Uma metodologia multiobjetivo para otimização topológica

Abstract

CAD systems that integrates Topological Optimization, automatic interpretation of topologies and their parameterization and Shape Optimization are of great interest given the complexity of the task of applying a post-processing procedure to a large set of proposed topologies. This thesis presents a multiobjective approach that integrates the Topological Optimization with the parameterization of the obtained topologies and the Shape Optimization for problems with several materials. A Multiobjective Ant Colony Algorithm is presented to solve the topological optimization. The topologies estimated by the Multiobjective Ant Colony Algorithm (MOACO) represent an initial set of compromise solutions, which are then parameterized using NURBS (NonUniform Rational B-Spline). Instead of applying an additional step performing Shape Optimization in all solutions of this set, PROMETHEE II is used as a decision-making method to select a topology or a small number of topologies to undergo the shape optimization. At the final stage, the Multiobjective Shape Optimization problem is solved by applying the NSGA-II algorithm to the variables associated to the coordinates of the control points and the weights of the internal border NURBS parametrization of the selected topologies. The proposed approach is illustrated in the design of a C-core magnetic actuator, which involves the distribution of three materials (air, permanent magnets and ferromagnetic materials) in a design space. The results obtained show the suitability and flexibility of the presented method, since good estimates of the Pareto-optimal front are obtained and the procedure of parameterization via NURBS and selection of the solutions using PROMETHEE II integrates automatically the process of topological and shape optimization leading to a small set of solutions.