Otimização estrutural multi-objetivo de pórticos espaciais em aço com variáveis de projeto não usuais

Abstract

In structural engineering problems, it is of great interest to the designer to find the most economical solution possible, which meets the requirements imposed by technical standards. Finding the most economical solutions, meeting the safety requirements, may demand a trial and error process with high computational cost. To work out this issue, structural optimization problems are formulated to find an optimal solution, or close to the optimum, as desired. Structural optimization problems can have one or more objectives. In most of the cases, the weight of the structure or the total cost is the main objective to be minimized. However, if it is desired to increase the structural performance of the building, the problem have conflicting objectives. To solve it, one can resort to multi-objective optimization, where objective functions related to displacement minimization, stability maximization, and better dynamic behavior are also present. This work objective is to formulate, solve and analyse several multi-objective optimization of steel space frames considering these objective functions, combined in multiple ways. When one of these aspects is not an objective, it is considered as a constraint. Furthermore, in addition to considering the traditional design variables related to the cross-sections designated to a group of members, the orientation of the columns and their positions are also considered as design variables. In the studied examples, the search for the best solutions is done using algorithms based in Differential Evolution to multi-objective problems. Pareto fronts in two, three and four dimension are presented. A detailed analysis about the non-dominated solutions presented in the Pareto fronts is done. A multi-criteria tournament decisionmaking method is used in multi-objective problems to extract the adequate solutions to the criteria defined by the designer and performance metrics are applied to compare the algorithms.