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Saint-Venant's principle on unbounded regions

Published online by Cambridge University Press:  14 November 2011

R. J. Knops ,
S. Rionero  and
L. E. Payne
R. J. Knops
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, U.K.
S. Rionero
Affiliation:
Istituto di Matematica, Università di Napoli, Cap 80134, Napoli, Italy
L. E. Payne
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853, U.S.A.
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Synopsis

We consider an anisotropic non-homogeneous linear elastic material in equilibrium and occupying an open region with non-compact boundary. In both the linearised and classical linear theories the asymptotic behaviour of the solution is determined and a clear relationship established with Saint-Venant's principle on such regions. Although the treatment is discussed with special reference to elasticity, it is equally applicable to general systems of elliptic differential equations, and thus reveals a relationship with the classical theorems of Phragmèn-Lindelöf and Liouville.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 3-4 , 1990 , pp. 319 - 336
Copyright
Copyright © Royal Society of Edinburgh 1990

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