Buckling and Postbuckling Behavior of Cross-Ply Composite Plate Subjected to Nonuniform In-Plane Loads
Publication: Journal of Engineering Mechanics
Volume 137, Issue 9
Abstract
This paper presents a study of buckling and postbuckling behaviour of simply supported composite plates subjected to nonuniform in-plane loading. The mathematical model is based on higher order shear deformation theory incorporating von Kármán nonlinear strain displacement relations. Because the applied in-plane edge load is nonuniform, in the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using these stress distributions, the governing equations for postbuckling analysis of composite plates are obtained through the theorem of minimum potential energy. Adopting Galerkin’s approximation, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations in the case of postbuckling analysis, and homogeneous linear algebraic equations in the case of buckling analysis. The critical buckling load is obtained from the solution of associated linear eigenvalue problem. Postbuckling equilibrium paths are obtained by solving nonlinear algebraic equations employing the Newton-Raphson iterative scheme. Explicit expressions for the plate in-plane stress distributions within the prebuckling range are reported for isotropic and composite plates subjected to parabolic in-plane edge loading. Buckling loads are determined for three plate aspect ratios (, 1, 1.5) and three different types of in-plane load distributions. The effect of shear deformation on the buckling loads of composite plate is reported. The present buckling results are compared with previously published results wherever possible.
Get full access to this article
View all available purchase options and get full access to this article.
References
Benoy, M. B. (1969). “An energy solution for buckling of rectangular plate under non-uniform in-plane loading.” Aeronautical J., 73, 974–977.
Bert, C. W., and Devarakonda, K. K. (2003). “Buckling of rectangular plates subjected to nonlinearly distributed in-plane loading.” Int. J. Solids Struct., 40(16), 4097–4106.
Jana, P., and Bhaskar, K. (2006). “Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions.” Thin-Walled Struct., 44(5), 507–516.
Leissa, A. W., and Ayoub, E. F. (1988). “Vibration and buckling of simply supported rectangular plate subjected to pair of in-plane concentrated forces.” J. Sound Vib., 127(1), 155–171.
Leissa, A. W., and Kang, J. H. (2002). “Exact solution for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses.” Int. J. Mech. Sci., 44(9), 1925–1945.
Reddy, J. N. (1984). “A simple higher-order theory for laminated composite plates.” J. Appl. Mech., 51(4), 745–752.
Shames, I. H., and Dym, C. L. (1991). Energy and finite element methods in structural mechanics, New Age International Publications, Delhi, India.
Shi, Y., Lee, R. Y. Y., and Mei, C. (1999). “Thermal postbuckling analysis of composite plates using the finite element modal coordinate method.” J. Therm. Stresses, 22(6), 595–614.
Sundaresan, P., Singh, G., and Rao, V. G. (1998). “Buckling of moderately thick rectangular composite plate subjected to partial edge compression.” Int. J. Mech. Sci., 40(11), 1105–1117.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, McGraw-Hill, New York.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, McGraw-Hill, New York.
von der Neut, A. (1958). “Buckling caused by thermal stresses.” High temperature effects in aircraft structures, AGARDograph, No. 28, Pergamon Press, London, 215–247.
Wang, X., Wang, X., and Shi, X. (2007). “Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method.” Int. J. Mech. Sci., 49(4), 447–453.
Zhong, H., and Gu, C. (2006). “Buckling of simply supported rectangular Reissner-Mindlin plates subjected to linearly varying in-plane loading.” J. Eng. Mech., 132(5), 578–581.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 137 • Issue 9 • September 2011
Pages: 589 - 597
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jul 8, 2008
Accepted: Mar 9, 2011
Published online: Mar 10, 2011
Published in print: Sep 1, 2011
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.