Checkerboard-free topology optimization for compliance minimization of continuum elastic structures based on the generalized finite-volume theory

Marcelo Vitor Oliveira Araujo, Eduardo Nobre Lages, Márcio André Araújo Cavalcante
2020 Latin American Journal of Solids and Structures  
Topology optimization is a well-suited method to establish the best material distribution inside an analysis domain. It is common to observe some numerical instabilities in its gradient-based version, such as the checkerboard pattern, mesh dependence, and local minima. This research demonstrates the generalized finite-volume theory's checkerboard-free property by performing topology optimization algorithms without filtering techniques. The formation of checkerboard regions is associated with
more » ... associated with the finite element method's displacement field assumptions, where the equilibrium and continuity conditions are satisfied through the element nodes. On the other hand, the generalized finite-volume theory satisfies the continuity conditions between common faces of adjacent subvolumes, which is more likely from the continuum mechanics point of view. Also, the topology optimization algorithms based on the generalized finite-volume theory are performed using a mesh independent filter that regularizes the subvolume sensitivities, providing optimum topologies that avoid the mesh dependence and length scale issues. Keywords Topology optimization, checkerboard-free approach, generalized finite-volume theory, continuum elastic structures, and finite element method. Graphical Abstract Checkerboard-free topology optimization for compliance minimization of continuum elastic structures based on the generalized finite-volume theory
doi:10.1590/1679-78256053 fatcat:ey2odkyq4jdftod7ivttgewfiq