FEA TUTORIAL – 2D STRESS ANALYSIS OF A THIN BAR

(Using ProMechanica – Wildfire 1.0) Introduction: A simple 2D stress analysis of a thin bar with a hole will be performed using Pro/Mechanica. The bar will be subjected to a loading that produces both axial and bending stresses. Instructions will be provided to complete all steps necessary for the analysis and review of the analysis results. Bar Specifications: (all dimensions are in inches)

b = 2 a = 4 d = 1.5 L = 16 Thickness (into page) = 0.25 Px = 1000 lbs Py = 2500 lbs 6061 Aluminum

b

Py L

Px b

d

a

© 2005 by Martin E. Gordon, PE Page 1 Rev. A

Overview: We will run Pro/Mechanica Wildfire 2.0 in independent mode. This tutorial will introduce the basic features of Pro/Mechanica and allow us to work through a complete analysis. The following basic steps will be performed for most simple 2D analyses:

1. Geometry Creation 2. Element Creation (meshing) 3. Assigning Material and Other Properties 4. Applying Constraints and Loads 5. Creating a Static Analysis 6. Run the Analysis 7. Review the Results

While you are working through this tutorial please think about what the purpose of each step is. You might want to quickly flip quickly through the entire lesson to get the overall scope of the tasks required. Often, many of the steps won’t make sense the first time you work through the tutorial. It is suggested that a second workthrough be performed for optimal understanding. Starting ProMechanica: Before starting Pro/Mechnica make sure that you have read and write access to the “Start In” directory:

Start>Programs>{right click}Structure>Create Shortcut{place on desktop}

{right click}Structure{shortcut}>Properties

Make sure that you have full access to this directory

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After making any necessary changes, start up ProMechanica “Structure” from your desktop.

Structure After some time – the following screen will appear:

Pull-Down Menus

Command/Message Window

Main Menu

Graphics Window Graphics Window: This is where the model and analysis results will be shown. Main Menu: This contains the major ProMechanica command submenus. Pull-Down Menus: Contains utility tools, screen display tools and editing tools. Command/Message Window: Gives progress, displays data and prompts for data entry.

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The Main Menu contains most of the ProMechanica command sub-menus: Geometry: Sub-menus to create 2D and 3D geometric features. Model: Sub-menus for specifying model type, elements, properties, loads,

constraints, measures. Analysis: Sub-menus for creating analyses. Design Study: Sub-menus for advanced design study and optimization features. Run: Sub-menu for setting run parameters, starting an analysis, and

monitoring the run of an analysis. Results: Sub-menus for displaying result windows based on the results of an

analysis.

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Geometry Creation: We will start our 2D model creation by entering points at the vertices of our bar. Main>Geometry>Point>Single Points Select the “Point” button. We will enter the x,y coordinates for each vertex point. The origin will be the lower left hand corner of our bar.

Continue entering the remainder of the vertices. To bring all points into view: View>Fit Add a point at the center of the hole. After entering all vertex points your graphic window should look like this:

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We will now add lines to connect the vertex points and put a circle at the hole location: Main>Geometry>Curve>Line>Two Points Select two points and a line will be drawn between the points. Now, lets add the circle. Main>Geometry>Curves>Circle>Radius – Center In the Command/Message Window enter the correct hole radius at the prompt. You will then be asked for the center of the circle – select the point at the center of the hole location. We can control what the points look like in the graphics window, lets change the points to “dots”. In the Pull-Down Menus select: Display>Settings Using the drop-down list for points, choose “DOT”, accept your choice. Your model should now look like this:

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The last step in geometry creation will be to create a surface. Our surface will consist of the rectangular bar minus the hole: Main>Geometry>Surface>Planar Carefully follow the prompts that will appear in the Command/Message Window. Your model should look like this when you are finished. Notice that the fainter lines indicating a surface do not pass through the hole. This indicates that you have “empty space” for your hole:

At this point, you should save your model. It is a very good idea to “save and save often” since some installations / computers are more stable than others. File>Save As You can use the “..\” in the window to go up in the directory structure. Select a meaningful name and then write down where you are saving your model to. As a suggestion, you can manually increment the model name so that you can go back to previous versions that you have saved. For instance, save this model as “bar_hole01” this time and then “Save As” “bar_hole02” next time, etc.

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Element Creation: We will now “mesh” our model by creating elements

Main>Model The first time you select the “Model” submenu ProMechanica will ask you for a “Structural Model Type”. We will select “Plane Stress”. Remember to “Accept” your selection. We will let Pro/Mechanica generate a mesh for us by using the AutoGEM feature. First we need to check the AutoGEM settings: Main>Model>Elements>AutoGEM>Settings

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Now, click the “Define/Review…” button, enter values as shown in the window below. Define/Review… We will force ProMechanica to make smaller elements by increasing the Min. Allowable Angle and decreasing the Max Allowable Angle. Also - change the Max Allowable Edge Turn and the Max Allowable Aspect Ratio. Don’t forget to Accept. (Changes are frequently lost by canceling instead of accepting.) Accept>Accept We are now ready to let ProMechanica create elements for us: Main>Model>Elements>AutoGEM>Surface Select the surface that we just created. The following summary is displayed once meshing is complete:

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It’s a good idea to take a few seconds and review the summary. Can you see that a total of 41 elements were created? 11 elements are triangles and 30 elements are quadrilaterals. (You may notice that your totals are slightly different) Click OK. The meshed model is now displayed. To make it easier to see the individual elements we will “shrink” the display of the elements (this does not change the “mathematical” element). Using the Main Menu: Display>Settings Select “Shrink All Elements”. The Model should now look like this:

If you look carefully you’ll see that ProMechanica (with our help by changing the AutoGEM settings) has placed more elements around the hole. This will make our analysis more accurate. Generally speaking it is a good idea to have a higher “mesh density” near stress concentrations. Now that we have a meshed model lets assign some material and other property values.

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Assigning Material and Other Properties: We will need to select a material and also tell ProMEchanica how thick our bar is. To assign a material: Main>Model>Properties>Material A material selection window will open, select the proper material and then assign the material to our surface. Highlight “AL6061_IPS” and then use the right pointing “three arrows button” to bring AL6061_IPS into the model . The “IPS” in the material name refers to inch – pound – seconds – the US system of measure. By using this unit system we can enter our forces in lbf and the stress results will be in psi. It is very important to select the correct unit system.

This button will “light-up” after a material is selected from the left-hand

This is what the window looks like after the AL6061_IPS is added.

We still need to “Assign” the material. We will assign the material to our surface. Assign>Surface>{click on the surface}>{press enter} HAVE YOU SAVED YOUR MODEL RECENTLY?? – remember to numerically “index” the name.

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We can create new materials or edit existing materials by using the New and Edit buttons respectively. If we’d like to edit the properties of AL6061_IPS click the Edit button. The following window is displayed that shows properties such as Modulus of Elasticity, Poisson’s Ratio and Density: Edit

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We won’t change any of the material properties. Cancel or close all windows until none are showing. Now we will specify the thickness of our bar: Main>Model>Properties>Shell Property>2D Plate Select “All”. All of the elements should now be “red”. Return to continue. The following window allows the thickness do be defined – you must enter a “Shell Property Name” and a thickness for the material. Accept when done. Our next step will be to define the loads and constraints.

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Applying Constraints and Loads: When working on a 2D analysis you should never define a point load or point constraint. Instead, define a curve constraint or curve load. This avoids “hotspots” , or discontinuities, in the model and provides more accurate results. We will apply a cantilever support along the left edge of the bar: Main>Model>Constraints>Curve

Click the arrow button to select a curve to be constrained.

The “depressed” button indicates that the curve will be constrained in the x and y directions.

Select this curve. Press return to continue.

:

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Your model is now displayed with a “constraint symbol” on the left edge. A constraint symbol is useful for determining what directions are constrained. A “filled-in” block indicates a constraint in a certain linear or rotational direction:

rx ry rz

tx ty tz

tx – translation in the x direction. ty –translation in the y direction tz –translation in the z direction rx –rotation about the x axis ry – rotation about the y axis rz – rotation about the z axis

For a 2D analysis only the tx and ty are valid. For our model all 6 blocks are filled in meaning (for a 2D model) that the end of the bar is constrained in the x and y directions.

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We will now apply our load to the right edge of the bar. Main>Model>Loads>Curve Select the right edge curve using the same method we used to select the curve when we applied a constraint. Insert values for the x and y components of the force: : Click “OK” to accept and return. Our model should now look like this: OK

Now is a good time to check that your force is pointing in the direction that you expected. We are now finished setting up our FEA model. The next step will be to choose the type of analysis we would like ProMechanica to perform.

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Creating a Static Analysis: ProMechanica is capable of running several different types of analyses. We will select a “Static Analysis”. Main>Analyses then select “new” The following window will open, you’ll need to assign a meaningful name and select the method of convergence. Since this is a 2D model with very few elements the analysis should run very quickly. Select a “Multi-Pass Adaptive” convergence method. This is the most popular convergence method.

OK>close We are finally ready to Run our analysis.

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Run the Analysis: To run the analysis we will select the directory locations for our temporary working files and our result files. Because of the massive amount of disk read and write that occurs during solution a local drive must be selected!!! Many students have made the mistake of selecting a network drive only to fall asleep at their computer waiting for their run to finish. It is also critical to select the proper “RAM Allocation”. You should usually select a RAM Allocation to be 40% of the total RAM. Main>Run then select “Settings…” By now you have probably noticed that buttons ending with “…” have additional windows that will need to be completed. Notice that both directories are physically located on the computer you are now using. At the completion of the tutorial you will need to copy your model and the directory containing your results (the “result” directory will have the same name as the Analysis eg. /bar_hole_01) to a location that will not get “wiped clean” as soon as you log off of your machine.

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We can start the analysis by selecting the Start button, use the Summary button to check the progress of your solution. Start When prompted for error detection select “yes”. It is always a good idea to allow error detection the first time an analysis is run.

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You can check if the analysis has finished by clicking “Summary”. When the analysis has completed the end of the summary should look like this:

If the words “Fatal Error” occur here you did something wrong. Review the summary for clues.

After the analysis has finished running it is time to check and review your results.

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Review the Results: The first step in reviewing the results is to check the validity of the results. There is nothing more embarrassing than showing off your beautiful results only to have some nice individual point out that your stress numbers don’t make a bit of sense. Often, there is a tendency to jump right to the Von Mises stress plots. The danger here is that the stress plots might look pretty but contain garbage. There are several easy methods to check the validity of a model. You should use as many methods as possible to check the validity of your results, especially when you are new to FEA.

1. Perform a hand calculation and compare to your FEA results. 2. Observe an animation of the displacement – is the part moving correctly? 3. Check the convergence of a stress measure that is close to the area most likely to fail

in your part. 4. Check the convergence of “Strain Energy”. 5. Perform a test of the part and correlate to the FEA results. 6. Make sure that the fringe plot contours are not discontinuous or blotchy across

elements. 7. Do higher stresses appear near stress concentrations, is the stress distribution what you

expect? The best result to review first is displacement. You can create a separate “Result Window” for each result. A “result” might be a Von Mises Stress Fringe Plot (fringe plots look like nice, colored weather maps); or a plot of Strain Energy Convergence; or a displacement animation. We will start by looking at an animation of the displacement. The animation will indicate if the model is behaving the way we want the model to behave. Main>Results The following window will appear:

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We will first need to “Create” a result window: Create Accept the default name of “Window 1”. Highlight but DO NOT double click the directory that has the same name as the analysis you just ran:

Highlight, DO NOT double clicks!!

Accept, a window will appear that allows you to select what type of Result Window you are creating.

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Make changes to the window in the areas noted below: Accept The Result Window Console is presented. There are two column in the console. The left column selects which Result Window(s) to display (show). The right column lets you select a window to edit. Make sure that “window1” is highlighted in the “show” column. Click this to

display the result window.

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An animation showing an upward deflection of the bar should now be on your screen:

Moves up and down

Click “Done” to leave the animation. The Result Window Console will again be displayed. We will now copy the animation window into a new result window and then edit the new result window to display Maximum Principal Stress. By reviewing Maximum Principal Stress we can see what areas of our model are in tension and what areas are in compression. Use the color code scale to determine tension or compression. Done>Copy>Accept Make sure that window2 is highlighted in the right (edit) column, click review. Review

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Make changes to the window as shown below: Accept>Show

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Now, assuming you had both window1 and window2 highlighted in the left column, the following should appear: Zoom into the area near the hole in the Fringe Plot of Maximum Principal Stress: View>Window{click and drag to form “viewfinder”} Notice that there is an increase in stress near the hole. However the maximum stress seems to occur on the bottom left of the bar. Copy window2 into window3. Change “Quantity” to Measure, using the “Select…” button choose “Strain Energy” (at the end of the pre-defined list). Accept>Accept Un-highlight window1 in the “show” column. Then show window2 and window3. Show

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The result window on the right shows a “convergence plot” for strain energy. Any measure can be plotted in this way to check for convergence. Can you see the convergence?

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Review window3 and make changes to create a result window showing Von Mises Stress. Review {then make changes to window} Deselect window1 in the left column, show window2 and window3. By using Dynamic Query the maximum or minimum stress value shown in a window can be displayed. Dynamic Query>{select the Max Principal Stress Window}>Show View Max The maximum stress should be approximately 7.1E+04. This stress is shown both in the result window and up in the Command/Message Window. Zoom into a specific area and try this again. Notice that the max value changes based on the view shown on your screen. This is a great tool to pick out stress values at specific locations on your part. This is the end of the tutorial – nice work – it’s a good idea to go through a second time Don’t forget to save your work in a directory that won’t get erased.

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