Abstract
In this paper, second order statistics of thermally induced post buckling response of elastically supported piezoelectric laminated composite plate using micromechanical approach is examined. A Co finite element has been used for deriving eigenvalue problem using higher order shear deformation theory (HSDT) with von-Karman nonlinearity. The uncertain system properties such as material properties of fiber and matrix of composite and piezoelectric, fiber volume fraction, plate thickness, lamination angle and foundation are modeled as random variables. The temperature field considered to be uniform temperature distributions through the plate thickness. A direct iterative based nonlinear finite element method combined with mean-centered second order perturbation technique (SOPT) is used to find the mean and coefficient of variance of the post buckling temperature. The effects of volume fraction, fiber orientation, and length to thickness ratio, aspect ratios, foundation parameters, position and number of piezoelectric layers, amplitude and boundary conditions with random system properties on the critical temperature are analysed. It is found that small amount of variations of uncertain system parameters of the composite plate significantly affect the initial and post buckling temperature of laminated composite plate. The results have been validated with independent Monte Carlo simulation (MCS) and those available in literature.
References
[1] Prabhu M.R., Dhanaraj R., Thermal buckling of laminated composite plates, Comp. Struct., 1994, 53, 1193-1204. 10.1016/0045-7949(94)90166-XSearch in Google Scholar
[2] Chen Lien-wen, Chen Lei-Yi., Thermal buckling behaviour of laminated composite plates with temperature-dependent properties, Compos. Struct., 1989, 13(4), 275–87. 10.1016/0263-8223(89)90012-3Search in Google Scholar
[3] Shen H.S., Thermal post buckling behaviour of imperfect shear deformable laminated plates with temperature-dependent properties, Comput. Meth. Appl. Mech. Eng. 2001, 190, 5377–90. Search in Google Scholar
[4] Srikanth G., Kumar A. Post buckling response and failure of symmetric laminates under uniform temperature rise, Compos. Struct., 2003, 59, 109–18. 10.1016/S0263-8223(02)00186-1Search in Google Scholar
[5] Shariyat M., Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layer wise theory, Thin-Walled Struct., 2007, 45(4), 439–52. 10.1016/j.tws.2007.03.004Search in Google Scholar
[6] Pandey R., Shukla K.K., Jain A., Thermoelastic stability analysis of laminated composite plates, an analytical approach, Commun. Nonl. Sci. Numer. Simulat., 2008, 14(4), 1679–99. 10.1016/j.cnsns.2008.02.010Search in Google Scholar
[7] Shukla K.K., Huang J.H., Nath Y., Thermal post buckling of laminated composite plates with temperature dependent properties, J. Engin.Mech., ASCE, 2004, 130(7), 818-825. 10.1061/(ASCE)0733-9399(2004)130:7(818)Search in Google Scholar
[8] Jifeng Xu, Qun Zhao, Pizhong Qiao, A Critical Review on Buckling and Post-Buckling Analysis of Composite Structures, Fron. Aero. Eng., 2013, 2(3), 157-168. Search in Google Scholar
[9] Fatima Zohra Kettaf, Mohammed Sid Ahmed Houari, Mohamed Benguediab, Abdelouahed Tounsi, Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model, Steel and Compos. Struct., 2013,15(4), 399-423. 10.12989/scs.2013.15.4.399Search in Google Scholar
[10] Grover N., Singh B. N., Maiti D. K., Free vibration and buckling characteristics of laminated composite and sandwich plates implementing a secant function based shear deformation theory, Proceed. Instit. Mech. Eng., Part C: J. Mech. Eng. Sc, 2015, 229(3), 391-405. 10.1177/0954406214537799Search in Google Scholar
[11] Patel B.P., Ganapati M., Prasad K.R., Makhecha D.P., Dynamic stability of layered anisotropic composite plates resting on elastic foundation, Eng. Struct., 1999, 35, 345-355. Search in Google Scholar
[12] Shen H.S., Zheng J.J., Huang X.L., Dynamic response of shear deformable plates under thermomechancial loadings, and resting on elastic foundation. Compos. Struct., 2003,60, 57-66. 10.1016/S0263-8223(02)00295-7Search in Google Scholar
[13] Setoodes A.R., Karmi G., Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using 3-D layer wise FEM, Eng. Struct., 2004, 26, 211-220. 10.1016/j.engstruct.2003.09.009Search in Google Scholar
[14] Jayachandran S.A., Vaidynathan C.V., Post critical behavior of biaxial compressed plate on elastic foundations, Comput. Struct., 1995,54(2), 239-246. 10.1016/0045-7949(94)00317-VSearch in Google Scholar
[15] Shen H.S., Williams F.W., Biaxial buckling and post buckling of composite laminated plates on two parameters elastic foundations, Comput. Struct., 1997, 63(6), 1177-1185. 10.1016/S0045-7949(96)00398-7Search in Google Scholar
[16] Shen H.S., Post buckling of shear deformable laminated plates under biaxial compression and lateral pressure and resting on elastic foundation, Int. J. Mech. Scien., 2000, 42 (6), 1171-1195. 10.1016/S0020-7403(99)00044-2Search in Google Scholar
[17] Shen H.S., Post buckling analysis of composite plates on two parameters elastic foundation, Int. J. Mech. Scien., 1995, 37 (12), 1307-1316. 10.1016/0020-7403(95)00040-5Search in Google Scholar
[18] Xia X.K., Shen H.S., Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators, Compos. Struct., 2009, 90, 254–262. 10.1016/j.compstruct.2009.03.018Search in Google Scholar
[19] Shen H.S., A comparison of buckling and post buckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators, Compos. Struct., 2009, 91, 375–384. 10.1016/j.compstruct.2009.06.005Search in Google Scholar
[20] Shen H., Zheng Hong Zhu, Compressive and thermal post buckling behaviors of laminated plates with piezoelectric fiber reinforced composite actuators, Appli. Math. Model., 2011, 35(4), 1829–1845. 10.1016/j.apm.2010.10.013Search in Google Scholar
[21] Naveen C., Singh B. N., Thermal buckling and post-buckling of laminated composite plates with sma fibers using layerwise theory. Int. J. Comput.l Meth. Engin. Sci. Mechan, 2009.10 (6), 423-429 10.1080/15502280903108024Search in Google Scholar
[22] Panda S. K., Singh B. N., Thermal Post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method by Compos. Struct., 2009,91(3), 366-374. 10.1016/j.compstruct.2009.06.004Search in Google Scholar
[23] Chamis C.C., Simplified composite micromechanics equations for mechanical, thermal and moisture related properties. Engin. Guide to comp.mater. ASMInt.,Materials Park, Ohio, 1987, 3.8– 3.24. Search in Google Scholar
[24] Chamis C.C., Sinclair J.H., Durability/life of fiber composites in hygrothermomechanical environments. Composite Materials: Testing and Design (Sixth Conf.) STP 787, ASTM, West Conshohocken, Pa., 1982, 498–512. 10.1520/STP28497SSearch in Google Scholar
[25] Chandra R., Singh S.P., Gupta K., Micromechanical damping models for fiber-reinforced composites: A comparative study.Composites, 2002, Part A. 33, 787–796. 10.1016/S1359-835X(02)00019-2Search in Google Scholar
[26] Chao L.P., Shyu S.L., Nonlinear buckling of fiber reinforced composite plates under hygrothermal effects. J. Chinese Inst. Eng. 1996, 19, 657–667. Search in Google Scholar
[27] Pandey R., Upadhyay A.K., Shukla K.K., Hygrothermoelastic post buckling response of laminated composite plates, J. Aeros. Engg., ASCE, 2010, 23(1), 1-13. 10.1061/(ASCE)0893-1321(2010)23:1(1)Search in Google Scholar
[28] Graham L.L., Siragy E.F., Stochastic finite element for elastic buckling of stiffened panels, ASCE J Eng. Mech., 2001, 127(1), 91-97. 10.1061/(ASCE)0733-9399(2001)127:1(91)Search in Google Scholar
[29] Onkar A.K., Upadhyay C.S., Yadav D., Stochastic finite element analysis buckling analysis of laminatedwith circular cutouts under uniaxial compression. Trans ASME J Appl. Mech. 2007, 74, 789–809. Search in Google Scholar
[30] Verma V.K., Singh B.N., Thermal buckling of laminated composite plates with random geometric and material properties, Int. J.Struct. Stab. Dynam., 9(2), 2009, 187-211. 10.1142/S0219455409002990Search in Google Scholar
[31] Lal A., Singh B. N., Thermal buckling response of laminated composite plate with random system properties, Int. J. Comput. Meth. 2009, 6(2), 447-471. Search in Google Scholar
[32] Lal A., Singh B.N., Kumar R., Effects of random system properties on the thermal buckling analysis of laminated composite plates, Comput. Struct., 2009, 87 (17-18), 1119. 10.1016/j.compstruc.2009.06.004Search in Google Scholar
[33] Singh B. N., Jibumon B., Thermal buckling of conical panel/shell embedded with and without piezoelectric layers with random material properties. Int. J. Crashworthiness, 2009, 14(1), 73-81. 10.1080/13588260802517352Search in Google Scholar
[34] Kumar R., Patil H.S., Lal A., Hygrothermoelastic buckling response of laminated composite plates with random system properties:macromechanical and micromechanical model, J. Aerosp. Eng., 2012, 10.1061/(ASCE)AS.1943-5525.0000241, 04014123. Search in Google Scholar
[35] Reddy J. N., A simple higher-order theory for laminated composite plates, J. Appl. Mech. 1984, 51, 745-752. Search in Google Scholar
[36] Kleiber M., Hien T.D., The stochastic finite element method, John Wiley and Sons, 1992. Search in Google Scholar
[37] Haldar A.,Mahadevan S., Reliability assessment using stochastic finite element analysis. John Willey and Sons, 2000. Search in Google Scholar
[38] Gibson R. F., Principles of composite material mechanics, McGraw-Hill, 1994. Search in Google Scholar
[39] Jones R. M., Mechanics of composite materials, McGraw-Hill, New York, 1975. 10.1115/1.3423688Search in Google Scholar
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