Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme

Abstract

In the topology optimization of structures, compliant mechanisms or materials, a density-like func- tion is often used for material interpolation to overcome the computational difficulties encountered in the large "0-1" type integer programming problem. In this paper, we illustrate that a gradually formed continuous peak function can be used for material interpolation. One of the advantages of introducing the peak function is that multiple materials can easily be incorporated into the topology optimization without increasing the number of design variables. By using the peak function and the op- timality criteria method, we synthesize compliant mech- anisms with multiple materials with and without the ma- terial resource constraint. The numerical examples in- clude the two-phase, three-phase, and four-phase materi- als where void is treated as one material. This newdesign method enables us to optimally juxtapose stiff and flex- ible materials in compliant mechanisms, which can be built using modern manufacturing methods.