Elastic Buckling of Moderately Thick Homogeneous Circular Plates of Variable Thickness

Document Type: Research Paper


Faculty of Mechanical Engineering, College of Engineering, University of Tehran


In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal thickness distribution over the plate with respect to buckling is presented. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved. The influence of the boundary conditions, the thickness variation profile and aspect ratio on the buckling behavior is examined.  The comparison shows that the results derived, using the current method, compare very well with those available in the literature.


[1] Timoshenko S.P., Gere J.M., 1961, Theory of Elastic Stability, McGraw-Hill, New York, Second Edition.

[2] Brush D.O., Almroth B.O., 1975, Buckling of Bars, Plates and Shells, McGraw-Hill, New York.

[3] Turvey G.J., Marshall I.H., 1995, Buckling and Postbuckling of Composite Plates, Chapman & Hall, London, First Edition.

[4] Turvey G.J., 1987, Axisymmetric snap buckling of imperfect, tapered circular plates, Computers & Structures 9: 551-558.

[5] Raju K.K., Rao G.V., 1985, Post-buckling of cylindrically orthotropic linearly tapered circular plates by finite element method, Computers & Structures 21(5): 969-972.

[6] Mizusawa T., 1993, Buckling of rectangular Mindlin plates with tapered thickness by the Spline Strip method, International Journal of Solids and Structures 30(12): 1663-1677.

[7] Wang C.M., Hong G.M., Tan T.J., 1995, Elastic buckling of tapered circular plates, Computers & Structures 55(6): 1055-1061.

[8] Gupta U.S., Ansari A.H., 1998, Asymmetric vibrations and elastic stability of polar orthotropic circular plates of linearly varying profile, Journal of Sound and Vibration 215(2): 231-250.

[9] Dumir P.C., Khatri K.N., 1984, Axisymmetric postbuckling of orthotropic thin tapered circular plates,Fibre Science and Technology 21: 233-245.

[10] Özakça M., Taysi N., Kolcu F., 2003, Buckling analysis and shape optimization of elastic variable thickness circular and annular plates-I. Finite element formulation, Engineering Structures 25: 181-192.

[11] Shufrin I., Eisenberger M., 2005, Stability of variable thickness shear deformable plates-First order and high order analyses, Thin-Walled Structures 43: 189-207.

[12] Boyd J.P., 2000, Chebyshev and Fourier Spectral Methods, Dover, New York.

[13] Lee J., Schultz W.W., 2004, Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method, Journal of Sound and Vibration 269: 609-621.

[14] Wang C.M., Xiang Y., Kitipornchai S., Liew K.M., 1993, Axisymmetric buckling of circular Mindlin plates with ring supports, Journal of Structural Engineering 119: 782-793.

[15] Raju K.K., Rao G.V., 1983, Finite element analysis of post-buckling behavior of cylindrical orthotropic circular plates, Fibre Technology 19: 145–154.