Two-dimensional unsteady-state problem of elasticity with diffusion for isotropic one-component half-plane

A two-dimensional unsteady-state problem for the isotropic elastic half-plane with diffusion effect is investigated in this paper. In order to solve the problem, the local-equilibrium model of mechanical diffusion is used. This model consists of a system of equations, which describe the law of motion and mass transfer. The solution is found with the help of sine and cosine transformation of the space variable. Additionally, the Laplace transformation of the time variable is applied. The inverse Laplace transformation is reduced to the calculation of the originals of rational functions. Quadrature formulas are used for the inverse sine and cosine transformation.