Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T01:04:35.201Z Has data issue: false hasContentIssue false
  • English
  • Français

Bending of a simply-supported shallow spherical shell under a uniform line load on a part of a parallel circle

Published online by Cambridge University Press:  24 October 2008

D. N. Mitra
D. N. Mitra
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur
Get access Rights & Permissions [Opens in a new window]

Abstract

The two fourth-order partial differential equations giving the transverse displacement and the stress functions for shallow shells are reduced to a sixth-order differential equation in one variable which has been solved, and the values of displacements, stress resultants and couples are all expressed in terms of Bessel Functions of imaginary argument. Numerical values of the displacement presented for points on the shell on different meridian lines, showed that on the symmetrical line deflexion is maximum at the point of loading but the point of maximum deflexion shifts gradually towards the pole.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 239 - 246
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)Archer, R. R.Quart. Appl. Math. 15 (1958), 355–366.Google Scholar
(2)Bateman, H.Higher transcendental functions, vol. II, Staff of the Bateman Manuscript Project (McGraw Hill, 1953).Google Scholar
(3)Budiansky, B.Proc. I.U.T.A.M. (1959), pp. 64–94.Google Scholar
(4)Jahnke, E. and Emde, F.Table of functions with formulae (1945).Google Scholar
(5)Johnson, M. W. and Reissner, E.Quart. Appl. Math. 15 (1957), 367–380.Google Scholar
(6)Marguerre, K.Proc. 5th Inter. Congr. Appl. Mech. (1938), 93.Google Scholar
(7)Paria, G.Bull. Calcutta Math. Soc. 52 (1960), 79–86.Google Scholar
(8)Reissner, E.J. Mathematical Phys. 25 (1946), 279–300.Google Scholar
(9)Reissner, E.J. Mathematical Phys. 38 (1959), 16–35.Google Scholar
(10)Reismann, H., Thurston, G. A. and Holston, A.ZAMM, 45 (1965), 95–103.Google Scholar
(11)Saito, Atsushi.Proc. Japan Nat. Congr. Appl. Mech. (1959), 55–60.Google Scholar