A SIMP-based algorithm to maximize natural frequencies in two- dimensional structures

Resumo

This paper aims to study the topology optimization of two-dimensional structures based on their
dynamic response by implementing a computational algorithm that optimally distributes the material in a project
domain based on the SIMP approach (Solid Isotropic Material with Penalization). It allows for a well-defined
result and therefore a layout that can be manufactured since it penalizes intermediate densities thus eliminating
them from the final result. The model uses the Finite Element Method (FEM) for spatial discretization and to
evaluate the objective function, the restraints, and the sensitivities through iterations. Since it does not depend on
the initial representation, the solution of a topology optimization problem can be represented with a high degree
of geometric complexity, requiring a certain level of refinement of the finite element mesh. This refinement can
cause sub-regions of the domain resembling a checkerboard pattern, which is avoided when a sensitivity filter is
used. The optimization objective function is taken as the lowest eigenfrequency of the structure, as to avoid
resonance, a common problem in civil and mechanical structures.