Abstract Despite the accelerated deployment of laminated composites in a wide variety of markets due to their peculiar engineering features, the design of those materials is often restrained by the lack of cost-efficient modeling techniques. In fact, the existing strategies allowing for cheap simulations usually fail to directly capture out-of-plane through-the-thickness stresses, which prove to be typically responsible of delamination failure modes. In this paper, we introduce a fast and accurate stress recovery strategy to model the out-of-plane behavior of Kirchhoff laminated plates. The proposed technique can be regarded as a two-step approach: First, the classical composite plates theory, providing the lowest computational cost among known literature strategies, is applied to obtain a coarse displacement solution; afterwards, this solution is used to compute the necessary in-plane derivatives to recover the out-of-plane stresses directly imposing equilibrium in strong form. Since this a posteriori step relies on high-order in-plane continuity requirements, isogeometric analysis (IGA) represents a natural simulation framework given its accuracy and higher continuity properties. Both isogeometric Galerkin and collocation formulations are herein considered. The effectiveness of the proposed approach is proven by extensive numerical tests.

中文翻译：

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基于精确平衡的等几何层压复合基尔霍夫板的层间应力恢复

摘要 尽管层压复合材料由于其特殊的工程特征而在各种市场中加速部署，但这些材料的设计往往受到缺乏具有成本效益的建模技术的限制。事实上，允许廉价模拟的现有策略通常无法直接捕获平面外的全厚度应力，这证明通常是造成分层失效模式的原因。在本文中，我们引入了一种快速准确的应力恢复策略来模拟 Kirchhoff 层压板的平面外行为。所提出的技术可以看作是一个两步法：首先，经典的复合板理论，在已知的文献策略中提供最低的计算成本，用于获得粗略的位移解；然后，该解决方案用于计算必要的面内导数，以恢复以强形式直接施加平衡的面外应力。由于这个后验步骤依赖于高阶面内连续性要求，等几何分析 (IGA) 代表了一种自然的模拟框架，因为它具有准确性和更高的连续性特性。本文考虑了等几何 Galerkin 和搭配公式。大量数值试验证明了所提出方法的有效性。本文考虑了等几何 Galerkin 和搭配公式。大量数值试验证明了所提出方法的有效性。本文考虑了等几何 Galerkin 和搭配公式。大量数值试验证明了所提出方法的有效性。