Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

This paper presents the application of the boundary element method to the shape design sensitivity analysis of composite structures with holes and cutouts. A two-dimensional (2D) anisotropic domain, which contains a number of voids of arbitrary shapes will be considered. The objective is to perform the design sensitivity analysis of the structure with respect to the translation and rotation of the voids using the boundary element method. A directly differentiated form of the boundary integral equation, with respect to geometric design variables is used to calculate the shape design sensitivities for anisotropic materials. The response sensitivity analysis, with respect to the design variables such as feature positions and orientations, is achieved by the definition of appropriate design velocity fields for these variables. To find the optimum positions of the features within an anisotropic structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses and geometry. Due to the non-linear nature of the mean compliance and stresses, the numerical optimisation algorithm used is the feasible direction method, together with the golden section method for the 1D search. A couple of test cases have been performed to verify the proposed method.