Nonlinear Flexural Response of Laminated Composite Plates on a Nonlinear Elastic Foundation with Uncertain System Properties under Lateral Pressure and Hygrothermal Loading: Micromechanical Model
Publication: Journal of Aerospace Engineering
Volume 27, Issue 3
Abstract
This paper investigates the stochastic nonlinear flexural response of laminated composite plates resting on a two-parameter Pasternak elastic foundation with Winkler cubic nonlinearity and random system properties subjected to transverse uniform lateral pressure and hygrothermal loading. System properties, such as the lamina material properties, coefficients of thermal expansion, coefficients of hygroscopic expansion, and lateral load, are modeled as basic random variables using a micromechanical model. A higher-order shear deformation theory in the von Kármán sense is used to model the system behavior of the laminated plate. A direct iterative-based nonlinear FEM, in conjunction with the first-order perturbation technique previously developed by the authors, is extended for the hygrothermal problem to obtain the second-order response statistics, i.e., the mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results for the second-order statistics of the nonlinear transverse central deflection of composite plates subjected to uniform temperature and moisture distribution over the plate surface and through the plate thickness are obtained for various combinations of foundation parameters, uniform lateral pressures, staking sequences, volume fraction, aspect ratio, plate thickness ratio, and boundary conditions under environmental conditions. The approach has been compared with those available in the literature and an independent Monte Carlo simulation (MCS).
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References
Chandrashekhara, K., and Tenneti, R. (1994). “Non-linear static and dynamic analysis of heated laminated plates; A finite element approach.” Compos. Sci. Technol., 51(1), 85–94.
Chia, Y. A. (1980). Nonlinear analysis of plates, McGraw Hill, New York.
Fares, M. E., and Zenkour, A. M. (1999). “Mixed variational formula for the thermal bending of laminated plates.” J. Therm. Stresses, 22(3), 347–365.
Huang, N. N., and Tauchert, T. R. (1988). “Large deformation of antisymmetric angle-ply laminates resulting from nonuniform temperature loading.” J. Therm. Stresses, 11(3), 287–297.
Jones, R. M. (1998). Mechanics of composite materials, 2nd Ed., Taylor & Francis, Philadelphia.
Kaminski, M. M. (2002). Computational mechanics of composite materials: Sensitivity, randomness and multiscale behavior, Springer, London.
Khdeir, A. A., and Reddy, J. N. (1991). “Thermal stresses and deflections of cross-ply laminated plates using refined plate theories.” J. Therm. Stresses, 14(4), 419–438.
Kleiber, M., and Hien, T. D. (1992). The stochastic finite element method, Wiley, New York.
Lal, A., Singh, B. N., and Kumar, R. (2007). “Static response of laminated composite plates resting on elastic foundation with uncertain system properties.” J. Reinf. Plast. Compos., 26(8), 807–829.
Lal, A., Singh, B. N., and Kumar, R. (2011). “Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading.” Arch. Appl. Mech., 81(6), 727–743.
Lin, R. M., Lim, M. K., and Du, H. (1994). “Large deflection analysis of plates under thermal loading.” Comput. Methods Appl. Mech. Eng., 117(3–4), 381–390.
Liu, W. K., Belytschko, T., and Mani, A. (1986). “Random field finite elements.” Int. J. Numer. Methods Eng., 23(10), 1831–1845.
Navaneentha Raj, B., Iyengar, N. G. R., and Yadav, D. (1998). “Response of composite plates with random material properties using FEM and MCS.” Adv. Compos. Mater., 7(3), 219–237.
Nigam, N. C., and Narayanan, S. (1994). Applications of random vibrations, Narosa, New Delhi.
Noh, H. C. (2006). “Effects of multiple uncertain material properties on the response variability of in-plane and plate structures.” Comput. Methods Appl. Mech. Eng., 195(19–22), 2697–2718.
Onkar, A. K., and Yadav, D. (2003). “Non-linear response statistics of composite laminates with random material properties under random loading.” Compos. Struct., 60(4), 375–383.
Pandit, M. K., Sheikh, A. H., and Singh, B. N. (2008). “An improved higher order Zigzag theory for the static analysis of laminated sandwich plate with soft core.” Finite Elem. Anal, 44(9–10), 602–610.
Pandit, M. K., Singh, B. N., and Sheikh, A. H. (2009). “Stochastic perturbation based finite element for deflection statistics of soft core sandwich plate with random material properties.” Int. J. Mech. Sci., 51(5), 363–371.
Park, J. S., Kim, C. G., and Hong, C. S. (1995). “Stochastic finite element method for laminated composite structures.” J. Reinf. Plast. Compos., 14(7), 675–693.
Peng, X. Q., Geng, L., Liyan, W., Liu, G. R., and Lam, K. Y. (1998). “A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending.” Comput. Mech., 21(3), 253–261.
Reddy, J. N. (1984). “A simple higher order theory for laminated composite plates.” J. Appl. Mech., 51(4), 745–752.
Reddy, J. N. (1996). Mechanics of laminated composite plates: Theory and analysis, CRC Press, Boca Raton, FL.
Salim, S., Yadav, D., and Iyengar, N. G. R. (1993). “Analysis of composite plates with random material characteristics.” Mech. Res. Commun., 20(5), 405–414.
Shankara, C. A., and Iyengar, N. G. R. (1996). “A element for analysis of laminated composite plate.” J. Sound Vib., 191(5), 721–738.
Shen, H.-S. (2000a). “Nonlinear analysis of composite laminated thin plates subjected to lateral pressure and thermal loading resting on elastic foundation.” Compos. Struct., 49(2), 115–128.
Shen, H.-S. (2000b). “Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations.” J. Strain Anal. Eng. Des., 35(2), 93–108.
Shen, H.-S. (2002). “Hygrothermal effects on the nonlinear bending of shear deformable laminated plates.” J. Eng. Mech., 493–496.
Shen, H.-S. (2004). “Nonlinear bending analysis of unsymmetric cross-ply laminated plates with piezoelectric actuators in thermal environment.” Comput. Struct., 63(2), 167–177.
Singh, B. N., Lal, A., and Kumar, R. (2008). “Nonlinear bending response of laminated composite plates on nonlinear elastic foundation with uncertain system properties.” Eng. Struct., 30(4), 1101–1112.
Upadhyay, A. K., Pandey, R., and Shukla, K. K. (2010). “Nonlinear flexural response of laminated composite plates under hygro-thermo-mechanical loading.” Commun. Nonlinear Sci. Numer. Simul., 15(9), 2634–2650.
Yang, J., Liew, K. M., and Kitipornchai, S. (2005). “Stochastic analysis of compositionally graded plates with system randomness under static loading.” Int. J. Mech. Sci., 47(10), 1519–1541.
Zenkour, A. M. (2004). “Analytical solution for bending of cross ply laminated plates under thermo-mechanical loading.” Compos. Struct., 65(3–4), 367–379.
Zhang, J., and Ellingwood, B. (1995). “Effects of uncertain material properties on structural stability.” J. Struct. Eng., 705–716.
Zhang, Y., Chen, S., Liu, Q., and Liu, T. (1996). “Stochastic perturbation finite elements.” Comput. Struct., 59(3), 425–429.
Zhang, Z., and Chen, S. (1991). “The standard deviations of the eigensolutions for random MDOF systems.” Comput. Struct., 39(6), 603–607.
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Published In
Journal of Aerospace Engineering
Volume 27 • Issue 3 • May 2014
Pages: 529 - 547
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jul 13, 2011
Accepted: Mar 2, 2012
Published online: Mar 8, 2012
Published in print: May 1, 2014
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