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Rational approach for assumed stress finite elements
Author(s) -
Pian T. H. H.,
Sumihara K.
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.1620200911
Subject(s) - mathematics , finite element method , mathematical analysis , mixed finite element method , stress (linguistics) , plane stress , variational principle , element (criminal law) , geometry , structural engineering , engineering , linguistics , philosophy , political science , law
A new method for the formulation of hybrid elements by the Hellinger‐Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co‐ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4‐node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.