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Buckling of elastic plates by the method of constant deflection lines

Published online by Cambridge University Press:  09 April 2009

J. Mazumdar
J. Mazumdar
Affiliation:
Department of Applied Mathematics The University of Adelaide
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In a previous paper of this series – hereinafter to be referred to as [1] – the author introduced a new method for a large class of boundary value problems connected with the flexure analysis of elastic plates of arbitrary shape where the concept of ‘Lines of Equal Deflection’, i.e. lines which are obtained by intersecting the bent plate by planes parallel to the original plane of the plate, was introduced. The present paper extends this analysis to the buckling analysis of thin elastic plates with various forms of boundary conditions. It is shown that the proposed method appears to be a powerful tool for the investigation of those problems of elastic stability which could not be solved by conventional methods because of the difficulty of the mathematical treatment.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 91 - 103
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Mazumdar, J., ‘A Method for Solving Problems of Elastic Plates of Arbitrary Shape’, Journal of Australian Mathematical Society 11 (1970), 95–112.CrossRefGoogle Scholar
[2]Timoshenko, S., Gere, J. M., Theory of Elastic Stability (Second Edition, McGraw-Hill Book Co., 1961).Google Scholar
[3]Woinowsky-Krieger, S., ‘The Stability of a Clamped Elliptic Place under Uniform Compression’, J. Appl. Mech. 4 (1937), 177.CrossRefGoogle Scholar
[4]Shibaoka, Y., ‘On the Buckling of an Elliptic Plate with Clamped Edge’, Journal of the Physical Society of Japan 11 (1956), 1088–1091.CrossRefGoogle Scholar