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

•A new sensitivity field is proposed to minimize both compliance and stress of shell structures.•Boundary-conforming trimmed quadrilateral shell meshes are used to clearly represent the structural boundaries.•Trimmed quadrilateral shell meshes are generated by cutting a background mesh with the zero-isolines of a level set function.•Numerical results show that the present method can effectively minimize both the compliance and stress of shell structures. 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.