Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-22T21:34:04.359Z Has data issue: false hasContentIssue false

Complex potentials in shallow shells of revolution

Published online by Cambridge University Press:  24 October 2008

A. R. Yacoub
Affiliation:
Ain Shams University, Cairo

Abstract

By introducing complex variable techniques in the theory of shallow shells, the problem is reduced to the solution of one fourth-order differential equation, and the displacement components and stress resultants and couples are expressed in terms of four complex potentials. Two of these complex potentials are those of thin plate theory, thus admitting of deducing the solution of a shallow shell problem from the limiting case of the circular flat plate. These results are applied to a case of non-rotational symmetry, a special case of which has practical significance in the design of tanks and boilers.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Basali, W. A. and Dawoud, R. H.Proc. Math. Phys. Soc. Egypt 21 (1957), 1.Google Scholar
(2)Dawoud, R. H.Mathematika 7 (1960), 23.CrossRefGoogle Scholar
(3)Reissner, E.J. Math. Phys. 25, 1 (1946), 80.CrossRefGoogle Scholar
(4)Reissner, E.J. Math. Phys. 25, 4 (1947), 279.CrossRefGoogle Scholar
(5)Savidge, H. G.Rep. Brit. Assoc. Advancement of Science (1916), p. 108.Google Scholar