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A Note on the Choice of Co-ordinate Functions for the Rayleigh-Ritz Method

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 Rayleigh-Ritz method for approximate solution of equilibrium or stability problems in elasticity is based on the theorem of the minimum of the total potential. Hence the assumed displacements have to satisfy only the geometrical boundary conditions of the problem in order to be admissible. The displacements are expressed as a series of suitable chosen functions, called co-ordinate functions, multiplied by parameters which are determined by the minimisation procedure of the method. Except for the essential requirement that these co-ordinate functions have to satisfy the geometrical boundary conditions of the problem, no general rule for their choice can be given, and experience and physical considerations have to be relied upon.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 65 , Issue 611 , November 1961 , pp. 765 - 766
Copyright
Copyright © Royal Aeronautical Society 1961

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References

1.Hoff, Nicholas J. (1956). The Analysis of Structures, pp. 201, 254. John Wiley, New York, 1956.Google Scholar
2.Pflüger, Alf (1950). Stäbilitdtsprobleme der Elastostatik, p. 172. Springer-Verlag, Berlin, 1950.Google Scholar
3.Istvan, Szabó (1958). Höhere Technische Mechanik, 2nd Ed. p. 108. Springer-Verlag, Berlin, 1958.Google Scholar