductional Manual

Bo Torstenfelt

Contents

1 Introduction 1

2 Starting the Program 3

3 Basic Principles 5Editing of Integers, Floating-point numbers and Characters in the User

Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Function keys and short cuts . . . . . . . . . . . . . . . . . . . . . . . . 7

4 The Main Menu 9Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Domain Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Time Dependencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Analysis Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Single Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Animations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 A Getting Started Example 13The Physical Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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ii CONTENTS

• Geometry - Create Point - Create Points by the Cursor . . . . . 14• Geometry - Create Line - . . . . . . . . . . . . . . . . . . . . . . 15• Geometry - Modify Line - Spline a Line by the Cursor . . . . . . 16• Geometry - Create Surface . . . . . . . . . . . . . . . . . . . . . 17• Geometry - Create Volume - Create Volumes by picking Surfaces 17

Domain Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18• Domain Properties - Create a New Material - . . . . . . . . . . 18• Domain Properties - Connect a Material - . . . . . . . . . . . . 18

Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18• Boundary Conditions - Line Loads - Numeric Method . . . . . . 18• Boundary Conditions - Fix a Lines - ... . . . . . . . . . . . . . . . 19

Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19• Mesh - Create a Model Mesh from default higher-order Elements 20• Mesh - Modify Mesh - Change Number of Subdivision s along a

Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Analysis Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

• Analysis Type - Linear Static Stress Analysis - Start an Analysis 21Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

• Single Values - Pick Maximum Numeric Value . . . . . . . . . . . 22

Chapter 1Introduction

The TRINITAS program is an integrated graphical environment for Finite Ele-ment Analysis. The program includes activities for geometry modeling, boundarycondition definition, mesh generation, simulation and evaluation of the results.Boundary conditions can be defined on the geometry and/or on the mesh.

One important characteristics of the program is that it works in a what yousee is what you get (WYSIWYG) fashion today very common in other disciplinessuch as in for instance word processing. This also means that there exist no inputor output file formats. All data are saved on a database file. That is the programcan looked upon as a browser for the problem definition and the result. It is alsoan editor of the problem definition and a monitor for ongoing calculations.

The program is written in FORTRAN and in C. An Object-based program-ming technique has been utilized through out the entire program development.The graphical user interface (GUI) has a hierarchical structure where all differentactivities can be reached.

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2 1. Introduction

Chapter 2Starting the Program

On a PC computer a copy of the executable file have to be available on thedirectory where you do your calculations. This executable file can be found onthe WEB.

On a UNIX computer you start the program by typing TRINITAS in theinput window will start the program.

The program uses two different data base files. One of these two files is calledTrinitas Data Base File by default and it contains information of all created andanalyzed models. The second file called Trinitas Program Settings contains onlyuser-chosen preferences for how the program shall behave. These files will beinitiated during a first run on a new directory and the files will be closed whenthe program is properly closed down.

The first file name, Trinitas Data Base File, is a default file name and can bechanged in the first menu appearing when the program is started. Both thesefiles are non-formatted direct access files.

It can be mentioned that the program do not support any backup or undo fea-tures so it can be useful to make your own backup copy of the Trinitas Data Base Filebefore starting a new session as a security.

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4 2. Starting the Program

Chapter 3Basic Principles

The TRINITAS program is entirely driven behind a Graphical User Interface(GUI). This interface has a hierarchical structure (tree structure) with 13 branchesstarting from the root (the Main Menu) and the leaves in tree are all differentactivities possible to activate in the program.

The Main Menu appears to the right of the program window. Each Menu con-sists of a number of rectangular boxes, called Target Areas in this documentation,containing text and sometimes also figures.

A Target Area flashes into a reversed color pattern when the mouse is movedover it and tells the User that something will happens if the Left mouse buttonis pushed in that part of the window.

Every menu appears in the same position of the window. This means thatonly one menu at the time can be activated. This makes the number of possiblealternatives for the User limited and increases the User-friendliness of the pro-gram especially for beginners. General Menu system principles can be identifiedand summarized as follows:

• Every menu is constructed in such a way that it indicates a logical sequenceof the work. Always start the work by putting focus at the target area atthe top of the menu and continue further downwards. Every activity are ofcourse not always needed.

• By pushing the right mouse button you will climb upward in the hierarchicaltree from the Main menu (root menu) and you will move back down againby pushing the left mouse button.

• In target areas with a filled triangle to the right in the box, you shall expecta new menu to appear when pushing the left mouse button.

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6 3. Basic Principles

• In target areas with an unfilled triangle to the right, you shall expect asmaller so called Cursor menu to appear on top of the previous menu.

• When pushing the left mouse button in a target area without any triangleto the right, you shall expect an activity to start. When starting an activitya message will occur in the Message Window at the bottom of the window.Two different situations can be identified:

• In activities where the message ends up with an exclamation mark (!) theUser is expected to do some mouse activity in the Viewport window (nor-mally picking of some kind of previously created entity)

• In activities where the message ends up without an exclamation mark (!)the message only tells the User what is ongoing in the program and nofurther mouse activities are expected from the User.

• In some rare cases you will found boxes of text inside a menu which donot flash into reversed color mode. Such boxes are actually no target areasbecause these are not connections to anything and the only purpose is togive the User some informational text.

Editing of Integers, Floating-point numbers andCharacters in the User Interface

In some target areas the text is moved a bit offset making space for a smallerbox-shaped area with a double-drawn border. In such a sub-area it is possible toedit variables of three different types (Integers, Reals and Characters).

In each of these cases, pushing the left mouse button inside this sub-areastarts an editing process. The area will then change into black text on a whitebackground with a thick red border. The focus, marked by a small filled trianglebelow the text, can be moved by using the arrows on the keyboard.

The editing process will be closed by pressing the carriage return button orby just moving the cursor out of the editing area.

• Integers: The ten digits from 0 to 9 and the minus sign can be used inthis case.

• Reals: Here, the dot and the small and big ”e” are also included in thepossible character set. Please observe, if you put in a number greater thanten powered by 8 or less than ten powered by minus 8 the program will usean exponential representation.

• Characters: In this case all characters are possible to use which are in-cluded in the standard character set defined by the ANSI FORTRAN 77standard.

3.0. Function keys and short cuts 7

Function keys and short cuts

In 3D problems the camera can be manipulated by the following commands:

• By pushing the character v for view and the left mouse button the anglein which the object is visualized is changed.

• By pushing the left mouse button and the character z for zoom the zoomdegree in the camera is changed.

• By pushing the character x and the left mouse button the object can bepanned over the screen.

• By pushing the character t and the left mouse button the camera is turnedand the object is rotated on the screen without changing the angle of ob-servation.

Some function keys can be used for some frequently used activities:

F1 Performs a redraw of the model with Auto-Zoom conditions which meansthat the bounding box of all defined Points and the corners of the workingplane raster, if any is activated, will be used for defining the degree of zoom.

F2 Starts an activity where it is possible to move the center of the picture ofthe model. You select the position in the picture of the model, which youwould like to see in the center of the view port window, by pushing the leftmouse button. The activity has to be closed by pushing the right mousebutton.

This is always done without changing the degree of zoom.

F3 This key starts an activity where it is possible to increase the degree ofzoom.

F4 This key starts an activity where it is possible to decrease the degree ofzoom.

F5 The same as F1 but the view is reset to the XY-plane

F6 The same as F1 but the view is reset to the XZ-plane

F7 The same as F1 but the view is reset to the YZ-plane

F8 Enters the View menu.

F9 Enters the Viewpoint menu.

F10 Enters the Draw - Option menu.

F11 Performs refresh of the model without any changes of how to draw themodel.

8 3. Basic Principles

Chapter 4The Main Menu

In this chapter, a short summary will be given telling what shall be expectedin the different branches of the program emanating from the main menu of theprogram.

Geometry

In this part of the program the shape of the analyzed object can be defined andmanipulated. A geometry definition can be two-dimensional, axi-symmetric orthree-dimensional. The shape of the object is defined in a ”bottom-up” fashionwhere the procedure always have to be started by creating Points and after thatLines, Surfaces and finally Volumes. You will also find extrusion, sweepingand mirroring activities.

As long as all Point definitions has a zero Z-value the model will be treatedas 2D. A 2D model will be turned into 3D by just defining of one Point which isnot in the z=0. plane. A 2D model will be turned into an Axi-symmetric modelby selecting torus-shaped Volumes running around what in the 2D case was theY-axes.

Domain Properties

Each created volume has, among several other attributes, a material definitionassociated. The material definition consists of a number of physical propertiesrelevant in different types of analysis. In this branch of the program, it is possibleto create, delete, modify and connect Material Definitions to previously createdVolumes. Please observe, that normally not all physical properties are relevantin a certain type of analysis.

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10 4. The Main Menu

Boundary Conditions

Under this sub-domain of the program, it is possible to define various types ofboundary conditions useful in different types of Boundary-value, Initial-valueand Eigenvalue problems. In case of elasticity problem it is possible to definePoint, Line, Surface, Pressure and Volume loads or prescribed displacements toPoints, Lines and Surfaces. It shall be noticed that boundary conditions can beconnected to geometrical entities such that Points, Lines, Surfaces and Volumes.These boundary conditions will remain when the mesh is changed. It shall alsobe mentioned that boundary conditions also can be connected to mesh entitiessuch as nodes but it must be remembered that such definitions will be removedwhen the mesh changes.

Constraints

In program, it is possible to impose a variety different connections between dif-ferent types of elements. Also Rigid links and Cyclic symmetry can be definedin this branch of the program.

Time Dependencies

In cases where the problem simulated includes time-dependencies, quasi-static ortruly dynamic effect, it is possible to define how different entities vary over timein this part of the program.

It is also possible to define various types of initial conditions necessary indifferent types of analysis (defining the entity at time t = 0.)

The total time domain of interest is also defined under this menu in theprogram.

Mesh

Under this branch of the program an approximation of the geometry definedabove can be created in terms of a finite element mesh. Here it is also possible tocontrol how many elements shall be used along each Line used in the geometryand how these element edges shall be distributed along the Line. It is also possibleto select the type of elements to be used in different parts (Volumes) of the model.

A free mesh technique is available for two-dimensional and axi-symmetriccases.

4.0. Analysis Type 11

Analysis Type

Under this branch of the program a number of algorithms for different problemclasses are available:

• Linear static stress analysis with adaptivity and shape optimization

• Topology optimization

• Linear buckling analysis

• Dynamic eigenvalue analysis

• Linear dynamic transient stress analysis

• Linear heat transfer analysis

• Linear transient heat transfer analysis

Single Values

In this branch of the program, after that some kind of results exists, it is possi-ble to pick single numerical values associated to nodes or elements in the finiteelement mesh. It is possible to pick both scalar- and vector-valued entities.

Graphs

After that results has been calculated, it is also possible to create 2D graphsof different calculated entities along different physical paths in the global co-ordinate space or as function of time. It is also possible to plot one calculated oruser-defined entity as function of another.

Animations

It is possible to view some previously calculated results as an animation sequence.

Models

In this branch of the program, it is possible to select between, at the maximum,nine previously created models belonging to a project. You may also utilize up tonine projects. Adding different models into another model is also activity foundin under this sub-menu.

12 4. The Main Menu

Communication

The program can both import and export Point definitions in various formatspecifications. The program can also export and import single model definitionsin the TRINITAS internal format for further use in other data base files.

Options

In this branch of the program you may manipulate some user-defined preferencesfor how the program is asked to work in some general aspects.

Draw

In this branch, you can force the program to redraw the current model. It is alsopossible to select between a lot of options for What to draw, How to drawand Where to draw.

Stop

This menu is used for making a proper termination of the program. Here youcan save your work. After that save has been done it is not be possible to reachany older versions of the database file unless it was copied before the last sessionwas started.

Chapter 5A Getting Started Example

The Physical Problem

Let a uniformly tensile loaded strip with a width-reduction serve as a first exampleexplaining how to use TRINITAS. The strip has a constant thickness of 5.0 mmand a 2D idealization will be possible. When starting the process of converting

Figure 5.1: A tensile loaded structure with a width-reduction

this physical object into a realistic and useful analysis model we can concludethat the object contains one symmetry line. Furthermore, far away from thewidth-reduction the stress field is known and homogeneous.

Thus, it is possible to use a 2D approximation with the following outline andboundary conditions.

In the following, it will be described how to realize an analysis of this modelunder these assumptions.

It shall be observed that the sequence described below is not the only possiblesequence when performing such an analysis. For example, it is possible to meshthe model before the boundary conditions are defined and vice versa.

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14 5. A Getting Started Example

Figure 5.2: An outline and the boundary conditions of the model to be analyzed

Geometry

Any geometry has to be built up from entities such as Points, Lines, Surfacesand Volumes. Here is a so-called ”bottom-up” concept used, which means thatPoints have to be created first and after that Lines and so on. By picking two ormore points different types of lines can be created. Four different line types areavailable; Straight lines, Parabolas, Circular Arcs and Cubic Bezier Splines.

Picking three or more lines constituting a closed loop creates a Surface. Fi-nally, picking one or more surfaces creates a Volume. You may select between2D, Axi-symmetric or 3D volumes, extruded, swept or general.

The entire model may consist of an arbitrary number of volumes.In the following you will find a number of headlines starting with a • bullet

telling the menu position (or target area) which will be described. (The minussigns means that another menu level is reached).

• Geometry - Create Point - Create Points by the Cursor

Here follows a description of how to create points by the cursor in a 2D spaceproblem (z = 0.) In 2D cases, it is recommended to first create the points andlines defining the outline of the object.

- Push left mouse button in the target area with the text Create Points bythe Cursor. The target area will remain in reversed color mode until theright mouse button quits the activity.

- The text ”Create Points!” will occur in the message window.

- Move the cursor into the Viewport window. Press the left mouse buttonand an unfilled circle will appear at the cursor. In the upper right corner of

5.0. Geometry 15

the Viewport window the current global co-ordinates will be shown. Movethe cursor without releasing the button until the desired position is caught

- Release the mouse button and a point will be defined and saved on thedatabase file.

- This sequence can be repeated a sufficient number of times

- Pushing the right mouse button anywhere in the window closes the activity.The target area will then go back to its normal color mode.

Remark 1:

A transformation between the screen co-ordinate system and a global 3D co-ordinate system is pre-defined. Such a transformation, called a ”Working Plane”in the program, can be created, deleted, modified and selected from the Workingplane menu under the Geometry menu.

Remark 2:

The accuracy of the created global co-ordinate values can be controlled by theactivities ”Point Aligning” and ”Point Aligning Tolerance” found in thePoint Aligning menu under the Geometry menu. There is an invisible raster withall possible point locations in the global space starting from origo which can beswitched on or of and the raster step can also be controlled.

• Geometry - Create Line -

Four different types of lines can be created. The line types are Straight line,Parabola, Cubic Bezier Spline and Circular Arc. The following are general duringcreation of any of these four line types:

- Select line type by pushing the left mouse button in the target area contain-ing the desired line type symbol. The target area will remain in reversedcolor mode until the activity is closed.

- The text ”Pick Points!” will occur in the message window.

- A line is defined by picking points in the Viewport window. The firstpoint(s) is(are) picked by pushing the left mouse button and the last pointis always defined by release of the button.

- This sequence may be repeated an arbitrary number of times.

- Pushing the right mouse button anywhere in the window closes the activity.The target area will go back to its normal color mode.


Remark 1:

During creation of a circular arc the following also must be paid attention to:

- The first picked point must be close to the expected center of the arc. Thesecond and third points define the endpoints of the arc.

- The distance between the first and the second point defines the radius ofthe arc. From the second and third points it is possible to calculate theexact center of the arc.

- Finally, how to define which of the two possible arcs is the desired one?This is achieved by using information from what side of the second pointthe mouse was pushed. The arc will run from the second point towards thecurrent cursor position and then end up in the third point.

Remark 2:

This concept makes it possible to define circular arcs in 3D space. But it isimpossible to define an arc where the three picked point are located on a straightline because in that case obviously, the three points don’t define the plane forthe circular arc. Actually, it is recommended, not to create arcs much greaterthe 90. degrees.

• Geometry - Modify Line - Spline a Line by the Cursor

After that the outline of the object is created, it should be decided if mappedmeshing or free meshing technique shall be utilized. In this getting started ex-ample it will be described how to use the mapped mesh facility.

In a 2D case, mapped meshes can be created in volumes with three or fourcorners. Therefore it is necessary to split the object into a suitable number of2D volume primitives. Before doing this, it is often convenient to use the splitline facility:

- Push the left mouse button in the target area. The target area will remainin the reversed color mode.

- The text ”Split Lines!” will occur in the message window.

- Move the cursor to the position where a line should be split into two inde-pendent lines. Push the left button and the splitting will be accomplished.

- This sequence can be repeated an arbitrary number of times.

- Pushing the right mouse button anywhere in the window closes the activity.The target area will then go back to the normal color mode.

5.0. Geometry 17

• Geometry - Create Surface

Three different types of surfaces can be created. There are surfaces with three,four or n number of edges. A surface with three edges can be meshed mappedor freely by triangular elements. A surface with four edges can be meshed bytriangular or quadrilateral elements with a mapped meshing technique or bytriangular elements by the free meshing technique. A surface with more than fouredges will always be meshed with triangular elements by the free mesh algorithm.Every of these surface types can be created by the following sequence:


- The text ”Pick Lines!” will occur in the message window.

- Start picking lines with the left mouse button. The sequence is not critical.When the program finds a closed loop it will accept the picked lines as aproper surface definition and a ”surface symbol” will appear in the centerof gravity of the surface calculated as the mean value of all involved points.


- Pushing the right mouse button anywhere in the window closes the activity.The target area will then go back to the normal colour mode.

• Geometry - Create Volume - Create Volumes by pickingSurfaces

The program can create a number of different types of volumes. There are,1D volumes (Straight Cylinders) used for creation of bar elements, 2D volumeswith constant thickness used for membrane and shell elements, Axi-symmetricvolumes used for axi-symmetric elements and pure 3D volumes used for solid 3Delements. The following describes how to create a 2D volume.


- The text ”Pick Surfaces!” will occur in the message window.

- Pick a surface symbol and a 2D volume with constant thickness will becreated.




Domain Properties

To every created volume it is possible to connect a material definition. By defaulta pre-defined material definition named SIS 1550-01 is used and connected to thevolume when it was created.

• Domain Properties - Create a New Material -

Creation of Material Definitions can be done by this activity. A default materialname will be given and menu where it is possible to change all involved materialparameters will occur. This menu is equivalent to the menu which will occurunder the target area modify a material.

• Domain Properties - Connect a Material -

By this activity it is possible to change the material definition connected to acertain Volume.

- Push the left mouse button in the target area. A sub menu will occur whereone of all previously defined material definitions can be selected by releaseof the mouse button.

- The text ”Pick Volumes!” will occur in the message window.

- Pick volume symbols showing the current material name defined in thevolume. The material definition will then change to the selected one.



Boundary Conditions

This group of activities are able to define different kinds of boundary conditions.It shall be described how to connect line loads and fixed displacement conditionsto the geometry model.

• Boundary Conditions - Line Loads - Numeric Method

Here it will be described how create a line load. Such a one must obviously alwaysbe connected to a Line and the dimension is [N/unit length]. This activity willbe described in the following:

- First, adjust the X = and Y = target areas to the desired values

5.0. Mesh 19

- Push the left mouse button in the target area ”Create a New Line Load”.It will now be possible to connect the load conditions above to any line inthe model. Along a picked line the load will be visualized by one or anothertechnique depending on if a mesh is defined or not.

When defining the first line load in the model the program will automati-cally try to select an appropriate scale factor for drawing of the load con-ditions. During definition of further line loads no further automatical loadscale factor change will take place.

- Pushing the right mouse button anywhere in the window closes the activityand target area will go back to its normal color mode.

- The scale factor may be change afterwards in the last target area in thismenu. This has no influence on the results of the calculations. It is onlya factor used for creating a nice visualization of the given boundary condi-tions.

• Boundary Conditions - Fix a Lines - ...

By this activity it is possible to prevent different parts of the model to move inone or several directions.

- Select the target area with the appropriate text ”Fix in Current ?-direction”and push the left mouse button. The target area will then stay in reversedcolor mode until the activity is closed.

- Start picking lines with the left mouse button and along each picked line aboundary condition symbol will occur in every position where an elementcorner is expected.


- Pushing the right mouse button anywhere closes the activity.

If boundary conditions are connected to mesh entities such as nodes it shallbe noticed that those conditions will be removed when the mesh is modified.

Mesh

In every created Volume it is possible use one or several finite element types fordiscretization (meshing) of the volume. Some volume types may be meshed bothby a free and a mapped meshing techniques.


• Mesh - Create a Model Mesh from default higher-orderElements

This activity will create meshes in every volume defined in the model in accor-dance to the ”default meshing rule” currently used in the different Volumes.

The activity will also create a so-called Model mesh, which consists of onecontinuous sequence of node numbers used in the element definitions of the entiremodel.

Please observe that initially every volume edge only will contain one elementedge. Therefore, it is normally necessary to modify the mesh immediately afterits first creation.

Figure 5.3: A 2D free-meshed Model

Figure 5.4: A mapped meshed alternative

5.0. Analysis Type 21

• Mesh - Modify Mesh - Change Number of Subdivision salong a Line

This activity is a possibility to change the number of elements along certain linesin the geometry model.

- Push the left mouse button in the target area. A sub-menu with threedifferent alternatives will occur. By releasing the mouse button in ”ByIncrement” it is possible to change the current number of elements along aline by adding the current increment value present in a target area abovein this menu.

- Start picking lines. If there are meshes in the different volumes includingthe currently picked line these meshes will automatically be recreated. Ifthe meshing rule used in the volume is a mapped meshing technique alsoopposite lines in other volumes also will be changed.

- This sequence can be repeated until the mesh is satisfactory.

- Pushing the right mouse button anywhere in the window closes the activity.The menu will be redrawn and any other activity may be selected. In acase with the Model mesh present at the time for the start of the activityit will automatically be recreated after closure of the activity.

There is also possible to the change the number elements along different linesto a fixed value or by multiplying the current value by a factor.

Please note, that the number of element edges, which will be used along aline, is visualized as small filled red dots along the line. These element markswill only occur when there is no mesh in the Volume.

Analysis Type

Under this branch of the program, it is possible to select between a number ofdifferent types of analysis. In the getting started example a linear static stressanalysis is chosen.

• Analysis Type - Linear Static Stress Analysis - Start anAnalysis

During the calculation a sequence of graphical activities will take place.

- Each element will be drawn as a blue contour as soon as its element stiffnessmatrix is calculated and assembled into the structural stiffness matrix.


- During the Crout factorization of the stiffness matrix a slider will move hor-izontally giving an impression of the relative number of columns currentlyprocessed by the factorization procedure.

- After that the solution of the system of linear equations has been carriedout, each element will be redrawn in its deformed shape.

- The last step in the calculation is to calculate the stresses. This is doneelement by element and the equivalent von Mises’ stress is visualized as afilled contour plot over the element.

- Finally, all used boundary conditions are drawn. A number of differentoptions and combinations can be selected.

When the calculation is performed the cursor changes from a watch to thearrow previously used and the target area will go back to its normal color mode.

Figure 5.5: The von Mises’ stress

Evaluation

The program contains activities for visualization of single numerical values asso-ciated to a certain positions in the structure (most commonly nodes), 2D Graphswhere selected entities can be plotted against a location in space, in time or an-other selected entity. Animations of contour plots on a deformed structure canbe continuously displayed as function of time.

• Single Values - Pick Maximum Numeric Value

- Pushing the left mouse button in the target area ”Pick Maximum NumericValue” starts this activity. A sub-menu will then appear where it is possible

5.0. Evaluation 23

to select any of all currently calculated or defined entities such as displace-ments, stresses or applied loads. The target area will stay in reversed colormode.

- By pushing the left mouse button inside the Viewport window the closestmodel node will be selected and its numeric value will be visualized in arectangular label which can be positioned by a second click on the leftmouse button.

- By using a push and drag technique during the first mouse button click itis possible to define a region where a search for the maximum value willtake place.

- Such requests for a numeric value will still be alive after that the meshhas been changed and a second analysis is performed. The same searchtechnique will be used around the same geometrical positions in the globalspace.

- The activity is closed by pushing the right mouse button anywhere in thewindow

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