Concurrent Design of Hierarchical Structures with Multi-morphology Lattices Considering Geometric Nonlinearity

Lattice structures are widely used in aerospace vehicles due to their characteristics of slender members, light weight, and small damping ratios. Traditional design methods mostly focus on single-form lattice structures and often neglect geometric nonlinearity, resulting in deviations between actual performance and expectations, which poses challenges to efficient collaborative optimization. This study proposes a novel design method for obtaining multiscale lattice hierarchical structures considering geometric nonlinearity. It addresses design issues at both macroscopic and microscopic scales simultaneously, defining two independent design variables in the macroscopic structural design domain and the microscopic material design domain, respectively. Based on homogenization theory and the porous anisotropic material penalty (PAMP) model, this study derives the equivalent properties of parameterized lattice microstructures. Therefore, this multiscale design method can optimize both the macroscopic distribution and its spatially varying microscopic configurations with acceptable computational cost. A collaborative optimization model for multiscale structures is established based on nonlinear finite element analysis (FEA), in which the overall stiffness is measured by complementary elastic work. Meanwhile, the sensitivity related to the geometric nonlinear iteration process is derived through the adjoint method. The effectiveness of this method is validated through numerical examples, including cantilever beam and bridge structures. The optimized examples maintain excellent load-bearing capacity under large deformations, while the multiscale lattices synergistically enhance the stiffness-to-weight ratio. This method breaks through the limitations of traditional design approaches, providing theoretical support for the refined design of hierarchical structures. It can guide the design of complex structures in additive manufacturing, being particularly applicable to lightweight components subjected to large deformations in the aerospace field. Additionally, it reduces computational costs and offers guidance for the multiscale design of other complex engineering structures.