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Solid elements with rotational degrees of freedom: Part II—tetrahedron elements
Author(s) -
Pawlak Timothy P.,
Yunus Shah M.,
Cook Robert D.
Publication year - 1991
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.1620310311
Subject(s) - tetrahedron , hexahedron , finite element method , stiffness matrix , stiffness , degrees of freedom (physics and chemistry) , node (physics) , element (criminal law) , geometry , structural engineering , mathematics , engineering , physics , quantum mechanics , political science , law
This is the second part of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part II introduces a solid tetrahedron element having 3 translational and 3 rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 10‐node tetrahedron element. To further enhance the element performance a least squares strain extraction technique is also implemented to develop the stiffness matrix with a desired field. The strain smoothing improves performance without causing a loss in generality. As with the hexahedron in Part I, the element stiffness is augmented with a small penalty stiffness to eliminate any possible spurious zero energy modes. The new tetrahedron element passes the patch test and demonstrates much improved performance over the 4‐node translational DOF only (constant strain) tetrahedron element.