Aplicação do modelo de kriging na otimização de estruturas de materiais compostos laminados - França, Gustavo Von Zeska de (2011)
Surrogate models (or metamodels) are mathematical approximations used to replace more detailed models, in order to reduce the computational time when many evaluations are necessary. They are obtained from mathematical approximation functions and detailed models previously calculated. Surrogate models are very useful in the optimization process of parts and structures, because in this case it is necessary to analyze the structural response of the system several times, each one with different values for the design variables. In this work, a Kriging model (KM) version was implemented in Matlab. Some parameters that govern the approximation were analyzed, in order to verify their influence on the surrogate model. Then, the Kriging model was applied to estimate the structural response of rectangular plates of laminated composite materials in which the exact response is given by the Classical Lamination Theory (CLT). The first analyses were made to check the approximation of the Tsai-Wu failure criterion and the buckling criterion. The obtained results were very consistent and they show that the Kriging model can be used to approximate the behavior of laminated composite materials. Next, the Genetic Algorithm (GA) optimization method was combined to the Kriging model to find the lay-up sequence of laminated composites aiming to minimize the possibilities of failure according to Tsai-Wu failure criterion and buckling. The results obtained in this cases showed a good convergence of the response to the optimal point. However, the computational time was lower only in the cases with a large number of design variables. Then, a commercial finite element, used to calculate the structural response, was associated with the Kriging model in order to optimize more complex geometries. The results from optimization problems using and not using de Kriging model were compared and it was verified that a significant computational time can be saved in the first case.