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Finite Element Approximation of a New Variational Principle for Compressible and Incompressible Linear Isotropic Elasticity

[+] Author and Article Information
Leopoldo P. Franca

Laboratório Nacional de Computação Científica, Rua Lauro Müller 455, 22290 Rio de Janeiro, RJ-Brazil

Rolf Stenberg

Institute of Mathematics, Helsinki University of Technology, 02150 Espoo, Finland

Appl. Mech. Rev 42(11S), S64-S68 (Nov 01, 1989) doi:10.1115/1.3152409 History: Online June 03, 2009

Abstract

Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure, and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations.

Copyright © 1989 by The American Society of Mechanical Engineers
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