ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
We present a simple calculation which seems at first to yield erroneous results when natural boundary conditions are not enforced. Our example is the static deformation of a cantilever beam under uniform loading. The corresponding variational principle is established and two applications of the Rayleigh-Ritz-Galerkin method are made.(1)The deflection is expanded in a series of cosines. The energy is rendered stationary subject to all boundary conditions, geometric and natural (they are imposed through Lagrange multipliers). The resulting function is exactly the Fourier cosine expansion of the true deflection-which is a fourth-degree polynomial.(2)The deflection is again expanded in a cosine series but now the natural boundary conditions are ignored. The resulting series does not converge to the true solution.Owing to the simplicity of the coefficients, exact summations are possible and the discrepancy is clear. The disagreement is large, and the object of the paper is to decide which method is right.
Additional Material:
2 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620261009
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