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Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

机译：用于异诊型层压弯曲结构的高效均衡应力恢复

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摘要

This work extends the stress recovery for laminated composite solid plates, proposed in [1,2], to curved structures. Based on 3D Isogeometric Analysis (IGA) computations and equilibrium, this procedure uses a single element through the thickness in combination with a calibrated layer-by-layer integration rule or a homogenized approach, allowing for an inexpensive and accurate approximation in terms of in-plane stresses (and their derivatives), while through-the-thickness stress components are poorly approximated. Relying on the highorder continuity properties of IGA shape functions, an accurate out-of-plane stress state can also be recovered by means of direct integration of the equilibrium equations in strong form. The a posteriori step application, which is straightforward in the context of solid plates, is not trivial in the case of curved geometries. In fact, the notion of in-plane and out-of-plane directions is not clear when modeling this kind of structures in the global reference system, while adopting curvilinear coordinates to express the equilibrium gives rise to additional coupled terms that require an iterative process to resolve the balance of momentum equation. Therefore, we propose to apply the recovery locally, which, despite leading to more elaborated stress derivative terms because of the increasing geometry complexity, still allows for a direct reconstruction as the resolvent system is uncoupled. Several numerical results show the good performance of this approach particularly for composite stacks with significant radius-to-thickness ratio and number of plies.
机译：该工作延伸了层压复合固体板的应力恢复，提出在[1,2]中，以弯曲结构。基于3D异构分析（IGA）计算和平衡，该过程使用单个元件与厚度结合校准的逐层集成规则或均质方法，允许在in-中允许廉价和准确的近似平面应力（及其衍生物），而通过厚度应力分量近似近似。依赖于IGA形状的高达连续性性能，还可以通过以强形式的平衡方程直接集成平衡方程来恢复精确的平面应力状态。在弯曲几何形状的情况下，在固体板的上下文中直截了当的后验台阶应用。实际上，在全局参考系统中建模这种结构时，飞机面内和平面方向的概念尚不清楚，同时采用曲线坐标以表达均衡，产生需要迭代过程的额外耦合术语解决动量方程的平衡。因此，我们建议在本地应用恢复，尽管由于几何复杂性增加而导致压力衍生术语更加精细，但仍允许直接重建，因为解决方案系统是未耦合的。几个数值结果表明了这种方法的良好性能，特别是对于具有明显的半径到厚度比和厚度的复合叠层。

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