A new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes

Abstract In this paper, a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes. Our approach consists of three main steps: (1) surface partitioning of polygonal meshes; (2) generation of shape design variables on the basis of partitioned surface patches; and (3) gradient‐based shape optimization of the structures by reducing a weighted compliance among all load cases. The main contributions of this paper include (i) that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times, compared to the conventional design variable scheme of using each mesh node; (ii) our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch, except on its boundary; and (iii) overall, our approach can be used to automate time‐consuming shape optimization of polygonal meshes to a greater extent. Numerical experiments have been conducted and the results indicate the effectiveness of the approach. Copyright © 2003 John Wiley & Sons, Ltd.