Topology Optimization for Variable Thickness Shell-Infill Composites Based on Stress Analysis Preprocessing

Inspired by natural biomimetic structures exemplified by femoral bones, the shell-infill composite design has emerged as a research focus in structural optimization. However, existing studies predominantly focus on uniform-thickness shell designs and lack robust methodologies for generating high-resolution porous infill configurations. To address these challenges, a novel topology optimization framework for full-scale shell-filled composite structures is developed in this paper. First, a physics-driven, non-uniform partial differential equation (PDE) filter is developed, enabling precise control of variable-thickness shells by establishing explicit mapping relationships between shell thickness and filter radii. Second, this study addresses the convergence inefficiency of traditional full-scale topology optimization methods based on local volume constraints. It is revealed that a reduced influence radius exacerbates algorithm convergence challenges, thereby impeding the design of intricate porous structures. To overcome this bottleneck, a physics-driven stress skeleton generation method is developed. By integrating stress trajectories and rasterization processing, this method constructs an initial density field, effectively guiding material evolution and significantly enhancing convergence in porous structural optimization within the full-scale framework. Classical numerical examples demonstrate that our proposed optimization framework achieves biomimetic non-uniform shell thickness optimization and enables precise control of the shell thickness. Additionally, density preprocessing effectively eliminates intermediate density regions and void aggregation. Moreover, the generated trabecular-like infill patterns with spatially graded porosity, akin to multiscale topology optimization (MTO), provide an innovative solution for multifunctional, lightweight, complex shell-infill composite structures in aerospace and biomedical applications.