Asymptotic ps-FEM for nonlinear analysis of composite shells

Nonlinear shell analysis relies typically on Finite Element Methods (FEMs) and Iterative-Incremental Procedures (IIPs). These methodologies can become computationally expensive whenever high-fidelity meshes are required to capture very localized features or extremely nonlinear responses. Aim of this study is presenting a novel computational tool based on an efficient finite element formulation, the ps-FEM, and a rapid perturbation solution procedure, the Asymptotic-Numerical Method (ANM). The proposed approach adopts a polynomial space enrichment strategy, the p-refinement, and a mesh superposition technique, the s-refinement, to build numerical models with quasi-optimal accuracy-to-error ratios. The introduced asymptotic framework enhances the effectiveness of solving nonlinear problems compared to IIPs. A set of test cases and new benchmarks is presented to validate the tool and demonstrate its potential. The present results show that challenging problems involving bifurcations, jumps, snap-backs and anisotropy-induced localizations can be solved with excellent degree of accuracy and relatively small modeling/computational effort.