EXISTENCE AND STABILITY, AND DISCRETE BB AND RANK CONDITIONS, FOR GENERAL MIXED-HYBRID FINITE ELEMENTS IN ELASTICITY.

W. M. Xue, S. N. Atluri

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations

Abstract

In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.

Original languageEnglish
Pages (from-to)91-112
Number of pages22
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume73
StatePublished - 1985

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