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Finite element criteria for some shells
Author(s) -
Morley L. S. D.
Publication year - 1984
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.1620200914
Subject(s) - finite element method , parametric statistics , quadratic equation , mathematics , representation (politics) , mixed finite element method , homogeneous , extended finite element method , shell (structure) , compatibility (geochemistry) , simple (philosophy) , mathematical analysis , geometry , structural engineering , engineering , mechanical engineering , combinatorics , philosophy , statistics , epistemology , chemical engineering , politics , political science , law
Abstract Simple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes, and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes. Curved finite elements of a quadratic parametric representation, which do not belong to the special class, are then studied. By using a series of exact inextensional bending displacements, it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow, as is usually the case in practice. Criteria for homogeneous membrane actions follow from Gol'denveizer's static–geometric analogue.