TRINITAS. a Finite Element stand-alone tool for Conceptual design, Optimization and General finite element analysis. Introductional Manual

Transcription

1 TRINITAS a Finite Element stand-alone tool for Conceptual design, Optimization and General finite element analysis Introductional Manual Bo Torstenfelt

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3 Contents 1 Introduction 1 2 Starting the Program 3 3 Basic Principles 5 Editing of Integers, Floating-point numbers and Characters in the User Interface Function keys and short cuts The Main Menu 9 Geometry Domain Properties Boundary Conditions Constraints Time Dependencies Mesh Analysis Type Single Values Graphs Animations Models Communication Options Draw Stop A Getting Started Example 13 The Physical Problem Geometry i

4 ii CONTENTS Geometry - Create Point - Create Points by the Cursor Geometry - Create Line Geometry - Modify Line - Spline a Line by the Cursor Geometry - Create Surface Geometry - Create Volume - Create Volumes by picking Surfaces 17 Domain Properties Domain Properties - Create a New Material Domain Properties - Connect a Material Boundary Conditions Boundary Conditions - Line Loads - Numeric Method Boundary Conditions - Fix a Lines Mesh Mesh - Create a Model Mesh from default higher-order Elements 20 Mesh - Modify Mesh - Change Number of Subdivision s along a Line Analysis Type Analysis Type - Linear Static Stress Analysis - Start an Analysis 21 Evaluation Single Values - Pick Maximum Numeric Value

5 Chapter 1 Introduction The TRINITAS program is an integrated graphical environment for Finite Element Analysis. The program includes activities for geometry modeling, boundary condition 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 you see is what you get (WYSIWYG) fashion today very common in other disciplines such as in for instance word processing. This also means that there exist no input or output file formats. All data are saved on a database file. That is the program can looked upon as a browser for the problem definition and the result. It is also an editor of the problem definition and a monitor for ongoing calculations. The program is written in FORTRAN and in C. An Object-based programming technique has been utilized through out the entire program development. The graphical user interface (GUI) has a hierarchical structure where all different activities can be reached. 1

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7 Chapter 2 Starting the Program On a PC computer a copy of the executable file have to be available on the directory where you do your calculations. This executable file can be found on the WEB. On a UNIX computer you start the program by typing TRINITAS in the input window will start the program. The program uses two different data base files. One of these two files is called Trinitas Data Base File by default and it contains information of all created and analyzed models. The second file called Trinitas Program Settings contains only user-chosen preferences for how the program shall behave. These files will be initiated during a first run on a new directory and the files will be closed when the program is properly closed down. The first file name, Trinitas Data Base File, is a default file name and can be changed in the first menu appearing when the program is started. Both these files are non-formatted direct access files. It can be mentioned that the program do not support any backup or undo features so it can be useful to make your own backup copy of the Trinitas Data Base File before starting a new session as a security. 3

8 4 2. Starting the Program

9 Chapter 3 Basic Principles The TRINITAS program is entirely driven behind a Graphical User Interface (GUI). This interface has a hierarchical structure (tree structure) with 13 branches starting from the root (the Main Menu) and the leaves in tree are all different activities possible to activate in the program. The Main Menu appears to the right of the program window. Each Menu consists 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 moved over it and tells the User that something will happens if the Left mouse button is pushed in that part of the window. Every menu appears in the same position of the window. This means that only one menu at the time can be activated. This makes the number of possible alternatives for the User limited and increases the User-friendliness of the program especially for beginners. General Menu system principles can be identified and summarized as follows: Every menu is constructed in such a way that it indicates a logical sequence of the work. Always start the work by putting focus at the target area at the top of the menu and continue further downwards. Every activity are of course not always needed. By pushing the right mouse button you will climb upward in the hierarchical tree from the Main menu (root menu) and you will move back down again by pushing the left mouse button. In target areas with a filled triangle to the right in the box, you shall expect a new menu to appear when pushing the left mouse button. 5

10 6 3. Basic Principles In target areas with an unfilled triangle to the right, you shall expect a smaller so called Cursor menu to appear on top of the previous menu. When pushing the left mouse button in a target area without any triangle to the right, you shall expect an activity to start. When starting an activity a 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 (!) the User is expected to do some mouse activity in the Viewport window (normally 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 no further mouse activities are expected from the User. In some rare cases you will found boxes of text inside a menu which do not flash into reversed color mode. Such boxes are actually no target areas because these are not connections to anything and the only purpose is to give the User some informational text. Editing of Integers, Floating-point numbers and Characters in the User Interface In some target areas the text is moved a bit offset making space for a smaller box-shaped area with a double-drawn border. In such a sub-area it is possible to edit variables of three different types (Integers, Reals and Characters). In each of these cases, pushing the left mouse button inside this sub-area starts an editing process. The area will then change into black text on a white background with a thick red border. The focus, marked by a small filled triangle below the text, can be moved by using the arrows on the keyboard. The editing process will be closed by pressing the carriage return button or by just moving the cursor out of the editing area. Integers: The ten digits from 0 to 9 and the minus sign can be used in this case. Reals: Here, the dot and the small and big e are also included in the possible character set. Please observe, if you put in a number greater than ten powered by 8 or less than ten powered by minus 8 the program will use an exponential representation. Characters: In this case all characters are possible to use which are included in the standard character set defined by the ANSI FORTRAN 77 standard.

11 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 angle in which the object is visualized is changed. By pushing the left mouse button and the character z for zoom the zoom degree in the camera is changed. By pushing the character x and the left mouse button the object can be panned over the screen. By pushing the character t and the left mouse button the camera is turned and the object is rotated on the screen without changing the angle of observation. Some function keys can be used for some frequently used activities: F1 F2 F3 F4 F5 F6 F7 F8 F9 Performs a redraw of the model with Auto-Zoom conditions which means that the bounding box of all defined Points and the corners of the working plane raster, if any is activated, will be used for defining the degree of zoom. Starts an activity where it is possible to move the center of the picture of the model. You select the position in the picture of the model, which you would like to see in the center of the view port window, by pushing the left mouse button. The activity has to be closed by pushing the right mouse button. This is always done without changing the degree of zoom. This key starts an activity where it is possible to increase the degree of zoom. This key starts an activity where it is possible to decrease the degree of zoom. The same as F1 but the view is reset to the XY-plane The same as F1 but the view is reset to the XZ-plane The same as F1 but the view is reset to the YZ-plane Enters the View menu. Enters the Viewpoint menu. F10 Enters the Draw - Option menu. F11 Performs refresh of the model without any changes of how to draw the model.

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13 Chapter 4 The Main Menu In this chapter, a short summary will be given telling what shall be expected in the different branches of the program emanating from the main menu of the program. Geometry In this part of the program the shape of the analyzed object can be defined and manipulated. A geometry definition can be two-dimensional, axi-symmetric or three-dimensional. The shape of the object is defined in a bottom-up fashion where the procedure always have to be started by creating Points and after that Lines, Surfaces and finally Volumes. You will also find extrusion, sweeping and mirroring activities. As long as all Point definitions has a zero Z-value the model will be treated as 2D. A 2D model will be turned into 3D by just defining of one Point which is not in the z=0. plane. A 2D model will be turned into an Axi-symmetric model by selecting torus-shaped Volumes running around what in the 2D case was the Y-axes. Domain Properties Each created volume has, among several other attributes, a material definition associated. The material definition consists of a number of physical properties relevant in different types of analysis. In this branch of the program, it is possible to create, delete, modify and connect Material Definitions to previously created Volumes. Please observe, that normally not all physical properties are relevant in a certain type of analysis. 9

14 10 4. The Main Menu Boundary Conditions Under this sub-domain of the program, it is possible to define various types of boundary conditions useful in different types of Boundary-value, Initial-value and Eigenvalue problems. In case of elasticity problem it is possible to define Point, Line, Surface, Pressure and Volume loads or prescribed displacements to Points, Lines and Surfaces. It shall be noticed that boundary conditions can be connected to geometrical entities such that Points, Lines, Surfaces and Volumes. These boundary conditions will remain when the mesh is changed. It shall also be mentioned that boundary conditions also can be connected to mesh entities such as nodes but it must be remembered that such definitions will be removed when the mesh changes. Constraints In program, it is possible to impose a variety different connections between different types of elements. Also Rigid links and Cyclic symmetry can be defined in this branch of the program. Time Dependencies In cases where the problem simulated includes time-dependencies, quasi-static or truly dynamic effect, it is possible to define how different entities vary over time in this part of the program. It is also possible to define various types of initial conditions necessary in different types of analysis (defining the entity at time t = 0.) The total time domain of interest is also defined under this menu in the program. Mesh Under this branch of the program an approximation of the geometry defined above can be created in terms of a finite element mesh. Here it is also possible to control how many elements shall be used along each Line used in the geometry and how these element edges shall be distributed along the Line. It is also possible to 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-symmetric cases.

15 4.0. Analysis Type 11 Analysis Type Under this branch of the program a number of algorithms for different problem classes 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 possible to pick single numerical values associated to nodes or elements in the finite element 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 graphs of different calculated entities along different physical paths in the global coordinate space or as function of time. It is also possible to plot one calculated or user-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 to nine projects. Adding different models into another model is also activity found in under this sub-menu.

16 12 4. The Main Menu Communication The program can both import and export Point definitions in various format specifications. The program can also export and import single model definitions in 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 preferences for 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 also possible to select between a lot of options for What to draw, How to draw and Where to draw. Stop This menu is used for making a proper termination of the program. Here you can save your work. After that save has been done it is not be possible to reach any older versions of the database file unless it was copied before the last session was started.

17 Chapter 5 A Getting Started Example The Physical Problem Let a uniformly tensile loaded strip with a width-reduction serve as a first example explaining how to use TRINITAS. The strip has a constant thickness of 5.0 mm and 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 conclude that the object contains one symmetry line. Furthermore, far away from the width-reduction the stress field is known and homogeneous. Thus, it is possible to use a 2D approximation with the following outline and boundary conditions. In the following, it will be described how to realize an analysis of this model under these assumptions. It shall be observed that the sequence described below is not the only possible sequence when performing such an analysis. For example, it is possible to mesh the model before the boundary conditions are defined and vice versa. 13

18 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, Surfaces and Volumes. Here is a so-called bottom-up concept used, which means that Points have to be created first and after that Lines and so on. By picking two or more points different types of lines can be created. Four different line types are available; Straight lines, Parabolas, Circular Arcs and Cubic Bezier Splines. Picking three or more lines constituting a closed loop creates a Surface. Finally, picking one or more surfaces creates a Volume. You may select between 2D, 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 minus signs 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 space problem (z = 0.) In 2D cases, it is recommended to first create the points and lines defining the outline of the object. - Push left mouse button in the target area with the text Create Points by the Cursor. The target area will remain in reversed color mode until the right 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 button and an unfilled circle will appear at the cursor. In the upper right corner of

19 5.0. Geometry 15 the Viewport window the current global co-ordinates will be shown. Move the cursor without releasing the button until the desired position is caught - Release the mouse button and a point will be defined and saved on the database 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 coordinate system is pre-defined. Such a transformation, called a Working Plane in the program, can be created, deleted, modified and selected from the Working plane menu under the Geometry menu. Remark 2: The accuracy of the created global co-ordinate values can be controlled by the activities Point Aligning and Point Aligning Tolerance found in the Point Aligning menu under the Geometry menu. There is an invisible raster with all possible point locations in the global space starting from origo which can be switched 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 during creation of any of these four line types: - Select line type by pushing the left mouse button in the target area containing the desired line type symbol. The target area will remain in reversed color 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 first point(s) is(are) picked by pushing the left mouse button and the last point is 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.

20 16 5. A Getting Started Example 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. The second and third points define the endpoints of the arc. - The distance between the first and the second point defines the radius of the arc. From the second and third points it is possible to calculate the exact 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 point the mouse was pushed. The arc will run from the second point towards the current 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 is impossible to define an arc where the three picked point are located on a straight line because in that case obviously, the three points don t define the plane for the circular arc. Actually, it is recommended, not to create arcs much greater the 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 mapped meshing or free meshing technique shall be utilized. In this getting started example 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 four corners. Therefore it is necessary to split the object into a suitable number of 2D volume primitives. Before doing this, it is often convenient to use the split line facility: - Push the left mouse button in the target area. The target area will remain in 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 independent 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.

21 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 mapped or freely by triangular elements. A surface with four edges can be meshed by triangular or quadrilateral elements with a mapped meshing technique or by triangular elements by the free meshing technique. A surface with more than four edges will always be meshed with triangular elements by the free mesh algorithm. Every of these surface types can be created by the following sequence: - Push the left mouse button in the target area. The target area will remain in the reversed color mode. - 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 a proper surface definition and a surface symbol will appear in the center of gravity of the surface calculated as the mean value of all involved points. - 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 colour mode. Geometry - Create Volume - Create Volumes by picking Surfaces The program can create a number of different types of volumes. There are, 1D volumes (Straight Cylinders) used for creation of bar elements, 2D volumes with constant thickness used for membrane and shell elements, Axi-symmetric volumes used for axi-symmetric elements and pure 3D volumes used for solid 3D elements. The following describes how to create a 2D volume. - Push the left mouse button in the target area. The target area will remain in the reversed color mode. - The text Pick Surfaces! will occur in the message window. - Pick a surface symbol and a 2D volume with constant thickness will be created. - 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.

22 18 5. A Getting Started Example Domain Properties To every created volume it is possible to connect a material definition. By default a pre-defined material definition named SIS is used and connected to the volume when it was created. Domain Properties - Create a New Material - Creation of Material Definitions can be done by this activity. A default material name will be given and menu where it is possible to change all involved material parameters will occur. This menu is equivalent to the menu which will occur under the target area modify a material. Domain Properties - Connect a Material - By this activity it is possible to change the material definition connected to a certain Volume. - Push the left mouse button in the target area. A sub menu will occur where one of all previously defined material definitions can be selected by release of the mouse button. - The text Pick Volumes! will occur in the message window. - Pick volume symbols showing the current material name defined in the volume. The material definition will then change to the selected one. - 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. 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 conditions to the geometry model. Boundary Conditions - Line Loads - Numeric Method Here it will be described how create a line load. Such a one must obviously always be connected to a Line and the dimension is [N/unit length]. This activity will be described in the following: - First, adjust the X = and Y = target areas to the desired values

23 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 in the model. Along a picked line the load will be visualized by one or another technique depending on if a mesh is defined or not. When defining the first line load in the model the program will automatically try to select an appropriate scale factor for drawing of the load conditions. During definition of further line loads no further automatical load scale factor change will take place. - Pushing the right mouse button anywhere in the window closes the activity and target area will go back to its normal color mode. - The scale factor may be change afterwards in the last target area in this menu. This has no influence on the results of the calculations. It is only a factor used for creating a nice visualization of the given boundary conditions. Boundary Conditions - Fix a Lines -... By this activity it is possible to prevent different parts of the model to move in one 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 reversed color mode until the activity is closed. - Start picking lines with the left mouse button and along each picked line a boundary condition symbol will occur in every position where an element corner is expected. - This sequence can be repeated an arbitrary number of times. - Pushing the right mouse button anywhere closes the activity. If boundary conditions are connected to mesh entities such as nodes it shall be 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 for discretization (meshing) of the volume. Some volume types may be meshed both by a free and a mapped meshing techniques.

24 20 5. A Getting Started Example Mesh - Create a Model Mesh from default higher-order Elements This activity will create meshes in every volume defined in the model in accordance to the default meshing rule currently used in the different Volumes. The activity will also create a so-called Model mesh, which consists of one continuous sequence of node numbers used in the element definitions of the entire model. Please observe that initially every volume edge only will contain one element edge. Therefore, it is normally necessary to modify the mesh immediately after its first creation. Figure 5.3: A 2D free-meshed Model Figure 5.4: A mapped meshed alternative

25 5.0. Analysis Type 21 Mesh - Modify Mesh - Change Number of Subdivision s along a Line This activity is a possibility to change the number of elements along certain lines in the geometry model. - Push the left mouse button in the target area. A sub-menu with three different alternatives will occur. By releasing the mouse button in By Increment it is possible to change the current number of elements along a line by adding the current increment value present in a target area above in this menu. - Start picking lines. If there are meshes in the different volumes including the currently picked line these meshes will automatically be recreated. If the meshing rule used in the volume is a mapped meshing technique also opposite 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 a case with the Model mesh present at the time for the start of the activity it will automatically be recreated after closure of the activity. There is also possible to the change the number elements along different lines to 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 a line, is visualized as small filled red dots along the line. These element marks will 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 of different types of analysis. In the getting started example a linear static stress analysis is chosen. Analysis Type - Linear Static Stress Analysis - Start an Analysis 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 stiffness matrix is calculated and assembled into the structural stiffness matrix.

26 22 5. A Getting Started Example - During the Crout factorization of the stiffness matrix a slider will move horizontally giving an impression of the relative number of columns currently processed by the factorization procedure. - After that the solution of the system of linear equations has been carried out, each element will be redrawn in its deformed shape. - The last step in the calculation is to calculate the stresses. This is done element by element and the equivalent von Mises stress is visualized as a filled contour plot over the element. - Finally, all used boundary conditions are drawn. A number of different options and combinations can be selected. When the calculation is performed the cursor changes from a watch to the arrow 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 associated to a certain positions in the structure (most commonly nodes), 2D Graphs where selected entities can be plotted against a location in space, in time or another selected entity. Animations of contour plots on a deformed structure can be continuously displayed as function of time. Single Values - Pick Maximum Numeric Value - Pushing the left mouse button in the target area Pick Maximum Numeric Value starts this activity. A sub-menu will then appear where it is possible

27 5.0. Evaluation 23 to select any of all currently calculated or defined entities such as displacements, stresses or applied loads. The target area will stay in reversed color mode. - By pushing the left mouse button inside the Viewport window the closest model node will be selected and its numeric value will be visualized in a rectangular label which can be positioned by a second click on the left mouse button. - By using a push and drag technique during the first mouse button click it is possible to define a region where a search for the maximum value will take place. - Such requests for a numeric value will still be alive after that the mesh has been changed and a second analysis is performed. The same search technique will be used around the same geometrical positions in the global space. - The activity is closed by pushing the right mouse button anywhere in the window