Nonlinear Buckling Analysis of Different Types of Porous FG Sandwich Beams with Temperature-Dependent

Subject Areas :

Mohsen Rahmani ¹ , Younes Mohammadi ² , Mahdi Abtahi ³

1 - Department of Mechanics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran
2 - Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Received: 2023-11-11 Accepted : 2024-01-06 Published : 2024-03-26

Keywords: Porosity, FGM, Boundary Condition, High-order Sandwich Beam Theory,

Abstract :

In this paper, the nonlinear buckling behavior of two types of functionally graded sandwich beams was studied using a high-order sandwich beam theory. Type I consists of functionally graded layers coating a homogeneous core, while type II features an FG core covered by homogeneous face sheets. All materials are considered temperature dependent, with FGM properties modified through even and uneven porosity distributions modeled by a power law rule. The sandwich beam theory was adjusted to account for nonlinear Lagrange strains, thermal stresses of the face sheets, in-plane strain, and the transverse flexibility of the core. The governing equations were derived from the minimum potential energy principle, and a Galerkin method was employed to solve them for simply supported and clamped boundary conditions. Comparisons with existing literature demonstrate good agreement. The resultes showed that critical load parameter decreases with increasing temperature, power law index, length-to-thickness ratio, thickness, and porosity volume fraction in both distributions, but increases with the wave number. Additionally, the stability of type II sandwich beams surpasses that of type I in high-temperature conditions.

References:

[1] Rahmani, M., Mohammadi, Y. and Kakavand, F. 2019. Vibration analysis of sandwich truncated conical shells with porous fg face sheets in various thermal surroundings. Steel and Composite Structures. 32(2): 239-252. doi:10.12989/scs.2019.32.2.239.
[2] Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. 2020. Vibration analysis of different types of porous fg conical sandwich shells in various thermal surroundings. Journal of Applied and Computational Mechanics. 6(3): 416-432. doi:10.22055/jacm.2019.29442.1598.
[3] Frostig, Y., Baruch, M., Vilnay, O. and Sheinman, I. 1992. High-order theory for sandwich-beam behavior with transversely flexible core. Journal of Engineering Mechanics. 118(5): 1026-1043. doi:10.1061/(ASCE)0733-9399(1992)118:5(1026).
[4] Fazzolari, F.A. 2018. Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous fg sandwich beams resting on elastic foundations. Composites Part B: Engineering. 136: 254-271. doi:10.1016/j.compositesb.2017.10.022.
[5] Wu, H., Kitipornchai, S. and Yang, J. 2015. Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. International Journal of Structural Stability and Dynamics. 15(07): 1540011. doi:10.1142/S0219455415400118.
[6] Li, Y., Dong, Y., Qin, Y. and Lv, H. 2018. Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam. International Journal of Mechanical Sciences. 138: 131-145. doi:10.1016/j.ijmecsci.2018.01.041.
[7] Nguyen, T.-K., Vo, T.P., Nguyen, B.-D. and Lee, J. 2016. An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3d shear deformation theory. Composite Structures. 156: 238-252. doi:10.1016/j.compstruct.2015.11.074.
[8] Kahya, V. and Turan, M. 2018. Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element. Composites Part B: Engineering. 146: 198-212. doi:10.1016/j.compositesb.2018.04.011.
[9] Tossapanon, P. and Wattanasakulpong, N. 2016. Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation. Composite Structures. 142: 215-225. doi:10.1016/j.compstruct.2016.01.085.
[10] Nguyen, T.-K., Nguyen, T.T.-P., Vo, T.P. and Thai, H.-T. 2015. Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Composites Part B: Engineering. 76: 273-285. doi:10.1016/j.compositesb.2015.02.032.
[11] Vo, T.P., Thai, H.-T., Nguyen, T.-K., Inam, F. and Lee, J. 2015. A quasi-3d theory for vibration and buckling of functionally graded sandwich beams. Composite Structures. 119: 1-12. doi:10.1016/j.compstruct.2014.08.006.
[12] Challamel, N. and Girhammar, U.A. 2011. Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects. Engineering structures. 33(8): 2297-2319. doi:10.1016/j.engstruct.2011.04.004.
[13] Bhangale, R.K. and Ganesan, N. 2006. Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core. Journal of Sound and Vibration. 295(1-2): 294-316. doi:10.1016/j.jsv.2006.01.026.
[14] Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. 2020. Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads. Steel and Composite Structures. 34(1): 75-89. DOI: doi:10.12989/scs.2020.34.1.075.
[15] Li, C., Shen, H.-S. and Wang, H. 2019. Thermal post-buckling of sandwich beams with functionally graded negative poisson's ratio honeycomb core. International Journal of Mechanical Sciences. 152: 289-297. doi:10.1016/j.ijmecsci.2019.01.002.
[16] Liu, Y., Su, S., Huang, H. and Liang, Y. 2019. Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Composites Part B: Engineering. 168: 236-242. doi:10.1016/j.compositesb.2018.12.063.
[17] Paul, A. and Das, D. 2017. A study on non-linear post-buckling behavior of tapered timoshenko beam made of functionally graded material under in-plane thermal loadings. The Journal of Strain Analysis for Engineering Design. 52(1): 45-56. doi:10.1177/0309324716671857.
[18] Yin, Z., Gao, H. and Lin, G. 2021. An efficient semi-analytical static and free vibration analysis of laminated and sandwich beams based on linear elasticity theory. The Journal of Strain Analysis for Engineering Design.): 03093247211062688. doi:10.1177/03093247211062688.
[19] Askari, M., Brusa, E. and Delprete, C. 2021. On the vibration analysis of coupled transverse and shear piezoelectric functionally graded porous beams with higher-order theories. The Journal of Strain Analysis for Engineering Design. 56(1): 29-49. doi:10.1177/0309324720922085
[20] Fouda, N., El-Midany, T. and Sadoun, A. 2017. Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of applied and computational mechanics. 3(4): 274-282. doi:10.22055/jacm.2017.21924.1121
[21] Gao, C. F., Pan, Y.-H., Zhang, W., Rao, J. X. and Huang, Y. 2021. Buckling of two-directional functionally graded cylindrical beams based on a high-order cylindrical beam model. International Journal of Structural Stability and Dynamics. 21(7): 2150099. doi:10.1142/S0219455421500991
[22] Basaglia, C. and Camotim, D. 2015. Buckling analysis of thin-walled steel structural systems using generalized beam theory (gbt). International Journal of Structural Stability and Dynamics. 15(1):1540004. doi:10.1142/S0219455415400040
[23] Akbaş, Ş.D. 2015. On post-buckling behavior of edge cracked functionally graded beams under axial loads. International Journal of Structural Stability and Dynamics. 15(4):1450065. doi:10.1142/S0219455414500655
[24] Grygorowicz, M., Magnucki, K. and Malinowski, M. 2015. Elastic buckling of a sandwich beam with variable mechanical properties of the core. Thin-Walled Structures. 87: 127-132. doi:10.1016/j.tws.2014.11.014
[25] Ellali, M., Bouazza, M. and Amara, K. 2022. Thermal buckling of a sandwich beam attached with piezoelectric layers via the shear deformation theory. Archive of Applied Mechanics. 92(3): 657-665. doi:10.1007/s00419-021-02094-x
[26] Nejati, M., Jafari, S.S., Dimitri, R. and Tornabene, F. 2022. Thermal buckling and vibration analysis of sma hybrid composite sandwich beams. Applied Sciences. 12(18): 9323. doi:10.3390/app12189323
[27] Chai, Y., Li, F. and Zhang, C. 2022. A new method for suppressing nonlinear flutter and thermal buckling of composite lattice sandwich beams. Acta Mechanica. 233:121–136. doi:10.1007/s00707-021-03107-0
[28] Safaei, B., Onyibo, E.C. and Hurdoganoglu, D. 2022. Thermal buckling and bending analyses of carbon foam beams sandwiched by composite faces under axial compression. Facta Universitatis, Series: Mechanical Engineering. 20(3): 589-615. doi:10.22190/FUME220404027S
[29] Mesmoudi, S., Askour, O., Rammane, M., Bourihane, O., Tri, A. and Braikat, B. 2022. Spectral chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams. International Journal for Numerical Methods in Engineering. 123(24): 6111-6126. doi:10.1002/nme.7105.
[30] Eltaher, M.A. and Mohamed, S.A. 2020. Buckling and stability analysis of sandwich beams subjected to varying axial loads. Steel and Composite Structures, An International Journal. 34(2): 241-260. doi:10.12989/scs.2020.34.2.241
[31] Liu, J., He, B., Ye, W. and Yang, F. 2021. High performance model for buckling of functionally graded sandwich beams using a new semi-analytical method. Composite Structures. 262: 113614. doi:10.1016/j.compstruct.2021.113614
[32] Belarbi, M. O., Garg, A., Houari, M. S. A., Hirane, H., Tounsi, A. and Chalak, H. 2021. A three-unknown refined shear beam element model for buckling analysis of functionally graded curved sandwich beams. Engineering with Computers. 38: 273–4300 1-28. doi:10.1007/s00366-021-01452-
[33] Waddar, S., Pitchaimani, J., Doddamani, M. and Barbero, E. 2019. Buckling and vibration behaviour of syntactic foam core sandwich beam with natural fiber composite facings under axial compressive loads. Composites Part B: Engineering. 175: 107133. doi:10.1016/j.compositesb.2019.107133
[34] Rahmani, M., Mohammadi, Y. and Kakavand, F. 2020. Buckling analysis of different types of porous fg conical sandwich shells in various thermal surroundings. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 42(4): 1-16. doi:10.1007/s40430-020-2200-2
[35] Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. 2019. Buckling behavior analysis of truncated conical sandwich panel with porous fg core in different thermal conditions. Amirkabir Journal of Mechanical Engineering. 52(10): 141-150. doi: 10.22060/mej.2019.15966.6240.
[36] Rahmani, M. and Dehghanpour, S. 2020. Temperature-dependent vibration of various types of sandwich beams with porous fgm layers. International Journal of Structural Stability and Dynamics. 21(2): 2150016. doi:10.1142/S0219455421500164
[37] Kheirikhah, M., Khalili, S. and Fard, K.M. 2012. Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory. European Journal of Mechanics-A/Solids. 31(1): 54-66. doi:10.1016/j.euromechsol.2011.07.003
[38] Rahmani, M. and Mohammadi, Y. 2021. Vibration of two types of porous fg sandwich conical shell with different boundary conditions. Structural Engineering and Mechanics. 79(4): 401-413. doi:10.12989/sem.2021.79.4.401
[39] Vo, T.P., Thai, H. T., Nguyen, T. K., Maheri, A. and Lee, J. 2014. Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Engineering structures. 64: 12-22. doi:10.1016/j.engstruct.2014.01.029
[40] Reddy, J.N. 2003. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition. CRC Press.