Topology optimization using the discrete element method. Part 1: Methodology, validation, and geometric nonlinearity

Abstract Structural Topology optimization is attracting increasing attention as a complement to additive manufacturing techniques. The algorithms usually employ continuum-based Finite Element analyses, but some important materials and processes are better described by discrete models, for example granular materials, powder-based 3D printing, or structural collapse. To address these systems, we adapt the established framework of SIMP system modelled with Discrete Method. We consider typical problem stiffness maximization which define objective function related sensitivity framework. method validated simply supported beams discretized interacting particles, whose predicted optimum solutions match those from classical algorithm. A parametric study then highlights effects mesh dependence filtering. An advantage Method that geometric nonlinearity captured without additional complexity; this illustrated when changing beam supports rollers hinges, indeed generates different structures. proposed Optimization enables future incorporation nonlinear interactions, well discontinuous such during fracture