A fictitious energy approach for shape optimization

Abstract

Abstract This paper deals with shape optimization of continuous structures. As in early works on shape optimization, coordinates of boundary nodes of the FE‐domain are directly chosen as design variables. Convergence problems and problems with jagged shapes are eliminated by a new regularization technique: an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design. The energy constraint defines a feasible design space whose size can be varied by one parameter, the upper energy limit. By construction, the proposed regularization is applicable to a wide range of problems; although in this paper, the application is restricted to linear elastostatic problems. Copyright © 2009 John Wiley & Sons, Ltd.