Buckling load relationship between Reddy and Kirchhoff circular plates

doi:10.1016/S0016-0032(97)00047-1

Journal of the Franklin Institute

Volume 335, Issue 6, August 1998, Pages 989-995

https://doi.org/10.1016/S0016-0032(97)00047-1 Get rights and content

Abstract

This paper presents an exact relationship between the buckling load of circular plates based on the Reddy (third-order shear deformation) plate theory and that of the classical Kirchhoff plate theory. The relationship allows one to obtain the exact buckling solutions of Reddy plates from the well-known Kirchhoff solutions for circular plates with (i) simply supported edges, (ii) clamped edges, (iii) simply supported edges with elastic rotational restraints, and (iv) free edges with the centre clamped. Unlike the Mindlin plate theory, there is no need for a shear correction factor in the Reddy plate theory. A comparison of buckling results between the Mindlin, Reddy and three-dimensional elasticity plates is also given.

References (7)

C.M. Wang
Buckling of polygonal and circular sandwich plates
AIAA J.
(1995)
C.M. Wang
Discussion on postbuckling of moderately thick plates with edge elastic restraint
J. Engrg. Mech. ASCE
(1996)
J.N. Reddy
A simple higher-order theory for laminated composite plates
J. Appl. Mech. Trans. ASME
(1984)

There are more references available in the full text version of this article.

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ArticleBuckling load relationship between Reddy and Kirchhoff circular plates

Abstract

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AIAA J.

Discussion on postbuckling of moderately thick plates with edge elastic restraint

J. Engrg. Mech. ASCE

A simple higher-order theory for laminated composite plates

J. Appl. Mech. Trans. ASME

Article
Buckling load relationship between Reddy and Kirchhoff circular plates