Otimização topológica aplicada ao problema de maximização da frequência natural

Abstract

The development of computational tools made possible the advancement of topology optimization applied to mechanical engineering systems. The method adjusts the best layout of a structure, optimally distributing the material in a design domain. The application of the SIMP method (Solid Isotropic Material with Penalization) allows for a well-defined layout, thus possible for fabrication as it penalizes intermediate densities, 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 the iterations. Since it doesn’t depend on the initial representation, the solution to a topology optimization problem can be represented with a high degree of geometric complexity. The topology optimization demands a certain level of refinement for the FE mesh, what may incur in sub-regions resembling a checkerboard pattern. Aiming towards eliminating this checkerboard instability and mesh dependency, a filter is used, either on the design variables or the sensitivities. Thus, this works aims at studying topology optimization for dynamic analysis of two-dimensional structures, presenting a Matlab cod that implements the topology optimization technique by distributing isotropic material applied to mechanical systems subject to free vibrations. As a demonstration of the efficiency of this algorithm, some numerical simulations of beams subject to different boundary conditions are presented.