Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T09:02:07.939Z Has data issue: false hasContentIssue false
  • English
  • Français

Green's functions for thin perforated elastic slabs

Published online by Cambridge University Press:  26 February 2010

W. A. Bassali
W. A. Bassali
Affiliation:
Faculty of Science, University of Alexandria, Egypt.
Get access

Summary

An exact expression in finite terms is found for the small deflexion at any point of an infinitely large plate clamped along an inner curvilinear edge, with outer edge free, and loaded by a concentrated force at an arbitrary point of the plate. The plate can be mapped on the area outside the unit circle by a rational mapping function involving two parameters. By varying these parameters holes having various shapes and several axes of symmetry are obtained. Infinite plates with holes in the forms of regular and approximately rectilinear polygons are included as special cases.

Type
Research Article
Information
Mathematika , Volume 7 , Issue 2 , December 1960 , pp. 101 - 112
Copyright
Copyright © University College London 1960

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., 53 (1957), 755.CrossRefGoogle Scholar
2.Bassali, W. A., Proc. Camb. Phil. Soc., 55 (1959), 121.Google Scholar
3.Bassali, W. A. and Gorgui, M. A., Proc. Camb. Phil. Soc., 56 (1960), 75.CrossRefGoogle Scholar
4.Dawoud, R. H., Ph.D. Thesis (London, 1950).Google Scholar
5.Dean, W. R., Proc. Camb. Phil. Soc., 49 (1953), 319.Google Scholar
6.Dean, W. R.Proc. Camb. Phil. Soc., 50 (1954), 623.CrossRefGoogle Scholar
7.Dean, W. R. and Harris, G. Z., Mathematika, 1 (1954), 18.Google Scholar
8.Dixon, A. C., Proc. Lond. Math. Soc. (2), 19 (1921), 373.Google Scholar
9.Dixon, A. C., Proc. Lond. Math. Soc. (2), 25 (1926), 417.CrossRefGoogle Scholar
10.Dixon, A. C., Lond, J.. Math. Soc., 9 (1934), 61.Google Scholar
11.Love, A. E. H., A treatise on the mathematical theory of elasticity, 4th ed. (Dover Publications, New York, 1944).Google Scholar
12.Saito, A., Kimura, S. and Shimazaki, T., Bull. Jap. Soc Mech. Engrs., 2 (1959), 299.Google Scholar
13.Scultz-Grunow, , Z. angew. Math. Mech., 33 (1953), 227.CrossRefGoogle Scholar
14.Singh, R. K. P., Mathematika, 4 (1957), 61.CrossRefGoogle Scholar
15.Stevenson, A. C., Phil. Mag., 34 (1943), 105.Google Scholar
16.Symonds, P. S., J. Appl. Mech., 13 (1946), 183.Google Scholar
17.Thorne, C. J., J. Appl. Mech., 15 (1948), 73.Google Scholar