Abstract The subject of the paper is a simply supported circular plate with symmetrically varying mechanical properties in the thickness direction. In extreme cases of this variability, the plate becomes a single-layer or three-layer structure. The main goal of the study is to develop a mathematical description of both a single-layer and three-layer structure using one formula. The mathematical model also includes all intermediate states of the plate in the axisymmetric bending and buckling problems with consideration of the shear effect. To this purpose, two dimensionless functions closely related to the variability of mechanical properties were introduced and the nonlinear hypothesis of deformation of the straight line normal to the plate neutral surface is assumed. Based on the principle of stationary potential energy two differential equations of equilibrium are obtained. The system of equations is analytically solved. The deflections and intensity of critical loads for example plates are derived and presented in Tables.

中文翻译：

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具有对称变化机械性能的圆板的弯曲和屈曲

摘要 本文的研究对象是一种在厚度方向上具有对称变化力学性能的简支圆板。在这种可变性的极端情况下，板变成单层或三层结构。该研究的主要目标是使用一个公式对单层和三层结构进行数学描述。数学模型还包括考虑剪切效应的轴对称弯曲和屈曲问题中板的所有中间状态。为此，引入了与机械性能变化密切相关的两个无量纲函数，并假设了垂直于板中性表面的直线变形的非线性假设。根据静止势能原理，得到两个平衡微分方程。方程组被解析解。临界载荷的挠度和强度（例如板）在表格中推导出和呈现。