# STANDARD FINITE VOLUME THEORY APPLIED TO TOPOLOGY OPTIMIZATION FOR COMPLIANCE MINIMIZATION OF CONTINUUM ELASTIC STRUCTURES

## Palavras-chave:

Finite Volume Theory, Topology Optimization, Sensitivity Filters, Continuum Elastic Structures, Compliance Minimization## Resumo

In topology optimization of structures, the objective is to establish the best material

distribution inside of an analysis domain given an objective function, as compliance minimization, and

mechanical restriction to the problem. Normally, in the gradient-based topology optimization

algorithms, there are some problems related to numerical instabilities, such as checkerboard pattern,

mesh dependence and local minima. The checkerboard effect is directly related to the assumptions of

the finite element method, as the satisfaction of equilibrium equations and continuity conditions

through the nodes. On the other hand, the finite volume theory satisfies the equilibrium equations at

the subvolume level, and the static and kinematic continuities are established through adjacent

subvolumes interfaces, as expected from the continuum mechanics point of view. To solve the

problems related to the checkerboard and mesh dependence in the finite element method, it is often

recommended the use of sensitivity or perimeter control filters. For the finite volume theory, the

sensitivity filter is employed with the purpose to control better the mesh dependence and length scale

numerical issues. Comparisons of the optimum topologies and computational performances of the

analyzed approaches are presented, demonstrating the influence of the adopted numerical method on

the obtaining optimal solution when a filtering technique is employed.