ASYMPTOTIC APPROACH TO THE PROBLEMS OF THE THEORY OF ELASTICITY OF BODIES OF FINITE DIMENSIONS.

A method is developed to solve the equilibrium problems of elastic bodies of fixed diemensions, based on a separation of the boundary-layer part of the solution by considering the problem for a half-strip. A closed solution in quadratures is constructed for the half-strip with a free lateral face and with given normal displaced longitudinal boundaries, using both symmetric and antisymmetric loading. When the normal stresses on the front boundaries are specified, the problem reduces to an integral equation of the first kind in a semi-infinite interval, the inversion of which is obtained by reduction to an infinite system of algebraic equations. The approach considered for problems of bodies of finite dimensions is asymptotic with respect to the small parameter characterizing the body's thickness. Testing of the method on a plane problem for an elastic rectangle enables the range of variation of this parameter to be investigated.