Bounds on Flexural Properties and Buckling Response for Symmetrically Laminated Composite Plates
Publication: Journal of Engineering Mechanics
Volume 133, Issue 11
Abstract
Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provide insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear, or pure in-plane bending loads are presented. The results indicate that the maximum gain in buckling resistance for tailored orthotropic laminates, with respect to the corresponding isotropic plate, is in the range of 26–36% for plates with simply supported edges, irrespective of the loading conditions. For the plates with clamped edges, the corresponding gains in buckling resistance are in the range of 9–12% for plates subjected to compression or pure in-plane bending loads and potentially up to 30% for plates subjected to shear loads.
Get full access to this article
View all available purchase options and get full access to this article.
References
Brunelle, E. J. (1985). “The fundamental constants of orthotropic affine slab/plate equations.” AIAA J., 23(12), 1957–1961.
Brunelle, E. J. (1986). “Eigenvalue similarity rules for symmetric cross-ply laminated plates.” AIAA J., 24(1), 151–154.
Brunelle, E. J., and Oyibo, G. A. (1983). “Generic buckling curves for specially orthotropic rectangular plates.” AIAA J., 21(8), 1150–1156.
Chamis, C. C. (1969). “Buckling of anisotropic composite plates.” J. Struct. Div., 95, 2119–2139.
Fukunaga, H., and Hirano, Y. (1982). “Stability optimization of laminated composite plates under in-plane loads.” Proc., 4th Int. Conf. on Composite Materials, Vol. 1, Tokyo, 565–572.
Fukunaga, H., and Sekine, H. (1992). “Stiffness design method of symmetric laminates using lamination parameters.” AIAA J., 30(11), 2791–2793.
Geier, B., and Singh, G. (1997). “Some simple solutions for buckling loads of thin and moderately thick cylindrical shells and panels made of laminated composite material.” Aerosp. Sci. Technol., 1, 47–63.
Grenestedt, J. L. (1991). “Lay-up optimization against buckling of shear panels.” Struct. Optim., 3(7), 115–120.
Huber, M. T. (1929). Problem der statik technisch wichtiger orthotroper platten, Warsaw, Poland.
Jones, R. M. (1999). Mechanics of composite materials, 2nd Ed., Taylor and Francis, Philadelphia.
Lempriere, B. M. (1968). “Poisson’s ratio in orthotropic materials.” AIAA J., 6(11), 2226–2227.
Mansfield, E. H. (1989). The bending and stretching of plates, 2nd Ed., Cambridge University Press, Cambridge, U.K.
Miki, M. (1982). “Material design of composite laminates with required in-plane elastic properties.” Proc., 4th Int. Conf. Composite Materials, Vol. 2, Tokyo, 1725–1731.
Nemeth, M. P. (1986). “Importance of anisotropy on buckling of composite-loaded symmetric composites plates.” AIAA J., 24(11), 1831.
Nemeth, M. P. (1992a). “Buckling behaviour of long symmetrically laminated plates subject to combined loadings.” NASA TP-3195, NASA, Washington, D.C.
Nemeth, M. P. (1992b). “Nondimensional parameters and equations for buckling of symmetrically laminated thin elastic shallow shells.” NASA TM-104060, NASA, Washington, D.C.
Nemeth, M. P. (1994). “Nondimensional parameters and equations for buckling of anisotropic shallow shells.” J. Appl. Mech., 61(9), 664–669.
Nemeth, M. P. (1995). “Buckling behavior of long anisotropic plates subject to combined loads.” NASA TP-3568, NASA, Washington, D.C.
Nemeth, M. P. (1997). “Buckling behavior of long symmetrically laminated plates subjected to shear or linearly varying axial loads.” NASA TP-3659, NASA, Washington, D.C.
Nemeth, M. P. (2000). “Buckling behaviour of long symmetrically laminated plates subjected to restrained thermal expansion and mechanical loads.” J. Therm. Stresses, 23, 873–916.
Oyibo, G. A., and Berman, J. (1985). “Influence of warpage on composite aeroelastic theories.” Proc., AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conf., Orlando, Fla., AIAA Paper No. 85-0673-CP.
Seydel, E. (1933). “The critical shear load of rectangular plates.” NACA TM 7005, NACA, Washington, D.C.
Skan, S. W., and Southwell, R. V. (1924). “On the stability under shearing stresses of a flat elastic strip.” Proc. R. Soc. London, Ser. A, 105, 582–607.
Shulesko, P. (1957). “A reduction method for buckling problems of orthotropic plates.” Aeronaut. Q., 8, 145–156.
Stein, M. (1983). “Postbuckling of orthotropic composite plates loaded in compression.” AIAA J., 12(12), 1729–1735.
Tsai, S. W., and Pagano, N. J. (1968). “Invariant properties of composite materials.” Proc., Composite Materials Workshop, U.S. Air Force, Univ. of California at Berkeley, Berkeley, Calif., 233–253.
Weaver, P. M. (2003). “On optimization of long anisotropic flat plates subject to compression buckling loads.” Proc., American Society of Composites 18th Technical Conf., Univ. of Florida, Gainesville, Fla., Paper No. 142.
Weaver, P. M. (2004). “On optimization of long anisotropic flat plates subject to shear buckling loads.” Proc., 45th AIAA, ASCE, ASME, AHS Structures, Structural Dynamics, and Materials Conf., Palm Springs, Calif.
Wittrick, W. H. (1952). “Correlation between some stability problems for orthotropic and isotropic plates under biaxial and uniaxial direct stress.” Aeronaut. Q., 4, 83–92.
Yang, I.-H., and Kuo, W.-S. (1986). “The global constants in orthotropic affine space.” J. Chin. Soc. Mech. Eng., 7(5), 355–360.
Zwillinger, D. (1996). Standard mathematical tables and formulae, 30th Ed., CRC, Boca Raton, Fla.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 11 • November 2007
Pages: 1178 - 1191
Copyright
© 2007 ASCE.
History
Received: Jul 12, 2006
Accepted: Feb 27, 2007
Published online: Nov 1, 2007
Published in print: Nov 2007
Notes
Note. Associate Editor: Khaled W. Shahwan
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.