Journal of Elasticity

, Volume 30, Issue 1, pp 1–54

# The invariant manifold of beam deformations

Part 1: the simple circular rod
• A. J. Roberts
Article

## 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.

### Key words

elastic beam theory subcentre invariant manifolds dynamical systems

### AMS (MOS) Classification

73C02 73C10 35A35 58G40

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## Copyright information

© Kluwer Academic Publishers 1993

## Authors and Affiliations

• A. J. Roberts
• 1
1. 1.Department of Applied MathematicsThe University of AdelaideAdelaideSouth Australia