Algorithms for point-wise state variable constraints in structural optimization

Abstract This paper presents algorithms to treat the point-wise state variable constraints in finite dimensional and distributed parameter structural optimization problems. The idea is to impose such constraints at all local maximum points, or over a small region around the maximum points. Therefore, methods for design sensitivity analysis to handle the constraints at some particular point for the distributed parameter problem are presented. The direct differentiation and adjoint variable methods are employed to derive the design sensitivity expressions. For the finite dimensional problem the new idea is easily carried out in optimization process. Simply supported and clamped beams are optimized using the new approach. These are modeled with nonuniform beam elements. Comparisons of finite dimensional and distributed parameter problems are also made.