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Discrete singular convolution and its application to the analysis of plates with internal supports. I: Theory and algorithm. (English) Zbl 1058.74643
Summary: This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either band-limited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in part II of the present paper [see the following review Zbl 1058.74644)] to plates with complex support conditions, which have not been fully addressed in the literature yet.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K20 Plates
74H45 Vibrations in dynamical problems in solid mechanics
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[1] Entdeckungen uber die Theorie des Klanges. Leipzig, 1787.
[2] Leissa, Shock and Vibration Digest 9 pp 13– (1977)
[3] Leissa, Shock and Vibration Digest 9 pp 21– (1977) · doi:10.1177/058310247700901005
[4] Leissa, Shock and Vibration Digest 13 pp 11– (1981)
[5] Leissa, Shock and Vibration Digest 13 pp 19– (1981)
[6] Leissa, Shock and Vibration Digest 19 pp 11– (1987)
[7] Leissa, Shock and Vibration Digest 19 pp 10– (1987)
[8] Vibration of Plates. NASA SP-160. Office of Technology Utilization, NASA: Washington, DC, 1969.
[9] Vibration of Mindlin Plates. Elsevier Science: Oxford, UK, 1998.
[10] Veletsos, Journal of Applied Mechanics 23 pp 97– (1956) · Zbl 0071.18901
[11] Ungar, Journal of Engineering for Industry 83 pp 434– (1961) · doi:10.1115/1.3664551
[12] Bolotin, Inzhenernyi Zhurnal 3 pp 86– (1961)
[13] Moskalenko, Prikladnaya Mekhanika 1 pp 59– (1965)
[14] Cheung, Journal of the Engineering Mechanics Division, American Society of Civil Engineers 97 pp 391– (1971)
[15] Elishakoff, Journal of Applied Mechanics 46 pp 656– (1979) · Zbl 0418.73062 · doi:10.1115/1.3424622
[16] Azimi, Journal of Sound and Vibration 93 pp 9– (1984)
[17] Mizusawa, Earthquake Engineering and Structural Dynamics 12 pp 847– (1984)
[18] Takahashi, Journal of Sound and Vibration 62 pp 455– (1979)
[19] Wu, Earthquake Engineering and Structural Dynamics 3 pp 3– (1974)
[20] Kim, Journal of Sound and Vibration 114 pp 129– (1987)
[21] Liew, Journal of Sound and Vibration 147 pp 255– (1991)
[22] Liew, Computers and Structures 49 pp 31– (1993)
[23] Zhou, International Journal of Solids and Structures 31 pp 347– (1994)
[24] Kong, Journal of Sound and Vibration 184 pp 639– (1995)
[25] Liew, Journal of Sound and Vibration 172 pp 527– (1994)
[26] Wei, Journal of Chemical Physics 110 pp 8930– (1999)
[27] Wei, Journal of Physics A 33 pp 4935– (2000)
[28] Wei, Journal of Physics A 33 pp 8577– (2000)
[29] Wei, Computer Methods in Applied Mechanics and Engineering 190 pp 2017– (2001)
[30] Théore des Distributions, Hermann: Paris, 1951.
[31] Wei, Journal of Physics B 33 pp 343– (2000)
[32] Wan, Journal of Computational Physics 180 pp 1– (2002)
[33] A unified method for computational mechanics. In Computational Mechanics for the Next Millennium, (eds). Amsterdam: Elsevier, 1999; 1049-1054. · Zbl 0937.60101
[34] Zhao, Journal of Sound and Vibration
[35] Wei, IEEE Signal Processing Letters 6 pp 165– (1999)
[36] Wei, Physica D 137 pp 247– (2000)
[37] Ablowitz, Journal of Computational Physics 126 pp 299– (1996)
[38] Guan, Physica D 151 pp 83– (2001)
[39] Mathematical Methods, vol. 1. Academic Press: New York, 1968.
[40] Walter, Annals of Statistics 7 pp 328– (1977)
[41] Winter, Annals of Statistics 3 pp 759– (1975)
[42] Wahba, Annals of Statistics 3 pp 15– (1975)
[43] Kronmal, Journal of the American Statistical Association 63 pp 925– (1968)
[44] Quantum Mechanics (3rd edn). Springer: Berlin, 1993.
[45] A note on regularized Shannon’s sampling formulae. Preprint arXiv:math.SC/0005003, 2000.
[46] Wei, Chemical Physics Letters 296 pp 215– (1998)
[47] Theory of Plates and Shells. McGraw-Hill: Singapore, 1970.
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