Shape optimization of two-dimensional anisotropic structures using the boundary element method

A shape optimization procedure is developed, using the boundary element method, for two-dimensional anisotropic structures to minimize weight while satisfying certain constraints upon stresses and geometry. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities of anisotropic materials. The boundary element method is very suitable for shape optimization and in comparison with the finite element method needs much fewer data, related only to the boundary of the structure being considered. Because a directly differentiated form of the boundary integral equation can be used to determine the derivatives of the objective and constraint functions, the accuracy of computation is very high. Because of the non-linear nature of weight and stresses, the numerical optimization method used in the program is the feasible direction approach, together with the golden section method for the one-dimensional search. Three example problems with anisotropic material properties are presented to demonstrate the applications of this general-purpose program.