Cálculo de sensibilidades: uma aplicação do método dos elementos de contorno à otimização de forma

Abstract

This work aims at the development of shape sensitivity analysis with the application of the Boundary Element Method (B.E.M.) and its use in the shape design optimization. A shape sensitivity procedure is developed in wich the standard discretized version of the boundary integral equation is differentiated. The sensitivities of the surface tractions and displacements are the new unknowns. They are computed by the solution of a system of linear equations that presents the same coeficient matrix of the original B.E.M. problem. The sensitivities for each design parameter are computed after the formation of the respective new right-hand-side term. With these results the stress sensitivities can also be calculated. The implementation uses constant elements in the case of torsion of prismatic bars and linear ones for plane elasticity. In the latter, special techniques for shape sensitivity analysis of symmetric structures and infinite regions were developed. It is also possible to analise structures where the sensitivities of the prescribed unknowns are not null. In a series of examples the convergence and precision of the method is verified. In adition, the applicability of the method is also tested through the adoption of a simple optimization algorithm.