Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T21:57:19.184Z Has data issue: false hasContentIssue false
  • English
  • Français

Bending of a thin semi-circular plate elastically restrained along the circular edge and clamped along the diameter

Published online by Cambridge University Press:  26 February 2010

W. A. Bassali  and
S. S. Mahmood
W. A. Bassali
Affiliation:
Department of Mathematics, Faculty of Science, Kuwait University, Kuwait.
S. S. Mahmood
Affiliation:
Department of Mathematics, Faculty of Science, Kuwait University, Kuwait.
Get access

Summary

This paper is concerned with the determination of the small deflexions and stresses in a thin isotropic homogeneous semi-circular plate subject to hydrostatic pressure distributed over the entire plate. The semi-circular plate is clamped along the bounding diameter and elastically restrained, against rotation along the circular edge, according to a general boundary condition including the simply supported and rigidly clamped boundaries as particular cases. The boundary conditions around the circular edge and the condition of zero deflexion on the straight edge are exactly satisfied while the remaining condition of zero slope on the bounding diameter is approximately satisfied. Calculations have been carried out corresponding to three cases of boundary constraint; namely, those for which the edge is fully restrained, the edge is simply supported and an intermediate case. Positions and magnitudes of maximum deflexions are determined. Numerical results are presented in tabular and graphical forms.

Type
Research Article
Information
Mathematika , Volume 20 , Issue 1 , June 1973 , pp. 34 - 46
Copyright
Copyright © University College London 1973

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

1. Bassali, W. A. and Dawoud, R. H., 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. and Dawoud, R. H., J. Appl. Mech., 25 (1958), 37.CrossRefGoogle Scholar
4. Bassali, W. A. and Halim, E., J. Mech. Phys. Solids, 9 (1961), 230; and 11 (1963), 79.CrossRefGoogle Scholar
5. Conway, H. D. and Huang, M. K., J. Appl. Mech., 19 (1952), 5.CrossRefGoogle Scholar
6. Grinberg, G. A., Prikl. Mat. Mekh., 17 (1953), 211.Google Scholar
7. Hassé, H. R., Quart. J. Mech., 3 (1950), 271.CrossRefGoogle Scholar
8. Jurney, W. R., J. Appl. Mech., 26 (1959), 224.CrossRefGoogle Scholar
9. Kalandia, A. I., Problems of Continuum Mechanics (Muskhelishvili Anniversary Volume), 219. (S. I. A. M. Philadelphia, Pa., 1961).Google Scholar
10. Kuno, R., J. Soc. Mech. Engrs., 37 (1934), 100.Google Scholar
11. Morley, L. S. D., Q. J. Mech. Appl. Math. 17 (1964), 293.CrossRefGoogle Scholar
12. Muster, D. F. and Sadowsky, M. A., J. Appl. Mech., 23 (1956), 329.CrossRefGoogle Scholar
13. Williams, M. L., U.S. Nat. Cong, of Appl. Mech. Illinois Inst. of Technology (1961), 325.Google Scholar
14. Woinowsky-Krieger, S., J. Appl. Mech., 22 (1955), 129.CrossRefGoogle Scholar