A Solid Isotropic Material with Parallel Penalization method for structural topology optimization with multiple materials

Abstract

This paper will conduct systematic research on structural shape and topology optimization in a multi-material domain. A Solid Isotropic Material with Parallel Penalization(SIMPP) method is presented. Central to the method is a parallel penalization that works by decomposing an overall multi-material optimization into a hierarchy of single material optimization and coordinating the sub-optimization so that the joint solution is consistent and optimal for the overall system. The single top-level element of the hierarchy represents the overall optimization of all materials and each lower level element represents optimization of single material where the synthesis of every component material is accomplished by the Solid Isotropic Material with Penalization(SIMP) method. The overall mechanical properties of a multi-material structure are generally formulated according to the tensor addition theorem, and the objective function is additively separable by element. The overall procedure has its unique benefits: it is simple in concept and practice; it is flexible to handle an arbitrary number of candidate materials; it can avoid fragile topologies and is therefore advantageous for manufacturing. Finally, the benefits and the advantages of the method are demonstrated with several examples of mean compliance minimization of multi-material structures.