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Basis of finite element methods for solid continua
Author(s) -
Pian Theodore H. H.,
Tong Pin
Publication year - 1969
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.1620010103
Subject(s) - finite element method , mixed finite element method , basis (linear algebra) , extended finite element method , mathematics , smoothed finite element method , boundary value problem , bending , basis function , mathematical optimization , mathematical analysis , computer science , boundary element method , boundary knot method , structural engineering , geometry , engineering
Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.