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.

With the continuous advancement in topology optimization and additive manufacturing (AM) technology, the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly. However, a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures, potentially resulting in diminished efficiency or macroscopic failure. A Hybrid Level Set Method (HLSM) is proposed, specifically designed to enhance connectivity among non-uniform microstructures, contributing to the design of functionally graded cellular structures. The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces. Initially, an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides. Subsequently, the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures. The method, seamlessly integrated into a multi-scale topology optimization framework using the level set method, exhibits its efficacy through numerical examples, showcasing its prowess in optimizing 2D and 3D functionally graded materials (FGM) and multi-scale topology optimization. In essence, the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced, substantiated by numerical evidence, advancing optimization capabilities in the realm of functionally graded materials and cellular structures.