Intrinsic methods in elasticity: a mathematical survey

Philippe G. Ciarlet; Liliana Gratie; Cristinel Mardare

doi:10.3934/dcds.2009.23.133

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2009, Volume 23, Issue 1&2: 133-164. Doi: 10.3934/dcds.2009.23.133

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Intrinsic methods in elasticity: a mathematical survey

1.
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
2.
Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
3.
Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Universite Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris

Received: September 30, 2007

Published: April 2009

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Abstract

In the classical approach to elasticity problems, the components of the displacement field are the primary unknowns. In an "intrinsic'' approach, new unknowns with more physical or geometrical meanings, such as a strain tensor field or a rotation field for instance, are instead taken as the primary unknowns. We survey here recent progress about the mathematical analysis of such methods applied to linear and nonlinear three-dimensional elasticity and shell problems.

Keywords:

Linearized and nonlinear three-dimensional elasticity,
linear and nonlinear shell theory,
intrinsic methods in elasticity.

Mathematics Subject Classification: Primary: 74-02; Secondary: 74G25, 74G65, 74K25.

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