Level set-based topology optimization for compliance and stress minimization of shell structures using trimmed quadrilateral shell meshes

In this paper, a novel level set-based topology optimization method for shell structures is presented to minimize both compliance and stress under a volume constraint. During the optimization process, trimmed quadrilateral shell meshes are generated by cutting a background quadrilateral shell mesh with the zero-isolines of a level set function. Polygonal shell elements with assumed strains are used for the trimmed quadrilateral shell elements created along the boundaries of shell structures. A new sensitivity field for the evolution of a level set function is proposed to minimize both compliance and stress of shell structures. A p -norm function is employed to aggregate local stresses into a single global stress measure in the sensitivity analysis. Several numerical examples are carried out to show the validity and effectiveness of the proposed method.