We proposed a new theory of bending of axisymmetrically loaded plates in the form of thick rings or disks for the case where their deflections are not large and the stressed state is not described by the Kirchhoff–Love or Timoshenko hypotheses. For bending of this kind, we use two harmonic functions that describe the axisymmetric stressed state. After integration over the thickness of the plate, the momentsand transverse forces are expressed via two functions. The relationships of the theory of elasticity are exactly satisfied and a closed system of equations for the introduced functions is constructed without using any hypotheses about the geometric nature of deformation of the plate. A method for the solution of these equations is developed. We also present the solution of various problems of bending of the plates with holes.

中文翻译：

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轴对称加载厚板的弯曲

我们提出了一种新的厚环或圆盘形式的轴对称加载板的弯曲理论，适用于它们的挠度不大且基尔霍夫-洛夫或铁木辛科假设未描述应力状态的情况。对于这种弯曲，我们使用两个谐波函数来描述轴对称应力状态。在对板的厚度积分后，力矩和横向力通过两个函数表示。完全满足弹性理论的关系，并且在不使用关于板变形几何性质的任何假设的情况下构建了引入函数的封闭方程组。开发了解决这些方程的方法。我们还介绍了带孔板弯曲的各种问题的解决方案。