Automated design optimization framework for geometrically nonlinear and dynamic structures based on a differentiable finite particle method

Structural design optimization accounting for geometric nonlinearity and dynamic effects remains challenging. Conventional finite element method (FEM)–based approaches often suffer from convergence difficulties and unreliable sensitivity evaluation when large deformations or instability phenomena occur. Moreover, the need for problem-specific formulations and different numerical schemes for static versus dynamic or linear versus nonlinear analyses further complicates gradient-based optimization. To address these issues, this study develops a finite particle method (FPM)–based optimization framework that provides a unified formulation for static and dynamic analyses, naturally accommodating large deformations and instability behaviors within a single explicit time-stepping scheme. Automatic differentiation (AD) is embedded directly into the FPM time-marching process, enabling fully automated and stable sensitivity evaluation without manual derivation or solver-specific adjoint formulations. Benchmark examples involving global buckling, snap-through instability, and dynamic loading demonstrate the effectiveness of the proposed approach. For optimization problems involving snap-through instability where FEM-based methods fail to converge or yield unreliable sensitivities, the proposed framework successfully guides the optimization and reduces structural compliance by over 98%, effectively preventing instability. For large-scale spatial trusses with up to 10,000 degrees of freedom under dynamic loading, computational time is reduced by more than 95% compared with FEM-based optimization. These results highlight the potential of the proposed framework for the optimization of structures subject to large deformations, instability, and dynamic excitations, providing clear numerical and practical advantages.