×

Elimination of spurious pressure and kinematic modes in biquadratic nine-node plane element. (English) Zbl 0846.73070

The authors propose \(Q9/3p\) elements which are free from spurious pressure. Complete theoretical development has been made, and the conclusions are illustrated by a number of numerical experiments together with the description of the program code.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
Full Text: DOI

References:

[1] Hermann, AIAA J. 3 pp 1896– (1965)
[2] Key, Int. J. Solids Struct. 5 pp 951– (1969)
[3] Plan, AIAA J. 14 pp 824– (1976)
[4] The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1987.
[5] and , The Finite Element Method, Vol. I–Basic Formulation and Linear Problems, 4th edn., McGraw-Hill New York, 1989.
[6] Sani, Int. j. numer. methods fluids 1 pp 17– (1981)
[7] Sani, Int. J. Numer. Methods Fluids 1 pp 171– (1981)
[8] and , ’Numerical analysis of incompressible flow using a new finite element formulation’, in et al. (eds.), Proc. 6th Int. Conf. Num. Meth. Laminar and Turbulent Flows, Pineridge Press, Swansea, 1989, pp. 169-177.
[9] Sussman, Comput. Struct. 26 pp 357– (1987)
[10] Babuška, Numer. Math. 20 pp 179– (1973)
[11] Brezzi, R.A.I.R.O. 8 pp 129– (1974)
[12] Sze, Int. j. numer. methods eng. 37 pp 2797– (1994)
[13] Sze, Int. j. numer. methods eng. 36 pp 3303– (1993)
[14] Sze, Int. j. numer. methods eng. 37 pp 2235– (1994)
[15] Sze, Comput. Methods Appl. Mech. Eng. 117 pp 361– (1994)
[16] Lee, Int. j. numer. methods eng. 21 pp 1629– (1986)
[17] Sze, Commun. Appl. Numer. Methods. 8 pp 385– (1992)
[18] Pian, Int. j. numer. methods eng. 20 pp 1685– (1984)
[19] Sze, Int. j. numer. methods eng. 35 pp 1– (1992)
[20] Wong, Eng. Comput. 4 pp 229– (1987)
[21] MacNeal, Finite Elements Analy. Des. 1 pp 3– (1985)
[22] and , Theory of Elasticity, 3rd edn, McGraw-Hill, New York, 1982.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.