1 / 24

Engineering Optimization

Concepts and Applications WB 1440. F. ?. Engineering Optimization. Fred van Keulen Matthijs Langelaar CLA H21.1 A.vanKeulen@tudelft.nl. Contents. Sensitivity analysis: Brief recap discrete / SA approach Adjoint method Continuum sensitivities Topology optimization Closure. E , n.

keaton
Download Presentation

Engineering Optimization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Concepts and Applications WB 1440 F ? Engineering Optimization • Fred van Keulen • Matthijs Langelaar • CLA H21.1 • A.vanKeulen@tudelft.nl

  2. Contents • Sensitivity analysis: • Brief recap discrete / SA approach • Adjoint method • Continuum sensitivities • Topology optimization • Closure

  3. E, n L t R h r Structural optimization

  4. ? F Topology optimization • Topology: topos (place), logos (study): ~ the way parts of an object are connected to each other • More general than shape optimization! No a prioriassumptions needed about shape

  5. Heuristic Methods • Hard-kill • Soft-kill • Etc. etc.

  6. Bendsoe & Kikuchi, 1988:Homogenization method Suzuki & Kikuchi (1991) Milestones • Michell, 1904: “Michell truss”Structures with optimal stiffness for a given weight

  7. Sheet thickness optimization (thickness sizing) ti • Homogenization approach (microstructure sizing) hi, bi “Classical” Approaches Ai • Various approaches: • Ground structure approach (truss sizing)

  8. Stiffest structure = structure with minimal compliance: Linear elasticity: Compliance: Compliance minimization • Classical problem: for a given amount of material, find the stiffest structure • Save material costs (bridge, building) • Improve dynamic performance (automotive, machines) • Save fuel costs (aerospace)

  9. Remedy 1: restrict solution to pure solid/void designs+ Manufacturable- Mesh refinement leads to more detailed solutions • Remedy 2: restrict minimal member sizes Compliance minimization (2) • Optimal solution has infinitely fine porous microstructure: impractical

  10. Solve optimization problem: ri Compliance minimization (3) • Conventional approach: • Assign density variables to every element • Young’s modulus depends on density:SIMP (Solid Isotropic Material with Penalization)

  11. p = 1; C = 184 p = 1.5; C = 210 p = 2; C = 220 p = 3; C = 229 SIMP • SIMP approach uses penalization to make intermediate densities unattractive: • Lower stiffness/weight ratio • Forces design to solid/void solution

  12. Heuristic solution: spatial filtering • Filtering of sensitivities or density values • Filter radius determines minimum member size r Mesh independence / checkerboard filtering • Problems: • Checkered solid/void patterns have artificially high stiffness (unrealistic) • Solution dependent on mesh size

  13. Solution procedure • Compliance minimization problem: • Solved by: • Constrained optimization algorithms (convex approximation methods: SLP, MMA) • Optimality criteria methods (heuristic)

  14. F Do it yourself! • See www.topopt.dtu.dk! • Online optimization • Matlab programs

  15. Recent progress in other applications • Topology optimization techniques also (being) developed for: • Multi-material designs, shells, 3D structures • Compliant mechanism design (large displacements) • Thermal actuator design (MEMS) • Crashworthiness design • PZT actuator design • Shape memory alloy actuator design

  16. Compliant mechanisms • Precise, frictionless motion, single structure (no joints) • Lu et al, 2003 • Wang et al, 2005

  17. Mechanism design • Inverter design, Kawamoto/Bendsoe/Sigmund, 2004

  18. Thermal actuator (Sigmund, 2000)

  19. To reduce number of DOFs, condensation is applied Uouter Original element properties Uinner kLi(g i) Element Connectivity Parameterization • Topology defined by elements connected with zero-length links • Stiffness of links controlled by design variables g • Elements maintain original properties!

  20. No numerical instabilities due to excessive distortion of weak elements 1: Extremedistortion Reference Density-based ECP F1 F2 1) Yoon and Kim, 2005 Compliant elements Advantages of ECP • No material model interpolation required • Straightforward sensitivity analysis

  21. SMAdesigndomain Shape memory alloy actuator • SMA: active material, actuation under temperature change

  22. Level sets • Topology optimization using an implicit boundary definition as the zero-level contour of a level-set function

  23. Geometrically nonlinear mechanism Compliant gripper Element-density field

  24. Topology optimization summary • Very versatile optimization technique: enormous variety of shapes possible • Recent development: area of active research • Improvements (accuracy, efficiency) • Extensions (nonlinearities, multiple physics, …) • Try it yourself: topology optimization Matlab program topopt.m available on Blackboard

More Related