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Bilinear finite elements for shells: Isoparametric quadrilaterals
Author(s) -
Niemi Antti H.,
Pitkäranta Juhani
Publication year - 2007
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.2252
Subject(s) - quadrilateral , finite element method , bilinear interpolation , norm (philosophy) , bilinear form , mathematics , strain energy , shell (structure) , structural engineering , mathematical analysis , engineering , mechanical engineering , statistics , political science , law
We study the accuracy and reliability of the lowest‐order bilinear shell finite element schemes. Our approach is based mainly on a simplified shallow shell model analogous to the Reissner–Mindlin model of plate bending. The numerical models are constructed by modifying the strain expressions within the usual energy principle so that error analysis in the energy norm framework is possible. Our theoretical predictions supported by numerical experiments indicate that the performance of the low‐order methods is both mesh and case dependent. Copyright © 2007 John Wiley & Sons, Ltd.