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On mixed boundary-value problems for inextensible elastic materials

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Summary

A class of mixed boundary-value problems is formulated for a linear elastic material subject to the internal constraint of inextensibility in a given direction. Due to the constraint, the usual prescription of boundary data has to be modified. A uniqueness theorem is established. For the particular cases of homogeneous isotropic and transversely isotropic materials, this theorem provides necessary and sufficient conditions for uniqueness of solution to the mixed problems posed.

Résumé

Des problèmes mixtes dans la théorie de l'élasticité linéaire sont formulés pour un matériel soumis à une contrainte d'inextensibilité dans une direction donnée. A cause de la contrainte, la façon dont on prescrit les données extrêmes doit être modifiée. Un théorème d'unicité est établi. Dans le cas particulier des matériaux homogènes isotropiques, ou des matériaux homogènes transversalement isotropiques, ce théorème donne les conditions nécessaires et suffisantes pour l'unicité de la solution des problèmes mixtes posés.

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Author notes

  1. Michael Hayes

    Present address: Dept. of Math. Physics, University College, Belfield, Dublin 4

Authors and Affiliations

  1. School of Mathematics and Physics, University of East Anglia, Norwich, England

    Michael Hayes & Cornelius O. Horgan

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  1. Michael Hayes
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  2. Cornelius O. Horgan
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Hayes, M., Horgan, C.O. On mixed boundary-value problems for inextensible elastic materials. Journal of Applied Mathematics and Physics (ZAMP) 26, 261–272 (1975). https://doi.org/10.1007/BF01590539

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  • DOI: https://doi.org/10.1007/BF01590539

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