Otimização estrutural multi-objetivo de treliças planas e espaciais considerando aspectos dinâmicos e de estabilidade global

Abstract

This dissertation presents the formulation of structural optimization problems (SOPs) containing three to six objective functions applied to plane and spatial trusses, focusing on considering objectives and constraints regarding the natural frequencies of vibration and the critical load factors. Solving SOPs helps engineering professionals find solutions and make decisions in developing a project. The application of multi-objective SOPs allows the decision-maker to find structural configurations that simultaneously serve all the desired criteria without solving several single-objective problems individually. To reduce costs and material consumption, the first objective, analyzed in all proposed problems, is to minimize the weight of the trusses. To avoid the resonance effect and find solutions with better dynamic behavior, other objectives used are the maximization of the first natural frequency of vibration and the maximization of the differences between the structure’s natural frequencies to avoid the superposition of their vibration modes. To guarantee the structural stability of the trusses, SOPs are also proposed with the objective functions of maximizing their first critical load factors related to global stability and maximizing the difference between their first two critical load factors. The meta-heuristics used to solve the optimization problems of this study are the GDE3 (Third Evolution Step of Generalized Differential Evolution), the SHAMODE (Success History–based Adaptive Multi-objective Differential Evolution), the SHAMODE-WO (Success History–based Adaptive Multi-objective Differential Evolution with Whale Optimisation) and the MM-IPDE (Multi-objective Meta-heuristic with Iterative Parameter Distribution Estimation). The non-dominated solutions obtained for each SOP are presented by graphs of the Pareto fronts and normalized parallel coordinate graphs (for the cases with more than three objective functions). A multi-criteria tournament decision-making method is applied to extract the desired solutions for each problem, according to the designer’s preferences. Finally, the performances of the four algorithms are compared through performance indicators found in the literature.