Abstract Out-of-plane failure is common in composite layered materials. Its detection in numerical simulations usually involves a high-level of spatial refinement which may lead to an excessive computational time for large structures. This paper presents a formulation for the recovery of the transverse stresses in conventional linear shell elements based on First-Order Shear Deformation Theory. Starting from the equilibrium equations, the proposed formulation allows the calculations to be made for arbitrary curvatures including variable ones. Compared to the Extended-2D method, it has the advantage of including all the contributions from the force and moment derivatives making it reliable in complex load cases. Several examples with different laminates, curvatures and loads are presented. The numerical results confirm the potential of the proposed method to be used both as post-processing tool for conventional models and as an enrichment criterion for adaptive modelling.

中文翻译：

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任意弯曲层合板中线性壳单元的完整横向应力恢复模型

摘要 平面外失效在复合层状材料中很常见。它在数值模拟中的检测通常涉及高级空间细化，这可能导致大型结构的计算时间过长。本文提出了基于一阶剪切变形理论的常规线性壳单元中横向应力恢复的公式。从平衡方程开始，建议的公式允许计算任意曲率，包括可变曲率。与 Extended-2D 方法相比，它的优点是包括力和力矩导数的所有贡献，使其在复杂载荷情况下可靠。介绍了几个具有不同层压板、曲率和载荷的示例。