Fundamental buckling of circular plates with elastically restrained edges and resting on concentric rigid ring support

Abstract

This work presents the existence of buckling mode switching with respect to the radius of concentric rigid ring support. The buckling mode may not be axisymmetric as previously assumed. In general, the plate may buckle in an axisymmetric mode but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. The optimum radius of the concentric rigid ring support for maximum buckling load is also determined. Introducing internal rigid ring support, when placed at an optimal position increases the elastic buckling load capacity by 149.39 percent. The numerical results obtained are in good agreement with the previously published data.

Key words： buckling; circular plate; elastically restrained edge; rigid ring support; mode switching

References

1 Bryan G H. On the Stability of a Plane Plate under Thrust in its own Plane with Application to the Buckling of the Side of a Ship. Proceedings of the London Mathematical Society, 1891, 22(1): 54–67

2 Walker A C. A Brief Review of Plate Buckling Research In Behaviour of Thin-Walled Structures, ed. by Rhodes J, Spence J, Elsevier: London, 1984, 375–397

3 Raju K K, Rao G V. Stability of moderately thick annular plates subjected to a uniform radial compressive load at the outer edge. Computers & Structures, 1989, 33(2): 477–482

4 Wang C M, Xiang Y, Kitipornchai S, Liew K M. Axisymmetric Buckling of Circular Mindlin Plates with Ring Supports. Journal of Structural Engineering, 1993, 119(3): 782–793

5 Liew K M, Xiang Y, Kitipornchai S, Wang C M. Buckling and vibration of annular Mindlin plates with internal concentric ring supports subject to in-plane radial pressure. Journal of Sound and Vibration, 1994, 177(5): 689–707

6 Laura P A A, Gutierrez R H, Sanzi H C, Elvira G. Buckling of Circular, Solid and Annular Plates with an Intermediate Circular Support. Ocean Engineering,2000, 27(7): 749–755

7 Timoshenko S P, Gere J M. Theory of Elastic Stability. New York: McGraw Hill, 1961

8 Szilard R. Theory and Analysis of Plates. NJ: Prentice-Hall, Englewood Cliffs, 1974

9 Wolkowisky J H. Buckling of the Circular Plate Embedded in Elastic Springs, an Application to Geophysics. Communications on Pure and Applied Mathematics, 1969, 22(5): 367–667

10 Brushes D O, Almroth B O. Buckling of Bars, Plates and Shells, New York: McGraw-Hill, 1975

11 Gerard C P. Asymmetric vibration and stability of circular plates. Computers & Structures, 1978, 9(1): 89–95

12 Thevendran V, Wang C M. Buckling of annular plates elastically restrained against rotation along edges. Thin-walled Structures, 1996, 25(3): 231–246

13 Wang C Y. Buckling of a Circular Plate with Internal Elastic Ring Support. Mechanics Based Design of Structures and Machines, 2003, 31(1): 93–102

14 Wang C Y, Wang C M. Buckling of Circular Plates with an Internal Ring Support and Elastically Restrained Edges. Thin-walled Structures, 2001, 39(9): 821–825

15 Kim C S, Dickinson S M. The Flexural Vibration of the Isotropic and Polar Orthotropic Annular and Circular Plates with Elastically Restrained Peripheries. Journal of Sound and Vibration, 1990, 143(1): 171–179

16 Yamaki N. Buckling of a Thin Annular Plate under Uniform Compression. Journal of Applied Mechanics, 1958, 25: 267–273

17 Bhaskara Rao L, Kameswara Rao C. Buckling analysis of circular plates with elastically restrained edges and resting on internal elastic ring support. Mechanics Based Design of Structures and Machines, 2010, 38(4): 440–452

18 Wang C M, Aung T M. Tun Myint Aung. Buckling of Circular Mindlin Plates with an Internal Ring Support and Elastically Restrained Edge. Journal of Engineering Mechanics, 2005, 131(4): 359–366