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The least‐squares finite element method in elasticity—Part I: Plane stress or strain with drilling degrees of freedom
Author(s) -
Jiang Bonan,
Wu Jie
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.290
Subject(s) - finite element method , elasticity (physics) , plane stress , compatibility (geochemistry) , mathematics , compressibility , rate of convergence , least squares function approximation , mathematical analysis , rotation (mathematics) , mixed finite element method , structural engineering , geometry , engineering , mechanics , physics , channel (broadcasting) , statistics , electrical engineering , estimator , chemical engineering , thermodynamics
A new least‐squares finite element method (LSFEM) for plane elasticity problems is developed based on the first‐order displacement–stress–rotation formulation which includes two new first‐order compatibility constraints among the stresses and the drilling rotation. This LSFEM can accommodate all kinds of equal‐order interpolations. Numerical experiments on various examples including incompressible materials show that the method achieves an optimal rate of convergence for all variables. Copyright © 2001 John Wiley & Sons, Ltd.

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