ДЕФОРМИРОВАНИЕ КОЛЬЦЕВЫХ ОРТОТРОПНЫХ ПЛАСТИН СРЕДНЕЙ ТОЛЩИНЫ ИЗ МАТЕРИАЛОВ, ЧУВСТВИТЕЛЬНЫХ К ВИДУ НАПРЯЖЕННОГО СОСТОЯНИЯ

Abstract

Discusses a model of a three-layer annular plate of medium thickness. It is assumed that the load on the plate is assumed to be uniformly distributed. The universal relations constructed in the normalized tensor stress space associated with the main axes of the anisotropy of the material are taken as the determining relations. The load was taken in such a way that the deflections of the middle surface of the plate were considered small in comparison with its thickness. The fixing of the plate is rigid along the external and internal contours. Since some orthotropic materials with different resistance exhibit a nonlinear dependence of deformations on stresses, the material characteristics are taken as functions of stress intensity. As a result of the formulation of the boundary value problem, a mathematical model was developed for the analyzed class of problems, implemented as a numerical algorithm integrated into the Mathcad software package. To solve the system of resolving differential equations of bending of annular orthotropic plates, the method of variable elasticity parameters with a finite-difference approximation of the second order of accuracy was used.