A sequential convex optimization method for multimaterial compliance design problems. (February 2019) - Kennedy, Graeme J.; Chin, Ting Wei
Highlights: Multimaterial and topology compliance designs are optimized via a sequential convex method. Discrete material optimization parametrization utilizes either RAMP or SIMP penalization. Compliance values obtained from the sequence of subproblems is non-increasing. Subproblems are optimized using an inexact Newton–Krylov interior point method. The algorithm is demonstrated on both multimaterial isotropic and orthotropic structures. 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.