TY - JOUR
T1 - EXISTENCE AND STABILITY, AND DISCRETE BB AND RANK CONDITIONS, FOR GENERAL MIXED-HYBRID FINITE ELEMENTS IN ELASTICITY.
AU - Xue, W. M.
AU - Atluri, S. N.
PY - 1985
Y1 - 1985
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0022269825&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:0022269825
SN - 0160-8835
VL - 73
SP - 91
EP - 112
JO - American Society of Mechanical Engineers, Applied Mechanics Division, AMD
JF - American Society of Mechanical Engineers, Applied Mechanics Division, AMD
ER -