Shape Optimal Design by the Convex Linearization Method

The main goal of the present paper is to discuss the choice of suitable numerical methods for shape optimal design of elastic structures discretized in finite elements. After a short description of the approach we followed to create an appropriate geometric model involving a relatively small number of design variables, attention is mainly directed toward the selection of an adequate optimization algorithm. To this aim the paper will briefly present the various attempts that we have successively undertaken before adopting the convex linearization method as the basic optimizer, not only for shape optimal design problems but also for all our other structural synthesis capabilities. Various examples of applications to optimum shape problems are offered to demonstrate the efficiency of this new algorithm. Finally some comments are made about future developments needed to effectively implement shape optimization concepts into the real design cycle.