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**Project 2: Torque-Arm Modeling, Simulation and Optimization**

Date: April 3

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Report Format Formal report, including title, summary, introduction, approach, results, discussion, appendix (programs), and/or references. Report must be self-explanatory; define all terms that you use and explain clearly what you did. Submit report (Word or PDF file, Max 10 pages) and CAE file of optimum design by 12:00 PM in Sakai Penalty or extra credit There will be additional extra credit of up to 10% for easy-to-understand (and grade) reports that would be given to at least 20% of the reports. 4/19 4/20 4/21 4/22 4/23 4/24 4/25 4/26 4/27 +6 +5 +4 +3 +2 +1 -5 -10

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Design of Torque Arm Used for transmitting load from a shaft to a wheel Goal: design the lightest structure with stress constraints Material properties E = GPa, Poisson’s ratio = 0.29, thickness = 1.0cm, density = 7850 kg/m3 Use cm for the length unit and make other units consistent (need to convert all values in cm units).

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Preliminary Analysis At the initial design (x1 = 12, x2 = 1, x3 = 27), estimate the vertical displacement at the center of the right hole and maximum von Mises stress using Mechanics of Materials. Explain your assumptions and approaches in the report. Later, compare your hand calculation with FE results and discuss the difference between them Remember that the purpose of preliminary analysis is to estimate the locations of max stress and displacement as well as their levels.

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Abaqus Modeling First task is to sketch the section geometry with fully constrained (curves will change to green color) This is necessary because you will change design and regenerate models several times How to apply BCs and loads? MPC constraint (control point = reference point, slave nodes = nodes on the circumference of the hole, MPC type = Beam).

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**Effect of Element Types**

Compare results using different elements (CST, LST, Q4 and Q8). Turn off “reduced integration” option in Element Type command Use plane stress element type Compare the maximum displacement at the load application point and maximum von Mises stress (provide a table) Try to use approximately the same number of nodes for all element types.

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Convergence Study FEA at the initial design (x1 = 12, x2 = 1, x3 = 27) with Q4 Carry out convergence study on the vertical displacement at the center of right shaft Determine reasonable mesh size (you are limited to 1,000 nodes!). Use this mesh size in the parameter study later. Use Richardson’s extrapolation to estimate the accurate vertical displacement at the load application point No. of Elements Displacement

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**Parameter Study Designer wants**

We simplify the design problem by one function with one variable (penalty parameter a = 100) The relationship between d and design variables is Change in d changes in x changes in FE geometry

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Parameter Study Perform a parameter study by changing d between 0 and 1 with 10 increments Plot a graph d versus f(d) and find an optimum design dopt that minimizes f(d) (graphically or approximated by polynomials) Report optimum design in terms of mass, stress and (x1, x2, x3) f(d) d dopt

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