Presentation on theme: "Project 2: Torque-Arm Modeling, Simulation and Optimization"— Presentation transcript:
1 Project 2: Torque-Arm Modeling, Simulation and Optimization Date: April 3
2 Report FormatFormal 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 SakaiPenalty or extra creditThere 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.4/194/204/214/224/234/244/254/264/27+6+5+4+3+2+1-5-10
3 Design of Torque ArmUsed for transmitting load from a shaft to a wheelGoal: design the lightest structure with stress constraintsMaterial propertiesE = GPa, Poisson’s ratio = 0.29, thickness = 1.0cm, density = 7850 kg/m3Use cm for the length unit and make other units consistent (need to convert all values in cm units).
4 Preliminary AnalysisAt 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 themRemember that the purpose of preliminary analysis is to estimate the locations of max stress and displacement as well as their levels.
5 Abaqus ModelingFirst 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 timesHow to apply BCs and loads?MPC constraint (control point = reference point, slave nodes = nodes on the circumference of the hole, MPC type = Beam).
6 Effect of Element Types Compare results using different elements (CST, LST, Q4 and Q8).Turn off “reduced integration” option in Element Type commandUse plane stress element typeCompare 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.
7 Convergence StudyFEA at the initial design (x1 = 12, x2 = 1, x3 = 27) with Q4Carry out convergence study on the vertical displacement at the center of right shaftDetermine 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 pointNo. of ElementsDisplacement
8 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 isChange in d changes in x changes in FE geometry
9 Parameter StudyPerform a parameter study by changing d between 0 and 1 with 10 incrementsPlot 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)ddopt