BENDING OF RING PLATES FROM ORTHOTROPIC NONLINEAR MISCELLANEOUS 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 uniformly distributed transverse load. An orthotropic plate made of a material whose mechanical characteristics nonlinearly depend on the type of stress state is considered. The most universal, constructed in the normalized tensor space of stresses associated with the main axes of anisotropy of the material are taken as the 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. Plate fasteners are available in two versions: 1) rigid fastening along the outer and inner contours; 2) hinge bearing on the outer and inner contours. Due to the fact that many orthotropic dissimilar materials exhibit a nonlinear stress-strain relationship, the material parameters are taken as functions of the stress intensity. 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, we used the method of variable elasticity parameters with a finite-difference approximation of the second order of accuracy.