Axisymmetric Nonlinear Stability of a Shallow Conical Shell with a Spherical Cap of Arbitrary Variable Shell Thickness
Publication: Journal of Engineering Mechanics
Volume 132, Issue 10
Abstract
The axisymmetric nonlinear stability of a shallow conical shell with a spherical cap was studied using the point collocation method with the cubic B-spline function as a trial function. Formulas were set up to consider arbitrary variable shell thickness and different boundary and loading conditions. A FORTRAN program was written to determine the critical loads and trace the stable parts of the equilibrium paths of the shell by method of gradually applied load. The upper and lower critical loads obtained in this technical note for some specific cases with constant shell thickness are of very good accuracy and agree very well with known solutions and finite-element method results. The method was then expanded successfully to arbitrary variable shell thickness and different boundary and loading conditions.
Get full access to this article
View all available purchase options and get full access to this article.
References
Archer, R. R. (1962). “On the numerical solution of nonlinear equations of revolution.” J. Math. Phys., 40(1), 165–178.
Banerjee, B. (1983). “Large deflections of circular plates of variable thickness.” Int. J. Solids Struct., 19(2), 179–182.
Budiansky, B. (1959). “Buckling of clamped shallow spherical shell.” Proc. Symp. on the Theory of Thin Elastic Shells, W. T. Koiter, ed., North-Holland, Amsterdam, The Netherlands, 64–69.
Gu, S. X. (1995). “Axisymmetrical buckling behavior of truncated shallow spherical shells subjected to line moment loads.” Int. J. Solids Struct., 32(15), 2245–2256.
Hou, C. S., Li, J., and Long, Q. (2003). “Cubic spline solutions of nonlinear bending and buckling of circular plates with arbitrarily variable thickness.” Trans. Tianjin Univ., 9(4), 321–325.
Lo, W. K., and Lee, T. L. (1996). “Equivalent systems for variable thickness circular plates.” Comput. Struct., 58(5), 957–977.
Niu, Z. R. (1993). “Nonlinear bending of the shallow spherical shells with variable thickness under axisymmetrical loads.” Appl. Math. Mech., 14(11), 1023–1031.
Varpasuo, P. (1980). “Incremental analysis of axisymmetric shallow shells with varying strain-displacement equations.” Comput. Methods Appl. Mech. Eng., 21(2), 153–169.
Yan, S. P. (1997). “Spline collocation method for nonlinear stability of shallow conical shell with spherical cap.” Chin. J. Eng. Mech., 14(3), 97–103 (in Chinese).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 10 • October 2006
Pages: 1146 - 1149
Copyright
© 2006 ASCE.
History
Received: Jun 2, 2004
Accepted: Jan 18, 2006
Published online: Oct 1, 2006
Published in print: Oct 2006
Notes
Note. Associate Editor: Hayden A. Rasheed
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.