General-purpose computer program for shape optimization of engineering structures using the boundary element method

Abstract

Optimization of the shape of structural components is often concerned with minimizing stress concentration effects to ensure a longer fatigue life. A general purpose computer program, STRESOPT, for shape optimal design of two-dimensional structures in order to smooth stress peaks is presented. The program has three main parts: the stress analyzer, design sensitivity analyzer and optimizer. The stress analyzer and design sensitivity analyzer use the boundary element method with isoparametric quadratic boundary elements. The boundary element method is very suitable for shape optimization and in comparison with the finite element method needs much less data, related only to the boundary of the structure being considered. Because a differentiated form of the boundary integral equation (on which the boundary element method is based) can be used directly to determine the derivatives of the objective and constraint functions, the accuracy of computation is very high. The numerical optimization method used in the program is the extended penalty function approach, using the BFGS variable metric for unconstrained minimization, together with the Golden Section method for the one-dimensional search. Initial mesh preparation and regeneration of the boundary elements during the iterative process of optimization is both straightforward and fast. Hermitian cubic splines are well suited for the boundary shape representation, and complex geometries can be described in a very compact way by a small number of design variables. Applications of the program to the optimum shape design of fillets and holes in plates and bars are presented.