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A mixed variational principle for finite element analysis
Author(s) -
Day Michael L.,
Yang T. Y.
Publication year - 1982
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.1620180808
Subject(s) - finite element method , variational principle , a priori and a posteriori , mixed finite element method , compatibility (geochemistry) , free energy principle , mathematics , extended finite element method , boundary value problem , mathematical analysis , domain (mathematical analysis) , mathematical optimization , structural engineering , engineering , philosophy , statistics , epistemology , chemical engineering
A mixed variational principle is developed and utilized in a finite element formulation. The procedure is mixed in the sense that it is based upon a combination of modified potential and complementary energy principles. Compatibility and equilibrium are satisfied throughout the domain a priori , leaving only the boundary conditions to be satisfied by the variational principle. This leads to a finite element model capable of relaxing troublesome interelement continuity requirements. The nodal concept is also abandoned and, instead, generalized parameters serve as the degrees‐of‐freedom. This allows for easier construction of higher order elements with the displacements and stresses treated in the same manner. To illustrate these concepts, plane stress and plate bending analyses are presented.