Exact Solutions for Buckling of Multispan Rectangular Plates
Publication: Journal of Engineering Mechanics
Volume 129, Issue 2
Abstract
This paper presents exact solutions for buckling of multispan rectangular plates having two opposite edges simply supported and the other two edges being either free, simply supported, or clamped. The Levy solution procedure is employed to develop an analytical approach for buckling analysis of multispan plates. The Levy solution for each span is derived and the continuity along the interface of two spans is ensured through the implementation of the essential and natural boundary conditions at the interface. Extensive buckling factors, most of which are first-known exact solutions, are given in tabular and design chart forms for two- and three-unequal-span square plates subjected to uniaxial in-plane load in the x or y directions and biaxial in-plane load. The influence of the span ratios and plate boundary conditions on the buckling factors is discussed. Buckling factors are also obtained for two-, three-, and four-equal-span rectangular plates with various edge support conditions. The exact buckling solutions presented in this paper are of benchmark values for such plates.
Get full access to this article
View all available purchase options and get full access to this article.
References
Braun, M. (1993). Differential equations and their applications, 4th Ed., Springer, New York.
Chen, W. C., and Liu, W. H.(1990). “Deflections and free vibrations of laminated plates—Levy-type solutions.” Int. J. Mech. Sci., 32, 779–793.
Cheung, Y. K., and Delcourt, C.(1977). “Buckling and vibration of thin flatwalled structures continuous over several spans.” Proc., Inst. Civ. Eng., Struct. Build., 63(2), 93–103.
Cheung, Y. K., and Kong, J.(1995). “Vibration and buckling of thin-walled structures by a new finite strip.” Thin-Walled Struct., 21(4), 327–343.
Khdeir, A. A., and Librescu, L.(1988). “Analysis of symmetric cross-ply elastic plates using a higher-order theory, Part II: Buckling and free vibration.” Compos. Struct., 9, 259–277.
Lee, S. Y., and Lin, S. M.(1993). “Levy-type solution for the analysis of nonuniform plates.” Comput. Struct., 49, 931–939.
Leissa, A. W. (1969). Vibration of Plates, National Aeronautics and Space Administration (NASA) SP-160, Office of Technology Utilization, NASA, Washington, DC.
Liew, K. M., and Wang, C. M.(1992). “Elastic buckling of rectangular plates with internal curved supports.” J. Struct. Eng., 118(6), 1480–1493.
Liew, K. M., Xiang, Y., and Kitipornchai, S.(1996). “Analytical buckling solutions for Mindlin plates involving free edges.” Int. J. Mech. Sci., 38, 1127–1138.
Puckett, J. A., Wiseman, D. L., and Chong, K. P.(1987). “Compound strip method for the buckling analysis of continuous plates.” Thin-Walled Struct., 5, 383–400.
Saadatpour, M. M., Azhari, M., and Bradford, M. A.(1998). “Buckling of arbitrary quadrilateral plates with intermediate supports using the Galerkin method.” Comput. Methods Appl. Mech. Eng., 164, 297–306.
Sakata, T.(1976). “A reduction method for vibration and buckling problems of orthotropic continuous plates.” J. Sound Vib., 49(1), 45–52.
Seide, P.(1975). “Compressive buckling of sandwich plates on longitudinal elastic line supports.” AIAA J., 13(6), 740–743.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, McGraw–Hill, New York.
Wang, C. M., Liew, K. M., Xiang, Y., and Kitipornchai, S.(1993). “Buckling of rectangular Mindlin plates with internal line supports.” Int. J. Solids Struct., 30(1), 1–17.
Wang, C. M., and Liew, K. M.(1994). “Buckling of triangular plates under uniform compression.” Eng. Struct., 16(1), 43–50.
Xiang, Y., Liew, K. M., and Kitipornchai, S.(1996). “Exact buckling solutions for composite laminates: Proper free edge conditions under in-plane loadings.” Acta Mech., 117, 115–128.
Xiang, Y., Zhao, Y. B., and Wei, G. W. (2002). “Levy solutions for vibration of multi-span rectangular plates.” Int. J. Mech. Sci., 44, 1195–1218.
Yamazaki, T., Hikisaka, H., and Katsuragi, K.(1968). “A calculation method of the buckling load for continuous orthotropic plates.” Tech. Rep., Kyusyu Univ., 41(1), 61–68.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 129 • Issue 2 • February 2003
Pages: 181 - 187
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Feb 22, 2001
Accepted: Jul 8, 2002
Published online: Jan 15, 2003
Published in print: Feb 2003
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.