Although the Green's function for an isotropic elastic half-space subjected to a line force or a line dislocation is well-known, the physical meaning of the solution is not clear. Green's functions for twodimensional plane-strain and plane-stress problems of an isotropic elastic half-space with a free or rigidly fixed surface subjected to line forces and line dislocations are reexamined in this study. The results are more explicit when compared with existing solutions in the literature. The Green's function for a half-space consists of four or five Green's functions for an infinite space, the number depending on the boundary condition at the half-space surface and the applied loading. One of the Green's functions in the infinite space has its singularity located in the half-space where the load is applied, and the other image singularities are located outside the half-space with the same distance from the surface as that of the applied load. The nature and magnitude of image singularities have been derived from the principle of superposition and classified according to different loads. The image singularities are found to possess some interesting properties. It is found that the fundamental solutions required to construct all the image singularities of applied forces and dislocations for the half-space are only forces and dislocations and their differentiations in the infinite space. Furthermore, the limiting case of the applied force or dislocation approaching the surface is also discussed in this study.
Green’s functions for anisotropic elastic multilayered media subjected to antiplane shear deformation are presented in this study. The antiplane shear deformation due to a concentrated shear force and screw dislocation in an arbitrary layer was investigated in detail. A linear coordinate transformation is introduced in this study to simplify the problem. The linear coordinate transformation reduces the anisotropic multilayered problem to an equivalent isotropic problem without complicating the geometry of the problem. Explicit analytical solutions were derived using the Fourier transform and the series expansion technique. The complete solutions for the multilayered problem consist only of the simplest solutions obtained from an infinite homogeneous medium with concentrated loadings. Numerical results for the full-field stress distribution in multilayered media subjected to a point body force are presented. These numerical results were compared with the solutions obtained by considering the multilayered medium as one layer with effective elastic constants determined from the averaged material constants of the multilayered medium. It is found that the shear stress τyz of the homogeneous one layer solution is a very good approximation of the result for the multilayered medium; however, the shear stress τxz in these two solutions has a large discrepancy due to the fact that τxz is discontinuous at the interfaces of the multilayered medium. [S0021-8936(00)01703-7]
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 halfplane 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.
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