Conformal-Mapping-Enhanced Topology Optimization of Core-Layer in Sandwich Shell Structures

Sandwich shell structures are used extensively in the aerospace, automotive, and marine engineering fields because of their favorable stiffness-to-weight characteristics and reliable fatigue performance. However, in most existing studies, the core layer is treated as a passive structural component, and the contribution of the core to the global mechanical performance of sandwich shell structures remains insufficiently explored. To fully exploit the structural potential of the core, in this paper, a topology optimization strategy is developed in which the core is treated as the primary design domain. A layered continuum material model (LCMM) that represents the three-layer sandwich shell as a unified equivalent shell is first developed; this enables the governing finite element equations to be derived while also accounting for mechanical interactions between the layers. Based on the proposed LCMM, a core-layer topology optimization model and the associated sensitivity analysis are established, allowing the effect of the core material distribution on the overall mechanical response of the sandwich shell to be accounted for during optimization. To cope with the geometric complexity of curved shell structures, conformal mapping is adopted to project the three-dimensional shell surface mesh onto a two-dimensional parameter domain. Within the parametric domain, the level set function is defined and updated to describe the topological evolution of the core. The feasibility and reliability of the proposed framework is verified by numerical simulations and experimental results.