An interactive capability for shape optimal design

Abstract

Shape optimal design of two-dimensional structures discretized in finite elements is investigated with emphasis on creating an interactive Computer-Aided Design capability. The paper will first provide a brief description of the approach followed to create an appropriate geometric model, involving a relatively small number of design variables. Next a general procedure to perform the sensitivity analysis is proposed, that takes advantage of the parametric modeling concepts used to create the design model. This sensitivity analysis method is based on the so-called semi-analytical approach, i.e. a finite difference approximation of the derivative of the stiffness matrix is employed. The numerical solution to the shape optimal design problem is obtained by resorting to an efficient optimizer based on the convex linearization method. A two-dimensional pre- and post-processing module is described, which is aimed at performing interactive shape optimal design on an engineering workstation. This module exhibits some innovative visualization techniques that should highly facilitate the task of a designer. Examples of application to shape optimal design problems are offered to illustrate the various functions of the new interactive optimization system. Although the described capability is restricted to simple two-dimensional structures, it is based upon very general concepts that could be readily implemented in general-purpose finite element systems.