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Exact Levy-type solutions for bending of thick laminated orthotropic plates based on 3-D elasticity and shear deformation theories

机译：基于3-D弹性和剪切变形理论的厚板正交异性板弯曲的精确Levy型解

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Exact solutions for static bending of symmetric laminated orthotropic plates with different Levy-type boundary conditions are developed. The shear deformation plate theories of Mindlin-Reissner and Reddy as well as the three-dimensional elasticity theory are employed. Using the minimum total potential energy principle, governing equilibrium equations of laminated orthotropic plates and pertaining boundary conditions are derived. Closed-form Levy-type solutions are obtained for the governing equations of both theories using separation of variables method and different types of classical boundary conditions, namely simply-supported, clamped and free edge, are exactly satisfied. Thereafter, 3-D elastostatic equations for orthotropic materials are solved for bending analysis of laminated plates using two different approaches. First, the method of separation of variables is utilised and an exact closed-from solution is achieved for simply-supported laminated orthotropic plates. Next, a combined Fourier Differential Quadrature (DQ) approach is employed to present a semi-numerical solution for bending of laminated orthotropic plates with Levy-type boundary conditions based on the three-dimensional elasticity theory. High accuracy of the presented solutions are proven and comprehensive comparative numerical results are provided and discussed. Presented comparative numerical results can serve as benchmark for investigating the correctness of new solution methods which may be established in the future. (C) 2016 Elsevier Ltd. All rights reserved.
机译：开发了具有不同Levy型边界条件的对称层状正交异性板的静态弯曲的精确解。运用了Mindlin-Reissner和Reddy的剪切变形板理论以及三维弹性理论。利用最小总势能原理，推导了正交各向异性层合板的控制平衡方程及相关边界条件。利用变量分离法对两种理论的控制方程都给出了封闭形式的Levy型解，并精确满足了不同类型的经典边界条件，即简单支撑，夹紧边和自由边。此后，使用两种不同的方法求解正交异性材料的3-D弹性方程，以进行层压板的弯曲分析。首先，利用变量的分离方法，并为简单支撑的正交各向异性板实现了精确的封闭解。接下来，基于三维弹性理论，采用组合傅立叶微分正交（DQ）方法提出具有Levy型边界条件的正交各向异性叠层板弯曲的半数值解。证明了所提出解决方案的高精度，并提供和讨论了全面的比较数值结果。提出的比较数值结果可作为研究将来可能建立的新求解方法正确性的基准。 （C）2016 Elsevier Ltd.保留所有权利。

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