Image Singularities of Green's Functions for Anisotropic Elastic Half-Spaces and Bimaterials,
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF CIVIL ENGINEERING MECHANICS AND METALL URGY
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Using Strohs formalism simple explicit expressions of Greens functions for anisotropic elastic half-spaces and bimaterials subject to line forces and line dislocations are presented. One of the novel features is that, knowing the Greens function for an infinite space, Greens functions for half-spaces and bimaterials can be written down immediately with very little derivation. The other novel feature is the physical interpretations of Greens functions. The Greens function for a half-space consists of ten Greens functions for the infinite space. One of the ten Greens functions has its singularities located in the half-space where they are prescribed. The other nine represent image singularities which are located outside of the half-space not occupied by the material. The locations of the nine image singularities as well as the nature of the singularities are presented explicitly. For bimaterials which consists of two anisotropic half-spaces bonded together, there are nine image singularities each for the two materials. Again the locations and the nature of the singularities are presented explicitly. We also suggest graphical solutions for finding the locations of these singularities. Since the Greens function for an infinite space has a real form solution this implies that Greens functions for half-spaces and bimaterials can have a real form solution.
- Theoretical Mathematics