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Flexural problems of circular ring plates and sectorial plates. I

Published online by Cambridge University Press:  24 October 2008

W. A. Bassali  and
M. A. Gorgui
W. A. Bassali
Affiliation:
Faculty of Science, University of Alexandria, Alexandria, Egypt
M. A. Gorgui
Affiliation:
Faculty of Science, University of Alexandria, Alexandria, Egypt
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Abstract

In this paper explicit expressions in closed forms are first obtained for the complex potentials and deflexion at any point of a circular annular plate under various edge conditions when the plate is acted upon by general line loadings distributed along the circumference of a concentric circle. These solutions are then used to discuss the bending of a circular plate with a central hole under a concentrated load or a concentrated couple acting at any point of the plate. Solutions for singularly loaded sectorial plates bounded by two arcs of concentric circles and two radii are also derived when the plate is simply supported along the straight edges. The boundary conditions along the circular edges include the cases of a free boundary as well as the elastically restrained boundary which covers the usual rigidly clamped and simply supported boundaries as special cases. The usual restrictions relating to the small deflexion theory of thin plates of constant thickness are assumed. Limiting forms of the resulting solutions are investigated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 1 , January 1960 , pp. 75 - 95
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Bassali, W. A.Proc. Camb. Phil. Soc. 52 (1956), 584.CrossRefGoogle Scholar
(2)Bassali, W. A. and Dawoud, R. H.Mathematika, 3 (1956), 144.CrossRefGoogle Scholar
(3)Bassali, W. A.Proc. Camb. Phil. Soc. 53 (1957), 248.CrossRefGoogle Scholar
(4)Bassali, W. A.Bull. Calcutta Math. Soc. 49 (1957), 119.Google Scholar
(5)Bassali, W. A.Proc. Camb. Phil. Soc. 53 (1957), 728.CrossRefGoogle Scholar
(6)Bassali, W. A. and Nassif, M.Proc. Camb. Phil. Soc. 54 (1958), 288.CrossRefGoogle Scholar
(7)Galerkin, B. G.Elastic thin plates (Moscow, 1933).Google Scholar
(8)Godfrey, D. E.R. Aero. Quart. 6 (1955), 196.CrossRefGoogle Scholar
(9)Holmyanskii, M. M.Inzen. Sb. 22 (1955), 199.Google Scholar
(10)Labrow, S.Proc. Instit. Mech. Engrs, 145 (1941), 115.CrossRefGoogle Scholar
(11)Reissner, H.Ingen.-Arch. 1 (1929), 72.CrossRefGoogle Scholar
(12)Saito, A. and Hirai, N.Proc. Jap. Nat. Congr. Appl. Mech. 6 (1956), 141.Google Scholar
(13)Sekiya, T., Saito, A. and Yamaha, S.Proc. Jap. Nat. Congr. Appl. Mech. 2 (1952), 113.Google Scholar
(14)Symonds, P. S.J. Appl. Mech. 13 (1946), 183.CrossRefGoogle Scholar
(15)Trumpler, W. E. Jr.Trans. ASME 65 (1943), 173.CrossRefGoogle Scholar
(16)Timoshenko, S.Theory of plates and shells (New York, 1940).Google Scholar
(17)Wahl, A. M. and Lobo, G. Jr.Trans. ASME 52 (1930), 29.Google Scholar
(18)Woinowsky-Kreiger, S.J. Appl. Mech. 20 (1953), 77.CrossRefGoogle Scholar