A model reduction procedure based on the ps-FEM for postbuckling analysis of composite shells

This paper presents a new computational framework for the efficient postbuckling analysis of laminated shell-like structures. The proposed approach is a two-step model reduction procedure that integrates the global/local refinement capabilities of the ps-Finite Element Method (ps-FEM) with a Ritz-based projection technique. First, the ps-FEM is used with a perturbation procedure to generate Ritz vectors with global/local representation capabilities. Then, the finite element equations are projected onto the reduced subspace spanned by these vectors, yielding a low-dimensional yet high-fidelity reduced-order model. The resulting reduced-order nonlinear equations are solved via the Asymptotic Numerical Method to ensure robustness and performance, even in the presence of strong nonlinearities. To further enhance the level of fidelity of the reduced solution, a subspace updating strategy is activated during the nonlinear solution process. The effectiveness of the proposed framework is demonstrated through a series of numerical benchmarks featuring bifurcation behavior, mode interaction, and unstable postbuckling responses. The results highlight the ability of the method to accurately capture both global and localized nonlinear structural phenomena, while requiring limited computational resources.