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The generalized differential quadrature rule for fourth-order differential equations. (English) Zbl 0999.74120
From the summary: The generalized differential quadrature rule (GDQR) proposed here is aimed at solving higher-order differential equations. The improved approach is completely free of the use of existing \(\delta\)-point technique by applying multiple conditions in a rigorous manner. The GDQR is applied to static and dynamic analysis of Bernoulli-Euler beams and classical rectangular plates. Numerical error analysis is carried out in the beam analysis.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K20 Plates
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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[1] Bellman, Journal of Mathematical Analysis and Applications 34 pp 235– (1971) · Zbl 0236.65020 · doi:10.1016/0022-247X(71)90110-7
[2] Jang, International Journal for Numerical Methods in Engineering 28 pp 561– (1989) · Zbl 0669.73064 · doi:10.1002/nme.1620280306
[3] Bert, Applied Mechanics Reviews 49 pp 1– (1996) · doi:10.1115/1.3101882
[4] Malik, International Journal for Numerical Methods in Engineering 39 pp 1237– (1996) · Zbl 0865.73079 · doi:10.1002/(SICI)1097-0207(19960415)39:7<1237::AID-NME904>3.0.CO;2-2
[5] Striz, Journal of Sound and Vibration 202 pp 689– (1997) · Zbl 1235.74124 · doi:10.1006/jsvi.1996.0846
[6] Chen, International Journal for Numerical Methods in Engineering 40 pp 1941– (1997) · Zbl 0886.73078 · doi:10.1002/(SICI)1097-0207(19970615)40:11<1941::AID-NME145>3.0.CO;2-V
[7] Wang, International Journal for Numerical Methods in Engineering 40 pp 759– (1997) · Zbl 0888.73078 · doi:10.1002/(SICI)1097-0207(19970228)40:4<759::AID-NME87>3.0.CO;2-9
[8] Wang, Communications in Numerical Methods in Engineering 14 pp 1133– (1998) · Zbl 0930.74080 · doi:10.1002/(SICI)1099-0887(199812)14:12<1133::AID-CNM213>3.0.CO;2-Q
[9] Gu, Journal of Sound and Vibration 202 pp 452– (1997) · doi:10.1006/jsvi.1996.0813
[10] Bellomo, Mathematical and Computer Modelling 26 pp 13– (1997) · Zbl 0898.65074 · doi:10.1016/S0895-7177(97)00142-8
[11] Quan, Computers in Chemical Engineering 13 pp 779– (1989) · doi:10.1016/0098-1354(89)85051-3
[12] Shu, International Journal for Numerical Methods in Fluids 15 pp 791– (1992) · Zbl 0762.76085 · doi:10.1002/fld.1650150704
[13] Introduction to Numerical Analysis. Springer: New York, 1992.
[14] Striz, ACTA Mechanics 111 pp 85– (1995) · Zbl 0854.73080 · doi:10.1007/BF01187729
[15] Leissa, Journal of Sound and Vibration 31 pp 257– (1973) · Zbl 0268.73033 · doi:10.1016/S0022-460X(73)80371-2
[16] Theory of Plates and Shells (2nd edn). McGraw-Hill: Singapore, 1970.
[17] Wu, Communications in Numerical Methods in Engineering
[18] Wu, Communications in Numerical Methods and Engineering
[19] A Generalized Differential Quadrature Rule for free vibration analysis of thin cylindrical shells. In Computational Mechanics for the Next Millennium, Proceedings of APCOM’99, (eds). Elsevier: Amsterdam, Vol. 1, 1999; 223-228.
[20] Wu, Journal of Sound and Vibration 233 pp 195– (2000) · Zbl 1237.65018 · doi:10.1006/jsvi.1999.2815
[21] A generalization of differential quadrature method. 20th ICTAM, Chicago, 2000, accepted.
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