Maximal Stiffness Design of Two-Material Structures by Topology Optimization with Nonprobabilistic Reliability

Basedon the multi-ellipsoid convex modelandthe quantified measure of the nonprobabilistic reliability, topology optimization of two-material structures in the presence of parameter uncertainties is investigated. The task of the optimal design problem is to distribute a given amount of two candidate materials into the design domain for acquiring the maximal stiffness while satisfying the reliability requirement. The extended power-law interpolation scheme for material properties is employed for relaxing the two-material topological design problem into a continuous-valued optimization problem. In addition, through transforming the minimax-type optimization problemintoaseriesofdeterministiconesbyusingasequentialapproximateprogrammingstrategy,thispaperaims tomaketheoptimizationdesignnumericallytractable.Theresultingmathematicalprogrammingproblemsarethen efficientlysolvedbytheassociationofthemethodofmovingasymptoteswithaheuristiciterativemanner.Numerical investigations reveal that system uncertainties may have considerable effects on the optimal material layout of twomaterial structures. The proposed topology optimization methodology could yield a more reasonable two-material structuraldesignthan theconventional deterministic counterpart whenthe samereliabilityrequirements need tobe achieved.

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