ES 230 Strengths Intro to Finite Element Modeling & Analysis Homework Assignment 2

Transcription

1 ES 230 Strengths Intro to Finite Element Modeling & Analysis Homework Assignment 2 In this homework assignment you will use your rapidly developing ANSYS skill set to model and analyze three different beam bending problems. Each problem will require some modifications of the ES230_Beam_Bending model you created in the 2 nd Tutorial. Therefore, for each of these problems you can start by creating a Duplicate of your previous Static Structure analysis block (if it is working correctly). Then you can modify the Material, Geometry and Model Blocks as needed to complete the three beam bending homework problems. Starting Homework Problem 1 In this problem you will create a model of a cantilever beam that has the same I-shaped cross-section as used in the 2 nd tutorial. The cantilever beam is also still made of Lafayette Steel. The change is that the new beam has a length of 120 inches instead of a length of 48 inches in Tutorial 2. Create a new beam bending model in ANSYS by using Duplicate to create a copy of your previous Static Structure analysis block (if it is working correctly). Change the Length of the Beam (Line) Element The length of the Beam (Line) element was defined as part of the Geometry operations in the DesignModeler window. Open the DesignModeler window by double clicking on the Geometry cell in the newly created Structural System Menu block. Once the window is open you may need to use the ISO tool or the Zoom tool from the top toolbar to get the view set. You may need to change the view to View->Cross Section Solids from the top View toolbar to view the 3D beam instead of the 1D line element.

2 The length of the beam (line) element is a property of the Line1 entity. In order to edit the Line1 properties, double click on the Line1 leaf in the LHS tree to expand its contents. Click on the Sketch1 geometry leaf that appears. In the boxes that appear in the bottom LHS menu, change the L1 length dimension to 120 inches from 48 inches. Double check your units. To set 120 inches as the new beam length, click on Generate in the toolbar. Under File select Save Project and go back to the ANSYS Main window and double click on the Model menu item to continue to update the model and to run a new analysis. Click OK in the dialog that popups to allow model updating to occur.

3 Updating the Model and Obtaining a New Solution In the Mechanical window you will see several items, including Mesh and Solution that have yellow lightning bolts next to them instead of green checkmarks. You will need to update these model items before you can obtain a new solution for the 120-inch cantilever beam. In addition, you can change the view to View->Cross Section Solids (Geometry) from the top View toolbar to view the 3D beam instead of the 1D line element. To update the Mesh, right-click on the Mesh leaf and select Update. In the view you now will see the new, 120-inch cantilever beam with a coarse mesh of elements defined. Left click on Static Structural leaf to help you visually confirm that the concentrated load and the fixed support are still assigned as need to the near and far ends of the beam. Now right-click on Solution and select Solve. If the analysis runs successfully all the result viewers listed will have green checkmarks. You can view the vertical deflection, bending moment, shear force and max/min combined stresses for the 120-inch long beam at this point in a similar manner as done in Tutorial 2. Use Tutorial 2 as a reference as needed. Save your model before moving on.

4 Problem 1 Homework 2 Assignment Part to Turn In A), B) and C): Due Tuesday, Nov. 3 rd Turn in the following items in hard copy form (print out) for grading. To get good views of the ANSYS Results you may need to zoom in or rotate the axial bar in the window as needed. A) Hand Calculations to turn in with Problem 1 Calculate the maximum vertical deformation of the free end of the cantilever for the 120-in long beam. Use the equation given on the first page of this assignment for a cantilever beam with a point load acting. Draw the shear force, V, and the bending moment, M, diagrams for the 120-in long beam. Determine the maximum shear force and the maximum bending moment for the 120-in long beam. Calculate the maximum tensile normal stress and the maximum compressive normal stress due to bending for the 120-in long beam. B) Screen Captured ANSYS analysis results to turn in with Problem 1: Screen-capture and print-out a view showing results for the vertical deformation of the 120-in long beam model. Make sure you can clearly see the color variation along the beam itself, the color legend and a few specific values of deformation identified using the Probe tool. Also make sure to show the undeformed beam shape in your view. Circle the units on the printed copy. Screen-capture and print-out views showing results for the shear force and the bending moment in the 120- in long beam model. Make sure you can clearly see the color variation across the beam itself, the color legend and a few specific values of force or moment identified using the Probe tool. Circle the units on each printed copy. Screen-capture and print-out a view showing results for the Maximum Combined Stress using the Beam Tool in the 120-in long beam model. Make sure you can clearly see the color variation across the beam itself, the color legend and a few specific values of stress identified using the Probe tool. Circle the units on each printed copy. C) Comparison of the Hand Calculations and the ANSYS Analysis Results to turn in with Problem 1: Compare the value of maximum vertical deformation obtained from your hand calculation with the maximum vertical deformation obtained from the ANSYS analysis results. Discuss any difference in these values. Calculate the error between the hand-calculated vertical deformation and the ANSYS vertical deformation values for the 120-in long beam. Also, compare the error between the hand and computational results obtained for the 48-in long beam in the 2 nd Tutorial and the 120-in long beam in this homework problem. Discuss why the error between the two models increased/decreased due to changing the length of the beam. Compare the values of shear force, bending moment, and maximum bending stress obtained from your hand calculations with the values of shear force, bending moment, and maximum combined stress obtained from the ANSYS analysis results. Discuss any difference in these values. Starting Homework Problem 2 In this problem you will create a model that has the same I-shaped cross-section as used in the 2 nd tutorial and that has the new 120-in length as run in Problem 1 of this homework. The difference will be that you will change the material from Lafayette Steel to Lafayette Aluminum.

5 To construct the new beam bending model in ANSYS, create a Duplicate of the Static Structure analysis block that you just created above and used to solve Problem 1 of this homework. You want this one since it already has the new cantilever beam length modeled. Change the Material to Lafayette Aluminum Make a copy of the Lafayette Aluminum.xml file that was ed to you by Prof. Raich. Save this file in the same directory as all of your ANSYS project files. Double click on the Engineering Data cell in the new Structural System Menu. Delete the current Lafayette Steel material table entry by right-clicking on that entry and selecting X Delete. Import the Lafayette Aluminum material from the file Lafayette Aluminum.xml using File->Import Engineering Data. Make sure to right-click on the Lafayette Aluminum material in the new table entry that is created and assign this material as the Default Solid Material for Model. If you forget this you will get a material assignment error later when you try to solve the problem. Save this material and then Close (X) the Engineering Data window. If you look at the Structural System Menu you will see several of those pesky yellow lightning bolts. This is to be expected since the model will need to be updated to reflect changing the material properties. Updating the Model and Obtaining a New Solution Double-Click on the Model Cell in the Structural System Menu. Click OK in the dialog that popups to allow model updating to occur. No update is required for the Geometry or the Mesh of this model since no changes were made to the cross-section or the length of the beam. Just click on Solution and then select Solve to run an analysis of the new Lafayette Aluminum cantilever beam model.

6 If you run an analysis over and over again, sometimes you will need to select Clear Generated Data under Solution before you can then select Solve under Solution again. Problem 2 Homework 2 Assignment Part to Turn In D), E) and F): Due Tuesday, Nov. 3 rd Turn in the following items in hard copy form (print out) for grading. To get good views of the ANSYS Results you may need to zoom in or rotate the axial bar in the window as needed. D) Hand Calculations to turn in with Problem 2: Calculate the maximum deformation that occurs at the free end of the cantilever with the Laf Aluminum material. Calculate the maximum tensile normal stress and the maximum compressive normal stress due to bending for cantilever beam with the Laf Aluminum material.

7 E) Screen Captured ANSYS analysis results to turn in with Problem 2: Screen-capture and print-out a view showing results for the vertical deformation of the 120-in long, Laf Aluminum beam. Make sure you can clearly see the color variation along the beam itself, the color legend and a few specific values of deformation identified using the Probe tool. Also make sure to show the undeformed beam shape in your view. Circle the units on the printed copy. Screen-capture and print-out a view showing results for the Maximum Combined Stress using the Beam Tool in the 120-in long, Laf Aluminum beam model. Make sure you can clearly see the color variation across the beam itself, the color legend and a few specific values of stress identified using the Probe tool. Circle the units on each printed copy. F) Comparison of the Hand Calculations and the ANSYS Analysis Results to turn in with Problem 2: Compare the value of maximum vertical deformation obtained from your hand calculation with the maximum vertical deformation obtained from the ANSYS analysis results for the 120-inch, Laf Aluminum beam. Discuss any difference in these values. Compare the value of maximum vertical deformation obtained from the ANSYS analysis results for the Laf Aluminum beam model with the value of maximum vertical deformation obtained from the ANSYS analysis results for the Laf Steel beam model solved in Problem 1 of this homework. Discuss any differences in these values. Compare the value of maximum normal stress obtained from your hand calculations with the value of maximum combined stress obtained from the ANSYS analysis results. Discuss any difference in these values. Compare the value of maximum normal stress obtained from the ANSYS analysis results for the Laf Aluminum beam model with the value of maximum normal stress obtained from the ANSYS analysis results for the Laf Steel beam model solved in Problem 1 of this homework. Discuss any difference in these values. Starting Homework Problem 3 In this problem you will create a model of a cantilever that is very similar to the one you just created for Homework Problem 2 above. The only difference is that the I-shaped cross-section is bending about its minor axis (y-axis) instead of the major axis of bending (z-axis) specified in Homework Problem 2. The cantilever beam will still have the 120-in length as well as be made out of Lafayette Aluminum. Z axis Y axis Major Axis Bending Minor Axis Bending To construct the new beam bending model in ANSYS, create a Duplicate of the Static Structure analysis block that you just created above and used to solve Homework Problem 2. You want this one since it already has the new cantilever beam length and aluminum materials modeled.

8 Change the Axis of Bending of the I-shaped Cross-Section Double-click on the Geometry cell in the new Structural System Menu to open the DesignModeler window. Click on the 1 Part, 1 Body leaf in the LHS tree and expand the leaf to see the Line Body leaf. Click on the Line Body leaf to open up the Details of Line Body options in the bottom, LHS menu. In the 2 nd Tutorial, you rotated the I-shape cross-section by 90 degrees in order to specify that the beam crosssection bend about the Z-axis, which is about the cross-section s major axis. For Homework Problem 2 you will need to rotate the I-shape cross-section back to bending about its y-axis, which is about the cross-section s minor axis. To do this, hover your cursor over the line element in the view on the beam element and click on the line to highlight it in the view.

9 This will open up the bottom, LHS menu for the Details-View. In the Angle text box enter 0 degrees to replace the current 90 degree value entered. Then hit Generate (lightning bolt) from the top tool bar. The I-shaped cross-section should rotate in the view. This orientation of the cross-section will have the beam bending about its minor axis instead of its major axis as in Homework Problem 2. Save Project your model at this point. If you look at the Structural System Menu you will see a check by Geometry but a circular arrow next to Model. Right-click on Model and select Update. Click OK in the dialog that popups to allow model updating to occur. This will update the current model to reflect any changes made to the Geometry of the model. This process will also open up the Mechanical window and will show a new view of the beam with its cross-section orientated as specified in Geometry.

10 Obtaining a New Solution Check the Mesh by clicking on the Mesh leaf in the LHS menu. Also check on the applied load and fixed support by clicking on Static Structural leaf in the LHS menu. These should be okay since no changes were made to the length of the beam. If these are not okay then Update the Mesh and Insert the load and fixed support condition as needed. Now click on Solution and then select Solve to run an analysis of the new minor-axis bending Lafayette Aluminum cantilever beam model. If you run an analysis over and over again, sometimes you will need to select Clear Generated Data under Solution before you can then select Solve under Solution again. You can view the two Moment of Inertias for this I-shaped cross-section listed under the Geometry Line Body Properties. Click on Line Body and view the bottom, LHS menu Properties. You may need to expand the options out with the + and scroll down to see the two I values listed for the cross-section. These two values

11 are listed taking into account the current local axes. So the Izz is the current axis of bending about the z-axis in the view and Iyy is the other axis of bending about the y-axis in the view. Therefore, Izz is smaller than Iyy for this orientation of the beam in the view. Izz = in 4 (minor axis) and Iyy = in 4 (major axis). Problem 3 Homework 2 Assignment Part to Turn In G) and H): Due Tuesday, Nov. 3 rd Turn in the following items in hard copy form (print out) for grading. To get good views of the ANSYS Results you may need to zoom in or rotate the axial bar in the window as needed. G) Hand Calculations to turn in with Problem 3: Calculate the maximum deformation that occurs at the free end of the cantilever with the Laf Aluminum material with the minor axis orientation of the cross-section. Calculate the maximum tensile normal stress and the maximum compressive normal stress due to bending for cantilever beam with the Laf Aluminum material and the minor axis orientation of the cross-section. H) Comparison of the Hand Calculations and the ANSYS Analysis Results to turn in with Problem 3: Compare the value of maximum vertical deformation obtained from your hand calculation with the maximum vertical deformation obtained from the ANSYS analysis results for the 120-inch, Laf Aluminum beam, minor cross-section bending. Discuss any difference in these values. Compare the value of maximum vertical deformation obtained from the ANSYS analysis results for the Laf Aluminum beam model with the major axis orientation of the cross-section (HW Prob 2) and the value of the maximum vertical deformation obtained from the ANSYS analysis results for the Laf Aluminum beam model with the minor axis orientation of the cross-section (this HW Prob 3). Discuss why one value is much larger than the other. Compare the value of maximum normal stress obtained from your hand calculations with the value of maximum combined stress obtained from the ANSYS analysis results. Discuss any difference in these values. Compare the value of maximum normal stress obtained from the ANSYS analysis results for the Laf Aluminum beam model with the major axis orientation of the cross-section (HW Prob 2) and the value of maximum normal stress obtained from the ANSYS analysis results for the Laf Aluminum beam model with the minor axis orientation of the cross-section (this HW Prob 3). Discuss why one value is much larger than the other.