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Analysis and finite element approximation of compressible and incompressible linear isotropic elasticity based upon a variational principle. (English) Zbl 0688.73044
Summary: We propose a variational principle for compressible and incompressible linear isotropic elasticity involving four dependent variables: the strain tensor, the augmented stress tensor, pressure and displacement. The variational formulation derived from the principle is analyzed employing a general result due to F. Brezzi [Revue Franç. Automat. Inform. Rech. Opérat. 8, R-2, 129-151 (1974; Zbl 0338.90047)]. Finite element methods using the Galerkin and SBB methods are shown to converge for a wide family of finite element interpolations.

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
Full Text: DOI
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