Stress-based topology optimization with discrete geometric components

In this paper, we introduce a framework for the stress-based topology optimization of structures made by the assembly of discrete geometric components, such as bars and plates, that are described by explicit geometry representations. To circumvent re-meshing upon design changes, we employ the geometry projection method to smoothly map the geometric components onto a continuous density field defined over a uniform finite element grid for analysis. The geometry projection is defined in a manner that prevents the singular optima phenomenon widely reported in the literature, and that effectively considers stresses only on the geometric components and not on the void region. As in previous work, a size variable is ascribed to each geometry component and penalized in the spirit of solid isotropic material with penalization (SIMP), allowing the optimizer to entirely remove geometric components from the design. We demonstrate our method on the L-bracket benchmark for stress-based optimization problems in 2-d and 3-d.