The Basic Stress—Strain State of a Circular Plate of Variable Thickness Based on a Nonclassical Theory

Аннотация

A mathematical model of the basic stress-strain state of a circular plate with thickness varying asymmetrically under axisymmetric loading is developed. The method of direct asymptotic integration of differential equations of the 3D theory of elasticity is used. A boundary value problem, which is a system of two second- and fourth-order displacement differential equations with variable coefficients and corresponding boundary conditions, is formulated. An example of plate calculation on the Matlab-14 system using the finite difference method is given.