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Direct Evaluation of Nonlinear Gradient Elasticity in 2D with C 1 Continuous Discretization Methods
Author(s) -
Fischer Paul,
Mergheim Julia,
Steinmann Paul
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010272
Subject(s) - discretization , finite element method , nonlinear system , elasticity (physics) , mathematics , linear elasticity , nonlinear elasticity , finite strain theory , mathematical analysis , discretization error , geometry , physics , quantum mechanics , thermodynamics
In this contribution, we present a study on the performance of four different subparametric triangular finite element formulations for linear and nonlinear strain gradient elastic continua. Fully C 1 and nonconforming C * finite elements are considered for a numerical analysis. The results are demonstrated by means of two computational examples together with the L 2 , H 1 and H 2 error norms. An interesting aspect concerning the linear geometry approximation is revealed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)