Topology optimization with multiple phase projection

Topology optimization is a powerful tool capable of generating new solutions to engineering design problems. While these designs may offer optimal performance in a computational setting, it is not uncommon for them to be impractical or unrealizable from engineering or fabrication points-of-view. This challenge motivates the present work. A methodology is proposed for restricting the minimum length scale of each material phase used in the design. The technique allows a designer to, for example, prescribe a minimum allowable length scale of structural members (solid phase) as well as the minimum allowable length scale on holes (void phase). The proposed approach utilizes the Heaviside Projection Method (HPM) to continuum topology optimization. Each material phase is associated with a design variable field that is projected onto element space using regularized Heaviside functions. The fields are independently projected and the resulting distributions are assembled to yield topology. The technique is demonstrated on classic topology optimization problems including minimum compliance, heat conduction, and compliant mechanisms. Solutions are shown to be near-discrete topologies satisfying minimum length scale criterion placed on each phase. Control over length scale is achieved implicitly and therefore the technique does not require additional constraints.