CALCULATION OF THE STRESS-STRAIN STATE OF ISOTROPIC PLATE WITH A CURVILINEAR OPENING, THE CONTOUR OF WHICH HAS BEEN PARTIALLY REINFORCED BY A THIN ELASTIC RING

Abstract

The article constructs an approximate solution of the problem of partial amplification of the contour of a curvilinear
opening of an infinite isotropic plate by a closed elastic edge. The plate at infinity is in conditions of cylindrical bending evenly
distributed moments. It is believed that under such a load, a closed isotropic rib of constant thickness and width does not come
into contact with the plate in the area that is not attached to it.
Modeling an edge with an elastic line endowed with bending and torsional rigidity, the mathematical model of the
problem is in in the form of a system of singular integral equations with Hilbert kernels.
Finding the exact solution of the system is associated with significant mathematical difficulties. To find an
approximate solution, the type of functions sought at the junction was set. Numerical implementation of the problem is carried
out using the method of mechanical squaring and collocation, which on a specific example, the influence of physical
characteristics of the reinforcement and theplate on their stress-strain state has been investigated.