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http://dx.doi.org/10.12989/sem.2019.71.6.669

Nonlinear thermal buckling of bi-directional functionally graded nanobeams  

Gao, Yang (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University)
Xiao, Wan-shen (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University)
Zhu, Haiping (School of Computing, Engineering and Mathematics, Western Sydney University)
Publication Information
Structural Engineering and Mechanics / v.71, no.6, 2019 , pp. 669-682 More about this Journal
Abstract
We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton's principle and the von $K{\acute{a}}rm{\acute{a}}n$ geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams.
Keywords
Bi-directional FGMs; Nonlocal strain gradient theory; Nonlinear thermal buckling;
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Times Cited By KSCI : 45  (Citation Analysis)
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93 Karami, B., Shahsavari, D, Janghorban, M and Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", Int. J. Mech. Sci. 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.   DOI
94 Karami, B., Janghorban, M. and Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using threedimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech. 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.   DOI
95 Karami, B., Shahsavari, D. and Janghorban, M.A. (2018e), "Comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Tech., 82, 499-512. https://doi.org/10.1016/j.ast.2018.10.001.   DOI
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97 Karami, B. and Janghorban, M. (2019), "Characteristics of elastic waves in radial direction of anisotropic solid sphere, a new closed-form solution", Eur. J.Mech.-A/Solid.,76, 36-45. https://doi.org/10.1016/j.euromechsol.2019.03.008.   DOI
98 Karami, B and Maziar, J. (2019), "On the dynamics of porous nanotubes with variable material properties and variable thickness", Int. J. Eng. Sci. 136, 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002.   DOI
99 Karami, B. and Janghorban, M. and Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech. 70 (1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.   DOI
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106 Abdelaziz, H. H., Meziane, M. A. A., Bousahla, A. A., Tounsi, A., Mahmoud, S. R., and Alwabli, A. S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25, 693-704. https://doi.org/10.12989/scs.2017.25.6.693.   DOI
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116 Besseghier, A., Houari, M. S. A., Tounsi, A., and Mahmoud, S. R. (2017a), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601 - 614. https://doi.org/10.12989/sss.2017.19.6.601.   DOI
117 Hamidi, A., Houari, M. S. A., Mahmoud, S. R., and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235 - 253. https://doi.org/10.12989/scs.2015.18.1.235.   DOI
118 Gao, Y., Xiao, W. and Zhu, H. (2019b), "Nonlinear vibration analysis of different types of functionally graded beams using nonlocal strain gradient theory and a two-step perturbation method", Eur. Phys. J. Plus, 134(23), 1-24. https://doi.org/10.1140/epjp/i2019-12446-0.   DOI
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125 Besseghier, A., Houari, M. S. A., Tounsi, A., and Mahmoud, S. R. (2017b), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601 - 614. https://doi.org/10.12989/sss.2017.19.6.601.   DOI
126 Bouadi, A., Bousahla, A. A., Houari, M. S. A., Heireche, H., and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.   DOI
127 Bounouara, F., Benrahou, K. H., Belkorissat, I., and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227.   DOI
128 Artioli, E. (2018), "Asymptotic homogenization of fibrereinforced composites: a virtual element method approach", Meccanica, 53(6), 1187-1201. https://doi.org/10.1007/s11012-018-0818-2.   DOI
129 Bouafia, K., Kaci, A., Houari, M. S. A., Benzair, A., and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19, 115-126. https://doi.org/10.12989/sss.2017.19.2.115.   DOI
130 Bouderba, B., Houari, M. S. A., Tounsi, A., and Mahmoud, S. R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397.   DOI
131 Boukhari, A., Atmane, H. A., Tounsi, A., Adda Bedia, E. A., and Mahmoud, S. R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837.   DOI
132 Bourada, F., Amara, K., Bousahla, A. A., Tounsi, A., and Mahmoud, S. R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661.   DOI
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135 Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. http://dx.doi.org/10.12989/sem.2015.53.6.1143.   DOI
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138 Yengejeh, S.I., Kazemi, S.A. and Andreas, O. (2017), "Carbon nanotubes as reinforcement in composites: A review of the analytical, numerical and experimental approaches", Comp. Mater. Sci., 136, 85-101. https://doi.org/10.1016/j.commatsci.2017.04.023.   DOI
139 Younsi, A., Tounsi, A., Zaoui, F. Z., Bousahla, A. A., and Mahmoud, S. R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14, 519-532. https://doi.org/10.12989/gae.2018.14.6.519.   DOI