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The Analysis of Cooling Towers by the Matrix Finite Element Method

Part II.*Large Displacements

Published online by Cambridge University Press:  04 July 2016

A. S. L. Chan  and
A. Firmin
A. S. L. Chan
Affiliation:
Department of Aeronautics, Imperial College, London
A. Firmin
Affiliation:
Department of Aeronautics, Imperial College, London
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Extract

As a necessary first step towards the large displacement analysis of the cooling tower structure by the finite element method, an account of the small displacement theory of the SABA family of elements has been given in the first part of the paper. It may be worth repeating the basic considerations which influenced the philosophy in the design of the element: for an economical large displacement analysis to be successful it is essential that the structure should be represented by as few displacement parameters as possible, consistent with an accurate description of the structural behaviour. The SABA element is an axi-symmetrical thin shell element which describes the displacement variation in the circumferential direction by a Fourier series, each term of which is associated with a polynomial for interpolation in the meridional direction. By the devise of interpolating the meridional geometry in the same way, no strain is induced in a rigid-body movement, thus achieving true equilibrium and avoiding serious error in a large displacement calculation. Results of the small displacement analysis by this element for various examples given in Part I agreed accurately with existing solutions by other methods.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 74 , Issue 720 , December 1970 , pp. 971 - 982
Copyright
Copyright © Royal Aeronautical Society 1970 

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Footnotes

*

Part I. (misprinted as Part II) appeared in the October 1970 issue of the Journal.

References

1. Chan, A. S. L. and Firmin, A. The Analysis of Cooling Towers by the Finite Element Method. Aeronautical Journal. Vol. 74, October 1970.Google Scholar
2. Argyris, J. H. and Scharpf, D. W. Some General ConsiderationsoftheNaturalModeTechnique—PartII. Aeronautical Journal, Vol. 73, May 1969.Google Scholar
3. Kalnins, A. On Non-linear Analysis of Elastic Shells of Revolution. J App Mechs, March 1967.Google Scholar
4. Ewing, D. Buckling of Cooling Tower Shells. CEGB Internal Report, November 1970.Google Scholar
5. Argyris, J. H. Continua and Discontinua. Proceedings of the 1st International Conference on Matrix Methods of Structural Mechanics, held in October, 1965, at Dayton, Ohio.Google Scholar
6. Oden, J. T. and Key, J. E. Numerical Analysis of Finite Axisymmetric Deformations of Incompressible Solids of Revolution. Int J. Solids & Struct, 1970.Google Scholar
7. Hibbitt, H. D. et al A Finite Element Formulation for Problems of Large Strain and Large Displacement. Int J Solids Struct, August 1970.Google Scholar
8. Novozhilov, V. The Theory of Thin Shells. P. Noordhoff, 1959.Google Scholar
9. Kaplan, A. and Fung, Y. C. A Non-Linear Theory of Bending and Buckling of Thin Elastic Spherical Shells. NACA TN 3212.Google Scholar
10. Gallagher, R. H. et al. A Discrete Element Procedure for Thin Shell Instability Analysis, AIAA Journal, January 1967.Google Scholar
11. Budiansky, B. Buckling of Clamped Shallow Spherical Shells. Proceedings of the IUTUM Symposium on the Theory of Thin Elastic Shells. North Holland Pub. Co. Amsterdam, 1960.Google Scholar
12. Ball, R. E. A Geometrically Non-linear Analysis of ArbitrarilyLoadedShells ofRevolution. NASA CR 909, January 1968.Google Scholar
13. Flügge, W. Stresses in Shells. Springer-Verlag. 1960.Google Scholar
14. Timoshenko, S. P. and Gere, J. M. Theory of Elastic Stability. McGraw-Hill, 1961.Google Scholar
15. Gerrard, G. Introduction to Structural Stability Theory. McGraw-Hill, 1962.Google Scholar