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A closed-form 3D shell solution for multilayered structures subjected to different load combinations

机译：适用于承受不同载荷组合的多层结构的封闭形式3D壳体解决方案

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摘要

Multilayered composite and sandwich plates and shells are typical aerospace structures. They introduce complicating effects such as in-plane and transverse anisotropy which lead to zigzag forms of displacement and interlaminar continuity problems. The present closed-form 3D shell solution allows the static analysis of simply-supported cross-ply laminated and sandwich plates, cylinders and cylindrical/spherical shell panels subjected to different harmonic load types. It is possible to consider transverse normal and transverse shear loads simultaneously or separately applied at the top and at the bottom of the considered structure. The present work extends the previous exact 3D shell model developed for the static analysis of plates and shells in the case of transverse normal load applied at the top or at the bottom of the investigated structure. This new extension is still based on the 3D equilibrium equations written in general orthogonal curvilinear coordinates. The obtained system is solved using simply supported boundary conditions, harmonic forms for loads and displacements, a general layer wise approach and the exponential matrix method for the solution of the differential equations in z. However, the load boundary conditions introduced in the proposed shell model have been opportunely modified in order to allow the combination of different transverse normal and transverse shear loads applied at the external surfaces. The new proposed benchmarks fill the gap present in the literature where the proposed 3D exact models always use a transverse normal load applied at the external surfaces. The present paper investigates the zigzag effects, the interlaminar continuity, the equilibrium and compatibility conditions, the load boundary conditions, the symmetry characteristics, the thickness ratio effect and the 3D behavior in laminated and sandwich plates and shells in the case of different load applications. The new proposed benchmarks will be fundamental for the validation of those new refined 2D shell models which want to capture all these features for different load types. (C) 2017 Elsevier Masson SAS. All rights reserved.
机译：多层复合材料，夹心板和壳体是典型的航空航天结构。它们引入了诸如平面内和横向各向异性之类的复杂效应，这导致了曲折形位移和层间连续性问题。本封闭形式的3D外壳解决方案可以对承受不同谐波载荷类型的简单支撑的交叉层压板和夹心板，圆柱体以及圆柱/球形外壳面板进行静态分析。可以考虑同时或分别施加在所考虑结构的顶部和底部的横向法向和横向剪力。本工作扩展了先前精确的3D壳体模型，该模型是在被研究结构的顶部或底部施加横向法向载荷的情况下为板和壳体的静态分析而开发的。此新扩展仍基于以一般正交曲线坐标编写的3D平衡方程。使用简单支持的边界条件，载荷和位移的简谐形式，一般的逐层方法和指数矩阵方法求解z中的微分方程，即可解决获得的系统。但是，在建议的壳模型中引入的载荷边界条件已经过适当修改，以允许组合施加在外表面的不同横向法向载荷和横向剪力。新提出的基准填补了文献中存在的空白，其中提出的3D精确模型始终使用施加在外表面的横向法向载荷。本文研究了在不同载荷应用情况下层压板和夹心板和壳体的之字形效应，层间连续性，平衡和相容性条件，载荷边界条件，对称特性，厚度比效应以及3D行为。新提出的基准测试将是验证那些想要捕获不同负载类型的所有这些功能的新精制2D壳模型的基础。 （C）2017 Elsevier Masson SAS。版权所有。

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