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Mesh distortion insensitive and locking-free Petrov–Galerkin low-order EAS elements for linear elasticity

Pfefferkorn, Robin ORCID iD icon 1; Betsch, Peter 1
1 Institut für Mechanik (IFM), Karlsruher Institut für Technologie (KIT)


One of the most successful mixed finite element methods in solid mechanics is the enhanced assumed strain (EAS) method developed by Simo and Rifai in 1990. However, one major drawback of EAS elements is the highly mesh dependent accuracy. In fact, it can be shown that not only EAS elements, but every finite element with a symmetric stiffness matrix must either fail the patch test or be sensitive to mesh distortion in bending problems (higher order displacement modes) if the shape of the element is arbitrary. This theorem was established by MacNeal in 1992. In the present work we propose a novel Petrov–Galerkin approach for the EAS method, which is equivalent to the standard EAS method in case of regular meshes. However, in case of distorted meshes, it allows to overcome the mesh-distortion sensitivity without loosing other advantages of the EAS method. Three design conditions established in this work facilitate the construction of the element which does not only fulfill the patch test but is also exact in many bending problems regardless of mesh distortion and has an exceptionally high coarse mesh accuracy. Consequently, high quality demands on mesh topology might be relaxed.

Verlagsausgabe §
DOI: 10.5445/IR/1000137764
Veröffentlicht am 23.09.2021
DOI: 10.1002/nme.6817
Zitationen: 2
Web of Science
Zitationen: 1
Zitationen: 2
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Mechanik (IFM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0029-5981, 1097-0207
KITopen-ID: 1000137764
Erschienen in International Journal for Numerical Methods in Engineering
Verlag John Wiley and Sons
Band 122
Heft 23
Seiten 6924-6954
Nachgewiesen in Scopus
Web of Science
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