A BIEM approach to an external problem of time-harmonic elastodynamics with elastic-type boundary conditions

This paper presents an application of boundary integral equation methods that are used to solve a stationary elastodynamic problem with elastic boundary conditions, in which the contact stresses are proportional to the corresponding boundary displacements. The solution is based on the single-layer potential, and is presented in the form of a Neumann series. The Green tensor estimation shows that the singular integrals can be regularised by applying a modified Perlin approach, which uses some specific properties of the integral equations’ kernels. A modified Shanks transform can be used to accelerate the Neumann series convergence. The implementation of the proposed method is demonstrated by a contact stress analysis around an oscillating inclusion, in an elastic plane where the inclusion is surrounded by an elastic intermediate layer. The peak stress and displacement dependence on the oscillation frequency was studied for various types of oscillations.