Engineering Optimization Contents Structural optimization Topology optimization Heuristic Methods

Engineering Optimization Contents Structural optimization Topology optimization Heuristic Methods www.phwiki.com

Engineering Optimization Contents Structural optimization Topology optimization Heuristic Methods

Balazs, Diana, Paradise Valley Reporter has reference to this Academic Journal, PHwiki organized this Journal Engineering Optimization Concepts in addition to Applications WB 1440 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 Structural optimization

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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 priori assumptions needed about shape Heuristic Methods Hard-kill Soft-kill Etc. etc. Milestones Michell, 1904: “Michell truss” Structures with optimal stiffness as long as a given weight

“Classical” Approaches Various approaches: Ground structure approach (truss sizing) Ai Compliance minimization Classical problem: as long as a given amount of material, find the stiffest structure Save material costs (bridge, building) Improve dynamic per as long as mance (automotive, machines) Save fuel costs (aerospace) Compliance minimization (2) Optimal solution has infinitely fine porous microstructure: impractical

Compliance minimization (3) Conventional approach: Assign density variables to every element Young’s modulus depends on density: SIMP (Solid Isotropic Material with Penalization) SIMP SIMP approach uses penalization to make intermediate densities unattractive: Lower stiffness/weight ratio Forces design to solid/void solution Mesh independence / checkerboard filtering Problems: Checkered solid/void patterns have artificially high stiffness (unrealistic) Solution dependent on mesh size

Solution procedure Compliance minimization problem: Solved by: Constrained optimization algorithms (convex approximation methods: SLP, MMA) Optimality criteria methods (heuristic) Do it yourself! See www.topopt.dtu.dk! Online optimization Matlab programs Recent progress in other applications Topology optimization techniques also (being) developed as long as : 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

Compliant mechanisms Precise, frictionless motion, single structure (no joints) Lu et al, 2003 Wang et al, 2005 Mechanism design Inverter design, Kawamoto/Bendsoe/Sigmund, 2004 Thermal actuator (Sigmund, 2000)

Flow networks Flow network optimization (Klarbring et al, 2003) Ground structure approach Minimize dissipation / pressure drop Limit analysis Gilbert & Tyas, 2003; high-per as long as mance ground structure approach 116,288,875 potential members 6½ hours 13,263,825 potential members 42 minutes Element Connectivity Parameterization Topology defined by elements connected with zero-length links Stiffness of links controlled by design variables g Elements maintain original properties!

Advantages of ECP No material model interpolation required Straight as long as ward sensitivity analysis Shape memory alloy actuator SMA: active material, actuation under temperature change Level sets Topology optimization using an implicit boundary definition as the zero-level contour of a level-set function

Balazs, Diana Arizona Republic - Scottsdale Bureau, The Paradise Valley Reporter www.phwiki.com

Geometrically nonlinear mechanism Compliant gripper Element- density field 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

Balazs, Diana Paradise Valley Reporter

Balazs, Diana is from United States and they belong to Arizona Republic – Scottsdale Bureau, The and they are from  Scottsdale, United States got related to this Particular Journal. and Balazs, Diana deal with the subjects like City/Metropolitan News; Local Government and Politics

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