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Control of zero‐energy modes in 9‐node plane element
Author(s) -
Verhegghe Benedict,
Powell Graham H.
Publication year - 1986
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.1620230508
Subject(s) - quadrilateral , quadrature (astronomy) , spurious relationship , node (physics) , offset (computer science) , element (criminal law) , topology (electrical circuits) , finite element method , plane (geometry) , structural engineering , geometry , mathematics , computer science , engineering , electronic engineering , combinatorics , statistics , law , political science , programming language
For plane stress/plane strain analysis, the 9‐node quadrilateral element performs better than the corresponding 8‐node element, especially for non‐rectangular shapes. For improved element flexibility and lower computer cost, 2 × 2 quadrature is generally preferable to 3 × 3 quadrature. Unfortunately the 9‐node element contains spurious zero‐energy modes when under‐integrated. A method is proposed to restrain these modes without significant loss of accuracy or added cost.

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