Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-18T23:45:14.313Z Has data issue: false hasContentIssue false
  • English
  • Français

Buckling analysis of plates of arbitrary shape

Published online by Cambridge University Press:  17 February 2009

D. Bucco  and
J. Mazumdar
D. Bucco
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia, 5001.
J. Mazumdar
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia, 5001.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A simple and efficient numerical technique for the buckling analysis of thin elastic plates of arbitrary shape is proposed. The approach is based upon the combination of the standard Finite Element Method with the constant deflection contour method. Several representative plate problems of irregular boundaries are treated and where possible, the obtained results are validated against corresponding results in the literature.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 1 , July 1984 , pp. 77 - 91
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Altiero, N. J. and Sikarskie, D. L., “A boundary integral method applied to plates of arbitrary plan form”, Comput. & Structures 9 (1978), 163–168.Google Scholar
[2]Ashton, J. E., “Stability of clamped skew plates under combined loads,” Trans. ASME Ser. E. J. Appl. Mech. 36 (1969), 139–140.CrossRefGoogle Scholar
[3]Bucco, D., Mazumdar, J. and Sved, G., “Application of the finite strip method combined with the deflection contour method to plate bending problems”, Comput. & Structures 10 (1979), 827–830.CrossRefGoogle Scholar
[4]Bucco, D., Mazumdar, J. and Sved, G., “Vibration analysis of plates of arbitrary shape-A new approach”, J. Sound Vibr. 67 (1979), 253–262.CrossRefGoogle Scholar
[5]Cheung, Y. K., The finite strip method in structural analysis (Pergamon Press, Oxford, 1976).Google Scholar
[6]Coleby, J. R. and Mazumdar, J., “Transient vibrations of elastic panels due to impact of shock waves”, J. Sound Vibr. 77 (1981), 481–494.CrossRefGoogle Scholar
[7]Dickinson, S. M., “The buckling and frequency of flexural vibration of rectangular isotropic and orthotropic plates using Rayleigh's method”, J. Sound Vibr. 61 (1978), 1–8.CrossRefGoogle Scholar
[8]Durvasula, S., “Natural frequencies and modes of clamped skew plates”, AIAA J. 7 (1969), 1164–1167.CrossRefGoogle Scholar
[9]Hearn, T. C., “An approximate expression for the fundamental frequency of a limacon-shaped membrane”, J. Sound Vibr. 67 (1979), 282–283.CrossRefGoogle Scholar
[10]Jones, R., “Application of the method of constant deflection contour to elastic plate and shell problems”, Ph.D. Thesis, The University of Adelaide, Adelaide, South Australia, 1973.Google Scholar
[11]Mazumdar, J., “Bucking of elastic plates by the method of constant deflection lines”, J. Austral. Math. Soc. 13 (1971), 91–103.CrossRefGoogle Scholar
[12]Richards, T. H. and Delves, B., “A semi-analytic finite element analysis of circular plate bending problems”, J. Strain Analysis 15 (1980), 75–82.CrossRefGoogle Scholar
[13]Sokolnikoff, I. S., Mathematical theory of elasticity (McGraw-Hill, New York, 1956).Google Scholar
[14]Stem, M., “A general boundary integral formulation for the numerical solution of plate bending problems”, Internat. J. Solids and Structures 15 (1979), 769–782.Google Scholar
[15]Szilard, R., Theory and analysis of plates, classical and numerical methods (Prentice-Hall, Englewood Cliffs, N. J., 1974).Google Scholar
[16]Timoshenko, S. and Gere, J. M., Theory of elastic stability (McGraw-Hill, New York, 2nd edition, 1961).Google Scholar
[17]Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of plates and shells (McGraw-Hill, Oxford, 2nd edition, 1959).Google Scholar
[18]Tottenham, H., “The boundary element method for plates and shells”, in Developments in boundary element methods-I (eds. Banaerjee, P. K. and Butterfield, R.), (Applied Science Publishers Ltd., London, 1979), 173–205.Google Scholar
[19]Woinowsky-Krieger, S., “The stability of a clamped triangular plate under uniform compression”, Ing. Archiv. 4 (1933), 254–262.CrossRefGoogle Scholar
[20]Zienkiewicz, O. C., The finite element method in engineering science (McGraw-Hill, London, 1971).Google Scholar