Local Buckling Analysis of Restrained Orthotropic Plates under Generic In-Plane Loading
Publication: Journal of Engineering Mechanics
Volume 139, Issue 8
Abstract
An analytical study of local buckling of discrete laminated plates or panels of fiber-reinforced plastic structural shapes is presented. Two cases of composite plate analyses with two opposite edges simply supported and the other two opposite edges either both rotationally restrained or one rotationally restrained and the other free, are studied. Generic loading cases with combined linearly varying axial and in-plane shear loading are considered. A variational formulation of the Ritz method is used to establish the eigenvalue problem for the local buckling behavior, and explicit expressions for predictions of the plate buckling stress resultants, in terms of the rotationally restrained stiffness, the plate aspect ratio, and the ratios of applied stress resultants, are developed. Based on different boundary and loading conditions, simple and explicit local buckling solutions for several special cases are further reduced. Validity of the explicit solutions presented is demonstrated by a good agreement of comparisons between the present predictions and available solutions in the literature. Parametric studies are further conducted, and the influences of several parameters such as the rotationally restrained stiffness, biaxial loading stress ratio, material flexural orthotropy, and linearly varying axial loading stress gradient on the local buckling stress resultants are discussed.
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References
Bank, L. C., and Yin, J. (1996). “Buckling of orthotropic plates with free and rotationally restrained unloaded edges.” Thin-walled Struct., 24(1), 83–96.
Barbero, E., and Raftoyiannis, I. (1993). “Local buckling of FRP beams and columns.” J. Mater. Civ. Eng., 5(3), 339–355.
Bedair, O. (1995). “Unified approach to local stability of plate/stiffener assemblies.” J. Eng. Mech., 121(2), 214–229.
Gibson, L. J., and Ashby, M. F. (1988). Cellular solids: Structure and properties, Pergamon Press, Oxford, U.K.
Herencia, J., Weaver, P., and Friswell, M. (2010). “Closed-form solutions for buckling of long anisotropic plates with various boundary conditions under axial compression.” J. Eng. Mech., 136(9), 1105–1114.
Kollar, L. (2002). “Buckling of unidirectionally loaded composite plates with one free and one rotationally restrained unloaded edge.” J. Struct. Eng., 128(9), 1202–1211.
Kollar, L. P., and Veres, I. A. (2001). “Buckling of rectangular orthotropic plates subjected to biaxial normal forces.” J, Comp, Mat,, 35(7), 625–635.
Lee, H. S., Hong, S. H., Lee, J. R., and Kim, Y. K. (2002). “Mechanical behavior and failure process during compressive and shear deformation of honeycomb composite at elevated temperatures.” J. Mater. Sci., 37(6), 1265–1272.
Masters, I. G., and Evans, K. E. (1996). “Models for the elastic deformation of honeycombs.” Compos. Struct., 35(4), 403–422.
Meirovitch, L., and Kwak, M. (1990). “Convergence of the classical Rayleigh-Ritz method and the finite-element method.” AIAA J., 28(8), 1509–1516.
Nemeth, M. P. (1992a). “Buckling behavior of long symmetrically laminated plates subjected to combined loadings.” NASA TP-3195, National Aeronautics and Space Administration, Washington, DC.
Nemeth, M. P. (1992b). “Buckling of symmetrically laminated plates with compression, shear, and in-plane bending.” Am. Inst. Aeronaut. Astronaut., 30(12), 2959–2965.
Nemeth, M. P. (1995). “Buckling behavior of long anisotropic plates subjected to combined loads.” NASA TP-3568, National Aeronautics and Space Administration, Washington, DC.
Nemeth, M. P. (1997). “Buckling behavior of long symmetrically laminated plates subjected to shear and linearly varying axial edge loads.” NASA TP-3659, National Aeronautics and Space Administration, Washington, DC.
Papka, S. D., and Kyriakides, S. (1994). “In-plane compressive response and crushing of honeycomb.” J. Mech. Phys. Solids, 42(10), 1499–1532.
Qiao, P. Z., and Huo, X. (2011). “Explicit local buckling analysis of rotationally restrained orthotropic plates under uniform shear.” Compos. Struct., 93(11), 2785–2794.
Qiao, P. Z., and Shan, L. (2005). “Explicit local buckling analysis and design of fiber–reinforced plastic composite structural shapes.” Compos. Struct., 70(4), 468–483.
Qiao, P. Z., and Shan, L. (2007). “Explicit local buckling analysis of rotationally restrained composite plates under biaxial loading.” Int. J. Struct. Stab. Dyn., 7(3), 487–517.
Qiao, P. Z., and Zou, G. (2002). “Local buckling of elastically restrained fiber-reinforced plastic plates and its application to box sections.” J. Eng. Mech., 128(12), 1324–1330.
Qiao, P. Z., Davalos, J. F., and Wang, J. L. (2001). “Local buckling of composite FRP shapes by discrete plate analysis.” J. Struct. Eng., 127(3), 245–255.
Qiao, P. Z., Davalos, J., Barbero, E. J., and Troutman, D. (1999). “Equations facilitate composite designs.” Modern Plast., 76(11), 77–80.
Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: Theory and analysis, CRC Press, Boca Raton, FL.
Shan, L., and Qiao, P. Z. (2008). “Explicit local buckling analysis of rotationally restrained composite plates under uniaxial compression.” Eng. Structures, 30(1), 126–140.
Shufrin, I., Rabinovitch, O., and Eisenberger, M. (2008a). “Buckling of laminated plates with general boundary conditions under combined compression, tension, and shear—a semi-analytical solution.” Thin-walled Struct., 46(7–9), 925–938.
Shufrin, I., Rabinovitch, O., and Eisenberger, M. (2008b). “Buckling of symmetrically laminated rectangular plates with general boundary conditions—a semi-analytical approach.” Compos. Struct., 82(4), 521–531.
Tarján, G., Sapkás, Á., and Kollár, L. P. (2009). “Stability analysis of long composite plates with restrained edges subjected to shear and linearly varying loads.” J. Reinforc. Plast. Compos., 29(9), 1386–1398.
Turvey, G. J., and Marshall, I. H. (1995). Buckling and postbuckling of composite plates, Chapman & Hall, London.
Wang, C. M., Wang, C. Y., and Reddy, J. N. (2004). Exact solutions for buckling of structural members, CRC Press, Boca Raton, FL.
Wang, C., Xiang, Y., and Kitipornchai, S. (1994). “Buckling solutions of rectangular Mindlin plates under uniform shear.” J. Eng. Mech., 120(11), 2462–2470.
Weaver, P. M. (2006). “Approximate analysis for buckling of compression loaded long rectangular plates with flexural/twist anisotropy.” Proc. Royal Soc A Math. Phys. Eng. Sci., 462(2065), 59–73.
Weaver, P., and Nemeth, M. (2007). “Bounds on flexural properties and buckling response for symmetrically laminated composite plates.” J. Eng. Mech., 133(11), 1178–1191.
Webber, J. P. H., Holt, P. J., and Lee, D. A. (1985). “Instability of carbon fiber reinforced flanges of I section beams and columns.” Compos. Struct., 4(3), 245–265.
Wright, H. (1995). “Local stability of filled and encased steel sections.” J. Struct. Eng., 121(10), 1382–1388.
Wu, Z., Raju, G., and Weaver, P. (2012). “A comparison of variational, differential quadrature and approximate closed form solution methods for buckling of highly flexurally anisotropic laminates.” J. Eng. Mech.. (Jul. 28, 2012).
Zhang, J., and Ashby, M. F. (1992). “The out-of-plane properties of honeycombs.” Int. J. Mech. Sci., 34(6), 475–489.
Zhu, H. X., and Mills, N. J. (2000). “The in-plane non-linear compression of regular honeycombs.” Int. J. Solids Struct., 37(13), 1931–1949.
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Information
Published In
Journal of Engineering Mechanics
Volume 139 • Issue 8 • August 2013
Pages: 936 - 951
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 6, 2012
Accepted: Sep 20, 2012
Published online: Sep 22, 2012
Published in print: Aug 1, 2013
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