Bending and buckling of a circular plate with symmetrically varying mechanical properties

Abstract

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.