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.

在本文中，提出了一种新的基于水平集的壳结构拓扑优化方法，以在体积约束下最小化柔量和应力。在优化过程中，修剪四边形壳网格是通过用水平集函数的零等值线切割背景四边形壳网格来生成的。具有假定应变的多边形壳单元用于沿壳结构边界创建的修剪四边形壳单元。提出了一个用于水平集函数演化的新灵敏度场，以最小化壳结构的柔度和应力。一种$磷$-norm 函数用于在敏感性分析中将局部应力聚合为单个全局应力度量。进行了几个数值例子来证明所提出方法的有效性和有效性。