Premium
A mixed finite element formulation for Reissner–Mindlin plates based on the use of bubble functions
Author(s) -
Pinsky Peter M.,
Jasti Raja V.
Publication year - 1989
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.1620280715
Subject(s) - finite element method , mathematics , mathematical analysis , displacement field , interpolation (computer graphics) , variational principle , degrees of freedom (physics and chemistry) , a priori and a posteriori , stress field , mixed finite element method , bubble , displacement (psychology) , geometry , classical mechanics , physics , mechanics , structural engineering , engineering , motion (physics) , psychology , philosophy , epistemology , quantum mechanics , psychotherapist
A new finite element formulation for Reissner–Mindlin plates, based on the Hellinger–Reissner variational principle, is proposed in which the displacement field is additively decomposed into two parts: a part associated with standard interpolation of nodal degrees of freedom and a part associated with a set of independent bubble functions expressed in terms of generalized parameters. The formulation employs independent approximations for every stress component so that the stress field does not a priori satisfy the homogeneous equilibrium equations. It is shown that the bubble functions provide additional variational constraints on the stress field, resulting in optimal accuracy for the mixed formulation, and also eliminating shear locking in the thin limit. A 4‐node and a 9‐node element are described in detail. Both elements pass the patch test for mixed elements described by Zienkiewicz et al. 1 and are stable in the sense of the Babuška–Brezzi condition. Numerical results indicate that the elements are accurate in displacements and stresses, including transverse shear, and insensitive to mesh distortion.