In this paper we study the procedure of reducing the three-dimensional problem of elasticity theory for a thin inhomogeneous anisotropic plate to a two-dimensional problem in the median plane. The plate is in equilibrium under the action of volume and surface forces of general form. À notion of internal force factors is introduced. The equations for force factors (the equilibrium equations in the median plane) are obtained from the thickness-averaged three-dimensional equations of elasticity theory. In order to establish the relation between the internal force factors and the characteristics of the deformed middle surface, we use some prior assumptions on the distribution of displacements along the thickness of the plate. To arrange these assumptions in order, the displacements of plate points are expanded into Taylor series in the transverse coordinate with consideration of the physical hypotheses on the deformation of a material fiber being originally perpendicular to the median plane. The well-known Kirchhoff—Love hypothesis is considered in detail. À closed system of equations for the theory of inhomogeneous anisotropic plates is obtained on the basis of the Kirchhoff—Love hypothesis. The boundary conditions are formulated from the Lagrange variational principle.

中文翻译：

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一般Kirchhoff问题的表述—非均质各向异性板的Love理论

在本文中，我们研究了将非均匀各向异性薄板的弹性理论的三维问题简化为中值平面的二维问题的过程。板在一般形式的体积和表面力的作用下处于平衡状态。介绍了内力因素的概念。力因数方程（中值平面中的平衡方程）是从弹性理论的厚度平均三维方程中获得的。为了建立内力因素与变形的中间表面的特性之间的关系，我们对沿板厚度的位移分布使用了一些先验的假设。为了按顺序排列这些假设，考虑到关于材料纤维最初垂直于中间平面变形的物理假设，板点的位移在横向坐标中扩展为泰勒级数。详细讨论了著名的基希霍夫-爱假设。基于Kirchhoff-Love假设，获得了非均质各向异性板理论的封闭方程组。边界条件是根据拉格朗日变分原理制定的。基于Kirchhoff-Love假设，获得了非均质各向异性板理论的封闭方程组。边界条件是根据拉格朗日变分原理制定的。基于Kirchhoff-Love假设，获得了非均质各向异性板理论的封闭方程组。边界条件是根据拉格朗日变分原理制定的。