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Solid elements with rotational degrees of freedom: Part 1—hexahedron elements
Author(s) -
Yunus Shah M.,
Pawlak Timothy P.,
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.1620310310
Subject(s) - hexahedron , spurious relationship , finite element method , node (physics) , degrees of freedom (physics and chemistry) , element (criminal law) , stiffness , topology (electrical circuits) , engineering , geometry , mathematics , structural engineering , physics , law , statistics , quantum mechanics , political science , electrical engineering
This is the first of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part I introduces an 8‐node solid hexahedron element having three translational and three rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 20‐node hexahedron element. The new element produces a much smaller effective band width of the global system equations than does the 20‐node hexahedron element having midside nodes. A small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present. The new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational DOF at the corner nodes.