Otimização de topologia de estruturas e componentes

Abstract

Topology optimization (TO) is an optimization technique that aims to help the designer in the phase of structural conception, seeking a better distribution of one fixed amount of material in a extended design domain. It combines a method of structural analysis with a mathematical programming (MP) algorithm. In this work, structural analysis is done by Finite Element Method (FEM) and the solution algorithm employed is the Optimality Criteria (OC). One of the main themes of research in TO refer to the regularization techniques, needed to make the solutions free of the classic numerical instabilities of the problem: the instability of the checkerboard and mesh dependency. The goal of this work is study the traditional regularization techniques found in literature as the sensitivity filter by Sigmund, Continuous Approximation of Material Distribution (CAMD) and projection techniques. A new projection technique is proposed in order to obtain solutions close to the void-solid form. The objective function is the mean compliance of the structure, and is imposed a restriction on the total volume of material to be distributed. Is used the model Solid Isotropic Material with Penalization (SIMP) to parameterize the distribution of isotropic materials, and their adaptation FGM-SIMP for functionally graded materials (FGM). To illustrate the behavior of these techniques examples of application are shown, fruits of the computational implementation.