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

• Published in: Latin American journal of solids and structures 2020, Vol.17 (8)
• Main Authors: Araujo, Marcelo Vitor Oliveira, Lages, Eduardo Nobre, Cavalcante, Márcio André Araújo
• Format: Article
• Language: English
• Subjects: ENGINEERING, CIVIL; ENGINEERING, MECHANICAL; MECHANICS
• ISSN: 1679-7817; 1679-7825; 1679-7825
• DOI: 10.1590/1679-78256053

Abstract 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 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.