ANSYS Tutorials

ANSYS is a general purpose finite element modeling package for numerically solving a wide variety of mechanical problems. These problems include: static/dynamic structural analysis (both linear and non-linear), heat transfer and fluid problems, as well as acoustic and electromagnetic problems. Most of these tutorials have been created using ANSYS 7.0, therefore, make note of small changes in the menu structure if you are using an older or newer version.

This manual has been organized into the following six sections.

ANSYS Utilities An introduction to using ANSYS. This includes a quick explanation of the stages of analysis, how to start ANSYS, the use of the windows in ANSYS, convergence testing, saving/restoring jobs, and working with Pro/E.

Basic Tutorials Detailed tutorials outlining basic structural analysis using ANSYS. It is recommended that you complete these tutorials in order as each tutorial builds upon skills taught in previous examples.

Intermediate Tutorials Complex skills such as dynamic analysis and nonlinearities are explored in this section. It is recommended that you have completed the Basic Tutorials prior to attempting these tutorials.

Advanced Tutorials Advanced skills such as substructuring and optimization are explored in this section. It is recommended that you have completed the Basic Tutorials prior to attempting these tutorials.

Postprocessing Tutorials Postprocessing tools available in ANSYS such as X-sectional views of the geometry are shown in this section. It is recommended that you have completed the Basic Tutorials prior to attempting these tutorials.

Command Line Files Example problems solved using command line coding only, in addition to several files to help you to generate your own command line files.

ANSYS Utilities

An introduction to using ANSYS, including a quick explanation of the stages of analysis, how to start ANSYS, and the use of the windows in ANSYS, and using Pro/ENGINEER with ANSYS.

• Introduction to Finite Element Analysis A brief introduction of the 3 stages involved in finite element analysis.

• Starting up ANSYS How to start ANSYS using windows NT and Unix X-Windows.

• ANSYS Environment An introduction to the windows used in ANSYS

• ANSYS Interface An explanation of the Graphic User Interface (GUI) in comparison to the command file approach.

• Convergence Testing This file can help you to determine how small your meshing elements need to be before you can trust the solution.

• Saving/Restoring Jobs Description of how to save your work in ANSYS and how to resume a previously saved job.

• ANSYS Files Definitions of the different files created by ANSYS.

• Printing Results Saving data and figures generated in ANSYS.

• Working with Pro Engineer A description of how to export geometry from Pro/E into ANSYS.

Basic Tutorials

The following documents will lead you through several example problems using ANSYS. ANSYS 7.0 was used to create some of these tutorials while ANSYS 5.7.1 was used to create others, therefore, if you are using a different version of ANSYS make note of changes in the menu structure. Complete these tutorials in order as each tutorial will build on skills taught in the previous example.

• Two Dimensional Truss Basic functions will be shown in detail to provide you with a general knowledge of how to use ANSYS. This tutorial should take approximately an hour and a half to complete.

• Bicycle Space Frame Intermediate ANSYS functions will be shown in detail to provide you with a more general understanding of how to use ANSYS. This tutorial should take approximately an hour and a half to complete.

• Plane Stress Bracket Boolean operations, plane stress and uniform pressure loading will be introduced in the creation and analysis of this 2-Dimensional object.

• Solid Modeling This tutorial will introduce techniques such as filleting, extrusion, copying and working plane orienation to create 3-Dimensional objects.

Intermediate Tutorials

The majority of these examples are simple verification problems to show you how to use the intermediate techniques in ANSYS. You may be using a different version of ANSYS than what was used to create these tutorials, therefore, make note of small changes in the menu structure. These tutorials can be completed in any order, however, it is expected that you have completed the Basic Tutorials before attempting these.

• Effect of Self Weight Incorporating the weight of an object into the finite element analysis is shown in this simple cantilever beam example.

• Distributed Loading The application of distributed loads and the use of element tables to extract data is expalined in this tutorial.

• NonLinear Analysis A large moment is applied to the end of a cantilever beam to explore Geometric Nonlinear behaviour (large deformations). There is also an associated tutorial for an explanation of the Graphical Solution Tracking (GST) plot.

• Buckling In this tutorial both the Eigenvalue and Nonlinear methods are used to solve a simple buckling problem.

• NonLinear Materials The purpose of the tutorial is to describe how to include material nonlinearities in an ANSYS model.

• Dynamic AnalysisThese tutorial explore the dynamic analyis capabilities of ANSYS. Modal, Harmonic, and Transient Analyses are shown in detail.

• Thermal ExamplesAnalysis of a pure conduction, a mixed convection/conduction/insulated boundary condition example, and a transient heat conduction analysis.

• Modelling Using Axisymmetry Utilizing axisymmetry to model a 3-D structure in 2-D to reduce computational time.

Postprocessing Tutorials

These tutorials were created to show some of the tools available in ANSYS for postprocessing. You may be using a different version of ANSYS than what was used to create these tutorials, therefore, make note of small changes in the menu structure. These tutorials can be completed in any order, however, it is expected that you have completed the Basic Tutorials.

• Viewing Cross Sectional Results The method to view cross sectional results for a volume are shown in this tutorial.

• Advanced X-Sectional Results: Using Paths to Post Process Results The purpose of this tutorial is to create and use 'paths' to provide extra detail during post processing.

• Data Plotting: Using Tables to Post Process Results The purpose of this tutorial is to outline the steps required to plot results using tables, a special type of array.

• Changing Graphical Properties This tutorial outlines some of the basic graphical changes that can be made to the main screen and model.

Advanced Tutorials

The majority of these examples are simple verification problems to show you how to use the more advanced techniques in ANSYS. You may be using a different version of ANSYS than what was used to create these tutorials, therefore, make note of small changes in the menu structure. These tutorials can be completed in any order, however, it is expected that you have completed the Basic Tutorials.

• Springs and Joints The creation of models with multiple elements types will be explored in this tutorial. Additionally, elements COMBIN7 and COMBIN14 will be explained as well as the use of parameters to store data.

• Design Optimization The use of Design Optimization in ANSYS is used to solve for unknown parameters of a beam.

• Substructuring The use of Substructuring in ANSYS is used to solve a simple problem.

• Coupled Structural/Thermal Analysis The use of ANSYS physics environments to solve a simple structural/thermal problem.

• Using P-Elements The stress distribution of a model is solved using p-elements and compared to h-elements.

• Melting Using Element Death Using element death to model a volume melting.

• Contact Elements Model of two beams coming into contact with each other.

• ANSYS Parametric Design Language Design a truss using parametric variables.

Command Line Files

The following files should help you to generate your own command line files.

• Creating Command Files Directions on generating and running command files.

• ANSYS Command File Programming Features This file shows some of the commonly used programming features in the ANSYS command file language known as ADPL (ANSYS Parametric Design Language). Prompting the user for parameters, performing calculations with paramaters and control structures are illustrated.

The following files include some example problems that have been created using command line coding.

Basic Tutorials This set of command line codes are from the Basic Tutorial section.

Intermediate Tutorials

This set of command line codes are from the Intermediate Tutorial section.

Advanced Tutorials This set of command line codes are from the Advanced Tutorial section.

PostProc Tutorials This set of command line codes are from the PostProc Tutorial section.

Radiation Analysis A simple radiation heat transfer between concentric cylinders.

Introduction

ANSYS is a general purpose finite element modeling package for numerically solving a wide variety of mechanical problems. These problems include: static/dynamic structural analysis (both linear and non-linear), heat transfer and fluid problems, as well as acoustic and electro-magnetic problems.

In general, a finite element solution may be broken into the following three stages. This is a general guideline that can be used for setting up any finite element analysis.

1. Preprocessing: defining the problem; the major steps in preprocessing are given below:

o Define keypoints/lines/areas/volumes o Define element type and material/geometric properties o Mesh lines/areas/volumes as required

The amount of detail required will depend on the dimensionality of the analysis (i.e. 1D, 2D, axi-symmetric, 3D).

2. Solution: assigning loads, constraints and solving; here we specify the loads (point or pressure), contraints (translational and rotational) and finally solve the resulting set of equations.

3. Postprocessing: further processing and viewing of the results; in this stage one may wish to see:

o Lists of nodal displacements o Element forces and moments o Deflection plots o Stress contour diagrams

Starting up ANSYS

Starting up ANSYS

Large File Sizes

ANSYS can create rather large files when running and saving; be sure that your local drive has space for it.

Getting the Program Started

In the Mec E 3-3 lab, there are two ways that you can start up ANSYS:

1. Windows NT application 2. Unix X-Windows application

Windows NT Start Up

Starting up ANSYS in Windows NT is simple:

• Start Menu • Programs • ANSYS 5.7 • Run Interactive Now

Unix X-Windows Start Up

Starting the Unix version of ANSYS involves a few more steps:

• in the task bar at the bottom of the screen, you should see something labeled X-Win32. If you don't see this minimized program, you can may want to reboot the computer, as it automatically starts this application when booting.

• right click on this menu and selection Sessions and then select Mece. • you will now be prompted to login to GPU... do this. • once the Xwindows emulator has started, you will see an icon at the bottom of the

screen that looks like a paper and pencil; don't select this icon, but rather, click on the up arrow above it and select Terminal

• a terminal command window will now start up

• in that window, type xansys57 • at the UNIX prompt and a small launcher menu will appear.

• select the Run Interactive Now menu item.

ANSYS 7.0 Environment

The ANSYS Environment for ANSYS 7.0 contains 2 windows: the Main Window and an Output Window. Note that this is somewhat different from the previous version of ANSYS which made use of 6 different windows.

1. Main Window

Within the Main Window are 5 divisions:

a. Utility Menu

The Utility Menu contains functions that are available throughout the ANSYS session, such as file controls, selections, graphic controls and parameters.

b. Input Lindow

The Input Line shows program prompt messages and allows you to type in commands directly.

c. Toolbar

The Toolbar contains push buttons that execute commonly used ANSYS commands. More push buttons can be added if desired.

d. Main Menu

The Main Menu contains the primary ANSYS functions, organized by preprocessor, solution, general postprocessor, design optimizer. It is from this menu that the vast majority of modelling commands are issued. This is where you will note the greatest change between previous versions of ANSYS and version 7.0. However, while the versions appear different, the menu structure has not changed.

e. Graphics Window

The Graphic Window is where graphics are shown and graphical picking can be made. It is here where you will graphically view the model in its various stages of construction and the ensuing results from the analysis.

2. Output Window

The Output Window shows text output from the program, such as listing of data etc. It is usually positioned behind the main window and can de put to the front if necessary.

ANSYS InterfaceGraphical Interface vs. Command File Coding

There are two methods to use ANSYS. The first is by means of the graphical user interface or GUI. This method follows the conventions of popular Windows and X-Windows based programs.

The second is by means of command files. The command file approach has a steeper learning curve for many, but it has the advantage that an entire analysis can be described in a small text file, typically in less than 50 lines of commands. This approach enables easy model modifications and minimal file space requirements.

The tutorials in this website are designed to teach both the GUI and the command file approach, however, many of you will find the command file simple and more efficient to use once you have invested a small amount of time into learning the code.

For information and details on the full ANSYS command language, consult:

Help > Table of Contents > Commands Manual.

FEM Convergence Testing

Introduction

A fundamental premise of using the finite element procedure is that the body is sub-divided up into small discrete regions known as finite elements. These elements defined by nodes and interpolation functions. Governing equations are written for each element and these elements are assembled into a global matrix. Loads and constraints are applied and the solution is then determined.

The Problem

The question that always arises is: How small do I need to make the elements before I can trust the solution?

What to do about it...

In general there are no real firm answers on this. It will be necessary to conduct convergence tests! By this we mean that you begin with a mesh discretization and then observe and record the solution. Now repeat the problem with a finer mesh (i.e. more elements) and then compare the results with the previous test. If the results are nearly similar, then the first mesh is probably good enough for that particular geometry, loading and constraints. If the results differ by a large amount however, it will be necessary to try a finer mesh yet.

The Consequences

Finer meshes come with a cost however: more calculational time and large memory requirements (both disk and RAM)! It is desired to find the minimum number of elements that give you a converged solution.

Beam Models

For beam models, we actually only need to define a single element per line unless we are applying a distributed load on a given frame member. When point loads are used, specifying more that one element per line will not change the solution, it will only slow the calculations down. For simple models it is of no concern, but for a larger model, it is desired to minimize the number of elements, and thus calculation time and still obtain the desired accuracy.

General Models

In general however, it is necessary to conduct convergence tests on your finite element model to confirm that a fine enough element discretization has been used. In a solid mechanics problem, this would be done by creating several models with different mesh sizes and comparing the resulting deflections and stresses, for example. In general, the stresses will converge more slowly than the displacement, so it is not sufficient to examine the displacement convergence.

ANSYS: Saving and Restoring Jobs

Saving Your Job

It is good practice to save your model at various points during its creation. Very often you will get to a point in the modeling where things have gone well and you like to save it at the point. In that way, if you make some mistakes later on, you will at least be able to come back to this point.

To save your model, select Utility Menu Bar -> File -> Save As Jobname.db. Your model will be saved in a file called jobname.db, where jobname is the name that you specified in the Launcher when you first started ANSYS.

It is a good idea to save your job at different times throughout the building and analysis of the model to backup your work incase of a system crash or other unforseen problems.

Recalling or Resuming a Previously Saved Job

Frequently you want to start up ANSYS and recall and continue a previous job. There are two methods to do this:

1. Using the Launcher... o In the ANSYS Launcher, select Interactive... and specify the

previously defined jobname. o Then when you get ANSYS started, select Utility Menu -> File ->

Resume Jobname.db . o This will restore as much of your database (geometry, loads, solution, etc)

that you previously saved. 2. Or, start ANSYS and select Utitily Menu -> File -> Resume from... and

select your job from the list that appears.

ANSYS Files

Introduction

A large number of files are created when you run ANSYS. If you started ANSYS without specifying a jobname, the name of all the files created will be FILE.* where the * represents various extensions described below. If you specified a jobname, say Frame, then the created files will all have the file prefix, Frame again with various extensions: frame.db

Database file (binary). This file stores the geometry, boundary conditions and any solutions.

frame.dbb Backup of the database file (binary).

frame.err Error file (text). Listing of all error and warning messages.

frame.out

Output of all ANSYS operations (text). This is what normally scrolls in the output window during an ANSYS session.

frame.log Logfile or listing of ANSYS commands (text). Listing of all equivalent ANSYS command line commands used during the current session.

etc... Depending on the operations carried out, other files may have been written. These files may contain results, etc.

What to save?

When you want to clean up your directory, or move things from the /scratch directory, what files do you need to save?

• If you will always be using the GUI, then you only require the .db file. This file stores the geometry, boundary conditions and any solutions. Once the ANSYS has started, and the jobname has been specified, you need only activate the resume command to proceed from where you last left off (see Saving and Restoring Jobs).

• If you plan on using ANSYS command files, then you need only store your command file and/or the log file. This file contains a complete listing of the ANSYS commands used to get you model to its current point. That file may be rerun as is, or edited and rerun as desired (Command File Creation and Execution).

If you plan to use the command mode of operation, starting with an existing log file, rename it first so that it does not get over-written or added to, from another ANSYS run.

Printing and Plotting ANSYS Results to a File

Printing Text Results to a File

ANSYS produces lists and tables of many types of results that are normally displayed on the screen. However, it is often desired to save the results to a file to be later analyzed or included in a report.

1. Stresses: instead of using 'Plot Results' to plot the stresses, choose 'List Results'. Select 'Elem Table Data', and choose what you want to list from the menu. You can pick multiple items. When the list appears on the screen in its own window, Select 'File'/'Save As...' and give a file name to store the results.

2. Any other solutions can be done in the same way. For example select 'Nodal Solution' from the 'List Results' menu, to get displacements.

3. Preprocessing and Solution data can be listed and saved from the 'List' menu in the 'Utility Menu bar'. Save the resulting list in the same way described above.

Plotting of Figures

There are two major routes to get hardcopies from ANSYS. The first is a quick a raster-based screen dump, while the second is a scalable vector plot.

1.0 Quick Image Save

When you want to quickly save an image of the entire screen or the current 'Graphics window', select:

• 'Utility menu bar'/'PlotCtrls'/'Hard Copy ...'. • In the window that appears, you will normally want to select 'Graphics window',

'Monochrome', 'Reverse Video', 'Landscape' and 'Save to:'. • Then enter the file name of your choice. • Press 'OK'

This raster image file may now be printed on a PostScript printer or included in a document.

2.0 Better Quality Plots

The second method of saving a plot is much more flexible, but takes a lot more work to set up as you'll see...

RedirectionNormally all ANSYS plots are directed to the plot window on the screen. To save some plots to a file, to be later printed or included in a document or what have you, you must first 'redirect' the plots to a file by issuing: 'Utility menu bar'/'PlotCtrls'/'Redirect Plots'/'To File...'.

Type in a filename (e.g.: frame.pic) in the 'Selection' Window.

Now issue whatever plot commands you want within ANSYS, remembering that the plots will not be displayed to the screen, but rather they will be written to the selected file. You can put as many plots as you want into the plot file. When you are finished plotting what you want to the file, redirect plots back to the screen using:

'Utility menu bar'/'PlotCtrls'/'Redirect Plots'/'To Screen'.

Display and ConversionThe plot file that has been saved is stored in a proprietary file format that must be converted into a more common graphic file format like PostScript, or HPGL for example. This is performed by running a separate program called display. To do this, you have a couple of options:

1. select display from the ANSYS launcher menu (if you started ANSYS that way) 2. shut down ANSYS or open up a new terminal window and then type display at

the Unix prompt.

Either way, a large graphics window will appear. Decrease the size of this window, because it most likely covers the window in which you will enter the display plotting commands. Load your plot file with the following command: file,frame,pic

if your plot file is 'plots.pic'. Note that although the file is 'plots.pic' (with a period), Display wants 'plots,pic'(with a comma). You can display your plots to the graphics window by issuing the command like plot,n

where n is plot number. If you plotted 5 images to this file in ANSYS, then n could be any number from 1 to 5.

Now that the plots have been read in, they may be saved to printer files of various formats:

1. Colour PostScript: To save the images to a colour postscript file, enter the following commands in display:

2. pscr,color,23. /show,pscr4. plot,n

where n is the plot number, as above. You can plot as many images as you want to postscript files in this manner. For subsequent plots, you only require the plot,n command as the other options have now been set. Each image is plotted to a postscript file such as pscrxx.grph, where xx is a number, starting at 00.

Note: when you import a postscript file into a word processor, the postscript image will appear as blank box. The printer information is still present, but it can only be viewed when it's printed out to a postscript printer.

Printing it out: Now that you've got your color postscript file, what are you going to do with it? Take a look here for instructions on colour postscript printing at a couple of sites on campus where you can have your beautiful stress plot plotted to paper, overheads or even posters!

5. Black & White PostScript: The above mentioned colour postscript files can get very large in size and may not even print out on the postscript printer in the lab because it takes so long to transfer the files to the printer and process them. A way around this is to print them out in a black and white postscript format instead of colour; besides the colour specifications don't do any good for the black and white lab printer anyways. To do this, you set the postscript color option to '3', i.e. and then issue the other commands as before

6. pscr,color,37. /show,pscr8. plot,n

Note: when you import a postscript file into a word processor, the postscript image will appear as blank box. The printer information is still present, but it can only be viewed when it's printed out to a postscript printer.

9. HPGL: The third commonly used printer format is HPGL, which stands for Hewlett Packard Graphics Language. This is a compact vector format that has the advantage that when you import a file of this type into a word processor, you can actually see the image in the word processor! To use the HPGL format, issue the following commands:

10. /show,hpgl11. plot,n

Final Steps

It is wise to rename these plot files as soon as you leave display, for display will overwrite the files the next time it is run. You may want to rename the postscript files with an '.eps' extension to indicate that they are encapsulated postscript images. In a similar way, the HPGL printer files could be given an '.hpgl' extension. This renaming is done at the Unix commmand line (the 'mv' command).

A list of all available display commands and their options may be obtained by typing:

help

When complete, exit display by entering

finish

Finite Element Method using Pro/ENGINEER and ANSYS

Notes by R.W. Toogood

The transfer of a model from Pro/ENGINEER to ANSYS will be demonstrated here for a simple solid model. Model idealizations such as shells and beams will not be treated. Also, many modeling options for constraints, loads, mesh control, analysis types will not be covered. These are fairly easy to figure out once you know the general procedures presented here.

Step 1. Make the part

Use Pro/E to make the part. Things to note are:

• be aware of your model units • note the orientation of the model (default coordinate system in ANSYS will be the

same as in Pro/E) • IMPORTANT: remove all unnecessary and/or cosmetic features like rounds,

chamfers, holes, etc., by suppressing them in Pro/E. Too much small geometry will cause the mesh generator to create a very fine mesh with many elements which will greatly increase your solver time. Of course, if the feature is critical to your design, you will want to leave it. You must compromise between accuracy and available CPU resources.

The figure above shows the original model for this demonstration. This is a model of a short cantilevered bracket that bolts to the wall via the thick plate on the left end. Model units are inches. A load is applied at the hole in the right end. Some cosmetic features are located on the top surface and the two sides. Several edges are rounded. For this model, the interest is in the stress distribution around the vertical slot. So, the plate and the loading hole are removed, as are the cosmetic features and rounds resulting in the "de-featured" geometry shown below. The model will be constrained on the left face and a uniform load will be applied to the right face.

Step 2. Create the FEM model

In the pull-down menu at the top of the Pro/E window, select

Applications > Mechanica

An information window opens up to remind you about the units you are using. Press Continue

In the MECHANICA menu at the right, check the box beside FEM Mode and select the command Structure.

A new toolbar appears on the right of the screen that contains icons for creating all the common modeling entities (constraints, loads, idealizations). All these commands are also available using the command windows that will open on the right side of the screen or in dialog windows that will open when appropriate.

Notice that a small green coordinate system WCS has appeared. This is how you will specify the directions of constraints and forces. Other coordinate systems (eg cylindrical) can be created as required and used for the same purpose.

The MEC STRUCT menu appears on the right. Basically, to define the model we proceed down this menu in a top-down manner. Model is already selected for you which opens the STRC MODEL menu. This is where we specify modeling information. We proceed in a top-down manner. The Features command allows you to create additional simulation features like datum points, curves, surface regions, and so on. Idealizations lets you create special modeling entities like shells and beams. The Current CSYS command lets you create or select an alternate coordinate system for specifying directions of constraints and loads.

Defining Constraints

For our simple model, all we need are constraints, loads, and a specified material. Select

Constraints > New

We can specify constraints on four entity types (basically points, edges, and surfaces). Constraints are organized into constraint sets. Each constraint set has a unique name (default of the first one is ConstraintSet1) and can contain any number of individual constraints of different types. Each individual constraint also has a unique name (default of the first one is Constraint1). In the final computed model, only one set can be included, but this can contain numerous individual constraints.

Select Surface. We are going to fully constrain the left face of the cantilever. A dialog window opens as shown above. Here you can give a name to the constraint and identify which constraint set it belongs to. Since we elected to create a surface constraint, we now select the surface we want constrained (push the Surface selection button in the window and then click on the desired surface of the model). The constraints to be applied are selected using the buttons at the bottom of the window. In general we specify constraints on translation and rotation for any mesh node that will appear on the selected entity. For each direction X, Y, and Z, we can select one of the four buttons (Free, Fixed, Prescribed, and Function of Coordinates). For our solid model, the rotation constraints are irrelevant (since nodes of solid elements do not have this degree of freedom anyway). For beams and shells, rotational constraints are active if specified.

For our model, leave all the translation constraints as FIXED, and select the OK button. You should now see some orange symbols on the left face of the model, along with some text labels that summarize the constraint settings.

Defining Loads

In the STRC MODEL menu select

Loads > New > Surface

The FORCE/MOMENT window opens as shown above. Loads are also organized into named load sets. A load set can contain any number of individual loads of different types. A FEM model can contain any number of different load sets. For example, in the analysis of a pressurized tank on a support system with a number of nozzle connections to other pipes, one load set might contain only the internal pressure, another might contain the support forces, another a temperature load, and more might contain the forces applied at each nozzle location. These can be solved at the same time, and the principle of superposition used to combine them in numerous ways.

Create a load called "end_load" in the default load set (LoadSet1)

Click on the Surfaces button, then select the right face of the model and middle click to return to this dialog. Leave the defaults for the load distribution. Enter the force components at the bottom. Note these are relative to the WCS. Then select OK. The load should be displayed symbolically as shown in the figure below.

Note that constraint and load sets appear in the model tree. You can select and edit these in the usual way using the right mouse button.

Assigning Materials

Our last job to define the model is to specify the part material. In the STRC MODEL menu, select

Materials > Whole Part

In the library dialog window, select a material and move it to the right pane using the triple arrow button in the center of the window. In an assembly, you could now assign this material to individual parts. If you select the Edit button, you will see the properties of the chosen material.

At this point, our model has the necessary information for solution (constraints, loads, material).

Step 3. Define the analysis

Select

Analyses > New

Specify a name for the analysis, like "ansystest". Select the type (Structural or Modal). Enter a short description. Now select the Add buttons beside the Constraints and Loads panes to add ConstraintSet1 and LoadSet1 to the analysis. Now select OK.

Step 4. Creating the mesh

We are going to use defaults for all operations here. The MEC STRUCT window, select

Mesh > Create > Solid > Start

Accept the default for the global minimum. The mesh is created and another dialog window opens (Element Quality Checks).

This indicates some aspects of mesh quality that may be specified and then, by selecting the Check button at the bottom, evaluated for the model. The results are indicated in columns on the right. If the mesh does not pass these quality checks, you may want to go back to specify mesh controls (discussed below). Select Close. Here is an image of the default mesh, shown in wire frame.

Improving the Mesh

In the mesh command, you can select the Controls option. This will allow you to select points, edges, and surfaces where you want to specify mesh geometry such as hard points, maximum mesh size, and so on. Beware that excessively tight mesh controls can result in meshes with many elements.

For example, setting a maximum mesh size along the curved ends of the slot results in the following mesh. Notice the better representation of the curved edges than in the previous figure. This is at the expense of more than double the number of elements. Note that mesh controls are also added to the model tree.

Step 5. Creating the Output file

All necessary aspects of the model are now created (constraints, loads, materials, mesh). In the MEC STRUCT menu, select

Run

This opens the Run FEM Analysis dialog window shown here. In the Solver pull-down list at the top, select ANSYS. In the Analysis list, select Structural. You pick either Linear or Parabolic elements. The analysis we defined (containing constraints, loads, mesh, and material) is listed. Select the Output to File radio button at the bottom and specify the output file name (default is the analysis name with extension .ans). Select OK and read the message window.

We are now finished with Pro/E. Go to the top pull-down menus and select

Applications > Standard

Save the model file and leave the program.

Copy the .ans file from your Pro/E working directory to the directory you will use for running ANSYS.

Step 6. Importing into ANSYS

Launch ANSYS Interactive and select

File > Read Input From...

Select the .ans file you created previously. This will read in the entire model. You can display the model using (in the pull down menus) Plot > Elements.

Step 7. Running the ANSYS solver

In the ANSYS Main Menu on the left, select

Solution > Solve > Current LS > OK

After a few seconds, you will be informed that the solution is complete.

Step 8. Viewing the results

There are myriad possibilities for viewing FEM results. A common one is the following:

General Postproc > Plot Results > Contour Plot > Nodal Solu

Pick the Von Mises stress values, and select Apply. You should now have a color fringe plot of the Von Mises stress displayed on the model.

Two Dimensional Truss

Introduction

This tutorial was created using ANSYS 7.0 to solve a simple 2D Truss problem. This is the first of four introductory ANSYS tutorials.

Problem Description

Determine the nodal deflections, reaction forces, and stress for the truss system shown below (E = 200GPa, A = 3250mm2).

(Modified from Chandrupatla & Belegunda, Introduction to Finite Elements in Engineering, p.123)

Preprocessing: Defining the Problem

1. Give the Simplified Version a Title (such as 'Bridge Truss Tutorial').

In the Utility menu bar select File > Change Title:

The following window will appear:

Enter the title and click 'OK'. This title will appear in the bottom left corner of the 'Graphics' Window once you begin. Note: to get the title to appear immediately, select Utility Menu > Plot > Replot

2. Enter Keypoints

The overall geometry is defined in ANSYS using keypoints which specify various principal coordinates to define the body. For this example, these keypoints are the ends of each truss.

o We are going to define 7 keypoints for the simplified structure as given in the following table

keypointcoordinate

x y

1 0 0

2 1800 3118

3 3600 0

4 5400 3118

5 7200 0

6 9000 3118

7 10800 0

o (these keypoints are depicted by numbers in the above figure) o From the 'ANSYS Main Menu' select:

Preprocessor > Modeling > Create > Keypoints > In Active CS

The following window will then appear:

o To define the first keypoint which has the coordinates x = 0 and y = 0: Enter keypoint number 1 in the appropriate box, and enter the x,y coordinates: 0, 0 in their appropriate boxes (as shown above). Click 'Apply' to accept what you have typed.

o Enter the remaining keypoints using the same method.

Note: When entering the final data point, click on 'OK' to indicate that you are finished entering keypoints. If you first press 'Apply' and then 'OK' for the final keypoint, you will have defined it twice!If you did press 'Apply' for the final point, simply press 'Cancel' to close this dialog box.

UnitsNote the units of measure (ie mm) were not specified. It is the responsibility of the user to ensure that a consistent set of units are used for the problem; thus making any conversions

where necessary.

Correcting MistakesWhen defining keypoints, lines, areas, volumes, elements, constraints and loads you are bound to make mistakes. Fortunately these are easily corrected so that you don't need to begin from scratch every time an error is made! Every 'Create' menu for generating these various entities also has a corresponding 'Delete' menu for fixing things up.

3. Form Lines

The keypoints must now be connected

We will use the mouse to select the keypoints to form the lines.

o In the main menu select: Preprocessor > Modeling > Create > Lines > Lines > In Active Coord. The following window will then appear:

o Use the mouse to pick keypoint #1 (i.e. click on it). It will now be marked by a small yellow box.

o Now move the mouse toward keypoint #2. A line will now show on the screen joining these two points. Left click and a permanent line will appear.

o Connect the remaining keypoints using the same method. o When you're done, click on 'OK' in the 'Lines in Active Coord' window, minimize the

'Lines' menu and the 'Create' menu. Your ANSYS Graphics window should look

similar to the following figure.

Disappearing LinesPlease note that any lines you have created may 'disappear' throughout your analysis. However, they have most likely NOT been deleted. If this occurs at any time from the Utility Menu select:

Plot > Lines

4. Define the Type of Element

It is now necessary to create elements. This is called 'meshing'. ANSYS first needs to know what kind of elements to use for our problem:

o From the Preprocessor Menu, select: Element Type > Add/Edit/Delete. The following window will then appear:

o Click on the 'Add...' button. The following window will appear:

o For this example, we will use the 2D spar element as selected in the above figure. Select the element shown and click 'OK'. You should see 'Type 1 LINK1' in the 'Element Types' window.

o Click on 'Close' in the 'Element Types' dialog box. 5. Define Geometric Properties

We now need to specify geometric properties for our elements:

o In the Preprocessor menu, select Real Constants > Add/Edit/Delete

o Click Add... and select 'Type 1 LINK1' (actually it is already selected). Click on 'OK'. The following window will appear:

o As shown in the window above, enter the cross-sectional area (3250mm): o Click on 'OK'. o 'Set 1' now appears in the dialog box. Click on 'Close' in the 'Real Constants' window.

6. Element Material Properties

You then need to specify material properties:

o In the 'Preprocessor' menu select Material Props > Material Models

o Double click on Structural > Linear > Elastic > Isotropic

We are going to give the properties of Steel. Enter the following field:

EX 200000

o Set these properties and click on 'OK'. Note: You may obtain the note 'PRXY will be set to 0.0'. This is poisson's ratio and is not required for this element type. Click 'OK' on the window to continue. Close the "Define Material Model Behavior" by clicking on the 'X' box in the upper right hand corner.

7. Mesh Size

The last step before meshing is to tell ANSYS what size the elements should be. There are a variety of ways to do this but we will just deal with one method for now.

o In the Preprocessor menu select Meshing > Size Cntrls > ManualSize > Lines > All Lines

o In the size 'NDIV' field, enter the desired number of divisions per line. For this example we want only 1 division per line, therefore, enter '1' and then click 'OK'. Note that we have not yet meshed the geometry, we have simply defined the element sizes.

8. Mesh

Now the frame can be meshed.

o In the 'Preprocessor' menu select Meshing > Mesh > Lines and click 'Pick All' in the 'Mesh Lines' Window

Your model should now appear as shown in the following window

Plot NumberingTo show the line numbers, keypoint numbers, node numbers...

• From the Utility Menu (top of screen) select PlotCtrls > Numbering... • Fill in the Window as shown below and click 'OK'

Now you can turn numbering on or off at your discretion

Saving Your Work

Save the model at this time, so if you make some mistakes later on, you will at least be able to come back to this point. To do this, on the Utility Menu select File > Save as.... Select the name and location where you want to save your file.

It is a good idea to save your job at different times throughout the building and analysis of the model to backup your work in case of a system crash or what have you.

Solution Phase: Assigning Loads and Solving

You have now defined your model. It is now time to apply the load(s) and constraint(s) and solve the the resulting system of equations.

Open up the 'Solution' menu (from the same 'ANSYS Main Menu').

1. Define Analysis Type

First you must tell ANSYS how you want it to solve this problem:

o From the Solution Menu, select Analysis Type > New Analysis.

o Ensure that 'Static' is selected; i.e. you are going to do a static analysis on the truss as opposed to a dynamic analysis, for example.

o Click 'OK'. 2. Apply Constraints

It is necessary to apply constraints to the model otherwise the model is not tied down or grounded and a singular solution will result. In mechanical structures, these constraints will typically be fixed, pinned and roller-type connections. As shown above, the left end of the truss bridge is pinned while the right end has a roller connection.

o In the Solution menu, select Define Loads > Apply > Structural > Displacement > On Keypoints

o Select the left end of the bridge (Keypoint 1) by clicking on it in the Graphics Window and click on 'OK' in the 'Apply U,ROT on KPs' window.

o This location is fixed which means that all translational and rotational degrees of freedom (DOFs) are constrained. Therefore, select 'All DOF' by clicking on it and enter '0' in the Value field and click 'OK'.

You will see some blue triangles in the graphics window indicating the displacement contraints.

o Using the same method, apply the roller connection to the right end (UY constrained).

Note that more than one DOF constraint can be selected at a time in the "Apply U,ROT on KPs" window. Therefore, you may need to 'deselect' the 'All DOF' option to select just the 'UY' option.

3. Apply Loads

As shown in the diagram, there are four downward loads of 280kN, 210kN, 280kN, and 360kN at keypoints 1, 3, 5, and 7 respectively.

o Select Define Loads > Apply > Structural > Force/Moment > on Keypoints. o Select the first Keypoint (left end of the truss) and click 'OK' in the 'Apply F/M on

KPs' window.

o Select FY in the 'Direction of force/mom'. This indicate that we will be applying the load in the 'y' direction

o Enter a value of -280000 in the 'Force/moment value' box and click 'OK'. Note that we are using units of N here, this is consistent with the previous values input.

o The force will appear in the graphics window as a red arrow. o Apply the remaining loads in the same manner.

The applied loads and constraints should now appear as shown below.

4. Solving the System

We now tell ANSYS to find the solution:

o In the 'Solution' menu select Solve > Current LS. This indicates that we desire the solution under the current Load Step (LS).

o The above windows will appear. Ensure that your solution options are the same as

shown above and click 'OK'. o Once the solution is done the following window will pop up. Click 'Close' and close

the /STATUS Command Window..

Postprocessing: Viewing the Results

1. Hand Calculations

We will first calculate the forces and stress in element 1 (as labeled in the problem description).

2. Results Using ANSYS

Reaction Forces

A list of the resulting reaction forces can be obtained for this element

o from the Main Menu select General Postproc > List Results > Reaction Solu.

o Select 'All struc forc F' as shown above and click 'OK'

These values agree with the reaction forces claculated by hand above.

Deformation

o In the General Postproc menu, select Plot Results > Deformed Shape. The following window will appear.

o Select 'Def + undef edge' and click 'OK' to view both the deformed and the

undeformed object.

o Observe the value of the maximum deflection in the upper left hand corner (DMX=7.409). One should also observe that the constrained degrees of freedom appear to have a deflection of 0 (as expected!)

Deflection

For a more detailed version of the deflection of the beam,

o From the 'General Postproc' menu select Plot results > Contour Plot > Nodal Solution. The following window will appear.

o Select 'DOF solution' and 'USUM' as shown in the above window. Leave the other selections as the default values. Click 'OK'.

o Looking at the scale, you may want to use more useful intervals. From the Utility Menu select Plot Controls > Style > Contours > Uniform Contours...

o Fill in the following window as shown and click 'OK'.

You should obtain the following.

o The deflection can also be obtained as a list as shown below. General Postproc > List Results > Nodal Solution select 'DOF Solution' and 'ALL DOFs' from the lists in the 'List Nodal Solution' window and click 'OK'. This means that we want to see a listing of all degrees of freedom from the solution.

o Are these results what you expected? Note that all the degrees of freedom were constrained to zero at node 1, while UY was constrained to zero at node 7.

o If you wanted to save these results to a file, select 'File' within the results window (at the upper left-hand corner of this list window) and select 'Save as'.

Axial Stress

For line elements (ie links, beams, spars, and pipes) you will often need to use the Element Table to gain access to derived data (ie stresses, strains). For this example we should obtain axial stress to compare with the hand calculations. The Element Table is different for each element, therefore, we need to look at the help file for LINK1 (Type help link1 into the Input Line). From Table 1.2 in the Help file, we can see that SAXL can be obtained through the ETABLE, using the item 'LS,1'

o From the General Postprocessor menu select Element Table > Define Table o Click on 'Add...'

o As shown above, enter 'SAXL' in the 'Lab' box. This specifies the name of the item you are defining. Next, in the 'Item,Comp' boxes, select 'By sequence number' and 'LS,'. Then enter 1 after LS, in the selection box

o Click on 'OK' and close the 'Element Table Data' window. o Plot the Stresses by selecting Element Table > Plot Elem Table o The following window will appear. Ensure that 'SAXL' is selected and click 'OK'

o Because you changed the contour intervals for the Displacement plot to "User Specified" - you need to switch this back to "Auto calculated" to obtain new values for

VMIN/VMAX.

Utility Menu > PlotCtrls > Style > Contours > Uniform Contours ...

Again, you may wish to select more appropriate intervals for the contour plot

o List the Stresses From the 'Element Table' menu, select 'List Elem Table' From the 'List Element Table Data' window which appears ensure 'SAXL' is

highlighted Click 'OK'

Note that the axial stress in Element 1 is 82.9MPa as predicted analytically.

command language interface that you may want to browse. Open the .HTML version, copy and paste the code into Notepad or a similar text editor and save it to your computer. Now go to 'File > Read input from...' and select the file. A .PDF version is also available for printing.

Space Frame Example

| Verification Example | | Preprocessing | | Solution | | Postprocessing | | Command Line | | Bicycle Example | | Preprocessing | | Solution | | Postprocessing | | Command Line |

Introduction

This tutorial was created using ANSYS 7.0 to solve a simple 3D space frame problem.

Problem Description

The problem to be solved in this example is the analysis of a bicycle frame. The problem to be modeled in this example is a simple bicycle frame shown in the following figure. The frame is to be built of hollow aluminum tubing having an outside diameter of 25mm and a wall thickness of 2mm.

Verification

The first step is to simplify the problem. Whenever you are trying out a new analysis type, you need something (ie analytical solution or experimental data) to compare the results to. This way you can be sure that you've gotten the correct analysis type, units, scale factors, etc.

The simplified version that will be used for this problem is that of a cantilever beam shown in the following figure:

Preprocessing: Defining the Problem

1. Give the Simplified Version a Title (such as 'Verification Model').

Utility Menu > File > Change Title

2. Enter Keypoints

For this simple example, these keypoints are the ends of the beam.

o We are going to define 2 keypoints for the simplified structure as given in the following table

keypointcoordinate

x y z

1 0 0 0

2 500 0 0

o From the 'ANSYS Main Menu' select:Preprocessor > Modeling > Create > Keypoints > In Active CS

3. Form Lines

The two keypoints must now be connected to form a bar using a straight line.

o Select: Preprocessor > Modeling> Create > Lines > Lines > Straight Line. o Pick keypoint #1 (i.e. click on it). It will now be marked by a small yellow box. o Now pick keypoint #2. A permanent line will appear. o When you're done, click on 'OK' in the 'Create Straight Line' window.

4. Define the Type of Element

It is now necessary to create elements on this line.

o From the Preprocessor Menu, select: Element Type > Add/Edit/Delete. o Click on the 'Add...' button. The following window will appear:

o For this example, we will use the 3D elastic straight pipe element as selected in the above figure. Select the element shown and click 'OK'. You should see 'Type 1 PIPE16' in the 'Element Types' window.

o Click on the 'Options...' button in the 'Element Types' dialog box. The following window will appear:

o Click and hold the K6 button (second from the bottom), and select 'Include Output' and click 'OK'. This gives us extra force and moment output.

o Click on 'Close' in the 'Element Types' dialog box and close the 'Element Type'

menu. 5. Define Geometric Properties

We now need to specify geometric properties for our elements:

o In the Preprocessor menu, select Real Constants > Add/Edit/Delete o Click Add... and select 'Type 1 PIPE16' (actually it is already selected). Click on

'OK'. o Enter the following geometric properties: o Outside diameter OD: 25o Wall thickness TKWALL: 2

This defines an outside pipe diameter of 25mm and a wall thickness of 2mm.

o Click on 'OK'. o 'Set 1' now appears in the dialog box. Click on 'Close' in the 'Real Constants'

window. 6. Element Material Properties

You then need to specify material properties:

o In the 'Preprocessor' menu select Material Props > Material Models... o Double click Structural > Linear > Elastic and select 'Isotropic' (double click on

it) o Close the 'Define Material Model Behavior' Window.

We are going to give the properties of Aluminum. Enter the following field:

EX 70000PRXY 0.33

o Set these properties and click on 'OK'. 7. Mesh Size

o In the Preprocessor menu select Meshing > Size Cntrls > ManualSize > Lines > All Lines

o In the size 'SIZE' field, enter the desired element length. For this example we want an element length of 2cm, therefore, enter '20' (i.e 20mm) and then click 'OK'. Note that we have not yet meshed the geometry, we have simply defined the element sizes.

(Alternatively, we could enter the number of divisions we want in the line. For an element length of 2cm, we would enter 25 [ie 25 divisions]).

8. NOTEIt is not necessary to mesh beam elements to obtain the correct solution. However, meshing

is done in this case so that we can obtain results (ie stress, displacement) at intermediate positions on the beam.

9. Mesh

Now the frame can be meshed.

o In the 'Preprocessor' menu select Meshing > Mesh > Lines and click 'Pick All' in the 'Mesh Lines' Window

10. Saving Your Work

Utility Menu > File > Save as.... Select the name and location where you want to save your file.

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type o From the Solution Menu, select 'Analysis Type > New Analysis'. o Ensure that 'Static' is selected and click 'OK'.

2. Apply Constraints o In the Solution menu, select Define Loads > Apply > Structural > Displacement

> On Keypoints o Select the left end of the rod (Keypoint 1) by clicking on it in the Graphics Window

and click on 'OK' in the 'Apply U,ROT on KPs' window. o This location is fixed which means that all translational and rotational degrees of

freedom (DOFs) are constrained. Therefore, select 'All DOF' by clicking on it and enter '0' in the Value field and click 'OK'.

3. Apply Loads

As shown in the diagram, there is a vertically downward load of 100N at the end of the bar

o In the Structural menu, select Force/Moment > on Keypoints. o Select the second Keypoint (right end of bar) and click 'OK' in the 'Apply F/M'

window. o Click on the 'Direction of force/mom' at the top and select FY. o Enter a value of -100 in the 'Force/moment value' box and click 'OK'. o The force will appear in the graphics window as a red arrow.

The applied loads and constraints should now appear as shown below.

4. Solving the System

We now tell ANSYS to find the solution:

o Solution > Solve > Current LS

Postprocessing: Viewing the Results

1. Hand Calculations

Now, since the purpose of this exercise was to verify the results - we need to calculate what we should find.

Deflection:

The maximum deflection occurs at the end of the rod and was found to be 6.2mm as shown above.

Stress:

The maximum stress occurs at the base of the rod and was found to be 64.9MPa as shown above (pure bending stress).

2. Results Using ANSYS

Deformation

o from the Main Menu select General Postproc from the 'ANSYS Main Menu'. In this menu you will find a variety of options, the two which we will deal with now are 'Plot Results' and 'List Results'

o Select Plot Results > Deformed Shape. o Select 'Def + undef edge' and click 'OK' to view both the deformed and the

undeformed object.

o Observe the value of the maximum deflection in the upper left hand corner (shown here surrounded by a blue border for emphasis). This is identical to that obtained via hand calculations.

Deflection

For a more detailed version of the deflection of the beam,

o From the 'General Postproc' menu select Plot results > Contour Plot > Nodal Solution.

o Select 'DOF solution' and 'USUM'. Leave the other selections as the default values. Click 'OK'.

o You may want to have a more useful scale, which can be accomplished by going to the Utility Menu and selecting Plot Controls > Style > Contours > Uniform Contours

o The deflection can also be obtained as a list as shown below. General Postproc > List Results > Nodal Solution ... select 'DOF Solution' and 'ALL DOFs' from the lists in the 'List Nodal Solution' window and click 'OK'. This means that we want to see a listing of all translational and rotational degrees of freedom from the solution. If we had only wanted to see the displacements for example, we would have chosen 'ALL Us' instead of 'ALL DOFs'.

o Are these results what you expected? Again, the maximum deflection occurs at node 2, the right end of the rod. Also note that all the rotational and translational degrees of freedom were constrained to zero at node 1.

o If you wanted to save these results to a file, use the mouse to go to the 'File' menu (at the upper left-hand corner of this list window) and select 'Save as'.

Stresses

For line elements (ie beams, spars, and pipes) you will need to use the Element Table to gain access to derived data (ie stresses, strains).

o From the General Postprocessor menu select Element Table > Define Table... o Click on 'Add...'

o As shown above, in the 'Item,Comp' boxes in the above window, select 'Stress' and 'von Mises SEQV'

o Click on 'OK' and close the 'Element Table Data' window. o Plot the Stresses by selecting Plot Elem Table in the Element Table Menu o The following window will appear. Ensure that 'SEQV' is selected and click 'OK'

o If you changed the contour intervals for the Displacement plot to "User Specified" you may need to switch this back to "Auto calculated" to obtain new values for VMIN/VMAX.

Utility Menu > PlotCtrls > Style > Contours > Uniform Contours ...

Again, select more appropriate intervals for the contour plot

o List the Stresses From the 'Element Table' menu, select 'List Elem Table' From the 'List Element Table Data' window which appears ensure 'SEQV' is

highlighted Click 'OK'

Note that a maximum stress of 64.914 MPa occurs at the fixed end of the beam as predicted analytically.

Bending Moment Diagrams

To further verify the simplified model, a bending moment diagram can be created. First, let's look at how ANSYS defines each element. Pipe 16 has 2 nodes; I and J, as shown in the following image.

To obtain the bending moment for this element, the Element Table must be used. The Element Table contains most of the data for the element including the bending moment data for each element at Node I and Node J. First, we need to obtain obtain the bending moment data.

o General Postproc > Element Table > Define Table... . Click 'Add...'.

o In the window,

AA Enter IMoment as the 'User label for item' - this will give a name to the data

AA Select 'By sequence num' in the Item box AA Select 'SMISC' in the first Comp box DA Enter SMISC,6 in the second Comp box AA Click 'OK'

This will save all of the bending moment data at the left hand side (I side) of each element. Now we need to find the bending moment data at the right hand side (J side) of each element.

o Again, click 'Add...' in the 'Element Table Data' window. AA Enter JMoment as the 'User label for item' - again, this will give a

name to the data

AA Same as above AA Same as above DA For step D, enter SMISC,12 in the second Comp box AA Click 'OK'

o Click 'Close' in the 'Element Table Data' window and close the 'Element Table' Menu. Select Plot Results > Contour Plot > Line Elem Res...

o From the 'Plot Line-Element Results' window, select 'IMOMENT' from the pull down menu for LabI, and 'JMOMENT' from the pull down menu for LabJ. Click 'OK'. Note again that you can modify the intervals for the contour plot.

Now, you can double check these solutions analytically. Note that the line between the I and J point is a linear interpolation.

o Before the explanation of the above steps, enter help pipe16 in the command line as shown below and then hit enter.

o Briefly read the ANSYS documentation which appears, pay particular attention to the Tables near the end of the document (shown below).

Table 1. PIPE16 Item, Sequence Numbers, and Definitions for the ETABLE Commands

node I

name item e Definition

MFORX SMISC 1 Member forces at the

nodeMFORY SMISC 2

MFORZ SMISC 3

MMOMX SMISC 4 Member moments at

the nodeMMOMY SMISC 5

MMOMZ SMISC 6

Note that SMISC 6 (which we used to obtain the values at node I) correspond to MMOMZ - the Member moment for node I. The value of 'e' varies with different Element Types, therefore you must check the ANSYS Documentation files for each element to determine the appropriate SMISC corresponding to the plot you wish to generate.

Command File Mode of Solution

The above example was solved using the Graphical User Interface (or GUI) of ANSYS. This problem can also been solved using the ANSYS command language interface. To see the benefits of the command line clear your current file:

• From the Utility menu select: File > Clear and Start New • Ensure that 'Read File' is selected then click 'OK' • select 'yes' in the following window.

Copy the following code into the command line, then hit enter. Note that the text following the "!" are comments.

/PREP7 ! PreprocessorK,1,0,0,0, ! Keypoint, 1, x, y, zK,2,500,0,0, ! Keypoint, 2, x, y, zL,1,2 ! Line from keypoint 1 to 2!*ET,1,PIPE16 ! Element Type = pipe 16KEYOPT,1,6,1 ! This is the changed option to give the extra force and moment output!* R,1,25,2, ! Real Constant, Material 1, Outside Diameter, Wall thickness!* MP,EX,1,70000 ! Material Properties, Young's Modulus, Material 1, 70000 MPaMP,PRXY,1,0.33 ! Material Properties, Major Poisson's Ratio, Material 1, 0.33!* LESIZE,ALL,20 ! Element sizes, all of the lines, 20 mm LMESH,1 ! Mesh the linesFINISH ! Exit preprocessor/SOLU ! SolutionANTYPE,0 ! The type of analysis (static)!*DK,1, ,0, ,0,ALL ! Apply a Displacement to Keypoint 1 to all DOFFK,2,FY,-100 ! Apply a Force to Keypoint 2 of -100 N in the y direction

/STATUS,SOLUSOLVE ! Solve the problemFINISH

Note that you have now finished Postprocessing and the Solution Phase with just these few lines of code. There are codes to complete the Postprocessing but we will review these later.

Bicycle Example

Now we will return to the analysis of the bike frame. The steps which you completed in the verification example will not be explained in great detail, therefore use the verification example as a reference as required. We will be combining the use of the Graphic User Interface (GUI) with the use of command lines.

Recall the geometry and dimensions of the bicycle frame:

Preprocessing: Defining the Problem

1. Clear any old ANSYS files and start a new file

Utility Menu > File > Clear and Start New

2. Give the Example a Title

Utility menu > File > Change Title

3. Defining Some Variables

We are going to define the vertices of the frame using variables. These variables represent the various lengths of the bicycle members. Notice that by using variables like this, it is very easy to set up a parametric description of your model. This will enable us to quickly redefine the frame should changes be necessary. The quickest way to enter these variables is via the 'ANSYS Input' window which was used above to input the command line codes for the verification model. Type in each of the following lines followed by Enter.

x1 = 500 x2 = 825 y1 = 325 y2 = 400 z1 = 50

4. Enter Keypoints

For this space frame example, these keypoints are the frame vertices.

o We are going to define 6 keypoints for this structure as given in the following table (these keypoints are depicted by the circled numbers in the above figure):

keypointcoordinate

x y z

1 0 y1 0

2 0 y2 0

3 x1 y2 0

4 x1 0 0

5 x2 0 z1

6 x2 0 -z1

o Now instead of using the GUI window we are going to enter code into the 'command line'. First, open the 'Preprocessor Menu' from the 'ANSYS Main Menu'. The preprocessor menu has to be open in order for the preprocessor commands to be recognized. Alternatively, you can type /PREP7 into the command line. The command line format required to enter a keypoint is as follows:

o K, NPT, X, Y, Z

where, each Abbreviation is representative of the following:

Keypoint, Reference number for the keypoint, coords x/y/z

For a more detailed explanation, type help k into the command line

For example, to enter the first keypoint type:

K,1,0,y1,0

into the command line followed by Enter.

As with any programming language, you may need to add comments. The exclamation mark indicates that anything following it is commented out. ie - for the second keypoint you might type:

K,2,0,y2,0 ! keypoint, #, x=0, y=y2, z=0

o Enter the 4 remaining keypoints (listed in the table above) using the command line o Now you may want to check to ensure that you entered all of the keypoints

correctly:Utility Menu > List > Keypoints > Coordinates only(Alternatively, type 'KLIST' into the command line)

o If there are any keypoints which need to be re-entered, simply re-enter the code. A previously defined keypoint of the same number will be redefined. However, if there is one that needs to be deleted simply enter the following code:

o KDELE,#

where # corresponds to the number of the keypoint.

In this example, we defined the keypoints by making use of previously defined variables like y1 = 325. This was simply used for convenience. To define keypoint #1, for example, we could have alternatively used the coordinates x = 0, y = 325, z = 0.

5. Changing Orientation of the Plot o To get a better view of our view of our model, we'll view it in an isometric view: o Select Utility menu bar > PlotCtrls > Pan, Zoom, Rotate...'

In the window that appears (shown left), you have many controls. Try experimenting with them. By turning on the dynamic mode (click on the checkbox beside 'Dynamic Mode') you can use the mouse to drag the image, translating and rotating it on all three axes.

To get an isometric view, click on 'Iso' (at the top right). You can either leave the 'Pan, Zoom, Rotate' window open and move it to an empty area on the screen, or close it if your screen is already cluttered.

6. Create Lines

We will be joining the following keypoints together:

linekeypoint

1st 2nd

1 1 2

2 2 3

3 3 4

4 1 4

5 3 5

6 4 5

7 3 6

Again, we will use the command line to create the lines. The command format to create a straight line looks like:

L, P1, P2 Line, Keypoint at the beginning of the line, Keypoint at the end of line

For example, to obtain the first line, I would write: ' L,1,2 '

Note: unlike 'Keypoints', 'Lines' will automatically assign themselves the next available reference number.

8 4 6

o Enter the remaining lines until you get a picture like that shown below. o Again, check to ensure that you entered all of the lines correctly: type ' LLIST ' into

the command line o If there are any lines which need to be changed, delete the line by typing the

following code: ' LDELE,# ' where # corresponds to the reference number of the line. (This can be obtained from the list of lines). And then re-enter the line (note: a new reference number will be assigned)

You should obtain the following:

7. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete > Add

As in the verification model, define the type of element (pipe16). As in the verification model, don't forget to change Option K6 'Include Output' to obtain extra force and moment output.

8. Define Geometric Properties

Preprocessor > Real Constants > Add/Edit/Delete

Now specify geometric properties for the elements

Outside diameter OD: 25 Wall thickness TKWALL: 2

9. Element Material Properties

To set Young's Modulus and Poisson's ratio, we will again use the command line. (ensure that the preprocessor menu is still open - if not open it by clicking Preprocessor in the Main Menu)

MP, LAB, MAT, C0Material Property,Valid material property label, Material Reference

Number, value

o To enter the Elastic Modulus (LAB = EX) of 70000 MPa, type: ' MP,EX,1,70000 ' o To set Poisson's ratio (PRXY), type ' MP,PRXY,1,0.33 '

10. Mesh Size

As in the verification model, set the element length to 20 mmPreprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines

11. Mesh

Now the frame can be meshed.

o In the 'Preprocessor' menu select 'Mesh' > 'Lines' and click 'Pick All' in the 'Mesh Lines' Window

Saving Your JobUtility Menu > File > Save as...

Solution Phase: Assigning Loads and Solving

Close the 'Preprocessor' menu and open up the 'Solution' menu (from the same 'ANSYS Main Menu').

1. Define Analysis Type

Solution > Analysis Type > New Analysis... > Static

2. Apply Constraints

Once again, we will use the command line. We are going to pin (translational DOFs will be fixed) the first keypoint and constrain the keypoints corresponding to the rear wheel attachment locations in both the y and z directions. The following is the command line format to apply constraints at keypoints.

DK, KPOI, Lab, VALUE, VALUE2, KEXPND, Lab2, Lab3, Lab4, Lab5, Lab6Displacement on K, K #, DOF label, value, value2, Expansion key, other

DOF labels

Not all of the fields are required for this example, therefore when entering the code certain fields will be empty. For example, to pin the first keypoint enter:

DK,1,UX,0,,,UY,UZ

The DOF labels for translation motion are: UX, UY, UZ. Note that the 5th and 6th fields are empty. These correspond to 'value2' and 'the Expansion key' which are not required for this constraint. Also note that all three of the translational DOFs were constrained to 0. The DOFs can only be contrained in 1 command line if the value is the same.

To apply the contraints to Keypoint 5, the command line code is:

DK,5,UY,0,,,UZ

Note that only UY and UZ are contrained to 0. UX is not constrained. Again, note that the 5th and 6th fields are empty because they are not required.

o Apply the constraints to the other rear wheel location (Keypoint 6 - UY and UZ). o Now list the constraints ('DKLIST') and verify them against the following:

If you need to delete any of the constraints use the following command: 'DKDELE, K, Lab' (ie 'DKDELE,1,UZ' would delete the constraint in the 'z' direction for Keypoint 1)

3. Apply Loads

We will apply vertical downward loads of 600N at the seat post location (keypoint 3) and 200N at the pedal crank location (keypoint 4). We will use the command line to define these loading conditions.

FK, KPOI, Lab, value, value2Force loads at keypoints, K #, Force Label directions (FX, FY, FZ), value1, value2 (if req'd)

To apply a force of 600N downward at keypoint 3, the code should look like this: ' FK,3,FY,-600 '

Apply both the forces and list the forces to ensure they were inputted correctly (FKLIST).

If you need to delete one of the forces, the code looks like this: 'FKDELE, K, Lab' (ie 'FKDELE,3,FY' would delete the force in the 'y' direction for Keypoint 3)

The applied loads and constraints should now appear as shown below.

4. Solving the System

Solution > Solve > Current LS

Postprocessing: Viewing the Results

To begin Postprocessing, open the 'General Postproc' Menu

1. Deformation

Plot Results > Deformed Shape... 'Def + undef edge'

o You may want to try plotting this from different angles to get a better idea what's going on by using the 'Pan-Zoom-Rotate' menu that was earlier outlined.

o Try the 'Front' view button (Note that the views of 'Front', 'Left', 'Back', etc depend on how the object was first defined).

o Your screen should look like the plot below:

2. Deflections

Now let's take a look at some actual deflections in the frame. The deflections have been calculated at the nodes of the model, so the first thing we'll do is plot out the nodes and node numbers, so we know what node(s) we're after.

o Go to Utility menu > PlotCtrls > Numbering... and turn on 'Node numbers'. Turn everything else off.

o Note the node numbers of interest. Of particular interest are those nodes where the constraints were applied to see if their displacements/rotations were indeed fixed to zero. Also note the node numbers of the seat and crank locations.

o List the Nodal Deflections (Main Menu > General Postproc > List Results > Nodal Solution...'). Are the displacements and rotations as you expected?

o Plot the deflection as well.

General Postproc > Plot Results > (-Contour Plot-) Nodal Solution select 'DOF solution' and 'USUM' in the window

o Don't forget to use more useful intervals. 3. Element Forces

We could also take a look at the forces in the elements in much the same way:

o Select 'Element Solution...' from the 'List Results' menu. o Select 'Nodal force data' and 'All forces' from the lists displayed. o Click on 'OK'. o For each element in the model, the force/moment values at each of the two nodes

per element will be displayed. o Close this list window when you are finished browsing. o Then close the 'List Results' menu.

4. Stresses

As shown in the cantilever beam example, use the Element Table to gain access to derived stresses.

o General Postproc > Element Table > Define Table ... o Select 'Add' o Select 'Stress' and 'von Mises' o Element Table > Plot Elem Table

o Again, select appropriate intervals for the contour plot 5. Bending Moment Diagrams

As shown previously, the bending moment diagram can be produced.

Select Element Table > Define Table... to define the table (remember SMISC,6 and SMISC,12)

And, Plot Results > Line Elem Res... to plot the data from the Element Table

Plane Stress Bracket

| Verification Example | | Preprocessing | | Solution | | Postprocessing | | Command Line | | Bracket Example | | Preprocessing | | Solution | | Postprocessing | | Command Line |

Introduction

This tutorial is the second of three basic tutorials created to illustrate commom features in ANSYS. The plane stress bracket tutorial builds upon techniques covered in the first tutorial (3D Bicycle Space Frame), it is therefore essential that you have completed that tutorial prior to beginning this one.

The 2D Plane Stress Bracket will introduce boolean operations, plane stress, and uniform pressure loading.

Problem Description

The problem to be modeled in this example is a simple bracket shown in the following figure. This bracket is to be built from a 20 mm thick steel plate. A figure of the plate is shown below.

This plate will be fixed at the two small holes on the left and have a load applied to the larger hole on the right.

Verification Example

The first step is to simplify the problem. Whenever you are trying out a new analysis type, you need something (ie analytical solution or experimental data) to compare the results to. This way you can be sure that you've gotten the correct analysis type, units, scale factors, etc.

The simplified version that will be used for this problem is that of a flat rectangular plate with a hole shown in the following figure:

Preprocessing: Defining the Problem

1. Give the Simplified Version a Title

Utility Menu > File > Change Title

2. Form Geometry

Boolean operations provide a means to create complicated solid models. These procedures make it easy to combine simple geometric entities to create more complex bodies. Subtraction will used to create this model, however, many other Boolean operations can be used in ANSYS.

a. Create the main rectangular shape

Instead of creating the geometry using keypoints, we will create an area (using GUI)

Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners

Fill in the window as shown above. This will create a rectangle where the bottom left corner has the coordinates 0,0,0 and the top right corner has the coordinates 200,100,0.

(Alternatively, the command line code for the above command is BLC4,0,0,200,100)

b. Create the circle

Preprocessor > Modeling > Create > Areas > Circle > Solid Circle

Fill in the window as shown above. This will create a circle where the center has the coordinates 100,50,0 (the center of the rectangle) and the radius of the circle is 20 mm.

(Alternatively, the command line code for the above command is CYL4,100,50,20 )

c. Subtraction

Now we want to subtract the circle from the rectangle. Prior to this operation, your image should resemble the following:

To perform the Boolean operation, from the Preprocessor menu select:

Modeling > Operate > Booleans > Subtract > Areas

At this point a 'Subtract Areas' window will pop up and the ANSYS Input window will display the following message: [ASBA] Pick or enter base areas from which to subtract (as shown below)

Therefore, select the base area (the rectangle) by clicking on it. Note: The selected area will turn pink once it is selected.

The following window may appear because there are 2 areas at the location you clicked.

Ensure that the entire rectangular area is selected (otherwise click 'Next') and then click 'OK'.

Click 'OK' on the 'Subtract Areas' window. Now you will be prompted to select the areas to be subtracted, select the

circle by clicking on it and then click 'OK'.

You should now have the following model:

(Alternatively, the command line code for the above step is ASBA,1,2)

3. Define the Type of Element

It is now necessary to define the type of element to use for our problem:

Preprocessor Menu > Element Type > Add/Edit/Delete

o Add the following type of element: Solid (under the Structural heading) and the Quad 82 element, as shown in the above figure.

PLANE82 is a higher order version of the two-dimensional, four-node element (PLANE42). PLANE82 is an eight noded quadrilateral element which is better suited to model curved boundaries.

For this example, we need a plane stress element with thickness, therefore

o Click on the 'Options...' button. Click and hold the K3 button, and select 'Plane strs w/thk', as shown below.

(Alternatively, the command line code for the above step is ET,1,PLANE82 followed by KEYOPT,1,3,3)

2. Define Geometric Properties o As in previous examples Preprocessor menu > Real Constants >

Add/Edit/Delete

o Enter a thickness of 20 as shown in the figure below. This defines a plate thickness of 20mm)

(Alternatively, the command line code for the above step is R,1,20)

3. Element Material Properties o As shown in previous examples, select Preprocessor > Material Props >

Material models > Structural > Linear > Elastic > Isotropic

We are going to give the properties of Steel. Enter the following when prompted:

EX 200000PRXY 0.3

(Alternatively, the command line code for the above step is MP,EX,1,200000 followed by MP,PRXY,1,0.3)

4. Mesh Size

To tell ANSYS how big the elements should be, Preprocessor > Meshing > Size Cntrls > Manual Size > Areas > All Areas

o Select an element edge length of 25. We will return later to determine if this was adequate for the problem.

(Alternatively, the command line code for the above step is AESIZE,ALL,25,)

5. Mesh

Now the frame can be meshed.

o In the 'Preprocessor' menu select Meshing > Mesh > Areas > Free and select the area when prompted

(Alternatively, the command line code for the above step is AMESH,ALL)

You should now have the following:

Saving Your JobUtility Menu > File > Save as...

Solution Phase: Assigning Loads and Solving

You have now defined your model. It is now time to apply the load(s) and constraint(s) and solve the the resulting system of equations.

1. Define Analysis Type o Ensure that a Static Analysis will be performed (Solution > Analysis Type >

New Analysis).

(Alternatively, the command line code for the above step is ANTYPE,0)

2. Apply Constraints

As shown previously, the left end of the plate is fixed.

o In the Solution > Define Loads > Apply > Structural > Displacement > On Lines

o Select the left end of the plate and click on 'Apply' in the 'Apply U,ROT on Lines' window.

o Fill in the window as shown below.

o This location is fixed which means that all DOF's are constrained. Therefore, select 'All DOF' by clicking on it and enter '0' in the Value field as shown above.

You will see some blue triangles in the graphics window indicating the displacement contraints.

(Alternatively, the command line code for the above step is DL,4,,ALL,0)

3. Apply Loads o As shown in the diagram, there is a load of 20N/mm distributed on the right hand

side of the plate. To apply this load:

Solution > Define Loads > Apply > Structural > Pressure > On Lines

o When the window appears, select the line along the right hand edge of the plate and click 'OK'

o Calculate the pressure on the plate end by dividing the distributed load by the thickness of the plate (1 MPa).

o Fill in the "Apply PRES on lines" window as shown below. NOTE: The pressure is uniform along the surface of the plate, therefore the last

field is left blank. The pressure is acting away from the surface of the plate, and is therefore

defined as a negative pressure.

o The applied loads and constraints should now appear as shown below.

o

4. Solving the System

Solution > Solve > Current LS

Postprocessing: Viewing the Results

1. Hand Calculations

Now, since the purpose of this exercise was to verify the results - we need to calculate what we should find.

Deflection: The maximum deflection occurs on the right hand side of the plate and was calculated to be 0.001 mm - neglecting the effects of the hole in the plate (ie - just a flat plate). The actual deflection of the plate is therefore expected to be greater but in the same range of magnitude.

Stress: The maximum stress occurs at the top and bottom of the hole in the plate and was found to be 3.9 MPa.

2. Convergence using ANSYS

At this point we need to find whether or not the final result has converged. We will do this by looking at the deflection and stress at particular nodes while changing the size of

the meshing element.

Since we have an analytical solution for the maximum stress point, we will check the stress at this point. First we need to find the node corresponding to the top of the hole in the plate. First plot and number the nodes

Utility Menu > Plot > NodesUtility Menu > PlotCtrls > Numbering...

o The plot should look similar to the one shown below. Make a note of the node closest to the top of the circle (ie. #49)

o List the stresses (General Postproc > List Results > Nodal Solution > Stress, Principals SPRIN) and check the SEQV (Equivalent Stress / von Mises Stress) for the node in question. (as shown below in red)

The equivalent stress was found to be 2.9141 MPa at this point. We will use smaller elements to try to get a more accurate solution.

o Resize Elements a. To change the element size, we need to go back to the Preprocessor Menu

Preprocessor > Meshing > Size Cntrls > Manual Size > Areas > All Areas

now decrease the element edge length (ie 20)

b. Now remesh the model (Preprocessor > Meshing > Mesh > Areas > Free). Once you have selected the area and clicked 'OK' the following window will appear:

c. Click 'OK'. This will remesh the model using the new element edge length.

d. Solve the system again (note that the constraints need not be reapplied). ( Solution Menu > Current LS )

o Repeat steps 'a' through 'd' until the model has converged. (note - the number of the node at the top of the hole has most likely changed. It is essential that you plot the nodes again to select the appropriate node). Plot the stress/deflection at varying mesh sizes as shown below to confirm that convergence has occured.

Note the shapes of both the deflection and stress curves. As the number of elements in the mesh increases (ie - the element edge length decreases), the values converge towards a final solution.

The von Mises stress at the top of the hole in the plate was found to be approximatly 3.8 MPa. This is a mere 2.5% difference between the analytical solution and the solution found using ANSYS.

The approximate maximum displacement was found to be 0.0012 mm, this is 20%

greater than the analytical solution. However, the analytical solution does not account for the large hole in the center of the plate which was expected to significantly increase the deflection at the end of the plate.

Therefore, the results using ANSYS were determined to be appropriate for the verification model.

3. Deformation o General Postproc > Plot Results > Deformed Shape > Def + undeformd to

view both the deformed and the undeformed object.

o Observe the locations of deflection. 4. Deflection

o General Postproc > Plot Results > Nodal Solution... Then select DOF solution, USUM in the window.

o Alternatively, obtain these results as a list. (General Postproc > List Results > Nodal Solution...)

o Are these results what you expected? Note that all translational degrees of freedom were constrained to zero at the left end of the plate.

5. Stresses o General Postproc > Plot Results > Nodal Solution... Then select Stress, von

Mises in the window.

o You can list the von Mises stresses to verify the results at certain nodes

General Postproc > List Results. Select Stress, Principals SPRIN

Command File Mode of Solution

The above example was solved using a mixture of the Graphical User Interface (or GUI) and the command language interface of ANSYS. This problem has also been solved using the ANSYS command language interface that you may want to browse. Open the .HTML version, copy and paste the code into Notepad or a similar text editor and save it to your computer. Now go to 'File > Read input from...' and select the file. A .PDF version is also available for printing.

Bracket Example

Now we will return to the analysis of the bracket. A combination of GUI and the Command line will be used for this example.

The problem to be modeled in this example is a simple bracket shown in the following figure. This bracket is to be built from a 20 mm thick steel plate. A figure of the plate is shown below.

This plate will be fixed at the two small holes on the left and have a load applied to the larger hole on the right.

Preprocessing: Defining the Problem

1. Give the Bracket example a Title

Utility Menu > File > Change Title

2. Form Geometry

Again, Boolean operations will be used to create the basic geometry of the Bracket.

a. Create the main rectangular shape

The main rectangular shape has a width of 80 mm, a height of 100mm and the bottom left corner is located at coordinates (0,0)

Ensure that the Preprocessor menu is open. (Alternatively type /PREP7 into the command line window)

Now instead of using the GUI window we are going to enter code into the 'command line'. Now I will explain the line required to create a rectangle:

BLC4, XCORNER, YCORNER, WIDTH, HEIGHT BLC4, X coord (bottom left), Y coord (bottom left),

width, height

Therefore, the command line for this rectangle is BLC4,0,0,80,100 b. Create the circular end on the right hand side

The center of the circle is located at (80,50) and has a radius of 50 mm

The following code is used to create a circular area:

CYL4, XCENTER, YCENTER, RAD1CYL4, X coord for the center, Y coord for the center,

radius

Therefore, the command line for this circle is CYL4,80,50,50 c. Now create a second and third circle for the left hand side using the following

dimensions:

parameter circle 2 circle 3

XCENTER 0 0

YCENTER 20 80

RADIUS 20 20

d. Create a rectangle on the left hand end to fill the gap between the two small circles.

XCORNER -20

YCORNER 20

WIDTH 20

HEIGHT 60

e. Your screen should now look like the following...

f.g. Boolean Operations - Addition

We now want to add these five discrete areas together to form one area.

To perform the Boolean operation, from the Preprocessor menu select:

Modeling > Operate > Booleans > Add > Areas

In the 'Add Areas' window, click on 'Pick All'

(Alternatively, the command line code for the above step is AADD,ALL)

You should now have the following model:

h. Create the Bolt Holes

We now want to remove the bolt holes from this plate.

Create the three circles with the parameters given below:

parameter circle 1 circle 2 circle 3

WP X 80 0 0

WP Y 50 20 80

radius 30 10 10

Now select

Preprocessor > Modeling > Operate > Booleans > Subtract > Areas

Select the base areas from which to subract (the large plate that was created)

Next select the three circles that we just created. Click on the three circles that you just created and click 'OK'.

(Alternatively, the command line code for the above step is ASBA,6,ALL)

Now you should have the following:

3. Define the Type of Element

As in the verification model, PLANE82 will be used for this example

o Preprocessor > Element Type > Add/Edit/Delete o Use the 'Options...' button to get a plane stress element with thickness

(Alternatively, the command line code for the above step is ET,1,PLANE82 followed by KEYOPT,1,3,3)

o Under the Extra Element Output K5 select nodal stress. 2. Define Geometric Contants

o Preprocessor > Real Constants > Add/Edit/Delete o Enter a thickness of 20mm.

(Alternatively, the command line code for the above step is R,1,20)

3. Element Material Properties

o Preprocessor > Material Props > Material Library > Structural > Linear > Elastic > Isotropic

We are going to give the properties of Steel. Enter the following when prompted:

EX 200000PRXY 0.3

(The command line code for the above step is MP,EX,1,200000 followed by MP,PRXY,1,0.3)

4. Mesh Size o Preprocessor > Meshing > Size Cntrls > Manual Size > Areas > All Areas o Select an element edge length of 5. Again, we will need to make sure the model

has converged.

(Alternatively, the command line code for the above step is AESIZE,ALL,5,)

5. Mesh o Preprocessor > Meshing > Mesh > Areas > Free and select the area when

prompted

(Alternatively, the command line code for the above step is AMESH,ALL)

6.

7. Saving Your JobUtility Menu > File > Save as...

Solution Phase: Assigning Loads and Solving

You have now defined your model. It is now time to apply the load(s) and constraint(s) and solve the the resulting system of equations.

1. Define Analysis Type o 'Solution' > 'New Analysis' and select 'Static'.

(Alternatively, the command line code for the above step is ANTYPE,0)

2. Apply Constraints

As illustrated, the plate is fixed at both of the smaller holes on the left hand side.

o Solution > Define Loads > Apply > Structural > Displacement > On Nodes o Instead of selecting one node at a time, you have the option of creating a box,

polygon, or circle of which all the nodes in that area will be selected. For this case, select 'circle' as shown in the window below. (You may want to zoom in to select the points Utilty Menu / PlotCtrls / Pan, Zoom, Rotate...) Click at the center of the bolt hole and drag the circle out so that it touches all of the nodes on the border of the hole.

o Click on 'Apply' in the 'Apply U,ROT on Lines' window and constrain all DOF's in the 'Apply U,ROT on Nodes' window.

o Repeat for the second bolt hole. 3. Apply Loads

As shown in the diagram, there is a single vertical load of 1000N, at the bottom of the large bolt hole. Apply this force to the respective keypoint ( Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints Select a force in the y direction of -1000)

The applied loads and constraints should now appear as shown below.

4. Solving the System

Solution > Solve > Current LS

Post-Processing: Viewing the Results

We are now ready to view the results. We will take a look at the deflected shape and the stress contours once we determine convergence has occured.

1. Convergence using ANSYS

As shown previously, it is necessary to prove that the solution has converged. Reduce the mesh size until there is no longer a sizeable change in your convergence criteria.

2. Deformation o General Postproc > Plot Results > Def + undeformed to view both the

deformed and the undeformed object.

The graphic should be similar to the following

o Observe the locations of deflection. Ensure that the deflection at the bolt hole is indeed 0.

3. Deflection o To plot the nodal deflections use General Postproc > Plot Results > Contour

Plot > Nodal Solution then select DOF Solution - USUM in the window.

o Alternatively, obtain these results as a list. (General Postproc > List Results > Nodal Solution...)

o Are these results what you expected? Note that all translational degrees of freedom were constrained to zero at the bolt holes.

4. Stresses o General Postproc > Plot Results > Nodal Solution... Then select von Mises

Stress in the window.

o You can list the von Mises stresses to verify the results at certain nodes

General Postproc > List Results. Select Stress, Principals SPRIN

.

Effect of Self Weight on a Cantilever Beam

Introduction

This tutorial was completed using ANSYS 7.0 The purpose of the tutorial is to show the required steps to account for the weight of an object in ANSYS.

Loads will not be applied to the beam shown below in order to observe the deflection caused by the weight of the beam itself. The beam is to be made of steel with a modulus of elasticity of 200 GPa.

Preprocessing: Defining the Problem

1. Give example a Title

Utility Menu > File > Change Title .../title, Effects of Self Weight for a Cantilever Beam

2. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

3. Define Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CS...K,#,x,y,z

We are going to define 2 keypoints for this beam as given in the following table:

Keypoint Coordinates (x,y,z)

1 (0,0)

2 (1000,0)

4. Create Lines

Preprocessor > Modeling > Create > Lines > Lines > In Active CoordL,1,2

Create a line joining Keypoints 1 and 2

5. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the BEAM3 (Beam 2D elastic) element. This element has 3 degrees of freedom (translation along the X and Y axes, and rotation about the Z axis).

6. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for BEAM3' window, enter the following geometric properties:

i. Cross-sectional area AREA: 500 ii. Area moment of inertia IZZ: 4166.67

iii. Total beam height: 10

This defines a beam with a height of 10 mm and a width of 50 mm.

7. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200000 ii. Poisson's Ratio PRXY: 0.3

8. Define Element Density

Preprocessor > Material Props > Material Models > Structural > Linear > Density

In the window that appears, enter the following density for steel:

i. Density DENS: 7.86e-6 9. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines...

For this example we will use an element edge length of 100mm.

10. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > StaticANTYPE,0

2. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix keypoint 1 (ie all DOF constrained)

3. Define Gravity

It is necessary to define the direction and magnitude of gravity for this problem.

o Select Solution > Define Loads > Apply > Structural > Inertia > Gravity...

o The following window will appear. Fill it in as shown to define an acceleration of 9.81m/s2 in the y direction.

Note: Acceleration is defined in terms of meters (not 'mm' as used throughout the problem). This is because the units of acceleration and mass must be consistent to give the product of force units (Newtons in this case). Also note that a positive acceleration in the y direction stimulates gravity in the negative Y direction.

There should now be a red arrow pointing in the positive y direction. This indicates that an acceleration has been defined in the y direction.DK,1,ALL,0,ACEL,,9.8

The applied loads and constraints should now appear as shown in the figure below.

4. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Hand Calculations

Hand calculations were performed to verify the solution found using ANSYS:

The maximum deflection was shown to be 5.777mm

2. Show the deformation of the beam

General Postproc > Plot Results > Deformed Shape ... > Def + undef edgePLDISP,2

As observed in the upper left hand corner, the maximum displacement was found to be 5.777mm. This is in agreement with the theortical value.

Application of Distributed Loads

Introduction

This tutorial was completed using ANSYS 7.0. The purpose of this tutorial is to explain how to apply distributed loads and use element tables to extract data. Please note that this material was also covered in the 'Bicycle Space Frame' tutorial under 'Basic Tutorials'.

A distributed load of 1000 N/m (1 N/mm) will be applied to a solid steel beam with a rectangular cross section as shown in the figure below. The cross-section of the beam is 10mm x 10mm while the modulus of elasticity of the steel is 200GPa.

Preprocessing: Defining the Problem

1. Open preprocessor menu

/PREP7

2. Give example a Title

Utility Menu > File > Change Title .../title, Distributed Loading

3. Create Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CSK,#,x,y

We are going to define 2 keypoints (the beam vertices) for this structure as given in the following table:

Keypoint Coordinates (x,y)

1 (0,0)

2 (1000,0)

4. Define Lines

Preprocessor > Modeling > Create > Lines > Lines > Straight LineL,K#,K#

Create a line between Keypoint 1 and Keypoint 2.

5. Define Element Types

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the BEAM3 element. This element has 3 degrees of freedom (translation along the X and Y axis's, and rotation about the Z axis). With only 3 degrees of freedom, the BEAM3 element can only be used in 2D analysis.

6. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for BEAM3' window, enter the following geometric properties:

i. Cross-sectional area AREA: 100 ii. Area Moment of Inertia IZZ: 833.333

iii. Total beam height HEIGHT: 10

This defines an element with a solid rectangular cross section 10mm x 10mm.

7. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200000 ii. Poisson's Ratio PRXY: 0.3

8. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines...

For this example we will use an element length of 100mm.

9. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'

10. Plot Elements

Utility Menu > Plot > Elements

You may also wish to turn on element numbering and turn off keypoint numbering

Utility Menu > PlotCtrls > Numbering ...

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > StaticANTYPE,0

2. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Pin Keypoint 1 (ie UX and UY constrained) and fix Keypoint 2 in the y direction (UY constrained).

3. Apply Loads

We will apply a distributed load, of 1000 N/m or 1 N/mm, over the entire length of the beam.

o Select Solution > Define Loads > Apply > Structural > Pressure > On Beams

o Click 'Pick All' in the 'Apply F/M' window. o As shown in the following figure, enter a value of 1 in the field 'VALI

Pressure value at node I' then click 'OK'.

The applied loads and constraints should now appear as shown in the figure below.

Note:

To have the constraints and loads appear each time you select 'Replot' you must change some settings. Select Utility Menu > PlotCtrls > Symbols.... In the window that appears, select 'Pressures' in the pull down menu of the 'Surface Load Symbols' section.

4. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Plot Deformed Shape

General Postproc > Plot Results > Deformed ShapePLDISP.2

2. Plot Principle stress distribution

As shown previously, we need to use element tables to obtain principle stresses for line elements.

1. Select General Postproc > Element Table > Define Table 2. Click 'Add...' 3. In the window that appears

a. enter 'SMAXI' in the 'User Label for Item' section b. In the first window in the 'Results Data Item' section scroll down

and select 'By sequence num' c. In the second window of the same section, select 'NMISC, ' d. In the third window enter '1' anywhere after the comma

4. click 'Apply' 5. Repeat steps 2 to 4 but change 'SMAXI' to 'SMAXJ' in step 3a and change

'1' to '3' in step 3d. 6. Click 'OK'. The 'Element Table Data' window should now have two

variables in it. 7. Click 'Close' in the 'Element Table Data' window. 8. Select: General Postproc > Plot Results > Line Elem Res... 9. Select 'SMAXI' from the 'LabI' pull down menu and 'SMAXJ' from the

'LabJ' pull down menu

Note:

o ANSYS can only calculate the stress at a single location on the element. For this example, we decided to extract the stresses from the I and J nodes of each element. These are the nodes that are at the ends of each element.

o For this problem, we wanted the principal stresses for the elements. For the BEAM3 element this is categorized as NMISC, 1 for the 'I' nodes and NMISC, 3 for the 'J' nodes. A list of available codes for each element can be found in the ANSYS help files. (ie. type help BEAM3 in the ANSYS Input window).

As shown in the plot below, the maximum stress occurs in the middle of the beam with a value of 750 MPa.

NonLinear Analysis of a Cantilever Beam

Introduction

This tutorial was created using ANSYS 7.0 The purpose of this tutorial is to outline the steps required to do a simple nonlinear analysis of the beam shown below.

There are several causes for nonlinear behaviour such as Changing Status (ex. contact

elements), Material Nonlinearities and Geometric Nonlinearities (change in response due to large deformations). This tutorial will deal specifically with Geometric Nonlinearities .

To solve this problem, the load will added incrementally. After each increment, the stiffness matrix will be adjusted before increasing the load.

The solution will be compared to the equivalent solution using a linear response.

Preprocessing: Defining the Problem

1. Give example a Title

Utility Menu > File > Change Title ...

2. Create Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CS

We are going to define 2 keypoints (the beam vertices) for this structure to create a beam with a length of 5 inches:

Keypoint Coordinates (x,y)

1 (0,0)

2 (5,0)

3. Define Lines

Preprocessor > Modeling > Create > Lines > Lines > Straight Line

Create a line between Keypoint 1 and Keypoint 2.

4. Define Element Types

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the BEAM3 (Beam 2D elastic) element. This element has 3 degrees of freedom (translation along the X and Y axis's, and rotation about the Z axis). With only 3 degrees of freedom, the BEAM3 element can only be used in 2D analysis.

5. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for BEAM3' window, enter the following geometric properties:

i. Cross-sectional area AREA: 0.03125 ii. Area Moment of Inertia IZZ: 4.069e-5

iii. Total beam height HEIGHT: 0.125

This defines an element with a solid rectangular cross section 0.25 x 0.125 inches.

6. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 30e6 ii. Poisson's Ratio PRXY: 0.3

If you are wondering why a 'Linear' model was chosen when this is a non-linear example, it is because this example is for non-linear geometry, not non-linear material properties. If we were considering a block of wood, for example, we would have to consider non-linear material properties.

7. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines...

For this example we will specify an element edge length of 0.1 " (50 element divisions along the line).

8. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'LMESH,ALL

Solution: Assigning Loads and Solving

1. Define Analysis Type

Solution > New Analysis > StaticANTYPE,0

2. Set Solution Controls o Select Solution > Analysis Type > Sol'n Control...

The following image will appear:

Ensure the following selections are made (as shown above)

A. Ensure Large Static Displacements are permitted (this will include the effects of large deflection in the results)

B. Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails.

C. Enter 5 as the number of substeps. This will set the initial substep to 1/5 th of the total load.

The following example explains this: Assume that the applied load is 100 lb*in. If the Automatic Time Stepping was off, there would be 5 load steps (each increasing by 1/5 th of the total load):

20 lb*in 40 lb*in 60 lb*in 80 lb*in 100 lb*in

Now, with the Automatic Time Stepping is on, the first step size will still be 20 lb*in. However, the remaining substeps will be determined based on the response of the material due to the previous load increment.

D. Enter a maximum number of substeps of 1000. This stops the program if the solution does not converge after 1000 steps.

E. Enter a minimum number of substeps of 1. F. Ensure all solution items are writen to a results file.

NOTEThere are several options which have not been changed from their default values. For more information about these commands, type help followed by the command into the command line.

Function Command Comments

Load Step KBC Loads are either linearly interpolated (ramped) from the one substep to another (ie - the load will increase from 10 lbs to 20 lbs in a linear fashion) or they are step functions (ie. the load steps directly from 10 lbs to 20 lbs). By default, the load is ramped. You may wish to use the stepped loading for rate-dependent behaviour or transient load steps.

Output OUTRES This command controls the solution data written to the database. By default, all of the solution items are written at the end of each load step. You may select only a specific iten (ie Nodal DOF solution) to decrease processing time.

Stress Stiffness SSTIF This command activates stress stiffness effects in nonlinear analyses. When large static deformations are permitted (as they are in this case), stress stiffening is automatically included. For some special nonlinear cases, this can cause divergence because some elements do not provide a complete consistent tangent.

Newton Raphson NROPT By default, the program will automatically choose the Newton-Raphson options. Options include the full Newton-Raphson, the modified Newton-Raphson, the previously computed matrix, and the full Newton-

Raphson with unsymmetric matrices of elements.

Convergence Values CNVTOL By default, the program checks the out-of-balance load for any active DOF.

3. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix Keypoint 1 (ie all DOFs constrained).

4. Apply Loads

Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints

Place a -100 lb*in moment in the MZ direction at the right end of the beam (Keypoint 2)

5. Solve the System

Solution > Solve > Current LSSOLVE

The following will appear on your screan for NonLinear Analyses

This shows the convergence of the solution.

General Postprocessing: Viewing the Results

1. View the deformed shape

General Postproc > Plot Results > Deformed Shape... > Def + undeformedPLDISP,1

2. View the deflection contour plot

General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF solution, UYPLNSOL,U,Y,0,1

3. List Horizontal Displacement

If this example is performed as a linear model there will be no nodal deflection in the horizontal direction due to the small deflections assumptions. However, this is not realistic for large deflections. Modeling the system non-linearly, these horizontal deflections are calculated by ANSYS.General Postproc > List Results > Nodal Solution...> DOF solution, UX

Other results can be obtained as shown in previous linear static analyses.

Buckling

Introduction

This tutorial was created using ANSYS 7.0 to solve a simple buckling problem.

It is recommended that you complete the NonLinear Tutorial prior to beginning this tutorial

Buckling loads are critical loads where certain types of structures become unstable. Each load has an associated buckled mode shape; this is the shape that the structure assumes in a buckled condition. There are two primary means to perform a buckling analysis:

1. Eigenvalue

Eigenvalue buckling analysis predicts the theoretical buckling strength of an ideal elastic structure. It computes the structural eigenvalues for the given system loading and constraints. This is known as classical Euler buckling analysis. Buckling loads for several configurations are readily available from tabulated solutions. However, in real-life, structural imperfections and nonlinearities prevent most real-world structures from reaching their eigenvalue predicted buckling strength; ie. it over-predicts the expected buckling loads. This method is not recommended for accurate, real-world buckling prediction analysis.

2. Nonlinear

Nonlinear buckling analysis is more accurate than eigenvalue analysis because it employs non-linear, large-deflection, static analysis to predict buckling loads. Its mode of operation is very simple: it gradually increases the applied load until a load level is found whereby the structure becomes unstable (ie. suddenly a very small increase in the load will cause very large deflections). The true non-linear nature of this analysis thus permits the modeling of geometric imperfections, load perterbations, material nonlinearities and gaps. For this type of analysis, note that small off-axis loads are necessary to initiate the desired buckling mode.

This tutorial will use a steel beam with a 10 mm X 10 mm cross section, rigidly constrained at the bottom. The required load to cause buckling, applied at the top-center of the beam, will be calculated.

Eigenvalue Buckling Analysis

Preprocessing: Defining the Problem

1. Open preprocessor menu

/PREP7

2. Give example a Title

Utility Menu > File > Change Title .../title,Eigen-Value Buckling Analysis

3. Define Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CS ...K,#,X,Y

We are going to define 2 Keypoints for this beam as given in the following table:

Keypoints Coordinates (x,y)

1 (0,0)

2 (0,100)

4. Create Lines

Preprocessor > Modeling > Create > Lines > Lines > In Active CoordL,1,2

Create a line joining Keypoints 1 and 2

5. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the BEAM3 (Beam 2D elastic) element. This element has 3 degrees of freedom (translation along the X and Y axes, and rotation about the Z axis).

6. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for BEAM3' window, enter the following geometric properties:

i. Cross-sectional area AREA: 100 ii. Area moment of inertia IZZ: 833.333

iii. Total Beam Height HEIGHT: 10

This defines a beam with a height of 10 mm and a width of 10 mm.

7. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200000 ii. Poisson's Ratio PRXY: 0.3

8. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines...

For this example we will specify an element edge length of 10 mm (10 element divisions along the line).

9. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'LMESH,ALL

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > StaticANTYPE,0

2. Activate prestress effects

To perform an eigenvalue buckling analysis, prestress effects must be activated.

o You must first ensure that you are looking at the unabridged solution menu so that you can select Analysis Options in the Analysis Type submenu. The last option in the solution menu will either be 'Unabridged menu' (which means you are currently looking at the abridged version) or 'Abriged Menu' (which means you are looking at the unabridged menu). If you are looking at the abridged menu, select the unabridged version.

o Select Solution > Analysis Type > Analysis Options o In the following window, change the [SSTIF][PSTRES] item to 'Prestress

ON', which ensures the stress stiffness matrix is calculated. This is required in eigenvalue buckling analysis.

3. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix Keypoint 1 (ie all DOF constrained).

4. Apply Loads

Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints

The eignenvalue solver uses a unit force to determine the necessary buckling load. Applying a load other than 1 will scale the answer by a factor of the load.

Apply a vertical (FY) point load of -1 N to the top of the beam (keypoint 2).

The applied loads and constraints should now appear as shown in the figure below.

5. Solve the System

Solution > Solve > Current LSSOLVE

6. Exit the Solution processor

Close the solution menu and click FINISH at the bottom of the Main Menu.FINISH

Normally at this point you enter the postprocessing phase. However, with a buckling analysis you must re-enter the solution phase and specify the buckling analysis. Be sure to close the solution menu and re-enter it or the buckling analysis may not function properly.

7. Define Analysis Type

Solution > Analysis Type > New Analysis > Eigen BucklingANTYPE,1

8. Specify Buckling Analysis Options o Select Solution > Analysis Type > Analysis Options o Complete the window which appears, as shown below. Select 'Block

Lanczos' as an extraction method and extract 1 mode. The 'Block Lanczos' method is used for large symmetric eigenvalue problems and uses the sparse matrix solver. The 'Subspace' method could also be used, however

it tends to converge slower as it is a more robust solver. In more complex analyses the Block Lanczos method may not be adequate and the Subspace method would have to be used.

9. Solve the System

Solution > Solve > Current LSSOLVE

10. Exit the Solution processor

Close the solution menu and click FINISH at the bottom of the Main Menu.FINISH

Again it is necessary to exit and re-enter the solution phase. This time, however, is for an expansion pass. An expansion pass is necessary if you want to review the buckled mode shape(s).

11. Expand the solution o Select Solution > Analysis Type > Expansion Pass... and ensure that it is

on. You may have to select the 'Unabridged Menu' again to make this option visible.

o Select Solution > Load Step Opts > ExpansionPass > Single Expand > Expand Modes ...

o Complete the following window as shown to expand the first mode

12. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. View the Buckling Load

To display the minimum load required to buckle the beam select General Postproc > List Results > Detailed Summary. The value listed under 'TIME/FREQ' is the load (41,123), which is in Newtons for this example. If more than one mode was selected in the steps above, the corresponding loads would be listed here as well./POST1SET,LIST

2. Display the Mode Shape o Select General Postproc > Read Results > Last Set to bring up the data

for the last mode calculated. o Select General Postproc > Plot Results > Deformed Shape

Non-Linear Buckling Analysis

Ensure that you have completed the NonLinear Tutorial prior to beginning this portion of the tutorial

Preprocessing: Defining the Problem

1. Open preprocessor menu

/PREP7

2. Give example a Title

Utility Menu > File > Change Title .../TITLE, Nonlinear Buckling Analysis

3. Create Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CSK,#,X,Y

We are going to define 2 keypoints (the beam vertices) for this structure to create a beam with a length of 100 millimeters:

Keypoint Coordinates (x,y)

1 (0,0)

2 (0,100)

4. Define Lines

Preprocessor > Modeling > Create > Lines > Lines > Straight Line

Create a line between Keypoint 1 and Keypoint 2.L,1,2

5. Define Element Types

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the BEAM3 (Beam 2D elastic) element. This element has 3 degrees of freedom (translation along the X and Y axis's, and rotation about the Z axis). With only 3 degrees of freedom, the BEAM3 element can only be used in 2D analysis.

6. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for BEAM3' window, enter the following geometric properties:

i. Cross-sectional area AREA: 100 ii. Area Moment of Inertia IZZ: 833.333

iii. Total beam height HEIGHT: 10

This defines an element with a solid rectangular cross section 10 x 10 millimeters.

7. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200e3 ii. Poisson's Ratio PRXY: 0.3

8. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > Lines > All Lines...

For this example we will specify an element edge length of 1 mm (100 element divisions along the line).ESIZE,1

9. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'LMESH,ALL

Solution: Assigning Loads and Solving

1. Define Analysis Type

Solution > New Analysis > StaticANTYPE,0

2. Set Solution Controls o Select Solution > Analysis Type > Sol'n Control...

The following image will appear:

Ensure the following selections are made under the 'Basic' tab (as shown above)

A. Ensure Large Static Displacements are permitted (this will include the effects of large deflection in the results)

B. Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails.

C. Enter 20 as the number of substeps. This will set the initial substep to 1/20 th of the total load.

D. Enter a maximum number of substeps of 1000. This stops the program if the solution does not converge after 1000 steps.

E. Enter a minimum number of substeps of 1. F. Ensure all solution items are writen to a results file.

Ensure the following selection is made under the 'Nonlinear' tab (as shown below)

G. Ensure Line Search is 'On'. This option is used to help the Newton-Raphson solver converge.

H. Ensure Maximum Number of Iterations is set to 1000

NOTEThere are several options which have not been changed from their default values. For more information about these commands, type help followed by the command into the command line.

3. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix Keypoint 1 (ie all DOFs constrained).

4. Apply Loads

Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints

Place a -50,000 N load in the FY direction on the top of the beam (Keypoint 2). Also apply a -250 N load in the FX direction on Keypoint 2. This horizontal load will persuade the beam to buckle at the minimum buckling load.

The model should now look like the window shown below.

5. Solve the System

Solution > Solve > Current LSSOLVE

The following will appear on your screen for NonLinear Analyses

This shows the convergence of the solution.

General Postprocessing: Viewing the Results

1. View the deformed shape o To view the element in 2D rather than a line: Utility Menu > PlotCtrls >

Style > Size and Shape and turn 'Display of element' ON (as shown below).

o General Postproc > Plot Results > Deformed Shape... > Def + undeformedPLDISP,1

o View the deflection contour plot

General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF solution, UYPLNSOL,U,Y,0,1

Other results can be obtained as shown in previous linear static analyses.

Time History Postprocessing: Viewing the Results

As shown, you can obtain the results (such as deflection, stress and bending moment diagrams) the same way you did in previous examples using the General Postprocessor. However, you may wish to view time history results such as the deflection of the object over time.

1. Define Variables o Select: Main Menu > TimeHist Postpro. The following window should

open automatically.

If it does not open automatically, select Main Menu > TimeHist Postpro > Variable Viewer

o Click the add button in the upper left corner of the window to add a variable.

o Double-click Nodal Solution > DOF Solution > Y-Component of displacement (as shown below) and click OK. Pick the uppermost node on the beam and click OK in the 'Node for Data' window.

o To add another variable, click the add button again. This time select Reaction Forces > Structural Forces > Y-Component of Force. Pick the lowermost node on the beam and click OK.

o On the Time History Variable window, click the circle in the 'X-Axis' column for FY_3. This will make the reaction force the x-variable. The Time History Variables window should now look like this:

2. Graph Results over Time o Click on UY_2 in the Time History Variables window.

o Click the graphing button in the Time History Variables window.

o The labels on the plot are not updated by ANSYS, so you must change them manually. Select Utility Menu > Plot Ctrls > Style > Graphs > Modify Axes and re-label the X and Y-axis appropriately.

The plot shows how the beam became unstable and buckled with a load of approximately 40,000 N, the point where a large deflection occured due to a small increase in force. This is slightly less than the eigen-value solution of 41,123 N, which was expected due to non-linear geometry issues discussed above.

NonLinear Materials

Introduction

This tutorial was completed using ANSYS 7.0 The purpose of the tutorial is to describe how to include material nonlinearities in an ANSYS model. For instance, the case when a large force is applied resulting in a stresses greater than yield strength. In such a case, a multilinear stress-strain relationship can be included which follows the stress-strain curve of the material being used. This will allow ANSYS to more accurately model the plastic deformation of the material.

For this analysis, a simple tension speciment 100 mm X 5 mm X 5 mm is constrained at the bottom and has a load pulling on the top. This specimen is made out of a experimental substance called "WhoKilledKenium". The stress-strain curve for the substance is shown above. Note the linear section up to approximately 225 MPa where the Young's Modulus is constant (75 GPa). The material then begins to yield and the relationship becomes plastic and nonlinear.

Preprocessing: Defining the Problem

1. Give example a Title

Utility Menu > File > Change Title .../title, NonLinear Materials

2. Create Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CS/PREP7K,#,X,Y

We are going to define 2 keypoints (the beam vertices) for this structure to create a beam with a length of 100 millimeters:

Keypoint Coordinates (x,y)

1 (0,0)

2 (0,100)

3. Define Lines

Preprocessor > Modeling > Create > Lines > Lines > Straight Line

Create a line between Keypoint 1 and Keypoint 2.L,1,2

4. Define Element Types

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the LINK1 (2D spar) element. This element has 2 degrees of freedom (translation along the X and Y axis's) and can only be used in 2D analysis.

5. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for LINK1' window, enter the following geometric properties:

i. Cross-sectional area AREA: 25 ii. Initial Strain: 0

This defines an element with a solid rectangular cross section 5 x 5 millimeters.

6. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 75e3 ii. Poisson's Ratio PRXY: 0.3

Now that the initial properties of the material have been outlined, the stress-strain data must be included.

Preprocessor > Material Props > Material Models > Structural > Nonlinear > Elastic > Multilinear ElasticThe following window will pop up.

Fill in the STRAIN and STRESS boxes with the following data. These are points from the stress-strain curve shown above, approximating the curve with linear interpolation between the points. When the data for the first point is input, click Add Point to add another. When all the points have been inputed, click Graph to see the curve. It should look like the one shown above. Then click OK.

Curve Points

Strain Stress

1 0 0

2 0.001 75

3 0.002 150

4 0.003 225

5 0.004 240

6 0.005 250

7 0.025 300

8 0.060 355

9 0.100 390

10 0.150 420

11 0.200 435

12 0.250 449

13 0.275 450

To get the problem geometry back, select Utility Menu > Plot > Replot./REPLOT

7. Define Mesh Size

Preprocessor > Meshing > Manual Size > Size Cntrls > Lines > All Lines...

For this example we will specify an element edge length of 5 mm (20 element divisions along the line).

8. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'LMESH,ALL

Solution: Assigning Loads and Solving

1. Define Analysis Type

Solution > New Analysis > StaticANTYPE,0

2. Set Solution Controls o Select Solution > Analysis Type > Sol'n Control...

The following image will appear:

Ensure the following selections are made under the 'Basic' tab (as shown above)

A. Ensure Large Static Displacements are permitted (this will include the effects of large deflection in the results)

B. Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails.

C. Enter 20 as the number of substeps. This will set the initial substep to 1/20 th of the total load.

D. Enter a maximum number of substeps of 1000. This stops the program if the solution does not converge after 1000 steps.

E. Enter a minimum number of substeps of 1. F. Ensure all solution items are writen to a results file. This means

rather than just recording the data for the last load step, data for every load step is written to the database. Therefore, you can plot certain parameters over time.

Ensure the following selection is made under the 'Nonlinear' tab (as shown below)

G. Ensure Line Search is 'On'. This option is used to help the Newton-Raphson solver converge.

H. Ensure Maximum Number of Iterations is set to 1000

NOTEThere are several options which have not been changed from their default values. For more information about these commands, type help followed by the command into the command line.

3. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix Keypoint 1 (ie all DOFs constrained).

4. Apply Loads

Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints

Place a 10,000 N load in the FY direction on the top of the beam (Keypoint 2).

5. Solve the System

Solution > Solve > Current LSSOLVE

The following will appear on your screen for NonLinear Analyses

This shows the convergence of the solution.

General Postprocessing: Viewing the Results

1. To view the element in 2D rather than a line: Utility Menu > PlotCtrls > Style > Size and Shape and turn 'Display of element' ON (as shown below).

2. View the deflection contour plot

General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF solution, UYPLNSOL,U,Y,0,1

Other results can be obtained as shown in previous linear static analyses.

Time History Postprocessing: Viewing the Results

As shown, you can obtain the results (such as deflection, stress and bending moment diagrams) the same way you did in previous examples using the General Postprocessor. However, you may wish to view time history results such as the deflection of the object over time.

1. Define Variables o Select: Main Menu > TimeHist Postpro. The following window should

open automatically.

If it does not open automatically, select Main Menu > TimeHist Postpro > Variable Viewer

o Click the add button in the upper left corner of the window to add a variable.

o Select Nodal Solution > DOF Solution > Y-Component of displacement (as shown below) and click OK. Pick the uppermost node on the beam and click OK in the 'Node for Data' window.

o To add another variable, click the add button again. This time select Reaction Forces > Structural Forces > Y-Component of Force. Pick the lowermost node on the beam and click OK.

o On the Time History Variable window, click the circle in the 'X-Axis' column for FY_3. This will make the reaction force the x-variable. The Time History Variables window should now look like this:

2. Graph Results over Time o Click on UY_2 in the Time History Variables window.

o Click the graphing button in the Time History Variables window. o The labels on the plot are not updated by ANSYS, so you must change

them manually. Select Utility Menu > Plot Ctrls > Style > Graphs > Modify Axes and re-label the X and Y-axis appropriately.

This plot shows how the beam deflected linearly when the force, and subsequently the stress, was low (in the linear range). However, as the force increased, the deflection (proportional to strain) began to increase at a greater rate. This is because the stress in the beam is in the plastic range and thus no longer relates to strain linearly. When you verify this example analytically, you will see the solutions are very similar. The difference can be attributed to the ANSYS solver including large deflection calculations.

Modal Analysis of a Cantilever Beam

Introduction

This tutorial was created using ANSYS 7.0 The purpose of this tutorial is to outline the steps required to do a simple modal analysis of the cantilever beam shown below.

Preprocessing: Defining the Problem

The simple cantilever beam is used in all of the Dynamic Analysis Tutorials. If you haven't created the model in ANSYS, please use the links below. Both the command line

codes and the GUI commands are shown in the respective links.

Solution: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > ModalANTYPE,2

2. Set options for analysis type: o Select: Solution > Analysis Type > Analysis Options..

The following window will appear

o As shown, select the Subspace method and enter 5 in the 'No. of modes to extract'

o Check the box beside 'Expand mode shapes' and enter 5 in the 'No. of modes to expand'

o Click 'OK'

Note that the default mode extraction method chosen is the Reduced Method. This is the fastest method as it reduces the system matrices to only consider the Master Degrees of Freedom (see below). The Subspace Method extracts modes for all DOF's. It is therefore more exact but, it also takes longer to compute (especially when the complex geometries).

o The following window will then appear

For a better understanding of these options see the Commands manual.

o For this problem, we will use the default options so click on OK. 3. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix Keypoint 1 (ie all DOFs constrained).

4. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Verify extracted modes against theoretical predictions o Select: General Postproc > Results Summary...

The following window will appear

The following table compares the mode frequencies in Hz predicted by theory and ANSYS.

Mode Theory ANSYS Percent Error

1 8.311 8.300 0.1

2 51.94 52.01 0.2

3 145.68 145.64 0.0

4 285.69 285.51 0.0

5 472.22 472.54 0.1

Note: To obtain accurate higher mode frequencies, this mesh would have to be refined even more (i.e. instead of 10 elements, we would have to model the cantilever using 15 or more elements depending upon the highest mode frequency of interest).

2. View Mode Shapes o Select: General Postproc > Read Results > First Set

This selects the results for the first mode shape

o Select General Postproc > Plot Results > Deformed shape . Select 'Def + undef edge'

The first mode shape will now appear in the graphics window.

o To view the next mode shape, select General Postproc > Read Results > Next Set . As above choose General Postproc > Plot Results > Deformed shape . Select 'Def + undef edge'.

o The first four mode shapes should look like the following:

3. Animate Mode Shapes o Select Utility Menu (Menu at the top) > Plot Ctrls > Animate > Mode

Shape

The following window will appear

o Keep the default setting and click 'OK' o The animated mode shapes are shown below.

Mode 1

Mode 2

Mode 3

Mode 4

Using the Reduced Method for Modal Analysis

This method employs the use of Master Degrees of Freedom. These are degrees of freedom that govern the dynamic characteristics of a structure. For example, the Master Degrees of Freedom for the bending modes of cantilever beam are

For this option, a detailed understanding of the dynamic behavior of a structure is required. However, going this route means a smaller (reduced) stiffness matrix, and thus faster calculations.

The steps for using this option are quite simple.

• Instead of specifying the Subspace method, select the Reduced method and specify 5 modes for extraction.

• Complete the window as shown below

Note:For this example both the number of modes and frequency range was specified. ANSYS then extracts the minimum number of modes between the two.

• Select Solution > Master DOF > User Selected > Define • When prompted, select all nodes except the left most node (fixed).

The following window will appear:

• Select UY as the 1st degree of freedom (shown above).

The same constraints are used as above.

The following table compares the mode frequencies in Hz predicted by theory and ANSYS (Reduced).

Mode Theory ANSYS Percent Error

1 8.311 8.300 0.1

2 51.94 52.01 0.1

3 145.68 145.66 0.0

4 285.69 285.71 0.0

5 472.22 473.66 0.3

As you can see, the error does not change significantly. However, for more complex structures, larger errors would be expected using the reduced method.

Harmonic Analysis of a Cantilever Beam

Introduction

This tutorial was created using ANSYS 7.0 The purpose of this tutorial is to explain the steps required to perform Harmonic analysis the cantilever beam shown below.

We will now conduct a harmonic forced response test by applying a cyclic load (harmonic) at the end of the beam. The frequency of the load will be varied from 1 - 100 Hz. The figure below depicts the beam with the application of the load.

ANSYS provides 3 methods for conducting a harmonic analysis. These 3 methods are the Full , Reduced and Modal Superposition methods.

This example demonstrates the Full method because it is simple and easy to use as compared to the other two methods. However, this method makes use of the full stiffness and mass matrices and thus is the slower and costlier option.

Preprocessing: Defining the Problem

The simple cantilever beam is used in all of the Dynamic Analysis Tutorials. If you haven't created the model in ANSYS, please use the links below. Both the command line

codes and the GUI commands are shown in the respective links.

Solution: Assigning Loads and Solving

1. Define Analysis Type (Harmonic)

Solution > Analysis Type > New Analysis > HarmonicANTYPE,3

2. Set options for analysis type: o Select: Solution > Analysis Type > Analysis Options..

The following window will appear

o As shown, select the Full Solution method, the Real + imaginary DOF printout format and do not use lumped mass approx.

o Click 'OK'

The following window will appear. Use the default settings (shown below).

3. Apply Constraints o Select Solution > Define Loads > Apply > Structural > Displacement >

On Nodes

The following window will appear once you select the node at x=0 (Note small changes in the window compared to the static examples):

o Constrain all DOF as shown in the above window 4. Apply Loads:

o Select Solution > Define Loads > Apply > Structural > Force/Moment > On Nodes

o Select the node at x=1 (far right) o The following window will appear. Fill it in as shown to apply a load with

a real value of 100 and an imaginary value of 0 in the positive 'y' direction

Note: By specifying a real and imaginary value of the load we are providing information on magnitude and phase of the load. In this case the magnitude of the load is 100 N and its phase is 0. Phase information is important when you have two or more cyclic loads being applied to the structure as these loads could be in or out of phase. For harmonic analysis, all loads applied to a structure must have the SAME FREQUENCY.

5. Set the frequency range

o Select Solution > Load Step Opts > Time/Frequency > Freq and Substps...

o As shown in the window below, specify a frequency range of 0 - 100Hz, 100 substeps and stepped b.c..

By doing this we will be subjecting the beam to loads at 1 Hz, 2 Hz, 3 Hz, ..... 100 Hz. We will specify a stepped boundary condition (KBC) as this will ensure that the same amplitude (100 N) will be applyed for each of the frequencies. The ramped option, on the other hand, would ramp up the amplitude where at 1 Hz the amplitude would be 1 N and at 100 Hz the amplitude would be 100 N.

You should now have the following in the ANSYS Graphics window

6. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

We want to observe the response at x=1 (where the load was applyed) as a function of frequency. We cannot do this with General PostProcessing (POST1), rather we must use TimeHist PostProcessing (POST26). POST26 is used to observe certain variables as a function of either time or frequency.

1. Open the TimeHist Processing (POST26) Menu

Select TimeHist Postpro from the ANSYS Main Menu.

2. Define Variables

In here we have to define variables that we want to see plotted. By default, Variable 1 is assigned either Time or Frequency. In our case it is assigned Frequency. We want to see the displacement UY at the node at x=1, which is node #2. (To get a list of nodes and their attributes, select Utility Menu > List > nodes).

o Select TimeHist Postpro > Variable Viewer... and the following window should pop up.

o Select Add (the green '+' sign in the upper left corner) from this window and the following window should appear

o We are interested in the Nodal Solution > DOF Solution > Y-Component of displacement. Click OK.

o Graphically select node 2 when prompted and click OK. The 'Time History Variables' window should now look as follows

3. List Stored Variables o In the 'Time History Variables' window click the 'List' button, 3 buttons to

the left of 'Add'

The following window will appear listing the data:

4. Plot UY vs. frequency o In the 'Time History Variables' window click the 'Plot' button, 2 buttons to

the left of 'Add'

The following graph should be plotted in the main ANSYS window.

Note that we get peaks at frequencies of approximately 8.3 and 51 Hz. This corresponds with the predicted frequencies of 8.311 and 51.94Hz.

To get a better view of the response, view the log scale of UY.

o Select Utility Menu > PlotCtrls > Style > Graphs > Modify Axis

The following window will appear

o As marked by an 'A' in the above window, change the Y-axis scale to 'Logarithmic'

o Select Utility Menu > Plot > Replot o You should now see the following

This is the response at node 2 for the cyclic load applied at this node from 0 - 100 Hz.

o For ANSYS version lower than 7.0, the 'Variable Viewer' window is not available. Use the 'Define Variables' and 'Store Data' functions under TimeHist Postpro. See the help file for instructions.

Transient Analysis of a Cantilever Beam

Introduction

This tutorial was created using ANSYS 7.0 The purpose of this tutorial is to show the steps involved to perform a simple transient analysis.

Transient dynamic analysis is a technique used to determine the dynamic response of a structure under a time-varying load.

The time frame for this type of analysis is such that inertia or damping effects of the structure are considered to be important. Cases where such effects play a major role are under step or impulse loading conditions, for example, where there is a sharp load change in a fraction of time.

If inertia effects are negligible for the loading conditions being considered, a static analysis may be used instead.

For our case, we will impact the end of the beam with an impulse force and view the response at the location of impact.

Since an ideal impulse force excites all modes of a structure, the response of the beam should contain all mode frequencies. However, we cannot produce an ideal impulse force numerically. We have to apply a load over a discrete amount of time dt.

After the application of the load, we track the response of the beam at discrete time points for as long as we like (depending on what it is that we are looking for in the response).

The size of the time step is governed by the maximum mode frequency of the structure we wish to capture. The smaller the time step, the higher the mode frequency we will capture. The rule of thumb in ANSYS is

time_step = 1 / 20f

where f is the highest mode frequency we wish to capture. In other words, we must resolve our step size such that we will have 20 discrete points per period of the highest mode frequency.

It should be noted that a transient analysis is more involved than a static or harmonic analysis. It requires a good understanding of the dynamic behavior of a

structure. Therefore, a modal analysis of the structure should be initially performed to provide information about the structure's dynamic behavior.

In ANSYS, transient dynamic analysis can be carried out using 3 methods.

• The Full Method: This is the easiest method to use. All types of non-linearities are allowed. It is however very CPU intensive to go this route as full system matrices are used.

• The Reduced Method: This method reduces the system matrices to only consider the Master Degrees of Freedom (MDOFs). Because of the reduced size of the matrices, the calculations are much quicker. However, this method handles only linear problems (such as our cantilever case).

• The Mode Superposition Method: This method requires a preliminary modal analysis, as factored mode shapes are summed to calculate the structure's response. It is the quickest of the three methods, but it requires a good deal of understanding of the problem at hand.

We will use the Reduced Method for conducting our transient analysis. Usually one need not go further than Reviewing the Reduced Results. However, if stresses and forces are of interest than, we would have to Expand the Reduced Solution.

Preprocessing: Defining the Problem

The simple cantilever beam is used in all of the Dynamic Analysis Tutorials. If you haven't created the model in ANSYS, please use the links below. Both the command line

codes and the GUI commands are shown in the respective links.

Solution: Assigning Loads and Solving

1. Define Analysis Type o Select Solution > Analysis Type > New Analysis > Transient o The following window will appear. Select 'Reduced' as shown.

2. Define Master DOFs o Select Solution > Master DOFs > User Selected > Define o Select all nodes except the left most node (at x=0).

The following window will open, choose UY as the first dof in this window

For an explanation on Master DOFs, see the section on Using the

Reduced Method for modal analysis.

3. Constrain the Beam

Solution Menu > Define Loads > Apply > Structural > Displacement > On nodes

Fix the left most node (constrain all DOFs).

4. Apply Loads

We will define our impulse load using Load Steps. The following time history curve shows our load steps and time steps. Note that for the reduced method, a constant time step is required throughout the time range.

We can define each load step (load and time at the end of load segment) and save them in a file for future solution purposes. This is highly recommended especially when we have many load steps and we wish to re-run our solution.

We can also solve for each load step after we define it. We will go ahead and save each load step in a file for later use, at the same time solve for each load step after we are done defining it.

a. Load Step 1 - Initial Conditions i. Define Load Step

We need to establish initial conditions (the condition at Time = 0). Since the equations for a transient dynamic analysis are of second order, two sets of initial conditions are required; initial displacement and initial velocity. However, both default to zero. Therefore, for this example we can skip this step.

ii. Specify Time and Time Step Options Select Solution > Load Step Opts > Time/Frequenc >

Time - Time Step .. set a time of 0 for the end of the load step (as shown

below). set [DELTIM] to 0.001. This will specify a time

step size of 0.001 seconds to be used for this load step.

iii. Write Load Step File Select Solution > Load Step Opts > Write LS File

The following window will appear

Enter LSNUM = 1 as shown above and click 'OK'

The load step will be saved in a file jobname.s01

b. Load Step 2 i. Define Load Step

Select Solution > Define Loads > Apply > Structural > Force/Moment > On Nodes and select the right most node (at x=1). Enter a force in the FY direction of value -100 N.

ii. Specify Time and Time Step Options Select Solution > Load Step Opts > Time/Frequenc >

Time - Time Step .. and set a time of 0.001 for the end of the load step

iii. Write Load Step File

Solution > Load Step Opts > Write LS File

Enter LSNUM = 2

c. Load Step 3 i. Define Load Step

Select Solution > Define Loads > Delete > Structural > Force/Moment > On Nodes and delete the load at x=1.

ii. Specify Time and Time Step Options Select Solution > Load Step Opts > Time/Frequenc >

Time - Time Step .. and set a time of 1 for the end of the load step

iii. Write Load Step File

Solution > Load Step Opts > Write LS File

Enter LSNUM = 3

2. Solve the System

o Select Solution > Solve > From LS Files

The following window will appear.

o Complete the window as shown above to solve using LS files 1 to 3.

Postprocessing: Viewing the Results

To view the response of node 2 (UY) with time we must use the TimeHist PostProcessor (POST26).

1. Define Variables

In here we have to define variables that we want to see plotted. By default, Variable 1 is assigned either Time or Frequency. In our case it is assigned Frequency. We want to see the displacement UY at the node at x=1, which is node #2. (To get a list of nodes and their attributes, select Utility Menu > List > nodes).

o Select TimeHist Postpro > Variable Viewer... and the following window should pop up.

o Select Add (the green '+' sign in the upper left corner) from this window and the following window should appear

o We are interested in the Nodal Solution > DOF Solution > Y-Component of displacement. Click OK.

o Graphically select node 2 when prompted and click OK. The 'Time History Variables' window should now look as follows

2. List Stored Variables o In the 'Time History Variables' window click the 'List' button, 3 buttons to

the left of 'Add'

The following window will appear listing the data:

3. Plot UY vs. frequency o In the 'Time History Variables' window click the 'Plot' button, 2 buttons to

the left of 'Add'

The following graph should be plotted in the main ANSYS window.

A few things to note in the response curve

There are approximately 8 cycles in one second. This is the first mode of the cantilever beam and we have been able to capture it.

We also see another response at a higher frequency. We may have captured some response at the second mode at 52 Hz of the beam.

Note that the response does not decay as it should not. We did not specify damping for our system.

Expand the Solution

For most problems, one need not go further than Reviewing the Reduced Results as the response of the structure is of utmost interest in transient dynamic analysis.

However, if stresses and forces are of interest, we would have to expand the reduced solution.

Let's say we are interested in the beam's behaviour at peak responses. We should then expand a few or all solutions around one peak (or dip). We will expand 10 solutions within the range of 0.08 and 0.11 seconds.

1. Expand the solution o Select Finish in the ANSYS Main Menu o Select Solution > Analysis Type > ExpansionPass... and switch it to ON

in the window that pops open. o Select Solution > Load Step Opts > ExpansionPass > Single Expand >

Range of Solu's o Complete the window as shown below. This will expand 10 solutions

withing the range of 0.08 and 0.11 seconds

2. Solve the System

Solution > Solve > Current LSSOLVE

3. Review the results in POST1

Review the results using either General Postprocessing (POST1) or TimeHist Postprocessing (POST26). For this case, we can view the deformed shape at each of the 10 solutions we expanded.

Damped Response of the Cantilever Beam

We did not specify damping in our transient analysis of the beam. We specify damping at the same time we specify our time & time steps for each load step.

We will now re-run our transient analysis, but now we will consider damping. Here is where the use of load step files comes in handy. We can easily change a few values in these files and re-run our whole solution from these load case files.

• Open up the first load step file (Dynamic.s01) for editing Utility Menu > File > List > Other > Dynamic.s01. The file should look like the following..

• /COM,ANSYS RELEASE 5.7.1 UP20010418 14:44:02 08/20/2001• /NOPR• /TITLE, Dynamic Analysis • _LSNUM= 1• ANTYPE, 4• TRNOPT,REDU,,DAMP• BFUNIF,TEMP,_TINY• DELTIM, 1.000000000E-03• TIME, 0.00000000• TREF, 0.00000000• ALPHAD, 0.00000000• BETAD, 0.00000000• DMPRAT, 0.00000000• TINTP,R5.0, 5.000000000E-03,,,• TINTP,R5.0, -1.00000000 , 0.500000000 , -1.00000000• NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000• ERESX,DEFA• ACEL, 0.00000000 , 0.00000000 , 0.00000000• OMEGA, 0.00000000 , 0.00000000 , 0.00000000 , 0• DOMEGA, 0.00000000 , 0.00000000 , 0.00000000• CGLOC, 0.00000000 , 0.00000000 , 0.00000000• CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000• DCGOMG, 0.00000000 , 0.00000000 , 0.00000000•• D, 1,UX , 0.00000000 , 0.00000000 • D, 1,UY , 0.00000000 , 0.00000000

• D, 1,ROTZ, 0.00000000 , 0.00000000 • /GOPR

• Change the damping value BETAD from 0 to 0.01 in all three load step files. • We will have to re-run the job for the new load step files. Select Utility Menu >

file > Clear and Start New. • Repeat the steps shown above up to the point where we select MDOFs. After

selecting MDOFs, simply go to Solution > (-Solve-) From LS files ... and in the window that opens up select files from 1 to 3 in steps of 1.

• After the results have been calculated, plot up the response at node 2 in POST26. The damped response should look like the following

Simple Conduction Example

Introduction

This tutorial was created using ANSYS 7.0 to solve a simple conduction problem.

The Simple Conduction Example is constrained as shown in the following figure. Thermal conductivity (k) of the material is 10 W/m*C and the block is assumed to be infinitely long.

Preprocessing: Defining the Problem

1. Give example a Title 2. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

3. Create geometry

Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners > X=0, Y=0, Width=1, Height=1BLC4,0,0,1,1

4. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete... > click 'Add' > Select Thermal Mass Solid, Quad 4Node 55ET,1,PLANE55

For this example, we will use PLANE55 (Thermal Solid, Quad 4node 55). This element has 4 nodes and a single DOF (temperature) at each node. PLANE55 can only be used for 2 dimensional steady-state or transient thermal analysis.

5. Element Material Properties

Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic > KXX = 10 (Thermal conductivity)MP,KXX,1,10

6. Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Areas > 0.05AESIZE,ALL,0.05

7. Mesh

Preprocessor > Meshing > Mesh > Areas > Free > Pick AllAMESH,ALL

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > Steady-StateANTYPE,0

2. Apply Constraints

For thermal problems, constraints can be in the form of Temperature, Heat Flow, Convection, Heat Flux, Heat Generation, or Radiation. In this example, all 4 sides of the block have fixed temperatures.

o Solution > Define Loads > Apply Note that all of the -Structural- options cannot be selected. This is due to the type of element (PLANE55) selected.

o Thermal > Temperature > On Nodes o Click the Box option (shown below) and draw a box around the nodes on

the top line.

The following window will appear:

o Fill the window in as shown to constrain the side to a constant temperature of 500

o Using the same method, constrain the remaining 3 sides to a constant value of 100

Orange triangles in the graphics window indicate the temperature contraints.

3. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Results Using ANSYS

Plot Temperature

General Postproc > Plot Results > Contour Plot > Nodal Solu ... > DOF solution, Temperature TEMP

Note that due to the manner in which the boundary contitions were applied, the top corners are held at a temperature of 100. Recall that the nodes on the top of the plate were constrained first, followed by the side and bottom constraints. The top corner nodes were therefore first constrained at 500C, then 'overwritten' when the side constraints were applied. Decreasing the mesh size can minimize this effect, however, one must be aware of the limitations in the results at the corners.

Thermal - Mixed Boundary Example (Conduction/Convection/Insulated)

Introduction

This tutorial was created using ANSYS 7.0 to solve simple thermal examples. Analysis of a simple conduction as well a mixed conduction/convection/insulation problem will be demonstrated.

The Mixed Convection/Conduction/Insulated Boundary Conditions Example is constrained as shown in the following figure (Note that the section is assumed to be infinitely long):

Preprocessing: Defining the Problem

1. Give example a Title 2. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

3. Create geometry

Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners > X=0, Y=0, Width=1, Height=1BLC4,0,0,1,1

4. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete... > click 'Add' > Select Thermal Mass Solid, Quad 4Node 55ET,1,PLANE55

As in the conduction example, we will use PLANE55 (Thermal Solid, Quad 4node 55). This element has 4 nodes and a single DOF (temperature) at each node. PLANE55 can only be used for 2 dimensional steady-state or transient thermal analysis.

5. Element Material Properties

Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic > KXX = 10MP,KXX,1,10

This will specify a thermal conductivity of 10 W/m*C.

6. Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Areas > 0.05AESIZE,ALL,0.05

7. Mesh

Preprocessor > Meshing > Mesh > Areas > Free > Pick AllAMESH,ALL

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > Steady-StateANTYPE,0

2. Apply Conduction Constraints

In this example, all 2 sides of the block have fixed temperatures, while convection occurs on the other 2 sides.

o Solution > Define Loads > Apply > Thermal > Temperature > On Lines

o Select the top line of the block and constrain it to a constant value of 500 C

o Using the same method, constrain the left side of the block to a constant value of 100 C

3. Apply Convection Boundary Conditions o Solution > Define Loads > Apply > Thermal > Convection > On Lines o Select the right side of the block.

The following window will appear:

o Fill in the window as shown. This will specify a convection of 10 W/m2*C and an ambient temperature of 100 degrees Celcius. Note that VALJ and

VAL2J have been left blank. This is because we have uniform convection across the line.

4. Apply Insulated Boundary Conditions o Solution > Define Loads > Apply > Thermal > Convection > On Lines o Select the bottom of the block. o Enter a constant Film coefficient (VALI) of 0. This will eliminate

convection through the side, thereby modeling an insulated wall. Note: you do not need to enter a Bulk (or ambient) temperature

You should obtain the following:

5. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Results Using ANSYS

Plot Temperature

General Postproc > Plot Results > Contour Plot > Nodal Solu ... > DOF solution, Temperature TEMP

Transient Thermal Conduction Example

Introduction

This tutorial was created using ANSYS 7.0 to solve a simple transient conduction problem. Special thanks to Jesse Arnold for the analytical solution shown at the end of the tutorial.

The example is constrained as shown in the following figure. Thermal conductivity (k) of the material is 5 W/m*K and the block is assumed to be infinitely long. Also, the density of the material is 920 kg/m^3 and the specific heat capacity (c) is 2.040 kJ/kg*K.

It is beneficial if the Thermal-Conduction tutorial is completed first to compare with this solution.

Preprocessing: Defining the Problem

1. Give example a Title

Utility Menu > File > Change Title... /Title,Transient Thermal Conduction

2. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

3. Create geometry

Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners X=0, Y=0, Width=1, Height=1BLC4,0,0,1,1

4. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete... > click 'Add' > Select Thermal Mass Solid, Quad 4Node 55ET,1,PLANE55

For this example, we will use PLANE55 (Thermal Solid, Quad 4node 55). This element has 4 nodes and a single DOF (temperature) at each node. PLANE55 can only be used for 2 dimensional steady-state or transient thermal analysis.

5. Element Material Properties

Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic > KXX = 5 (Thermal conductivity)MP,KXX,1,10

Preprocessor > Material Props > Material Models > Thermal > Specific Heat > C = 2.04MP,C,1,2.04

Preprocessor > Material Props > Material Models > Thermal > Density > DENS = 920MP,DENS,1,920

6. Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Areas > 0.05AESIZE,ALL,0.05

7. Mesh

Preprocessor > Meshing > Mesh > Areas > Free > Pick AllAMESH,ALL

At this point, the model should look like the following:

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > TransientANTYPE,4

The window shown below will pop up. We will use the defaults, so click OK.

2. Set Solution Controls

Solution > Analysis Type > Sol'n Controls

The following window will pop up.

A) Set Time at end of loadstep to 300 and Automatic time stepping to ON. B) Set Number of substeps to 20, Max no. of substeps to 100, Min

no. of substeps to 20. C) Set the Frequency to Write every substep.

Click on the NonLinear tab at the top and fill it in as shown

D) Set Line search to ON . E) Set the Maximum number of iterations to 100.

For a complete description of what these options do, refer to the help file. Basically, the time at the end of the load step is how long the transient analysis will run and the number of substeps defines how the load is broken up. By writing the data at every step, you can create animations over time and the other options help the problem converge quickly.

3. Apply Constraints

For thermal problems, constraints can be in the form of Temperature, Heat Flow, Convection, Heat Flux, Heat Generation, or Radiation. In this example, 2 sides of the block have fixed temperatures and the other two are insulated.

o Solution > Define Loads > Apply Note that all of the -Structural- options cannot be selected. This is due to the type of element (PLANE55) selected.

o Thermal > Temperature > On Nodes o Click the Box option (shown below) and draw a box around the nodes on

the top line and then click OK.

The following window will appear:

o Fill the window in as shown to constrain the top to a constant temperature of 500 K

o Using the same method, constrain the bottom line to a constant value of 100 K

Orange triangles in the graphics window indicate the temperature contraints.

4. Apply Initial Conditions

Solution > Define Loads > Apply > Initial Condit'n > Define > Pick All

Fill in the IC window as follows to set the initial temperature of the material to 100 K:

5. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Results Using ANSYS

Plot Temperature

General Postproc > Plot Results > Contour Plot > Nodal Solu ... > DOF solution, Temperature TEMP

Animate Results Over Time

o First, specify the contour range.

Utility Menu > PlotCtrls > Style > Contours > Uniform Contours...

Fill in the window as shown, with 8 contours, user specified, from 100 to 500.

o Then animate the data.

Utility Menu > PlotCtrls > Animate > Over Time...

Fill in the following window as shown (20 frames, 0 - 300 Time Range, Auto contour scaling OFF, DOF solution > TEMP)

You can see how the temperature rises over the area over time. The heat flows from the higher temperature to the lower temperature constraints as expected. Also, you can see how it reaches equilibrium when the time reaches approximately 200 seconds. Shown below are analytical and ANSYS generated temperature vs time curves for the center of the block. As can be seen, the curves are practically identical, thus the validity of the ANSYS simulation has been proven.

Analytical Solution

ANSYS Generated Solution

Time History Postprocessing: Viewing the Results

1. Creating the Temperature vs. Time Graph o Select: Main Menu > TimeHist Postpro. The following window should

open automatically.

If it does not open automatically, select Main Menu > TimeHist Postpro > Variable Viewer

o Click the add button in the upper left corner of the window to add a variable.

o Select Nodal Solution > DOF Solution > Temperature (as shown below) and click OK. Pick the center node on the mesh, node 261, and click OK in the 'Node for Data' window.

o The Time History Variables window should now look like this:

2. Graph Results over Time o Ensure TEMP_2 in the Time History Variables window is highlighted.

o Click the graphing button in the Time History Variables window. o The labels on the plot are not updated by ANSYS, so you must change

them manually. Select Utility Menu > Plot Ctrls > Style > Graphs > Modify Axes and re-label the X and Y-axis appropriately.

Note how this plot does not exactly match the plot shown above. This is because the solution has not completely converged. To cause the solution to converge, one of two things can be done: decrease the mesh size or increase the number of substeps used in the transient analysis. From experience, reducing the mesh size will do little in this case, as the mesh is adequate to capture the response. Instead, increasing the number of substeps from say 20 to 300, will cause the solution to converge. This will greatly increase the computational time required though, which is why only 20 substeps are used in this tutorial. Twenty substeps gives an adequate and quick approximation of the solution.

Modelling Using Axisymmetry

Introduction

This tutorial was completed using ANSYS 7.0 This tutorial is intended to outline the steps required to create an axisymmetric model.

The model will be that of a closed tube made from steel. Point loads will be applied at the center of the top and bottom plate to make an analytical verification simple to calculate. A 3/4 cross section view of the tube is shown below.

As a warning, point loads will create discontinuities in the your model near the point of application. If you chose to use these types of loads in your own modelling, be very careful and be sure to understand the theory of how the FEA package is appling the load and the assumption it is making. In this case, we will only be concerned about the stress distribution far from the point of application, so the discontinuities will have a negligable effect.

Preprocessing: Defining the Problem

1. Give example a Title

Utility Menu > File > Change Title .../title, Axisymmetric Tube

2. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

3. Create Areas

Preprocessor > Modeling > Create > Areas > Rectangle > By DimensionsRECTNG,X1,X2,Y1,Y2

For an axisymmetric problem, ANSYS will rotate the area around the y-axis at x=0. Therefore, to create the geometry mentioned above, we must define a U-shape.

We are going to define 3 overlapping rectangles as defined in the following table:

Rectangle X1 X2 Y1 Y2

1 0 20 0 5

2 15 20 0 100

3 0 20 95 100

4. Add Areas Together

Preprocessor > Modeling > Operate > Booleans > Add > AreasAADD,ALL

Click the Pick All button to create a single area.

5. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the PLANE2 (Structural, Solid, Triangle 6node) element. This element has 2 degrees of freedom (translation along the X and Y axes).

Many elements support axisymmetry, however if the Ansys Elements Reference (which can be found in the help file) does not discuss axisymmetric applications for a particular element type, axisymmetry is not supported.

6. Turn on Axisymmetry

While the Element Types window is still open, click the Options... button.

Under Element behavior K3 select Axisymmetric.

7. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200000 ii. Poisson's Ratio PRXY: 0.3

8. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Areas

For this example we will use an element edge length of 2mm.

9. Mesh the frame

Preprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'

Your model should know look like this:

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

Solution > Analysis Type > New Analysis > StaticANTYPE,0

2. Apply Constraints o Solution > Define Loads > Apply > Structural > Displacement >

Symmetry B.C. > On Lines

Pick the two edges on the left, at x=0, as shown below. By using the symmetry B.C. command, ANSYS automatically calculates which DOF's should be constrained for the line of symmetry. Since the element we are using only has 2 DOF's per node, we could have constrained the lines in the x-direction to create the symmetric boundary conditions.

o Utility Menu > Select > Entities

Select Nodes and By Location from the scroll down menus. Click Y coordinates and type 50 into the input box as shown below, then click OK.

Solution > Define Loads > Apply > Structural > Displacement > On Nodes > Pick All

Constrain the nodes in the y-direction (UY). This is required to constrain the model in space, otherwise it would be free to float up or down. The location to constrain the model in the y-direction (y=50) was chosen because it is along a symmetry plane. Therefore, these nodes won't move in the y-direction according to theory.

3. Utility Menu > Select > Entities

In the select entities window, click Sele All to reselect all nodes. It is important to always reselect all entities once you've finished to ensure future commands are applied to the whole model and not just a few entities. Once you've clicked Sele All, click on Cancel to close the window.

4. Apply Loads o Solution > Define Loads > Apply > Structural > Force/Moment > On

Keypoints Pick the top left corner of the area and click OK. Apply a load of 100 in the FY direction.

o Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints

Pick the bottom left corner of the area and click OK. Apply a load of -100 in the FY direction.

o The applied loads and constraints should now appear as shown in the figure below.

5. Solve the System

Solution > Solve > Current LSSOLVE

Postprocessing: Viewing the Results

1. Hand Calculations

Hand calculations were performed to verify the solution found using ANSYS:

The stress across the thickness at y = 50mm is 0.182 MPa.

2. Determine the Stress Through the Thickness of the Tube o Utility Menu > Select > Entities...

Select Nodes > By Location > Y coordinates and type 45,55 in the Min,Max box, as shown below and click OK.

o General Postproc > List Results > Nodal Solution > Stress > Components SCOMP

The following list should pop up.

o If you take the average of the stress in the y-direction over the thickness of the tube, (0.18552 + 0.17866)/2, the stress in the tube is 0.182 MPa, matching the analytical solution. The average is used because in the analytical case, it is assumed the stress is evenly distributed across the thickness. This is only true when the location is far from any stress concentrators, such as corners. Thus, to approximate the analytical solution, we must average the stress over the thickness.

3. Plotting the Elements as Axisymmetric

Utility Menu > PlotCtrls > Style > Symmetry Expansion > 2-D Axi-symmetric...

The following window will appear. By clicking on 3/4 expansion you can produce the figure shown at the beginning of this tutorial.

4. Extra Exercise

It is educational to repeat this tutorial, but leave out the key option which enables axisymmetric modelling. The rest of the commands remain the same. If this is done, the model is a flat, rectangular plate, with a rectangular hole in the middle. Both the stress distribution and deformed shape change drastically, as expected due to the change in geometry. Thus, when using axisymmetry be sure to verify the solutions you get are reasonable to ensure the model is infact axisymmetric.