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Linearization stability and Signorini series for the traction problems in elastostatics

Marsden, J. E. and Wan, Y. H. (1983) Linearization stability and Signorini series for the traction problems in elastostatics. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 95 (1-2). pp. 171-180. ISSN 0308-2105.

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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 Stopelli.

Item Type:Article
Additional Information:© 1983, Royal Society of Edinburg. Research partially supported by NSF grant 81-07086, The Miller Institute and DOE, contract AT03-82ER12097. Research partially supported by NSF grant MCS 81-02463 and DOE contract DE-AT03-82ER12097. We thank Robin Knops and Clifford Truesdell for suggesting this area of research and David Chillingworth for valuable comments on the logical structure of the Signori scheme.
Funding AgencyGrant Number
Miller InstituteUNSPECIFIED
Department of Energy (DOE)DE-AT03-82ER-12097
NSFMCS 8102463
Issue or Number:1-2
Record Number:CaltechAUTHORS:20100922-100054148
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20085
Deposited On:22 Sep 2010 18:14
Last Modified:03 Oct 2019 02:05

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