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

In the topology optimization of structures, compliant mechanisms or materials, a density-like function 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 optimality criteria method, we synthesize compliant mechanisms with multiple materials with and without the material resource constraint. The numerical examples include the two-phase, three-phase, and four-phase materials where void is treated as one material. This new design method enables us to optimally juxtapose stiff and flexible materials in compliant mechanisms, which can be built using modern manufacturing methods.