Abstract
Closed-form analytical solutions for thin shell buckling problem are useful in a wide range of analysis and design problems. In this paper, the profile of a cylindrical shell in the post-buckling regime of axisymmetric deformation is analysed, and the solution is shown to be a Jacobi elliptic sine function, for any load and axial deformation. The exact solution of the non-linear differential equation for the thin elastic shell profile holds for any deformation, up to the limit in which the shell is almost flattened by the applied load. Closed-form expressions are derived also for the load dependent axial deflection and stored energy. The analytical solution of the buckling loads and deformed profile are found to agree well with an equivalent numerical solution. Results show that an axially compressed cylindrical shell exhibits ideal behaviour for a safety shock energy absorber.
Similar content being viewed by others
References
Byrd, P.F., Friedman, M.D.: Handbook of Elliptic Integrals for Engineers and Scientists, 2nd edn. Springer, New York (1971)
Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 7th edn. Academic, Burlington (2007)
Hunt, G.W., Lord, G.J., Peletier, M.A.: Cylindrical shell buckling: a characterization of localization and periodicity. Discret. Contin. Dyn. Syst. B 4, 505–518 (2003)
Kim, S.-E., Kim, C.-S.: Buckling strength of the cylindrical shell and tank subjected to axially compressive loads. Thin-walled Struct. 40, 329–353 (2002)
Paschero, M., Hyer, M.W.: Axial buckling of an orthotropic circular cylinder. Application to orthogrid concept. Int. J. Sol. Struct. 46, 2151–2171 (2009)
Pinna, R., Ronalds, B.F.: Buckling and postbuckling of cylindrical shells with one end pinned and the other end free. Thin-Walled Struct. 41, 507–527 (2003)
Simitses, G.J.: Buckling and postbuckling of imperfect cylindrical shells: a rewiew. Appl. Mech. Rev. 39, 1517–1524 (1986)
Wullschleger, L., Meyer-Piening, H.R.: Buckling of geometrically imperfect cylindrical shells-definition of a buckling load. Int. J. Non-Linear Mech. 37, 645–657 (2002)
Zozulya, V.V., Zhang, Ch.: A high order theory for functionally graded axisymmetric cylindrical shells. Int. J. Mech. Sci. 60, 12–22 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lagos, M., Das, R. Analytical solution for the axisymmetric buckling of cylindrical shells. Int J Mech Mater Des 11, 139–148 (2015). https://doi.org/10.1007/s10999-014-9259-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10999-014-9259-9