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Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D

✍ Scribed by K.S. Chavan; B.P. Lamichhane; B.I. Wohlmuth

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 394 KB
Volume: 196
Category: Article
ISSN: 0045-7825
DOI: 10.1016/j.cma.2007.03.022

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✦ Synopsis

The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases that are well known, as well as newly constructed bases. Starting from a suitable three-field problem, we extend our a-dependent three-field formulation to geometrically nonlinear elasticity with Saint-Venant Kirchhoff law. Additionally, an a-dependent three-field formulation for a general hyperelastic material model is proposed. A range of numerical examples using different material laws for small and large strain elasticity is presented.

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