A von Mises stress-based topology optimization applying the standard finite-volume theory for continuum elastic structures

Resumo

Topology optimization algorithms want to establish the best material distribution inside of an analysis
domain. In those optimization problems, usually there are some numerical problems to be overcome, such as the
checkerboard pattern, mesh dependence, local minima, and occurrence of gray regions. This paper addresses a
new topology optimization technique, where the objective is to minimize the equivalent average von Mises stress
subject to a volume constraint and to apply the standard finite-volume theory for elastic stress analysis. The solid
isotropic material with penalization (SIMP) approach is employed to avoid discrete optimization problems. The
proposed optimization problem has shown efficiency, avoiding the occurrence of numerical instabilities, such as
checkerboard pattern, mesh dependence, and local minima, when a sensitivity filter is employed. In the absence
of filtering techniques, the proposed approach has shown efficiency by producing checkerboard-free optimized
topologies with fewer bars, more robust bars, and well-defined “black and white” designs.