×
Sze, K. Y.

On immunizing five-beta hybrid-stress element models from ”trapezoidal locking” in practical analyses. (English) Zbl 0956.74065

Int. J. Numer. Methods Eng. 47, No. 4, 907-920 (2000).
Summary: When multiple trapezoidal four-node plane elements are used to model slender beams, it is found that the transverse bending stress/strain mode which should physically vanish is most detrimental to the element accuracy and leads to a deficiency which is sometimes known as ‘trapezoidal locking’. In this paper, immunity of four-node five-beta hybrid elements to ‘trapezoidal locking’ in practical analyses is obtained by a simple selective scaling procedure that judiciously reduces the stiffness arising from the two bending stress/strain modes in the elements.

Cited in 23 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

hybrid formulation; trapezoidal locking; slender beams; transverse bending stress/strain mode; four-node five-beta hybrid elements; selective scaling procedure
Cite Review PDF
Full Text: DOI

References:

[1] Pian, AIAA Journal 2 pp 1333– (1964) · doi:10.2514/3.2546
[2] Pian, International Journal for Numerical Methods in Engineering 20 pp 1685– (1984) · Zbl 0544.73095 · doi:10.1002/nme.1620200911
[3] Sze, International Journal for Numerical Methods in Engineering 35 pp 1– (1992) · doi:10.1002/nme.1620350102
[4] Yuan, International Journal for Numerical Methods in Engineering 36 pp 1747– (1992) · Zbl 0772.73086 · doi:10.1002/nme.1620361009
[5] Wu, Finite Elements in Analysis and Design 21 pp 111– (1995) · Zbl 0875.65070 · doi:10.1016/0168-874X(95)00023-0
[6] Yeo, International Journal for Numerical Methods in Engineering 40 pp 2933– (1997) · Zbl 0905.73073 · doi:10.1002/(SICI)1097-0207(19970830)40:16<2933::AID-NME198>3.0.CO;2-3
[7] Incompatible displacement models. In Numerical and Computer Methods in Structural Mechanics, et al. (eds). Academic Press: New York, 1973; 43-57. · doi:10.1016/B978-0-12-253250-4.50008-7
[8] Taylor, International Journal for Numerical Methods in Engineering 10 pp 1211– (1976) · Zbl 0338.73041 · doi:10.1002/nme.1620100602
[9] Simo, International Journal for Numerical Methods in Engineering 29 pp 1595– (1990) · Zbl 0724.73222 · doi:10.1002/nme.1620290802
[10] Belytschko, Computer Methods in Applied Mechanics and Engineering 54 pp 279– (1986) · Zbl 0579.73075 · doi:10.1016/0045-7825(86)90107-6
[11] Hughes, International Journal for Numerical Methods in Engineering 16 pp 1413– (1980) · Zbl 0437.73053 · doi:10.1002/nme.1620150914
[12] MacNeal, Nuclear Engineering and Design 70 pp 3– (1982) · doi:10.1016/0029-5493(82)90262-X
[13] On a formulation of the quadrilateral with highly accurate in-plane bending behavior. abstract, First U.S. National Congress on Computational Mechanics, July 21-24, Chicago, 1991.
[14] MacNeal, International Journal for Numerical Methods in Engineering 24 pp 1793– (1987) · Zbl 0625.73083 · doi:10.1002/nme.1620240913
[15] Finite Elements: Their Design and Performance. Marcel Dekker: New York, 1994.
[16] Allman, Computers and Structures 19 pp 1– (1984) · Zbl 0548.73049 · doi:10.1016/0045-7949(84)90197-4
[17] MacNeal, Finite Elements in Analysis and Design 5 pp 31– (1989) · doi:10.1016/0168-874X(89)90004-8
[18] Sze, Computers and Structures 42 pp 695– (1992) · Zbl 0825.73947 · doi:10.1016/0045-7949(92)90181-X
[19] Sze, International Journal for Numerical Methods in Engineering 40 pp 1785– (1997) · doi:10.1002/(SICI)1097-0207(19970530)40:10<1785::AID-NME137>3.0.CO;2-H
[20] Bergan, Computer Methods in Applied Mechanics and Engineering 50 pp 25– (1985) · Zbl 0593.73073 · doi:10.1016/0045-7825(85)90113-6
[21] The Finite Element Method?Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: New Jersey, 1987.
[22] The Finite Element Method, vol. 1-Basic Formulation and Linear Problems (4th edn). McGraw-Hill: London, 1989.
[23] Hauptmann, International Journal for Numerical Methods in Engineering 42 pp 49– (1998) · Zbl 0917.73067 · doi:10.1002/(SICI)1097-0207(19980515)42:1<49::AID-NME349>3.0.CO;2-2
[24] Sze, International Journal for Numerical Methods in Engineering 36 pp 1519– · Zbl 0772.73081 · doi:10.1002/nme.1620360907
[25] MacNeal, Finite Elements in Analysis and Design 1 pp 3– (1985) · doi:10.1016/0168-874X(85)90003-4
[26] Sze, Communications in Applied Numerical Methods 8 pp 385– (1992) · Zbl 0757.73060 · doi:10.1002/cnm.1630080605
[27] Lee, AIAA Journal 16 pp 29– (1978) · Zbl 0368.73067 · doi:10.2514/3.60853
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.