Technical Papers
May 26, 2018

Accuracy of the Buckling Predictions of Anisotropic Plates

Publication: Journal of Engineering Mechanics
Volume 144, Issue 8

Abstract

The aim of this work is to explore the potential of two hierarchic sets, one polynomial and the other trigonometric, in the construction of versatile Ritz bases to accurately solve the linear buckling of anisotropic Kirchhoff plates. Focus is placed on reporting the basis ability to surmount numerical degrading effects associated with anisotropy. Several examples are presented to illustrate the merits and demerits of each set in terms of accuracy and rate of convergence, mainly by comparing their results with those obtained from traditional Ritz bases and finite-element models.

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References

Bardell, N. S. 1991. “Free vibration analysis of a flat plate using the hierarchical finite element method.” J. Sound Vib. 151 (2): 263–289. https://doi.org/10.1016/0022-460X(91)90855-E.
Bassily, S. F., and S. M. Dickinson. 1975. “On the use of beam functions for problems of plates involving free edges.” J. Appl. Mech. 42 (4): 858–864. https://doi.org/10.1115/1.3423720.
Baucke, A., and C. Mittelstedt. 2015. “Closed-form analysis of the buckling loads of composite laminates under uniaxial compressive load explicitly accounting for bending-twisting-coupling.” Compos. Struct. 128: 437–454. https://doi.org/10.1016/j.compstruct.2014.12.054.
Beslin, O., and J. Nicolas. 1997. “A hierarchical functions set for predicting very high order plate bending modes with any boundary conditions.” J. Sound Vib. 202 (5): 633–655. https://doi.org/10.1006/jsvi.1996.0797.
Brukva, N. F. 1968. “Stability of rectangular orthotropic plates.” [In Russian.] Prikladnaya Mekhanika 4 (3): 77–85.
Cook, R. D., D. S. Malkus, M. E. Plesha, and R. J. Witt. 2002. Concepts and applications of finite element analysis. 4th ed. New York, NY: Wiley.
Dang, T. D., and R. K. Kapania. 2013. “Ritz approach for buckling prediction of cracked-stiffened structures.” J. Aircraft 50 (3): 965–974. https://doi.org/10.2514/1.C032173.
Daniel, I. M., and O. Ishai. 1994. Engineering mechanics of composite materials. 2nd ed. New York, NY: Oxford University Press.
Dickinson, S. M., and A. Di Blasio. 1986. “On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates.” J. Sound Vib. 108 (1): 51–62. https://doi.org/10.1016/S0022-460X(86)80310-8.
Dozio, L. 2011. “On the use of the trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates.” Thin-Walled Struct. 49 (1): 129–144. https://doi.org/10.1016/j.tws.2010.08.014.
Gawandi, A., J. M. Whitney, and R. A. Brockman. 2008. “Natural boundary conditions in the bending of anisotropic laminated plates.” Compos. Struct. 82 (2): 201–208. https://doi.org/10.1016/j.compstruct.2007.01.009.
Kumar, Y. V. S., and J. K. Paik. 2004. “Buckling analysis of cracked plates using hierarchical trigonometric functions.” Thin-Walled Struct. 42 (5): 687–700. https://doi.org/10.1016/j.tws.2003.12.012.
Leissa, A. W. 1985. Buckling of laminated composite plates and shell panels. Dayton, OH: Wright Patterson Air Force Base.
MacNeal, R. H. 1994. Finite elements: Their design and performance. New York, NY: Marcel Dekker.
Mallela, U. K., and A. Upadhyay. 2016. “Buckling load prediction of laminated composite stiffened panels subjected to in-plane shear using artificial neural networks.” Thin-Walled Struct. 102: 158–164. https://doi.org/10.1016/j.tws.2016.01.025.
Mansfield, E. H. 1964. The bending and stretching of plates. Oxford: Pergamon Press.
Meirovitch, L., and H. Baruh. 1983. “On the inclusion principle for the hierarchical finite element method.” Int. J. Numer. Methods Eng. 19 (2): 281–291. https://doi.org/10.1002/nme.1620190209.
Nallim, L. G., and R. O. Grossi. 2003. “On the use of orthogonal polynomials in the study of anisotropic plates.” J. Sound Vib. 264 (5): 1201–1207. https://doi.org/10.1016/S0022-460X(02)01523-7.
NX Nastran. 2014. Element library reference. Plano, TX: Siemens PLM Software.
Reddy, J. N. 2004. Mechanics of laminated composite plates and shells: Theory and analysis. Boca Raton, FL: CRC Press.
Szilard, R. 2004. Theories and applications of plate analysis: Classical, numerical and engineering methods. Hoboken, NJ: Wiley.
Vescovini, R., and L. Dozio. 2015. “Exact refined buckling solutions for laminated plates under uniaxial and biaxial loads.” Compos. Struct. 127: 356–368. https://doi.org/10.1016/j.compstruct.2015.03.003.
Washizu, K. 1982. Variational methods in elasticity and plasticity. 3rd ed. Oxford: Pergamon Press.
Weaver, P. M., and M. P. Nemeth. 2007. “Bounds on flexural properties and buckling response for symmetrically laminated composite plates.” J. Eng. Mech. 133 (11): 1178–1191. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:11(1178).
West, L. J., N. S. Bardell, J. M. Dunsdon, and P. M. Loasby. 1997. “Some limitations associated with the use of K-orthogonal polynomials in hierarchical versions of the finite element method.” In Vol. 1 of Proc., 6th Int. Conf. Recent Advances in Structural Dynamics, edited by N. S. Ferguson, H. F. Wolfe, and C. Mei. 217–231. Southampton, UK: ISVR, Univ. of Southampton.
Whitney, J. M. 1971. “Fourier analysis of clamped anisotropic plates.” J. Appl. Mech. 38 (2): 530–532. https://doi.org/10.1115/1.3408810.
Whitney, J. M. 1972. “Analysis of anisotropic rectangular plates.” AIAA J. 10 (10): 1344–1345. https://doi.org/10.2514/3.6610.
Whitney, J. M. 1987. Structural analysis of laminated anisotropic plates. Lancaster, UK: Technomic Publishing Company.
Wu, Z., G. Raju, and P. M. Weaver. 2013. “Comparison of variational, differential quadrature, and approximate closed-form solution methods for buckling of highly flexurally anisotropic laminates.” J. Eng. Mech. 139 (8): 1073–1083. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000468.
Zhu, D. C. 1986. “Development of hierarchical finite element methods at BIAA.” In Vol. 1 of Proc., Int. Conf. on Computational Mechanics, I-123–I-128. Tokyo, Japan.

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Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 144Issue 8August 2018

History

Received: Jul 27, 2017
Accepted: Feb 22, 2018
Published online: May 26, 2018
Published in print: Aug 1, 2018
Discussion open until: Oct 26, 2018

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Authors

Affiliations

L. N. Yshii [email protected]
Dept. of Civil Engineering, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil. Email: [email protected]
E. Lucena Neto [email protected]
Professor, Dept. of Civil Engineering, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil (corresponding author). Email: [email protected]
F. A. C. Monteiro [email protected]
Professor, Dept. of Civil Engineering, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil. Email: [email protected]
R. C. Santana [email protected]
M.Sc. Student, Dept. of Civil Engineering, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil. Email: [email protected]

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