Estudo e implementação computacional de problemas de otimização topológica 3D

• Ano de defesa: 2019
• Autor(a) principal: Alvarez, Gustavo David Quintero [UNIFESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Paulo (UNIFESP)
• Palavras-chave em Português: Topology Optimization; Nonlinear Optimization; Sequential Linear Programming; Three-Dimentional Structures; Otimização Topológica; Otimização Não Linear; Programação Linear Sequencial; Estruturas Tridimensionais
• Link de acesso: https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=8320258; https://repositorio.unifesp.br/handle/11600/59508

The topology optimization is a class of structural optimization problems to obtain a structure that is as rigid as possible, satisfying a constraint on the amount of material available inside a certain domain, and which is subjected to the application of external forces. In other words, the objective is to find the optimal distribution of the material that composing this structure, so that its average compliance is minimized (or, equivalently, its stiffness should be maximized). Initially, topology optimization problems are formulated in a continuous medium, so that at each point in the domain that contains the structure, it must be decide whether or not there will be material. In this case, we have an optimization problem with an infinite number of binary variables. In order to make the problem treatable from a numerical point of view, this continuous medium is replaced by a discrete medium through the application of the Finite Element Method. Thus, we obtain a nonlinear optimization problem with a finite number of variables, which represent the material density in each of the elements of the discretized domain. In this work, we performed a study on the formulation of topological optimization problems of three-dimensional structures (which have many applications in the automotive and aerospace industries), and implemented an optimization’s method denominated Sequential Linear Programming (SLP) to solve these problems. We perform several computational tests that prove the efficiency of this method in the resolution of topological optimization problems.