Nonlinear Analysis of Moderately Thick Laminated Rectangular Plates
Publication: Journal of Engineering Mechanics
Volume 126, Issue 8
Abstract
Analytical solutions to the geometrically nonlinear boundary value problems of laminated-composite plate undergoing moderately large deformations and subjected to various boundary conditions are presented in this paper. The nonlinear coupled partial differential equations are linearized using a quadratic extrapolation technique. The spatial discretization of the linear differential equations is carried out using fast-converging Chebyshev polynomials. A convergence study reveals that 8–10 terms of expansion of the function is sufficient to yield quite accurate results. The results for uniformly loaded, moderately thick laminated-composite plates with simply supported immovable edges, clamped immovable edges, free edges, and their combinations are presented. Some new results are presented, and it is observed that the present method is efficient and less expensive.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alwar, R. S., and Nath, Y. (1976). “Application of Chebyshev polynomials to nonlinear analysis of circular plates.” Int. J. Mech. Sci., 18, 589–595.
2.
Barbero, E. J., and Reddy, J. N. (1990). “Nonlinear analysis of composite laminates using a generalized laminated plate theory.” AIAA J., 28(11), 1987–1994.
3.
Bencharif, N., and Ng, S. F. (1994). “Linear and nonlinear deflection analysis of thick rectangular plates—II, numerical applications.” Comp. and Struct., 50(6), 763–776.
4.
Cheung, M. S., and Li, W. (1989). “A modified finite strip method for geometrically nonlinear analysis of plates.” Comp. and Struct., 33(4), 1031–1035.
5.
Chia, C. Y. (1988). “Geometrically nonlinear behaviour of composite plates: A review.” Appl. Mech. Rev., 41(12), 439–454.
6.
Fox, L., and Parker, I. B. (1968). Chebyshev polynomials in numerical analysis, Oxford University Press, London.
7.
Gunay, E., and Erdem, A. U. (1997). “A new hetersosis plate finite element for geometrically nonlinear finite element analysis of laminated composite plates.” Comp. and Struct., 65(6), 819–828.
8.
Nath, Y., and Sandeep, K. (1995). “Chebyshev series solution to nonlinear boundary value problems in rectangular domain.” Comp. Meth. in Appl. Mech. Engrg., 125, 41–52.
9.
Singh, G., Rao, G. V., and Iyengar, N. G. R. (1994). “Geometrically nonlinear flexural response characteristics of shear deformable unsymmetrically laminated plates.” Comp. and Struct., 53(1), 69–81.
10.
Turvey, G. J., and Marshall, I. H. (1995). Buckling and postbuckling of composite plates, Chapman & Hall, London.
11.
Turvey, G. J., and Osman, M. Y. (1990). “Elastic large deflection analysis of isotropic rectangular plates.” Int. J. Mech. Sci., 32(4), 315–328.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 8 • August 2000
Pages: 831 - 838
History
Received: Jun 30, 1999
Published online: Aug 1, 2000
Published in print: Aug 2000
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.