Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-24T20:59:49.111Z Has data issue: false hasContentIssue false
  • English
  • Français

A Study of the Various Boundary Conditions for Electrical Analogue Solutions of the Extension and Flexure of Flat Plates

Published online by Cambridge University Press:  07 June 2016

S. C. Redshaw  and
K. R. Rushton
S. C. Redshaw
Affiliation:
Department of Civil Engineering, University of Birmingham
K. R. Rushton
Affiliation:
Department of Civil Engineering, University of Birmingham
Get access

Summary

The application of electrical analogue methods to the analysis of the extension and flexure of flat plates is reviewed and the difficulties encountered in the satisfaction of the various boundary conditions are discussed. A new method for treating certain boundary conditions and the operation of the electrical analogue is described. New experimental results for two cases which present great analytical difficulty, the flexure of a plate with a free edge and a plate supported on columns, are given.

Type
Research Article
Information
Aeronautical Quarterly , Volume 12 , Issue 3 , August 1961 , pp. 275 - 292
Copyright
Copyright © Royal Aeronautical Society. 1961

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. Southwell, R. V. Relaxation Methods in Theoretical Physics. Clarendon Press, Oxford, Vol. 1, 1946; Vol. 2, 1956.Google Scholar
2. Palmer, P. J. and Redshaw, S. C. Experiments With an Electrical Analogue for the Extension and Flexure of Flat Plates. The Aeronautical Quarterly, Vol. VI, p.13, February 1955.Google Scholar
3. Redshaw, S. C. and Rushton, K. R. An Electrical Analogue Solution for the Stresses Near a Crack or Hole in a Flat Plate. Journal of the Mechanics and Physics of Solids, Vol. 8, p. 173, 1960.CrossRefGoogle Scholar
4. Fox, L. and Southwell, R. V. Relaxation Methods Applied to Engineering Problems VIIA, Biharmonic Analysis as Applied to the Flexure and Extension of Flat Elastic Plates. Phil. Trans. Roy. Soc. A, Vol. 239, p. 419, 1945.Google Scholar
5. Redshaw, S. C. Electrical Analogues for the Solution of Problems Concerning the Extension and Flexure of Flat Elastic Plates. A.R.C. 15,335, May 1952.Google Scholar
6. Liebmann, G. A Resistance-Network Analogue Method for Solving Plane Stress Problems. Nature, Vol. 172, p. 78, July 1953.Google Scholar
7. Boscher, J. and Malavard, L. Détermination Analogique des Fonctions Biharmoniques. Bulletin No. 8, Société Françhise des Mécaniciens, 1953.Google Scholar
8. Richardson, L. F. The Approximate Arithemetical Solution by Finite Differences, With an Application to the Stresses in Masonry Dams. Phil. Trans. Roy. Soc. A. Vol. 210, 1911.Google Scholar
9. Timoshenko, S. and Woinowsky-krieger, S. Theory of Plates and Shells. Second Edition, pp. 117, 133 and 208, McGraw-Hill, 1959.Google Scholar
10. Boscher, I. Sur 1’ Application de la Méthode des Réseaux Electriques au Calcul de la Deformation des Plaques Elastiques. Comptes Rendus, Academie des Sciences, Paris, Vol. 238, p. 1189, 1954.Google Scholar
11. Liebmann, G. The Solution of Plane Stress Problems by an Electrical Analogue Method. British Journal of Applied Physics, Vol. 6, p. 145, 1955.CrossRefGoogle Scholar
12. Nadai, A. Elastische Platten. Springer, Berlin, p. 155, 1925.Google Scholar