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A novel unsymmetric 8‐node plane element immune to mesh distortion under a quadratic displacement field
Author(s) -
Rajendran S.,
Liew K. M.
Publication year - 2003
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.836
Subject(s) - quadrilateral , quartic function , finite element method , quadratic equation , mathematics , displacement field , displacement (psychology) , element (criminal law) , mathematical analysis , compatibility (geochemistry) , node (physics) , geometry , topology (electrical circuits) , structural engineering , pure mathematics , combinatorics , engineering , psychology , political science , law , psychotherapist , chemical engineering
An 8‐node quadrilateral plane finite element is developed based on a novel unsymmetric formulation which is characterized by the use of two sets of shape functions, viz ., the compatibility enforcing shape functions and completeness enforcing shape functions. The former are chosen to satisfy exactly the minimum inter‐ as well as intra‐element displacement continuity requirements, while the latter are chosen to satisfy all the (linear and higher order) completeness requirements so as to reproduce exactly a quadratic displacement field. Numerical results from test problems reveal that the new element is indeed capable of reproducing exactly a complete quadratic displacement field under all types of admissible mesh distortions. In this respect, the proposed 8‐node unsymmetric element emerges to be better than the existing symmetric QUAD8, QUAD8/9, QUAD9, QUAD12 and QUAD16 elements, and matches the performance of the quartic element, QUAD25. For test problems involving a cubic or higher order displacement field, the proposed element yields a solution accuracy that is comparable to or better than that of QUAD8, QUAD8/9 and QUAD9 elements. Furthermore, the element maintains a good accuracy even with the reduced 2× 2 numerical integration. Copyright © 2003 John Wiley & Sons, Ltd.