ME 475 - Optimization of a Frame Analysis Problem Statement: The following problem will be analyzed using Abaqus. 4 7 7 5,000 N 5,000 N 0,000 N 6 6 4 3 5 5 4 4 3 3 Figure. Full frame geometry and loading (gravity load not shown). All units are in meters. Not shown is a gravity load. The structural members are made of a material with the following properties: E = 00 GPa, G = 66.7 GPa, 7,860 kg/m 3 ). The members are labeled as to what area cross-sectional properties will be assigned to them, listed below. Section-: Shape = Pipe, radius = 0. m, thickness = 0.00635 m Output points: (0, 0.00635); (0, -0.00635) Section-: Shape = Pipe, radius = 0.6 m, thickness = 0.07 m Output points: (0, 0.6); (0, -0.6)
Section-3: Shape = Pipe, radius = 0. m, thickness = 0.004 m Output points: (0, 0.); (0, -0.) Section-4: Shape = Pipe, radius = 0.6 m, thickness = 0.008 m Output points: (0, 0.6); (0, -0.6) Section-5: Shape = Pipe, radius = 0.08 m, thickness = 0.004 m Output points: (0, 0.08); (0, -0.08) Section-6: Shape = Pipe, radius = 0. m, thickness = 0.00635 m Output points: (0, 0.); (0, -0.) Section-7: Shape = I, l = 0.78 m, h = 0.356 m, b = b = 0.369 m, t = t = 0.08 m, t3 = 0.0 m Output points: (0, 0.78); (0, -0.78) Analysis Procedure:. Open Abaqus/CAE in a similar manner as with the last lab. a. Create a folder called BeamFEA in C:\temp b. Start Run type: cmd, press enter c. Type: C:, press enter d. Type cd C:\temp\BeamFEA e. type: abaqus cae. In the Part Module, draw the geometry as shown in Figure using the sketcher for a D, Deformable, Wire Part. 3. In the Property Module, create seven different Profiles, named Profile-, Profile-, etc., corresponding to those listed in the analysis problem statement. 4. In the Property Module, create seven different sections, named Section-, Section-, etc. a. Use beam sections with section integration occurring before the analysis. b. Choose the corresponding profile for the section (for example, Profile-3 goes with Section-3). c. Enter the Young s Modulus, Shear Modulus, and Section Material Density. d. Enter the output points as noted in the analysis problem statement. These are locations on the cross-section where stress will be calculated.
5. In the Property Module, assign each section to the corresponding member, based on the numbering shown in Figure. 6. Finally, assign the beam orientation for all of the members, use an n direction vector of (0,0,-). a. This affects the orientation of the profile on the beam elements. In this problem, only the section with an I-beam profile would be affected by different a different beam orientation. 7. To verify that the profiles and beam orientations were input properly, turn on beam profile rendering. a. View menu Part Display Options, check the box next to Render beam profiles toward the bottom of the General tab. 8. In the Assembly Module, instance the part as an independent part instance. 9. In the Step Module, create a Static Linear Perturbation step after the Initial step. 0. In the Load Module, apply the loading shown in Figure, as well as the gravity load (- 9.8 in the -direction).. Apply boundary conditions as shown in Figure.. In the Mesh Module, use a mesh seed of 0.5 on the assembly. 3. In the Mesh Module, assign the entire frame the element B3, a D beam element that uses the cubic formulation. 4. Mesh the assembly. 5. In the Job Module, create a job named: Kframe 6. Write the input deck of the job just created. 7. Save your CAE database and close Abaqus/CAE. 8. Run the analysis as in the previous lab. a. type in command prompt: abaqus interactive job=kframe 9. The analysis is now complete. Model Validation: It is not necessary to solve the entire structure to validate the FE solution. In fact, that would make performing the FEA useless for anything except visualization of the deformed state. To validate this structure, a comparison will be made to a uniform bar under a compressive axial 3
load. We will focus on the center region of the frame, highlighted in Figure. For the area of the bar, use the following value: A effective = ( θ ) + A cos ( ) Acolumn cos center θ where A column is the cross-sectional area of one of the outer columns (section 4), A center is the cross-sectional area of one of the inner supports (section 5), and θ and θ are shown on Figure. The cos () terms is used to rotate the stiffness of members into different coordinate systems, and will be further explained in lecture when FEA of trusses is covered. θ θ Figure. Regions for comparing to validation calculations. Use the following formula to find the predicted deflection of the bar: δ = PL EA effective where P is the total vertical load applied to the structure, 4
L is the height of the section of interest, E is the modulus of elasticity of the material, and δ is the axial deflection. Compare this value to the y-deflection of the center part of the frame, after rerunning without the gravity load. This means taking the difference in -displacement at the circled nodes in Figure. You should find that the frame deflection found through FEA is within 0% that of the bar with a cross-sectional area of A effective. If you keep the gravity load and add the (mass * g) to P, you should get larger error, but the displacements should be of the same order of magnitude. Present the results of both calculations (with and without gravity) in the validation section of the report. Why is the difference in predicted displacement so much different for the structure without the gravity load compared to with the gravity load? Report Requirements: A full report is required for this lab (see ME 475 Lab Report Format Guidelines). Present plots of the von Mises component of stress (for the top and the bottom section points, on separate plots, with the undeformed mesh superimposed) and the U component of displacement (with the undeformed mesh superimposed). Why is the S stress not asked for in this case? Assuming a yield stress of 380 MPa and the von Mises failure criterion, what is the factor of safety for the structure? 5