A layer-by-layer optimization strategy to constitute optimal material distribution of 3D spatial shells by stacking deformation-controlled 2D plain layers

The stiffness of a shell is conclusively influenced by the distribution of its material. To obtain the optimal material distribution of 3D spatial shells at a reasonable computational cost, this paper proposes a layer-by-layer optimization strategy with controllable deformation. In this strategy, the 3D spatial shell is divided into finite layers in the thickness dimension, and the deformations of each layer are constrained by the presupposed target volume in the matching optimization cycle. During the optimization cycle, to minimize the computational cost, we use a dimension-reduced level set method (DR-LSM), wherein the optimal 2D plane layers of the 3D spatial shell are iterated in the 2D domain using a uniform initial design. The optimized 2D plane layers are sequentially stacked to construct the optimal material distribution of the 3D spatial shell. Both numerical calculations and experimental results demonstrate that the proposed strategy successfully achieves an optimal material distribution for 3D spatial shells while preserving their original geometric characteristics and eliminating cavity structures. Notably, the stiffness of shells with different curvatures is significantly enhanced without altering its volume and mass, proving the stability and effectiveness of this strategy.