Strain-stress behaviour of elastic layer in local loading

The paper studies the problem of a local loading of an elastic layer in 3D perspective. The solution of the boundary value problem subject to a concentrated force is constructed as a combination of two components. The first component is a classical solution of A. Lyav theory of elasticity, the second one is a solution proposed by I.М. Rapoport. The second component is distinctive in that it describes a point edge effect rapidly damping while moving off from the point of force application. This solution is built in a series form, namely, proper decompositions of the auxiliary nonself-adjoint differential operator. The convergence of series is ensured by a rapid growth of eigenvalues. Dying-away to zero at infinity is caused by the exponential law of Macdonald functions damping. The solution of the concentrated force action is used as a kernel to determine displacement vector components, tensors of deformations and strains in the problem of arbitrary local loading of an elastic layer. Eventually, analytical solution of the singular problem makes it possible to reasonably determine the strain-stress state in a local loading zone.