Full–field analysis of a planar anisotropic layered half–plane for concentrated forces and edge dislocations

The problem of a planar anisotropic elastic layered half–plane subjected to concentrated forces and edge dislocations applied either in the layer or in the half–plane is analysed. One of the objectives of this study is to develop an effective analytical methodology to construct the exact full–field solution for this problem. By using the Lekhnitskii formalism for anisotropic elastic material with the Fourier–transformation technique, the explicit closed–form solutions for stresses in the layer and the half–plane are obtained. The solutions are suitable for loadings that are acting on the free surface or at the interface. The complete solutions for this problem consist only of the simplest solutions obtained from an infinite homogeneous medium with concentrated forces and edge dislocations. The solutions include Green's function for applied loadings in an infinite medium and an infinite number of image singularities that are induced to satisfy the boundary and interface conditions. It is shown that the physical meaning of the solution is the image method. The magnitudes and locations of image singularities are determined automatically from the mathematical method presented in this study. Numerical results for the full–field stress distribution in the layered half–plane medium subjected to concentrated forces or edge dislocations are discussed in detail.