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

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.