Elastic,Post-Buckling Behaviour of a Simply Supported Circular Plate

Abstract

A numerical method is presented for the elastic, post-buckling behaviour of a simply supported, mild-steel circular plate loaded in uniform compression around the edge of the plate. Such a procedure obviates the solution of the orthodox von Kármán large deflection equations, substituting, instead, a step-by-step integration of the differential equations of equilibrium and testing at each step to satisfy prescribed boundary conditions. The equations are programmed for a high-speed digital computer and the overall behaviour of the plate is obtained in terms of the applied edge load and the central deflection. The programme is evaluated for various plate sizes, and the edge load and central deflection are related through contours of moment and thrust at the centre of the plate.

Get full access to this article

View all access options for this article.

References

Bleich

1952 ‘Buckling Strength of Metal Structures’ (McGraw-Hill Book Co., New York).

Timoshenko

1936 ‘Theory of Elastic Stability’ (McGraw-Hill Book Co., New York).

Friedrichs

K. O.

Stoker

J. J.

1942 J. appl. Mech., vol. 9, p. A7, ‘Buckling of the Circular Plate beyond the Critical Thrust’.

Bodner

S. R.

1954 Quart. appl. Math., vol. 12, ‘Post-Buckling Behaviour of a Clamped Circular Plate’.

Keller

H. B.

Reiss

E. L.

1958 ‘Non-linear Bending and Buckling of Circular Plates’, Institute of Mathematical Sciences, New York University, February.

Wilkes

M. V.

Wheeler

D. J.

Gill

1951 ‘Preparation of Programmes for an Electronic Digital Computer (with special reference to the “Edsac” and the use of a Library of Subroutines)’ (Addison Wesley Press, Cambridge, Mass.).

Murray

N. W.

1956 Min. Proc. Instn civ. Engrs, vol. 5, part III, ‘Determination of the Collapse Loads of Rigidly Jointed Frameworks with Members in which the Axial Forces are Large’.