Abstract
In this paper Somigliana's method has been utilized to solve the two-dimensional boundary value problems of elastic half-spaces. We have considered traction and displacement problem, shear problem, contact and crack problems and the solutions, thus derived, have been compared with those derived from dislocation considerations.
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References
Lardner, R. W., Dislocation layers and boundary value problems of plane elasticity. Quart. J. Mech. Appl. Math. 25 (1972) 45–61.
Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. A 241 (1957) 376–396.
Maiti, M. and Makan, G. R., Somigliana's method applied to elastic inclusions and dislocations. Journal of Elasticity 3 (1973) 45–49.
Love, A. E. H., The mathematical theory of elasticity. Cambridge University Press 1952
Rizzo, F. J., An integral equation approach to boundary value problems of classical elasticity. Quart. Appl. Math. 25 (1967) 83–95
Rizzo, F. J. and Shippy, D. J., A formulation and solution procedure for the general non-homogeneous elastic inclusion problem. Int. J. Solids Structures 4 (1968) 1161–1179
Cruse, T. A., The direct potential method in three-dimensional elastostatics. SM-13, Dept. of Mech. Engg., Carnegie-Mellon University 1968
Cruse, T. A., Numerical solutions in three-dimensional elastostatics. Int. J. Solids Structures 5 (1969) 1259–1274
Maiti, M. and Palit, S. S., On the formulations of plane problems of elasticity in terms of dislocation layers (to appear)
Eshelby, J. D., Edge dislocations in anisotropic materials. Phil. Mag. 40 (1949) 903–912
Muskhelishvili, N. I., Some basic problems of mathematical theory of elasticity. Noordhoff, Groningen (1963)
Mushelishvili, N. I., Singular integral equations. Noordhoff, Groningen 1953
Gakhov, F. D., Boundary value problems. Pergamon Press, Oxford 1966
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Maiti, M., Das, B. & Palit, S.S. Somigliana's method applied to plane problems of elastic half-spaces. J Elasticity 6, 429–439 (1976). https://doi.org/10.1007/BF00040902
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DOI: https://doi.org/10.1007/BF00040902