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The Elastic Stability of a Corrugated Plate Under a Shearing Force

Published online by Cambridge University Press:  24 October 2008

A. E. Green
A. E. Green
Affiliation:
Jesus College
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Extract

1. The elastic stability of a long flat plate when acted on by a shearing force along its edges has been discussed by Southwell and Skan*, and Leggett† has solved the shearing problem when the plate has a small constant curvature. The present paper deals with the elastic stability of a long corrugated plate which is acted on by a shearing force along its generators, the work being applicable to plates with any given number of bays forming the corrugations. It is supposed that the plate is thin and that the depth d of a bay is a small multiple of the semithickness h; little progress has been made without some such assumption as the second, which enables us to reduce the fundamental equations to a soluble form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 4 , October 1937 , pp. 459 - 473
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

* Proc. Boy. Soc. 105 (1924), 582.Google Scholar

† proc. Roy. Soc. 162 (1937), 62.Google Scholar

* Proc. Roy. Soc. 107 (1925), 734Google Scholar, equations (30), (31) and (32). It is assumed that 1/ρ is small.

* These equations may also be obtained by using from the outset the theory of thin shells.

* It may actually be differentiated at least five times but we only need the third derivative in the boundary conditions.

* This shows that Ar is actually O(r–5).

* Proc. Camb. Phil. Soc. 31 (1935), 376.Google Scholar

* I wish to express my thanks to Mr Leggett for allowing me to reproduce his results from his manuscript.