Harmonic analysis of elliptical hollow section tubes in blending.

Conference item


McCann, F and Wadee, MA (2016). Harmonic analysis of elliptical hollow section tubes in blending. Engineering Mechanics Institute Conference 2016. Nashville, USA 22 - 25 May 2016 London South Bank University.
AuthorsMcCann, F and Wadee, MA
Abstract

When tubular members are in bending, they tend to flatten towards the axis of bending, thus
reducing their second moment of area. Eventually, a limit point is reached whereupon the
initial stability of the system is lost and unstable equilibrium prevails, thus reducing the load carrying
capacity of the member. This effect was originally described by Brazier (1927) for
circular tubular members. In the present study, the analysis of Brazier is adapted for elliptical
hollow section members, taking into account the additional geometric complexities inherent
in ellipses. An analytical method is presented whereby the initial geometry and the
displacement functions of the system are replaced by Fourier series, thus reducing the
analytical complexity of the problem. After formulating the potential energy functional, use
of a variational method allows for the amplitudes of the constituent harmonics of the Fourier
approximations of the displacement functions to be solved for, providing estimates of the
deformed geometry of the cross-section and the associated moment. In keeping with the
analogy of Brazier for circular sections, a limit point is observed. These analytical predictions
are then compared with the results of a complementary finite element analysis, whereupon it
is found that for smaller longitudinal curvatures there is close agreement between the
analytical and numerical methods. For larger curvatures and moments beyond the limit point
some divergence is observed between the predictions of the two methods, which can be
attributed to the lower-order approximations assumed in formulating the potential energy
functional in the analytical method

Year2016
PublisherLondon South Bank University
Accepted author manuscript
License
CC BY 4.0
Publication dates
Print22 May 2016
Publication process dates
Deposited12 Jun 2017
Accepted22 May 2016
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https://openresearch.lsbu.ac.uk/item/8740z

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