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On the Equivalence of the Galerkin and Rayleigh-Ritz Methods

Published online by Cambridge University Press:  04 July 2016

Josef Singer
Josef Singer*
Affiliation:
Department of Aeronautical Engineering, Technion, Israel Institute of Technology
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Extract

The Galerkin method for the approximate solution of elasticity problems (see e.g. Ref. 1) is usually presented as an alternative to the Rayleigh-Ritz method. The main distinction between the two methods is stated to be that the former begins with an equation of equilibrium, whereas the latter begins with a total potential energy expression. The two methods are not always equivalent, and the conditions for equivalence are given in Duncan's lucid presentation of the method (Refs. 2 and 3, which unfortunately have been out of print for some time). These conditions, however, are generally omitted from discussions of the Galerkin method, and it is the purpose of this note to re-emphasise them in a slightly different form.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 66 , Issue 621 , September 1962 , pp. 592
Copyright
Copyright © Royal Aeronautical Society 1962

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References

1.Biezeno, C. B. and Grammel, R. (1955), Engineering Dynamics. Vol. 1, p. 170. Blackie & Sons, Glasgow, 1955.Google Scholar
2.Duncan, W. J. (1937). Galerkin's Method in Mechanics and Differential Equations, R. & M. 1798, August 1937.Google Scholar
3.Duncan, W. J. (1938). The Principles of the Galerkin Method. R. & M. 1848, September 1938.Google Scholar
4.Hoff, Nicholas J. (1956), The Analysis of Structures, p. 206, John Wiley, New York. 1956.Google Scholar
5.Sokolnikoff, I. S. (1955), Mathematical Theory of Elasticity, p. 413, McGraw-Hill, New York. 2nd Edition, 1955.Google Scholar
6.Pflüger, Alf (1950), Stabilitätsprobleme der Elastostatik, p. 189, Springer-Verlag, Berlin, 1950.Google Scholar
7.Batdorf, S. B. (1947), A Simplified Method of Elastic Stability Analysis for Thin Cylindrical Shells, NACA Report 874, 1947.Google Scholar
8.Paul, Seide (1957), A Donnell Type Theory for Asymmetrical Bending and Buckling of Thin Conical Shells. Journal of Applied Mechanics. 24, 4, p. 547, December 1957.Google Scholar
9.Singer, Josef (1961), Buckling Circular Conical Shells Under Axisymmetrical External Pressure, 3, 4, p. 330, December 1961. Journal of Mechanical Engineering Science.Google Scholar