A multi-material Proportional Topology Optimization approach for compliant mechanism problems

Abstract

This paper presents an extension for the Proportional Topology Optimization (PTO) algorithm to solve multi-material topology optimization of compliant mechanism problems. The objective function is firstly transformed from maximization of output displacement into maximization of mutual strain energy. In this setting, the contribution of each element to the objective function can be evaluated, facilitating the application of the PTO algorithm. The objective function is further multiplied by minus one so that a familiar form of minimization can be obtained. When multiple materials are involved, the problem is decomposed into several two-phase sub-problems based on the alternating active phase algorithm (AAPA). Using the PTO algorithm, each material is distributed into elements proportionally to the contribution of that material in the mutual strain energy. Due to the fact that the mutual strain energy can be either negative or positive, a modification has been made in the PTO inner loop to update the pseudo-density (the design variables). The applicability and feasibility of the developed approach are illustrated through several numerical examples.