Shape Optimization for Beams Subject to Displacement Restrictions on the Basis of the Growing-Reforming Procedure

This paper deals with the shape optimizing problem for a structural beam where its allowable displacement is restricted under multiple loads. A Growing-Reforming Procedure proposed by the authors is employed. The Procedure is extended to the cases where a beam has to support a number of possible loads ; that is, a method to evaluate the envelope of the stress induced by the possible loads. In order to make allowable displacement within a restricted value, a combined method of sensitivity with the Growing-Reforming Procedure is introduced. A computational algorithm based on this method is established. Some typical applications are shown to demonstrate the effectiveness of these methods.