Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-19T01:35:52.726Z Has data issue: false hasContentIssue false
  • English
  • Français

The analysis of singularly loaded and rigidly clamped thin elastic slabs with curvilinear boundaries. I

Published online by Cambridge University Press:  24 October 2008

W. A. Bassali
W. A. Bassali
Affiliation:
Faculty of ScienceUniversity of AlexandriaAlexandria, Egypt
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper complex variable methods are used to derive exact solutions in closed forms for the small deflexions of certain thin elastic plates due to transverse concentrated forces or couples applied at arbitrary or specified points. The isotropic plates considered are bounded by curvilinear edges of certain types along which the plates are rigidly clamped. Plates bounded by quartic curves having the forms of the inverses of an ellipse with respect to its centre or its focus are included as special cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 1 , January 1959 , pp. 121 - 136
Copyright
Copyright © Cambridge Philosophical Society 1959

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)Aggarwala, B. D.Z. angew. Math. Mech. 34 (1954), 226.CrossRefGoogle Scholar
(2)Aggarwala, B. D.Bull. Calcutta Math. Soc. 47 (1955), 87.Google Scholar
(3)Bassali, W. A. and Dawoud, R. H.Mathematika, 3 (1956), 144.CrossRefGoogle Scholar
(4)Das, S. C.Bull. Calcutta Math. Soc. 42 (1950), 89.Google Scholar
(5)Dawoud, R. H. Thesis (London, 1950).Google Scholar
(6)Dean, W. R.Proc. Camb. Phil. Soc. 49 (1953), 319.CrossRefGoogle Scholar
(7)Dixon, A. C.Proc. Lond. Math. Soc. (2), 19 (1921), 373.CrossRefGoogle Scholar
(8)Dixon, A. C.Proc. Lond. Math. Soc. (2), 25 (1926), 417.CrossRefGoogle Scholar
(9)Dixon, A. C.J. Lond. Math. Soc. 9 (1934), 61.CrossRefGoogle Scholar
(10)Ghosh, S.Bull. Calcutta Math. Soc. 21 (1924), 191.Google Scholar
(11)Gray, C. A. M.J. Appl. Mech. 19 (1952), 422.CrossRefGoogle Scholar
(12)Happel, H.Math. Zeit. 11 (1921), 194.CrossRefGoogle Scholar
(13)Michel, J. H.Proc. Lond. Math. Soc. 34 (1901), 223.CrossRefGoogle Scholar
(14)Muskhelishvili, N. I.Some basic problems of the mathematical theory of elasticity, 3rd ed. (Moscow, 1949).Google Scholar
(15)Schultz-Grunow, Z. angew. Math. Mech. 33 (1953), 227.CrossRefGoogle Scholar
(16)Sen, B.Indian J. Phys. Math. 5 (1934), 17.Google Scholar
(17)Sengupta, H. M.Bull. Calcutta Math. Soc. 40 (1948), 17.Google Scholar
(18)Sengupta, H. M.Bull. Calcutta Math. Soc. 41 (1949), 163.Google Scholar
(19)Sokolnikoff, I. S.Mathematical theory of elasticity, 1st ed. (London, 1946).Google Scholar
(20)Stevenson, A. C.Phil. Mag. (7), 33 (1942), 639.CrossRefGoogle Scholar
(21)Stevenson, A. C.Phil. Mag. (7), 34 (1943), 105.CrossRefGoogle Scholar
(22)Timoshenko, S.Theory of plates and shells (London, 1940).Google Scholar