MIXED PLAIN BOUNDARY VALUE PROBLEM OF ELASTICITY FOR A RECTANGULAR DOMAIN

Abstract

Mixed plain boundary value problem is considered for the elastic rectangular domain. The conditions of first main elasticity problem are given at the lateral sides; the conditions of smooth contact are given at the base. The rectangular domain is under impact of the exterior static load at its upper edge. With the integral transformation method the problem is reduced to a vector boundary problem, where the unknown vector consists of the displacement`s transforms. The solution of vector boundary problem is constructed with the help of matrix differential calculations and has the unknown function. To find this function the integral singular equation is derived and solved with the help of the orthogonal polynomial method. The stress state of the rectangular domain is investigated depending on its size and kinds of impact.