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The numerical analysis of symmetric cross-ply laminates using the natural neighbour radial point interpolation method and high-order shear deformation theories
Engineering Structures ( IF 5.6 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.engstruct.2020.111247
D.E.S. Rodrigues , J. Belinha , L.M.J.S. Dinis , R.M. Natal Jorge

Abstract Composite structures are commonly analysed using the Finite Element Method (FEM). However, new accurate and efficient discrete numerical techniques have appeared recently – the meshless methods. Thus, this work uses a meshless method – the Natural Neighbour Radial Point Interpolation Method (NNRPIM) – to perform an elasto-static analysis of composite laminated plates. Meshless methods only require an unstructured nodal distribution to discretize the problem domain. In order to numerically integrate the integro-differential equation from the Galerkin weak formulation, a background integration mesh is constructed using the Voronoi diagram. Then, the nodal connectivity is enforced using the ‘influence-cell’ concept and the shape functions are obtained. In this work, laminated composite plates are analysed using distinct equivalent single layer theories, considering different transverse high-order shear deformation laws. Thus, several third-order, exponential and trigonometric transverse shear deformation theories are combined with the NNRPIM to analyse the structural response of composite laminated plates. In the end, composite laminated plates are numerically analysed and the meshless solutions are compared with the analytical solution available in the literature. Therefore, this works contributes with new solutions for classic composite symmetric cross-ply laminated plates and provides a comparative study on the accuracy of some high-order shear deformation theories (HSDTs).

中文翻译:

基于自然邻域径向点插值法和高阶剪切变形理论的对称交叉层板数值分析

摘要 复合结构通常使用有限元方法 (FEM) 进行分析。然而,最近出现了新的准确有效的离散数值技术——无网格方法。因此,这项工作使用无网格方法——自然邻域径向点插值法 (NNRPIM)——对复合层压板进行弹静力分析。无网格方法只需要一个非结构化的节点分布来离散化问题域。为了对来自 Galerkin 弱公式的积分微分方程进行数值积分,使用 Voronoi 图构建了背景积分网格。然后,使用“影响单元”概念强制节点连接并获得形状函数。在这项工作中,使用不同的等效单层理论分析层压复合板,考虑不同的横向高阶剪切变形规律。因此,将几种三阶、指数和三角横向剪切变形理论与 NNRPIM 相结合,分析复合层压板的结构响应。最后,对复合层压板进行数值分析,并将无网格解与文献中可用的解析解进行比较。因此,这项工作为经典复合对称交叉层合板提供了新的解决方案,并提供了对一些高阶剪切变形理论 (HSDT) 准确性的比较研究。指数和三角横向剪切变形理论与 NNRPIM 相结合,分析复合层压板的结构响应。最后,对复合层压板进行数值分析,并将无网格解与文献中可用的解析解进行比较。因此,这项工作为经典复合对称交叉层合板提供了新的解决方案,并提供了对一些高阶剪切变形理论 (HSDT) 准确性的比较研究。指数和三角横向剪切变形理论与 NNRPIM 相结合,分析复合层压板的结构响应。最后,对复合层压板进行数值分析,并将无网格解与文献中可用的解析解进行比较。因此,这项工作为经典复合对称交叉层合板提供了新的解决方案,并提供了对一些高阶剪切变形理论 (HSDT) 准确性的比较研究。
更新日期:2020-12-01
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