×

zbMATH — the first resource for mathematics

A triangular element based on Reissner-Mindlin plate theory. (English) Zbl 0728.73073
Summary: A new triangular plate bending element based on the Reissner-Mindlin theory is developed through a mixed formulation emanating from the Hu- Washizu variational principle. A main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges. The element is shown to avoid shear locking, converge to the Kirchhoff plate theory as the plate thickness approaches zero, and generally exhibit excellent behaviour on a series of standard problems and tests.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] and , ’Finite element stiffness matrices for analysis of plates in bending’, Proc. Conf. on Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, WPAFB, Ohio, 1966, pp. 515-545.
[2] Reissner, J. Appl. Mech. 12 pp 69– (1945)
[3] Mindlin, J. Appl. Mech. 18 pp 31– (1951)
[4] Zienkiewicz, Int. J. Numer. Methods Eng. 3 pp 275– (1971)
[5] Pawsey, Int. J. Numer. Methods Eng. 3 pp 575– (1971)
[6] Hughes, Int. J. Numer. Methods Eng. 11 pp 1529– (1977)
[7] Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford, 1982.
[8] Malkus, Comp. Methods Appl. Mech. Eng. 15 pp 63– (1978)
[9] Wempner, J. Eng. Mech. Div. Asce 94 pp 1273– (1968)
[10] Batoz, Int. J. Numer. Methods Eng. 15 pp 1771– (1980)
[11] Bathe, Int. J. Numer. Methods Eng. 21 pp 367– (1985)
[12] Huang, Eng. Comp. 1 pp 369– (1984)
[13] and , ’A uniformly accurate finite element method for the Mindlin-Reissner plate’, IMA Preprint 307, 1987.
[14] , and , ’Plate bending elements with discrete constraints: New triangular elements’, UCB/SEMM Report 89/09, Department of Civil Engineering, University of California, Berkeley, CA, 1989.
[15] The Finite Element Method, Prentice-Hall, Englewood Cliffs, N. J., 1987.
[16] Chrisfield, Comp. Methods Appl. Mech. Eng. 38 pp 93– (1983)
[17] and , The Finite Element Method, 4th edn, Vol. 1, McGraw-Hill, London, 1989.
[18] and (eds.), Handbook of Mathematical Functions; with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1970.
[19] Zienkiewicz, Comm. Appl. Numer. Methods 3 pp 301– (1987)
[20] Zienkiewicz, Int. J. Numer. Methods Eng. 23 pp 1873– (1986)
[21] and , Theory of Plates and Shells, McGraw-Hill, London, 1959.
[22] Yuan, Int. J. Numer. Methods Eng. 28 pp 109– (1989)
[23] Skew Plates and Structures, International Series of Monographs in Aeronautics and Astronautics, MacMillan, New York, 1963.
[24] Hughes, J. Appl. Mech. 46 pp 587– (1981)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.