Shape design sensitivity and optimization of anisotropic functionally graded smart structures using bicubic B-splines DRBEM

Abstract

A new shape optimization technique is developed, using bicubic B-splines dual reciprocity boundary element method, for anisotropic functionally graded smart structures to minimize weight while satisfying certain constraints upon stresses and geometry. An implicit differentiation of the boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities of anisotropic materials. This method allows the coupling of an optimizing technique and a boundary element elastic stress analyzer to form an optimum shape design algorithm in two dimensions and also allows high-accuracy computation. The boundary element method needs much fewer data related only to the considered boundary of the structure, so it is very suitable for shape optimization in comparison with the finite element method.Because of the non-linear behavior of weight and stresses, the numerical optimization method used in the program is the feasible direction approach, together with the one-dimensional golden-section search technique. The two-dimensional electric fillet knife used as the numerical example in order to verify the formulation and the implementation of the proposed method.