Data-Driven Multifidelity Generative Topology Optimization for Geometrically Nonlinear Structures

Building upon existing multifidelity topology optimization studies where geometric nonlinearity has been considered in high-fidelity models, this work introduces a generative learning framework to generate, evaluate, and select multiple nonlinear feasible designs with different compliance/volume-fraction tradeoffs, thereby improving Pareto-oriented design-space exploration for geometrically nonlinear topology optimization. Addressing the critical challenge of large-deformation behavior in lightweight aerospace components, the proposed method integrates computationally efficient linear topology optimization with high-fidelity nonlinear finite element analysis. A variational autoencoder learns the latent distribution of elite designs, enabling efficient exploration of high-performance structural configurations without repeated high-fidelity nonlinear sensitivity analysis. Through simplex crossover operations in the latent space and a competitive diversity preservation mechanism, the framework iteratively identifies an approximate Pareto set of high-fidelity-screened candidate designs. Numerical demonstrations on a large-deformation cantilever beam show that the proposed framework can generate multiple high-fidelity-screened designs with compliance/volume-fraction tradeoffs comparable to those of a gradient-based baseline. The results suggest that the framework is a practical design-space exploration tool for geometrically nonlinear topology optimization rather than a universal replacement for gradient-based nonlinear optimization.