BENDING OF RING PLATES, PERFORMED FROM AN ORTHOTROPIC NONLINEAR DIFFERENTLY RESISTANT MATERIAL

Abstract

This article proposes a mathematical model of axisymmetric transverse bending of an annular plate of average thickness, the loading of which is assumed to be on the upper surface of a transverse uniformly distributed load. An orthotropic plate made of a material whose mechanical characteristics nonlinearly depend on the type of stress state is considered. The most universal, built in the normalized tensor space of stresses associated with the main axes of anisotropy of the material are taken as defining relations. The loads were taken in such a way that the deflections of the middle surface of the plate could be considered small compared to its thickness. Fastening plates are presented in two versions: 1) rigid fastening on the outer and inner contours; 2) hinge bearing on the outer and inner contours. As a result of the formulation of the boundary value problem, a mathematical model was developed for the class of problems in question, implemented as a numerical algorithm integrated into the application package of the MatLAB environment. To solve the system of resolving differential equations of plate bending, the method of variable parameters of elasticity was used with a finite-difference approximation of the second order of accuracy.

Keywords

• transverse bending, axisymmetric deformation, ring plate, orthotropic material, nonlinear dis-sociation, small deflections