Buckling Analysis of Moderately Thick Rotational Shells under Uniform Pressure Using the Ritz Method
Publication: Journal of Structural Engineering
Volume 134, Issue 4
Abstract
This paper is concerned with an application of the Ritz method for elastic, axisymmetric, buckling analysis of moderately thick, rotational orthotropic shells under uniform external pressure. In order to capture the effect of transverse shear deformation, which is significant for thick shells, the Mindlin shell theory is used. In applying the Ritz method, the displacement components of the shell are approximated by the product of one-dimensional polynomial functions, and the boundary equations are raised to the appropriate powers so as to ensure the satisfaction of geometric boundary conditions a priori. The validity of the method, convergence and accuracy of solutions are demonstrated using spherical shells, which is a special case of rotational shells, where closed-form solutions exist for some cases. A parametric study is conducted on spherical and parabolic shells, considering the effects of height-to-base-radius ratios, thickness-to-radius ratios, and different support conditions on the buckling solutions. The new solutions should be useful to researchers and engineers who are developing analytical tools and designs of shells.
Get full access to this article
View all available purchase options and get full access to this article.
References
Archer, R. R. (1956). “On the post buckling behavior of thin spherical shells.” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Mass.
Budiansky, B. (1959). “Buckling of clamped shallow spherical shells.” Proc. Symp. on the Theory of Thin Elastic Shells, North Holland, Amsterdam, The Netherlands.
Bushnell, D. (1976). “BOSOR5-program for buckling of elastic-plastic complex shells of revolution including large deflections and creep.” Comput. Struct., 6(3), 221–239.
Bushnell, D. (1984). “Computerized analysis of shells-governing equations.” Comput. Struct., 18(3), 471–536.
Chao, C. C., Tung, T. P., and Chern, Y. C. (1988). “Buckling of thick orthotropic spherical shells.” Compos. Struct., 9(2), 113–137.
Cohen, G. A. (1981). “FASOR—A program for stress, buckling, and vibration of shells of revolutions.” Adv. Eng. Software, 3(4), 155–162.
Dumir, P. C., Gandhi, M. L., and Nath, Y. (1984). “Axisymmetric static and dynamic buckling of orthotropic shallow spherical caps with flexible supports.” Acta Mech., 52(2), 93–106.
Dym, C. L. (1974). Introduction to the theory of shells, Pergamon, Oxford, U.K.
Huang, N. C. (1964). “Unsymmetrical buckling of thin shallow spherical.” J. Appl. Mech., 31(3), 447–457.
Kalnins, A., and Lestingi, J. E. (1967). “On nonlinear analysis of elastic shells of revolution.” Trans. ASME, J. Appl. Mech., 37(1), 59–64.
Kawai, T. (1974). Analysis of buckling problems, Baifukan, Tokyo.
Kraus, H. (1967). Thin elastic shells, Wiley, New York.
Li, Q. S., Liu, J., and Tang, J. (2003). “Buckling of shallow spherical shells including the effects of transverse shear deformation.” Int. J. Mech. Sci., 45(9), 1519–1529.
Muc, A. (1992). “On the buckling of composite shells of revolution under external pressure.” Compos. Struct., 21(2), 107–119.
Rayleigh, J. W. (1987). Theory of sound, reprinted by Dover Publications, Vol. 1, Macmillan, New York.
Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: Theory and analysis, 2nd Ed., CRC Press, Boca Raton, Fla.
Ritz, W. (1909). “Uber eine neue Methode zur Lösung gewisser Variationprobleme der mathematischen Physik.” J. Reine Angew. Math., 135, 1–61.
Ross, C. T. F. (2000). Pressure vessels: External pressure technology, Horwood Publishing Ltd., Chichester, U.K.
Ross, C. T. F., Little, A. P. F., and Bartlett, C. (2003). “Buckling of a large ring stiffened prolate dome under external hydrostatic pressure.” Int. J. Struct. Stab. Dyn., 3(4), 491–502.
Ross, C. T. F., Youster, P., and Sadler, R. (2001). “The buckling of plastic oblate hemiellipsoidal dome shells under external hydrostatic pressure.” Ocean Eng., 28(7), 789–803.
Thurston, G. A. (1961). “A numerical solution of the nonlinear equations for axisymmetric bending of shallow spherical shells.” J. Appl. Mech., 28, 557.
Tsai, S. W., and Pagano, N. J. (1968). “Invariant properties of composite materials.” Composite materials workshop, Technomic, Stamford, Conn., 233–253.
Uddin, M. W. (1987). “Buckling of general spherical shells under external pressure.” Int. J. Mech. Sci., 29(7), 469–481.
Uddin, M. W., and Haque, M. M. (1994). “Instability of semiellipsoidal shells.” Int. J. Pressure Vessels Piping, 58, 65–74.
Wolfram, S. (1999). Mathematica, 4th Ed., Cambridge University Press, New York.
Zbigniew, E. M., and Roman, T. N. (1991). Shells of revolution, PWN-Polish Scientific Publishers, Warszawa, Poland.
Zoelly, R. (1915). “Über ein knickproblem an der kugelschale.” Ph.D. thesis, Zurich, Switzerland.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: Mar 26, 2007
Accepted: Jul 20, 2007
Published online: Apr 1, 2008
Published in print: Apr 2008
Notes
Note. Associate Editor: M. Asghar Bhatti
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.