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Advanced 4‐node tetrahedrons
Author(s) -
Tian Rong,
Matsubara Hitoshi,
Yagawa Genki
Publication year - 2006
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.1744
Subject(s) - tetrahedron , spurious relationship , partition (number theory) , consistency (knowledge bases) , computer science , algorithm , hexahedron , displacement (psychology) , finite element method , computational science , mathematics , geometry , engineering , structural engineering , combinatorics , psychology , machine learning , psychotherapist
Tetrahedral elements are indispensable to complex finite element structural analysis. Two existing and two newly developed advanced 4‐node tetrahedrons are studied in this paper. The existing elements that use complicated displacement fields are significantly simplified. The spurious zero‐energy modes typical of all these elements are identified to be rigid‐body‐alike modes and are found to be naturally suppressible, making it possible to avoid any stabilization techniques and unknown parameters in formulation. Through the simplified form, we connect these four tetrahedrons and view them in a general framework of the partition‐of‐unity‐based approximation. This general view allows us to reveal many promising features of the newly developed tetrahedrons by comparing them with their existing counterparts: the newly developed tetrahedrons have straightforward formulation, no unsuppressed zero‐energy modes, no stabilization required, no unknown parameters contained, and a high consistency in implementation, in addition to good accuracy and extremely straightforward mesh generation. Copyright © 2006 John Wiley & Sons, Ltd.