Método das somas ponderadas aplicado à otimização multiobjetivo de estruturas lineares e não lineares usando computação evolucionária

Abstract

Topological optimization of structures with static behavior, both linear and physical and geometric nonlinear, considering multi-objective problems is the main of this work. In order to do this process, an evolutionary and heuristic formulation called SESO (Smoothing Evolutionary Structural Optimization) is used together with the Finite Element Method (FEM). When considering a multi-objective problem, it is also necessary to select a methodology according to the alternatives available in order to choose the optimal topology. Therefore, the Analytic Hierarchy Process (AHP) has been used, since all the theory about this method is able to deal with evaluation of subjective alternatives, according to multiple criteria, in a simple and hierarchical manner. Furthermore, the Weighted Sum Method (WSM) works together with the AHP to organize numerically the set of alternatives available throughout the optimization analysis, in terms of decision criteria. During all this process, it was implemented in an algorithm developed in Python® programming language that serves as the input file to the free numerical software for multi-physics analysis Code-Aster®, which belongs to Salome-Meca® modeling program, which has a friendly GUI for pre and post processing analyses. Finally, in parallel, the work complements the development of a computational interface in Lazarus, that is a free alternative software comparing with Borland Delphi, for the necessary adjustments for the proper functioning of SESO algorithm in order to perform relevant analyzes and evaluate the results obtained by minimizing the vector that was generated by the WSM. The nine linear examples show the operation code, including the comparison of results that can be found in the literature. The three nonlinear examples show differences and/or similarities between the optimal topologies among the analysis performed in this thesis.