Optimum Shape Design of Composite Structures Using Boundary-Element Method

The boundary-element method, combined with a numerical optimization algorithm, has been employed for the shape optimization of two-dimensional anisotropic structures. To find the optimum shape of a structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses, weight, and geometry. The optimum shapes of a series of anisotropic structures are obtained for maximum stiffness and minimum weight and stress, for specified loading conditions. The results are compared with the optimum shapes, that were already created by the minimization of the structural 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. Because of the nonlinear nature of the mean compliance, weight, and stresses, the numerical optimization algorithm used is the feasible direction method, together with the golden section method for the one-dimensional search. Hermitian cubic spline functions are used to represent boundary shapes that offer considerable advantages in fitting a wide range of curves and in the automatic remeshing process. Five example problems with anisotropic material properties are presented to demonstrate the applications of this general-purpose program. Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.