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The polygon-circle paradox and convergence in thin plate theory

Published online by Cambridge University Press:  24 October 2008

N. W. Murray
N. W. Murray
Affiliation:
Technische Universität, München
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Abstract

The solution for a simply supported many-sided polygonal plate does not agree with that for the corresponding circular plate. This paper describes the earlier work of Rao and Rajaiah on polygonal plates and then explains why best convergence of series solutions occurs when the boundary conditions are defined as

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 279 - 282
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Rao, A. K. and Rajaiah, K.Polygon-circle paradox of simply supported thin plates under pressure. AIAA Journal 6 (1968), 155–6.Google Scholar
(2)Rajaiah, K. and Rao, A. K.Effect of boundary condition description on convergence of solution in a boundary value problem. J. Computational Phys. 3 (1968), 190–201.Google Scholar
(3)Rajaiah, K. and Rao, A. K.On limiting cases in the flexure of simply supported rectangular plates. Proc. Cambridge Philos. Soc. 65 (1969), 831–4.Google Scholar
(4)Lanzos, C.Linear differential operators (D. van Nostrand, 1961), pp. 195–8.Google Scholar