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Equivalent single-layer theory for a complete stress field in sandwich panels under arbitrarily distributed loading

机译：任意分布载荷作用下夹芯板完整应力场的等效单层理论

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摘要

In single-layer theory, the displacement components represent the weighted-average through the thickness of the sandwich panel. Although discrete-layer theories are more representative of sandwich construction than the single-layer theories, they suffer from an excessive number of field variables in proportion to the number of layers. In this study, utilizing Reissner's definitions for kinematics of thick plates, the displacement components at any point on the plate are approximated in terms of weighted-average quantities (displacements and rotations) that are functions of the in-plane coordinates. The equations of equilibrium and boundary conditions of the sandwich panel are derived by employing the principle of virtual displacements. The solution for an arbitrarily distributed load is obtained by employing Fourier series representations of the unknown field variables. This single-layer theory is validated against an analytical solution for simply supported square sandwich panels under pressure over a small region on the face sheet and is also compared with previous single-layer plate theories.
机译：在单层理论中，位移分量代表夹心板厚度的加权平均值。尽管离散层理论比单层理论更能代表三明治结构，但它们受与层数成比例的过多的场变量的影响。在这项研究中，利用Reissner的厚板运动学定义，可以根据作为平面坐标的函数的加权平均量（位移和旋转）来近似估算板上任意点的位移分量。利用虚拟位移原理推导了夹层板的平衡和边界条件方程。通过采用未知场变量的傅立叶级数表示，可以得到任意分布载荷的解。对该单层理论进行了验证，该分析方法是针对在面板上一小区域受压的简单支撑方形夹心板的解析解决方案进行验证的，并且还与以前的单层板理论进行了比较。

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