Some observations on Kelvin's solution in classical elastostatics as a double tensor field with implications for Somigliana's integral

Various possible component representations of Kelvin's tensor in orthogonal curvilinear coordinates are examined and discussed in the light of Kelvin's solution being a two-point or double tensor field. Guides for making the 'best' choice among component representations are consi...

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Bibliographic Details
Published in:Journal of elasticity 1983-05, Vol.13 (1), p.91-97
Main Authors: Rizzo, F. J., Shippy, D. J.
Format: Article
Language:English
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Summary:Various possible component representations of Kelvin's tensor in orthogonal curvilinear coordinates are examined and discussed in the light of Kelvin's solution being a two-point or double tensor field. Guides for making the 'best' choice among component representations are considered. Somigliana's surface integral identity is examined, including the surface effect of the body force derivable from a potential, and that identity is interpreted in curvilinear form. Throughout, the role played by the double tensor components called 'shifters' is emphasized. Finally, the necessary elements to construct component representations of the quantities pertinent to a cylindrical coordinate system are given.
ISSN:0374-3535
1573-2681
DOI:10.1007/BF00041318