An efficient method for shape and topology optimization of shell structures

In this paper, a novel method is proposed for shape and the topology optimization of shell structures. A gradient-based shape optimization method and a level set (LS)-based topology optimization method are employed to minimize the compliance of shell structures under volume constraints. During the optimization process, the shell mid-surface of a background quadrilateral shell (QS) mesh is iteratively moved to an optimal shape using a shape gradient function. In the optimization iterations, trimmed QS meshes are generated to obtain an optimal topology by cutting the background QS mesh on an evolving surface with the zero-isolines of an LS function. Polygonal shell elements with assumed strains are used for the trimmed QS elements created along the boundaries of shell structures. Numerical results show that the present shape and topology optimization method is efficient and effective to obtain an optimal design of shell structures with clear boundaries.