Investigation on Buckling of Orthotropic Circular and Annular Plates of Continuously Variable Thickness by Optimized Ritz Method

Document Type : Persian


1 Assistant Professor, Islamic Azad University, Khomeinishahr Branch

2 M.Sc. Student, Islamic Azad University, Khomeinishahr Branch


This paper investigates symmetrical buckling of orthotropic circular and annular plates of continuous variable thickness. Uniform compression loading is applied at the plate outer boundary. Thickness varies linearly along radial direction. Inner edge is free, while outer edge has different boundary conditions: clamped, simply and elastically restraint against rotation. The optimized RayLeigh-Ritz method is applied for buckling analysis. In this method, a polynomial function that is based on static deformation of orthotropic circular plates in bending is used. Also, byemploying an exponential parameter in deformation function, eigenvalue is minimized in respect to that parameter. The advantage of this procedure is simplicity in comparison with other methods, while whole algorithm for solution can be coded for computer programming. The effect of variation of radius, thickness, different boundary conditions, ratio of radial Young Modulus to circumferential one, ratio of outer radius to inner one in annular plates on critical buckling coefficient are investigated. The obtained results show that in plate with identical thickness, increasing of outer radius decreases the critical buckling coefficient. In addition increasing of thickness of the plates results in increase of critical buckling coefficient.


[1]        Woinowski-Krieger, S., Buckling stability of circularplates with circular cylindrical Aeolotropy, Ingenieur-Archiv, Vol. 26, 1958, pp. 129-131
[2]        Meink T., Huybrechts S., Ganley J., “The Effect of varying thickness on the buckling of orthotropic plates, J. Composite Materials, Vol. 33, 1999, pp. 1048-1061.
[3]        Laura P.A.A, Gutierrez R.H., Sanzi H.C., Elvira G., buckling of circular, solid and annular plates with an intermediate circular support, J. Ocean Engineering, Vol. 27, 2000,  pp.749-755
[4]        Ciancio P.M, Reyes J.A., Buckling of circular annular plates of continuously variable thickness used as internal bulkheads in submersibles, J. Ocean engineering, Vol. 30, 2003, pp. 1323-1333
[5]        Bostjan B., Kosel F., Thickness optimization of circular annular plates at buckling, Thin-Walled Structures, Vol. 32, 2006,74-81.
[6]        Gutierrez R.H., Romanlli E., Laura P.A.A., Vibration and elastic stability of thin circular plates with variable profile, J. Sound and Vibration, Vol. 195, 1996, 391-399.
[7]        Liang B., Zhang Sh, Dian-Yun Chen, Natural frequencies of circular annular plates with variable thickness by a new method, J.  Pressure Vessels and Piping, Vol. 84, 2007, 293-297.
[8]        Timoshenko, S. P., Gere, J. M., Theory of elastic stability, 2nd Ed, McGraw-Hill, New York, 1961.
[9]        Venstel E., Thin plates and shells, Dekker Publication, 2001.
[10]    Chuen-Yuan Chia, Nonlinear Analysis of Plates, McGraw-Hill, 1980.