Premium
The null space and non‐conventional basis functions in the mixed finite element method
Author(s) -
Robey T. H.,
Schreyer H. L.
Publication year - 1988
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.1620260407
Subject(s) - finite element method , basis (linear algebra) , mathematics , basis function , displacement field , mathematical analysis , matrix (chemical analysis) , field (mathematics) , space (punctuation) , displacement (psychology) , decomposition
The two matrix equations obtained from the mixed finite element method are uncoupled through the use of the QR decomposition. The procedure obtains the basis for the null space which is composed of solutions to the homogeneous flux‐equilibrium equation. The result is that, even for statically indeterminate problems, stresses can be obtained without solving for the displacement field. Furthermore, the stress field can be decomposed directly into contributions from applied forces and from prescribed displacements. The appearance of kinetic modes can easily be monitored. The possibility of utilizing non‐conventional basis functions for use in conjunction with the QR decomposition is explored briefly. Simple examples are given to illustrate the theoretical results.