On the Equivalence of the Galerkin and Rayleigh-Ritz Methods
- 1 February 1962
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Royal Aeronautical Society
- Vol. 66 (621) , 592
- https://doi.org/10.1017/s0368393100077403
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- Buckling of Circular Conical Shells under Axisymmetrical External PressureJournal of Mechanical Engineering Science, 1961
- A Donnell Type Theory for Asymmetrical Bending and Buckling of Thin Conical ShellsJournal of Applied Mechanics, 1957