Optimizing the layout of discrete objects in structures and materials: A projection-based topology optimization approach

Abstract

This paper uses topology optimization to optimize the layout of discrete objects, such as fixed-shape void, stiffening, or functional inclusions, in structures and periodic materials. The methodology follows a material distribution approach and the Heaviside Projection Method (HPM) is manipulated to ensure that the designed objects are discrete, of fixed size (length scale) and shape, and satisfy minimum spacing requirements. These restrictions are achieved implicitly through projection without additional constraints or heuristics. The methodology is built in the spirit of free-form topology optimization and thus discrete objects are shown to appear, vanish, or translate across the design domain during the design evolution. The technique is demonstrated on problems governed by mechanical stiffness including the design of structures and material microstructures whose elastic stiffness is to be enhanced by optimizing the location of stiff, circular inclusions.