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January & February  2009, 23(1&2): 133-164. doi: 10.3934/dcds.2009.23.133

Intrinsic methods in elasticity: a mathematical survey

Philippe G. Ciarlet 1, , Liliana Gratie 2, and  Cristinel Mardare 3,

1. 

Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
2. 

Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
3. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Universite Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France

Received  October 2007 Published  September 2008

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.
Citation: Philippe G. Ciarlet, Liliana Gratie, Cristinel Mardare. Intrinsic methods in elasticity: a mathematical survey. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 133-164. doi: 10.3934/dcds.2009.23.133
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