Flexure of thick plate with elastic inclusion

Abstract

In the analysis of the flexure problem for a thick circular plate rigidly clamped along the lateral edge [I] the forces deforming such a plate were assumed to be uniformly distributed over its end faces. For arriving at a solution to this problem, the principal parts of coefficients were extracted and the problem reduced to calculating them so as to simplify, in this way, the analysis of the stressed state of the plate in the vicinity of points of changing boundary conditions. Here this problem will be extended to the case of a plate containing a cavity filled with an elastic core. A numerical evaluation has revealed patternsof behavior which can be utilized in designing structures with composite materials. We consider a hollow cylinder in a cylindrical system of coordinates (~, 0), symmetrical with respect to the ~ = 0 coordinate plane, having a length 2H, outside radius 00 and inside radius 01. The interior of this cylinder is filled with an elastic inclusion which has been soldered or glued in without predeformation. We introduce the dimensionless quantities