Otimização estrutural topológica contínua utilizando uma microestrutura sólida isotrópica e penalizada aplicada em problemas de vibrações livres não amortecidas

Abstract

The present work focuses on solving a Continuous Topology Optimization of Continuum Structures problem using a material approach based on a Solid Isotropic Microstructure with Penalization. The problem aims at maximizing the fundamental frequency of a formulation of undamped free vibrations with constraint on the material volume. The Finite Element Method is used for discretization of the analysis domain in mechanical models. The Augmented Lagrangian Method is applied to solve the optimization problem. Furthermore, two regularizing functionals are used, one penalizing regions with intermediate densities and the other penalizing density gradients. These functional features, for example the complexity intent of possible meshes, for example, can be defined as the gray board and have a mesh dependency. The computational implementation is performed by Matlab® software. Two physical problems with different symmetry characteristics are analyzed. The results obtained are qualitatively and quantitatively compared with works present in the literature, analyzing aspects of mesh independence and the occurrence of both the chessboard phenomenon and regions with intermediate densities. The optimal topologies obtained, considering the comparisons already present, had the problems mitigated using functionals. The optimal topologies obtained present the mitigation of checkerboard problems and regions with relative densities under the influence of the penalizing functionals, they also present show a tendency to the phenomenon of mesh independence. Therefore, regarding the proposed methodology, it is possible to affirm that it is adequate with a view to the problems of undamped free vibrations.