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BRIEF NOTES

Coincidence of Boobnov-Galerkin and Closed-Form Solutions in an Applied Mechanics Problem

[+] Author and Article Information
I. Elishakoff

Dept. of Mechanical Engineering, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431-0991, USA

M. Zingales

Dip. di Ingegneria Strutturale e Geotecnica, Viale delle Scienze, Palermo I-90128, Italy

J. Appl. Mech 70(5), 777-779 (Oct 10, 2003) (3 pages) doi:10.1115/1.1598474 History: Received October 30, 2001; Revised November 08, 2002; Online October 10, 2003
Copyright © 2003 by ASME
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References

Galerkin,  B. G., 1915, “Beams and Plates,” Vestnik Inzhenerov, 1, pp. 897–908, (see also Collected Works, USSR Academy of Sciences Publishing, 1952, pp. 182–183).
Duncan, W. J., 1937, “Galerkin’s Method in Mechanics and Differential Equations,” Aeronautical Research Council Reports and Memoranda No. 1798.
Duncan, W. J., 1938, “The Principles of the Galerkin Method,” Aeronautical Research Report and Memoranda No. 1894.
Mikhlin, S. G., 1964, Variational Methods in Mathematical Physics, Pergamon Press, Oxford.
Hoff, N. J., 1956, The Analysis of Structures, Wiley, New York.
Kantorovich, L. V., and Krylov, V. I., 1958, Approximate Method for Higher Analysis, Interscience (English translation), New York.
Ishlinski, A. Ju. (Editor), 1975, Advances of Mechanics of Deformable Continua (dedicated to the 100th Anniversary of the Birth of B. G. Galerkin), Nauka, Moscow (in Russian).
Strang, G., and Fix, G. J., 1973, An Analysis of the Finite Element Method, Prentice-Hall Englewood Cliffs, New Jersey.
Leipholz,  H. H. E., 1976, “Use of Galerkin’s Method for Vibration Problems,” Shock Vib. Dig., 8, pp. 3–18.
Singer,  J., 1962, “On the Equivalence of Galerkin’s and Rayleigh Ritz Methods,” Journal of the Royal Aeronautical Society,66, p. 592.
Elishakoff,  I., and Lee,  L. H. N., 1986, “On Equivalence of the Galerkin and Fourier Series Methods for one Class of Problems,” J. Sound Vib., 109, pp. 174–177.
Filonenenko-Borodich,  M. M., 1946, “On a Certain System of Functions and its Applications in the Theory of Elasticity,” Prikl. Mat. Mekh., 10, pp. 193–208 (in Russian).
Stepanov, V. V., 1945, “On Some Complete Non-Orthogonal Systems,” Proceedings of the USSR Academy of Sciences, Vol. XL VIII, No. 6 (in Russian).
Gradshteyn, I. S., and Ryzhik I. M., 1980, Tables of Integrals Series and Products, Academic Press, New York.
Vilenkin,  N. Ya., 1952, “On Some Nearly Periodic Systems of Functions,” PMM, 16 (3), pp. 812–814 (in Russian).

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