A sequential convex optimization method for multimaterial compliance design problems

Abstract This paper presents a sequential convex optimization method for minimum compliance design of multimaterial problems. The proposed method uses a multimaterial parametrization based on SIMP or RAMP penalization. At each iteration of the algorithm, a convex subproblem is constructed by forming a nonlinear, convex approximation of the penalized compliance based on a linearization of the stiffness matrix. Subsequent solutions of the convex subproblems form a non-increasing sequence of compliance values. The subproblems are solved using a tailored inexact Newton–Krylov interior point method that leverages relatively inexpensive Hessian-vector products. The algorithm is demonstrated on a series of isotropic and orthotropic multimaterial plane stress design problems.

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