Construction of the Transfer Function of the Poincaré–Steklov Operator for a Coated Elastic Half-Plane

For a homogeneous isotropic elastic half-plane with a stratified elastic coating we considerthe Poincaré–Steklov operator that maps normal stresses into normal displacements onpart of the boundary. To construct the transfer function of this operator, the variationalformulation of the boundary value problem for transforms of displacements is used. A definition isgiven and the existence and uniqueness are proved for a generalized solution to the variationalproblem. This problem is approximated by the finite element method. The preconditionedconjugate gradient method is used to numerically solve the resulting system of linear algebraicequations. The developed computational algorithm was verified.