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Large plane deformations of rectangular elastic sheets

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Abstract

The large deformation of a plane Mooney sheet is considered. The total potential energy of the deformed sheet is written in terms of the gradient of functions describing the deformed configuration. The minimum potential energy principle and the Ritz procedure are used to obtain the solution. Nonhomogeneous deformations of a rectangular sheet under uniaxial stretching are given as an example.

Résumé

Nous considérons ici la déformation extrême d'une feuille plate de Mooney. L'énergie potentielle totale da la feuille déformée peut se décrire au moyen du gradient des fonctions qui décrivent la configuration de la feuille. Le principe de l'énergie potentielle minimum et le procédé de Ritz nous permettent alors de résoudre le problème. Nous discutons, à titre d'exemples, des déformations nonhomogènes d'une feuille rectangulaire qui subit des tensions uniaxiales.

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References

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Authors and Affiliations

  1. Lawrence Livermore Laboratory, University of California, Livermore, California, USA

    William W. Feng

  2. Mechanics and Materials Research Center, Texas A & M University, College Station, Texas, USA

    John T. Tielking

Authors
  1. William W. Feng
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  2. John T. Tielking
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Feng, W.W., Tielking, J.T. Large plane deformations of rectangular elastic sheets. Journal of Applied Mathematics and Physics (ZAMP) 27, 781–789 (1976). https://doi.org/10.1007/BF01595129

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  • DOI: https://doi.org/10.1007/BF01595129

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