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The axisymmetric contact interaction of an infinite elastic plate with an absolutely rigid inclusion
(Odessa I.I. Mechnikov National University, 2015) Vaisfeld, Natalia D.; Popov, H. Ya.; Reut, Viktor V.; Вайсфельд, Наталья Даниловна; Вайсфельд, Наталя Данилiвна; Реут, Віктор Всеволодович
In the proposed paper, the analytical solution of the problem on an axisymmetric stress-strength state of an infinite elastic layer (a plate) with an absolutely rigid inclusion, coupled with this plate, is solved. The upper plate plane side is under the axisymmetric compressive load. The bottom side of the plate could be in different conditions with the absolutely rigid base: it can be the conditions of a smooth contact or the conditions of a full adhesion. The integral Weber-type transformation is applied to the axisymmetric Lamé equations for the displacements and stress field construction. It leads to a one-dimensional vector inhomogeneous boundary problem. With the help of this problem solution, after satisfying a boundary condition, the initial problem is reduced by solving an integral singular equation on the finite interval. The equation is solved approximately by the orthogonal polynomial method with the previous extraction of the solution’s singularities on the interval ends.