Abstract
The paper presents and analytical investigation of the properties of the integral terms in the Somigliana stress identity which are associated with a perceived hypersingular nature of the integral equations in three dimensional elasticity. The nature of the integral equations is, in fact, found to be non-hypersingular, thereby permitting direct evaluation of the jump terms in the stress identity for a solution point taken, in the limit, to the surface of the body. The continuity requirements on the boundary conditions are found to be more liberal than previously reported. A weakly-singular form of the Somigliana identity is found that is easily used for BEM implementations that use Gaussian integrations. Demonstration of the boundary form of the Somigliana stress identity is given for a three dimensional elasticity problem.
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Communicated by S. N. Atluri, April 20, 1992
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Cruse, T.A., Suwito, W. On the Somigliana stress identity in elasticity. Computational Mechanics 11, 1–10 (1993). https://doi.org/10.1007/BF00370069
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DOI: https://doi.org/10.1007/BF00370069