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Linearization stability and Signorini Series for the traction problem in elastostatics

Published online by Cambridge University Press:  14 November 2011

J. E. Marsden  and
Y. H. Wan
J. E. Marsden
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720, U.S.A
Y. H. Wan
Affiliation:
Department of Mathematics, State University of New York, Buffalo, New York 14214, U.S.A
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Synopsis

This paper uses previous results of Chillingworth, Marsden and Wan on symmetry and bifurcation for the traction problem in three dimensional elastostatics to establish new results on the Signorini expansion. We show that the Signorini compatibility conditions are necessary and sufficient for linearization stability and analogies with results known for other field theories are pointed out. Under an explicit non-degeneracy condition, a new series expansion is given in which successive terms are inductively determined in pairs rather than singly. Our results include as special cases, classical results of Signorini, Tolotti and Stoppelli.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 171 - 180
Copyright
Copyright © Royal Society of Edinburgh 1983

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