Otimização sequencial aproximada de estruturas laminadas de material compósito

Abstract

The optimization of fiber reinforced composite structures is a problem whose solution has a high computational cost, especially when using metaheuristic methods such as Genetic Algorithms and Particle Swarm Optimization. These methods require a large number of evaluations of the objective function and constraints, which combined with the high processing time of the analysis by the Finite Element Method (MEF) and Isogeometric Analysis (AIG), makes it difficult to apply optimization techniques in solving a structural engineering problem. An alternative to reduce processing time is the use of Sequential Approximate Optimization (SAO) using surrogate models that approximate but efficiently represent the MEF and AIG results. The SAO is a technique that requires the creation of an interface between an optimization program and a numerical simulation program. In this work, the interface was performed using the Biologically Inspired Optimization System (BIOS) for optimization and the Finite element AnalysiS Tool (FAST) for numerical simulation. The Radial Base Functions (RBF) were used in SAO and the Support Vector Regression (SVR) were used in Static Optimization (SO) as surrogate models to approximate the structural analysis responses of the laminated structures. Initially, training samples were generated by the Hammersley Sequence to construct the initial surrogate model. In the SAO the initial RBF model was updated during the optimization in a sequence of generations, in the SO the surrogate model was not updated. The updating was accomplished through the insertion of new points in the training sample that were obtained through two different approaches: the first was the insertion of the best individual of each generation; in the second, insertions of new points located in the sparse regions of space of the design variables by minimizing the Density Function (DF). In the evaluation of SAO and SO, the performance of laminated plate and shell structures was maximized. The results showed the feasibility of using SAO with RBF in the optimization of laminated structures due to the reduction of computational cost and the admissible error values when the approximate solutions were compared to the optimal designs. The SO, in turn, showed that the computational cost was reduced to the extreme, but that there is a need to insert new points to improve the quality of the approaches.