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On the unity of the constant strain/constant moment finite element methods
Author(s) -
Hellan Kåre
Publication year - 1973
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.1620060205
Subject(s) - constant (computer programming) , bending moment , analogy , finite element method , mathematics , mathematical analysis , shear and moment diagram , bending , moment (physics) , geometry , classical mechanics , physics , bending stiffness , computer science , thermodynamics , philosophy , linguistics , programming language
The paper is an attempt to unify the finite element methods of ‘first’ order in plate stretching and plate bending, i.e. those assuming in each element constant strains in stretching or constant moments in bending. Reference is made to the stretching–bending analogy between the method of Turner, Clough, Martin and Topp and the method of Elias. By another analogy property a plate stretching method which is the dual to the constant moment method of Herrmann (and Hellan) is derived. The transformation of variables which carries the last pair of dual methods identically into the first pair is finally demonstrated.