Nonlinear Stability Analysis of Laminated Composite Simply Supported Circular Cylindrical Shells Subjected to Partial Axial Loading
Publication: Journal of Engineering Mechanics
Volume 140, Issue 8
Abstract
The present investigation deals with the nonlinear stability behavior of cross-ply laminated composite circular cylindrical shells subjected to partial and complete edge loading along with uniform external pressure. The shell is modeled using Donnell’s shell theory including the first-order shear deformation theory (FSDT). The analysis uses the simply supported boundary condition (at , , ). The equations governing the nonlinear stability behavior of cylindrical shells are derived in terms of displacements () and rotations (, ). The applied partial edge loading is expressed in terms of Fourier series, and stress distributions within the cylindrical shell are determined by prebuckling analysis. The study uses multiterm Galerkin’s method along with the Newton-Raphson method to solve the governing partial differential equations of the shell nonlinear stability. With the help of numerical investigations, the authors present the number of modes required for the postbuckling analysis and the influence of initial geometric imperfections on the equilibrium path in the presence of partial edge loading. They have developed a simple algorithm based on potential theory to locate the exact location of bifurcation and limit points on the equilibrium path using the bisection method.
Get full access to this article
View all available purchase options and get full access to this article.
References
Catellani, G., Pellicano, F., Dall’Asta, D., and Amabili, M. (2004). “Parametric instability of a circular cylindrical shell with geometric imperfections.” Comput. Struct., 82(31–32), 2635–2645.
Crisfield, M. A. (1983). “An arc-length method including line searches and accelerations.” Int. J. Numer. Methods Eng., 19(9), 1269–1289.
Girish, J., and Ramachandra, L. S. (2006). “Thermomechanical postbuckling analysis of cross-ply laminated cylindrical shell panels.” J. Eng. Mech., 133–140.
Goldfeld, Y. (2009). “An alternative formulation in linear bifurcation analysis of laminated shells.” Thin-Walled Struct., 47(1), 44–52.
Goldfeld, Y., and Ejgenberg, E. A. (2007). “On the different formulations in linear bifurcation analysis of laminated cylindrical shells.” Int. J. Solids Struct., 44(25–26), 8613–8626.
Goncalves, P. B., and Del Prado, Z. J. G. N. (2002). “Nonlinear oscillations and stability of parametrically excited cylindrical shells.” Meccanica, 37(6), 569–597.
Guggenberger, W., Greiner, R., and Rotter, J. M. (2000). “The behavior of locally-supported cylindrical shells: Unstiffened shells.” J. Constr. Steel Res., 56(2), 175–197.
Han, B., and Simitses, G. J. (1991). “Analysis of anisotropic laminated cylindrical shells subjected to destabilizing loads. Part II: Numerical results.” Compos. Struct., 19(2), 183–205.
Iu, V. P., and Chia, C. Y. (1988). “Non-linear vibration and postbuckling of unsymmetric cross-ply circular cylindrical shells.” Int. J. Solids Struct., 24(2), 195–210.
Li, Z. M., and Lin, Z. Q. (2010). “Non-linear buckling and postbuckling of shear deformable anisotropic laminated cylindrical shells subjected to varying external pressure loads.” Compos. Struct., 92(2), 553–567.
Panda, S. K., and Ramachandra, L. S. (2010). “Postbuckling analysis of cross-ply laminated cylindrical shell panels under parabolic mechanical edge loading.” Thin-Walled Struct., 48(8), 660–667.
Papadakis, G. (2008). “Buckling of thick cylindrical shells under external pressure: A new analytical expression for the critical load and comparison with elasticity solutions.” Int. J. Solids Struct., 45(20), 5308–5321.
Riks, E. (1979). “An incremental approach to the solution of snapping and buckling problems.” Int. J. Solids Struct., 15(7), 529–551.
Sheinman, I., and Goldfeld, Y. (2001). “Buckling of laminated cylindrical shells in terms of different theories and formulation.” AIAA J., 39(9), 1773–1781.
Sheinman, I., and Goldfeld, Y. (2003). “Imperfection sensitivity of laminated cylindrical shells according to different shell theories.” J. Eng. Mech., 1048–1053.
Sheinman, I., and Jabareen, M. (2005). “Postbuckling of laminated cylindrical shells in different formulations.” AIAA J., 43(5), 1117–1123.
Sheinman, I., Shaw, D., and Simitses, G. J. (1983). “Non-linear analysis of axially-loaded laminated cylindrical shells.” Comput. Struct., 16(1–4), 131–137.
Shen, H. S. (2002). “Postbuckling of shear deformable laminated cylindrical shells.” J. Eng. Mech., 296–307.
Shen, H. S. (2008). “Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell. Part I: prediction under axial compression.” Compos. Struct., 82(3), 346–361.
Simitses, G. J., Shaw, D., and Sheinman, I. (1985). “Imperfection sensitivity of laminated cylindrical shells in torsion and axial compression.” Compos. Struct., 4(4), 335–360.
Song, C. Y., Teng, J. G., and Rotter, J. M. (2004). “Imperfection sensitivity of thin elastic cylindrical shells subjected to partial axial compression.” Int. J. Solids Struct., 41(24–25), 7155–7180.
Wagner, W., and Wriggers, P. (1988). “A simple method for the calculation of postcritical branches.” Eng. Comput., 5(2), 103–109.
Wriggers, P., and Simo, J. C. (1990). “A general procedure for the direct computation of turning and bifurcation points.” Int. J. Numer. Methods Eng., 30(1), 155–176.
Wriggers, P., Wagner, W., and Miehe, C. (1988). “A quadratically convergent procedure for the calculation of stability points in finite element analysis.” Comput. Methods Appl. Mech. Eng., 70(3), 329–347.
Yamaki, N., and Kodama, S. (1976). “Postbuckling behavior of circular cylindrical shells under compression.” Int. J. Non-Linear Mech., 11(2), 99–111.
Zhang, X., and Han, Q. (2007). “Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion.” Thin-Walled Struct., 45(12), 1035–1043.
Zhu, D. S., and Cheung, Y. K. (1996). “Postbuckling analysis of circular cylindrical shell under combined loads.” Comput. Struct., 58(1), 21–26.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 20, 2013
Accepted: Dec 13, 2013
Published online: Feb 11, 2014
Discussion open until: Jul 11, 2014
Published in print: Aug 1, 2014
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.