Deformation relations for an elastic half-plane with a weakly distorted boundary

Relations between the boundary stresses and displacements are derived for an elastic half-plane with a weakly distorted boundary. To do this, the stress-strain state of the half-plane is expressed by means of two harmonic functions using the general Papkovich–Neuber solution and the distorted half-plane is conformally mapped onto a canonical (flat) half-plane. As a result, a system of boundary value problems for the harmonic functions is obtained from which the required deformation relations follow using a Fourier transform. The effect of the distortion of the boundary on its deformation is analysed.