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Significance of norms and completeness in variational based methodsBy means of a simple structural problem, an important requirement often overlooked in practice on the basis functions used in Rayleigh-Ritz-Galerkin type methods is brought into focus. The problem of the static deformation of a uniformly loaded beam is solved variationally by expanding the beam displacement in a Fourier Cosine series. The potential energy functional is rendered stationary subject to the geometric boundary conditions. It is demonstrated that the variational approach does not converge to the true solution. The object is to resolve this paradox, and in so doing, indicate the practical implications of norms and completeness in an appropriate inner product space.
Document ID
19900013762
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Storch, Joel A. (Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
September 6, 2013
Publication Date
December 15, 1989
Publication Information
Publication: Proceedings of the 3rd Annual Conference on Aerospace Computational Control, Volume 2
Subject Category
Computer Programming And Software
Accession Number
90N23078
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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