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Digitale Medien

The invariant manifold of beam deformations (1993)

Roberts, A. J.

Springer

Journal of elasticity 30 (1993), S. 1-54

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ISSN: 1573-2681

Schlagwort(e): elastic beam theory ; subcentre invariant manifolds ; dynamical systems ; 73C02 ; 73C10 ; 35A35 ; 58G40

Quelle: Springer Online Journal Archives 1860-2000

Thema: Maschinenbau , Physik

Notizen: Abstract The subcentre invariant manifold of elasticity in a thin rod may be used to give a rigorous and appealing approach to deriving one-dimensional beam theories. Here I investigate the analytically simple case of the deformations of a perfectly uniform circular rod. Many, traditionally separate, conventional approximations are derived from within this one approach. Furthermore, I show that beam theories are convergent, at least for the circular rod, and obtain an accurate estimate of the limit of their validity. The approximate evolution equations derived by this invariant manifold approach are complete with appropriate initial conditions, forcing and, in at least one case, boundary conditions.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00041769

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