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 -FEM, and a rapid perturbation solution procedure, the Asymptotic-Numerical Method (ANM). The proposed approach adopts a polynomial space enrichment strategy, the -refinement, and a mesh superposition technique, the -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.

中文翻译：

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复合材料壳非线性分析的渐近[公式省略]-FEM

非线性壳分析通常依赖于有限元方法 (FEM) 和迭代增量过程 (IIP)。当需要高保真网格来捕获非常局部的特征或极其非线性的响应时，这些方法在计算上可能会变得昂贵。本研究的目的是提出一种基于高效有限元公式 -FEM 和快速微扰求解程序渐近数值方法 (ANM) 的新型计算工具。所提出的方法采用多项式空间丰富策略（-refinement）和网格叠加技术（-refinement）来构建具有准最佳准确度与误差比的数值模型。与 IIP 相比，引入的渐近框架增强了解决非线性问题的有效性。提供了一组测试用例和新基准来验证该工具并展示其潜力。目前的结果表明，涉及分叉、跳跃、回弹和各向异性引起的定位等具有挑战性的问题可以通过出色的精度和相对较小的建模/计算工作来解决。