In a geometrically linear formulation based on the use of variation principles of elasticity theory, the twodimensional equations of statics and the boundary conditions at the edge of an orthotropic bending plate are obtained within the framework of the classical theory and two low-order nonclassical theories: Reddy–Nemirovskii and Margueere–Timoshenko–Naghdi ones. It is shown that using the hypotheses of the classical theory, the two-dimensional static equations and the corresponding boundary conditions ensure the equilibrium of an arbitrary subarea of the structure and of the entire plate as a rigid whole; within the framework of the Reddy–Nemirovskii theory, this equilibrium is disturbed in moments and forces in the transverse direction; within the framework of the Margueere–Timoshenko–Naghdi theory, the equilibrium is disturbed in the membrane forces and moments. An example of cylindrical bending of rectangular elongate orthotropic and isotropic plates clamped along one longitudinal edge and loaded in the transverse direction on the other longitudinal edge is considered. It is shown that, within the framework of the classical, Reissner, and Ambartsumyan theories, this problem is statically determinate and the shearing force, according to these theories, is determined elementary by the method of sections. According to the Reddy–Nemirovskii theory, this problem is statically indeterminate and has a rather awkward solution. It is demonstrated that, within the framework of the Reddy–Nemirovskii theory, the shearing force is zero on the clamped edge, i.e., the plate as a whole cannot be in equilibrium. In the vicinity of such an edge, there arises a pronounced false boundary effect, which does not take place in reality, because it is located inside the zone of the boundary layer and cannot be calculated by this theory.

中文翻译：

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基于弹性理论的变分原理对复合板弯曲理论中静力学方程的批判性分析 2. 特殊低阶理论

在基于弹性理论变分原理的几何线性公式中，在经典理论和两个低阶非经典理论的框架内，得到静力学二维方程和正交各向异性弯板边缘的边界条件： Reddy-Nemirovskii 和 Margueere-Timoshenko-Naghdi 的。结果表明，利用经典理论的假设，二维静力方程和相应的边界条件保证了结构任意分区和整个板作为刚性整体的平衡；在 Reddy-Nemirovskii 理论的框架内，这种平衡受到横向力矩和力的干扰；在 Margueere-Timoshenko-Naghdi 理论的框架内，膜力和力矩的平衡受到干扰。考虑沿一个纵向边缘夹紧并在另一纵向边缘横向加载的矩形细长各向异性和各向同性板的圆柱弯曲示例。结果表明，在经典、Reissner 和 Ambartsumyan 理论的框架内，这个问题是静态确定的，根据这些理论，剪切力是由截面法基本确定的。根据 Reddy-Nemirovskii 理论，这个问题是静态不确定的，并且有一个相当笨拙的解决方案。结果表明，在 Reddy-Nemirovskii 理论的框架内，夹紧边缘上的剪切力为零，即板作为一个整体不能处于平衡状态。在这样的边缘附近，