Otimização de estruturas através de uma técnica de programação semidefinida de grande porte

• Autor(a) principal: Castro, André Francisco Coêlho
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/123456789/13378
• topic: programação semidefinida; algoritmo de pontos interiores por direções viáveis; maximização da frequência natural de estruturas mecânicas; semidefinite programming; feasible direction interior point algorithm; maximization of the natural frequency of mechanical structures; Modelagem matemática e computacional; Programação semidefinida; Algoritmo de pontos interiores; Otimização estrutural; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

The semidefinite programming techniques, which allow to work with optimization problems subject to matrix constraints, are very efficient in structural optimization applications. Using these techniques, the present dissertation presents a new numerical algorithm, the FDIPA-GSDP(3), belonging to the family FDIPA-SDP-NL, capable to solve large optimization problems. Its differential is in the formulation of a new Newton system, whose function is to find a direction that is at the same time descent and viable, with dimensions quite reduced compared to previous versions, which facilitates their storage in memory and makes possible its application in problems that require a great number of elements in the discretization of the structure. In order to show the performance of this algorithm, numerical results of the applications developed in a classical problem of structural optimization are presented: maximization of the natural frequency of structures subject to volume and compliance constraints.