FINITE-VOLUME THEORY APPLIED TO TOPOLOGY OPTIMIZATION OF CONTINUUM LINEAR ELASTIC STRUCTURES
Marcelo Vitor Oliveira Araujo1; Eduardo Nobre Lages1; Márcio André Araújo Cavalcante1
1 Federal University of Alagoas
doi:10.20906/CPS/CILAMCE2017-1247
Resumo
Numerical stability is an important issue for the gradient-based optimization algorithms based on finite-element method, and is currently one of the main research areas. Numerical issues of the gradient-based optimization algorithms are checkerboards, mesh dependence and local optima. Possible solutions for the checkerboard-problem and mesh dependence are the adoption of higher order elements or filtering techniques based on image processing. The issues of the gradient-based optimization algorithms are mainly related to the displacement based finite-element method assumptions, as the satisfaction of equilibrium and compatibility conditions between elements are enforced only at the nodes, in terms of nodal displacements and forces. Also, the equilibrium equations are not satisfied at the element level, only when a sufficiently refined mesh is employed. Differently of the finite element method, the finite volume theory satisfies the equilibrium equations at the subvolume level, and also the equilibrium and compatibility conditions at the subvolumes' interfaces, in terms of displacements and tractions. The finite volume theory is an elasticity-based approach, so, the connections between subvolumes occur through the subvolumes' faces, as expected from a continuum mechanics point-of-view, which is not true for the displacement based finite-element approach, where the connections between elements occur through the nodes, sometimes resulting in unrealistic optimized geometries with checkerboard patterns, not suitable for manufacturing. A topology optimization approach based on the finite volume theory is proposed to solve these issues of the gradient-based topology optimization algorithms based on finite-element analysis, resulting in an efficient computational tool for topological optimization of continuum linear elastic structures.
Palavras-chave: Finite-Volume Theory; Finite Element Method; Gradient-based Optimization Algorithm; Topology Optimization; Continuum Linear Elastic Structures