Strain Gradient–Based Thermomechanical Nonlinear Stability Behavior of Geometrically Imperfect Porous Functionally Graded Nanoplates
Publication: Journal of Engineering Mechanics
Volume 149, Issue 7
Abstract
This paper studied the thermomechanical nonlinear stability analysis of simply supported geometrically imperfect porous functionally graded nanoplates (FG-nPs) resting on an elastic medium. The inverse trigonometric shear deformation theory was used in conjunction with the nonlocal strain gradient theory, which accounts for small-scale effects. The non-linear stability equations using the von Karman sense of the strain–displacement relation and generic imperfection function were derived for FG-nPs under thermomechanical loading conditions. The FG-nP was subjected to mechanical and thermal loading. An expression for the critical buckling load and temperature of a geometrically imperfect porous FG-nP was obtained. The impact of geometric imperfection, porosity inclusion, and geometric and boundary conditions on the nonlinear stability characteristics of FG-nPs was addressed thoroughly after validation of the superior accuracy of the derived expression.
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Data Availability Statement
All data, or models used during the study are available from the corresponding author by request.
References
Addou, F. Y., M. Meradjah, A. A. Bousahla, A. Benachour, F. Bourada, A. Tounsi, and S. R. Mahmoud. 2019. “Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT.” Comput. Concr. 24 (4): 347–367. https://doi.org/10.12989/cac.2019.24.4.347.
Adhikari, S., T. Murmu, and M. A. McCarthy. 2014. “Frequency domain analysis of nonlocal rods embedded in an elastic medium.” Physica E 59 (May): 33–40. https://doi.org/10.1016/j.physe.2013.11.001.
Aifantis, E. C. 1996. “Non-linearity, periodicity and patterning in plasticity and fracture.” Int. J. Non-Linear Mech. 31 (6): 797–809. https://doi.org/10.1016/S0020-7462(96)00107-2.
Aifantis, E. C. 2003. “Update on a class of gradient theories.” Mech. Mater. 35 (3–6): 259–280. https://doi.org/10.1016/S0167-6636(02)00278-8.
Alzahrani, E. O., A. M. Zenkour, and M. Sobhy. 2013. “Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium.” Compos. Struct. 105 (Nov): 163–172. https://doi.org/10.1016/j.compstruct.2013.04.045.
Atmane, H. A., E. A. A. Bedia, M. Bouazza, A. Tounsi, and A. Fekrar. 2016. “On the thermal buckling of simply supported rectangular plates made of a sigmoid functionally graded based material.” Mech. Solids 51 (2): 177–187. https://doi.org/10.3103/S0025654416020059.
Boroujerdy, M. S., and M. R. Eslami. 2013. “Thermal buckling of piezoelectric functionally graded material deep spherical shells.” J. Strain Anal. Eng. Des. 49 (1): 51–62. https://doi.org/10.1177/0309324713484905.
Bouazza, M. 2009. “Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings.” Multidiscip. Model. Mater. Struct. 5 (1): 59–76. https://doi.org/10.1108/MMMS-02-2015-0008.
Bouazza, M., T. Becheri, A. Boucheta, and N. Benseddiq. 2016a. “Thermal buckling analysis of nanoplates based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler–Pasternak elastic foundation.” Int. J. Comput. Methods Eng. Sci. Mech. 17 (5–6): 362–373. https://doi.org/10.1080/15502287.2016.1231239.
Bouazza, M., A. Lairedj, N. Benseddiq, and S. Khalki. 2016b. “A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates.” Mech. Res. Commun. 73 (Apr): 117–126. https://doi.org/10.1016/j.mechrescom.2016.02.015.
Bouazza, M., A. Tounsi, E. A. Adda-Bedia, and A. Megueni. 2010. “Thermoelastic stability analysis of functionally graded plates: An analytical approach.” Comput. Mater. Sci. 49 (4): 865–870. https://doi.org/10.1016/j.commatsci.2010.06.038.
Bouazza, M., A. Tounsi, E. A. Adda-Bedia, and A. Megueni. 2011. “Thermal buckling of simply supported FGM square plates.” Appl. Mech. Mater. 61 (Jun): 25–32. https://doi.org/10.4028/www.scientific.net/AMM.61.25.
Bouazza, M., and A. M. Zenkour. 2018. “Free vibration characteristics of multilayered composite plates in a hygrothermal environment via the refined hyperbolic theory.” Eur. Phys. J. Plus 133 (6): 217. https://doi.org/10.1140/epjp/i2018-12050-x.
Bouazza, M., and A. M. Zenkour. 2021. “Hygrothermal environmental effect on free vibration of laminated plates using nth-order shear deformation theory.” Waves Random Complex Medium https://doi.org/10.1080/17455030.2021.1909173.
Bouazza, M., A. M. Zenkour, and N. Benseddiq. 2018. “Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects.” Acta Mech. 229 (5): 2251–2265. https://doi.org/10.1007/s00707-017-2097-8.
Bouiadjra, M. B., M. S. Ahmed Houari, and A. Tounsi. 2012. “Thermal buckling of functionally graded plates according to a four-variable refined plate theory.” J. Therm. Stresses 35 (8): 677–694. https://doi.org/10.1080/01495739.2012.688665.
Chan, D. Q., T. Q. Quan, B. G. Phi, D. V. Hieu, and N. D. Duc. 2022. “Buckling analysis and dynamic response of FGM sandwich cylindrical panels in thermal environments using nonlocal strain gradient theory.” Acta Mech. 233 (6): 2213–2235. https://doi.org/10.1007/s00707-022-03212-8.
Ebrahimi, F., and M. Zia. 2015. “Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities.” Acta Astronaut. 116 (Nov): 117–125. https://doi.org/10.1016/j.actaastro.2015.06.014.
Eringen, A. C. 1972. “Nonlocal polar elastic continua.” Int. J. Eng. Sci. 10 (1): 1–16. https://doi.org/10.1016/0020-7225(72)90070-5.
Eringen, A. C. 1983. “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves.” J. Appl. Phys. 54 (9): 4703–4710. https://doi.org/10.1063/1.332803.
Eringen, A. C., and J. L. Wegner. 2003. “Nonlocal continuum field theories.” Appl. Mech. Rev. 56 (2): B20–B22. https://doi.org/10.1115/1.1553434.
Gupta, A., and M. Talha. 2015. “Recent development in modeling and analysis of functionally graded materials and structures.” Prog. Aerosp. Sci. 79 (Nov): 1–14. https://doi.org/10.1016/j.paerosci.2015.07.001.
Gupta, A., and M. Talha. 2017. “Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment.” Int. J. Struct. Stab. Dyn. 18 (1): 1850013. https://doi.org/10.1142/S021945541850013X.
Gupta, A., and M. Talha. 2018. “Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates.” Mech. Based Des. Struct. Mach. 46 (6): 693–711. https://doi.org/10.1080/15397734.2018.1449656.
Hamid, M. S., and S. Ashkan. 2017. “Static and dynamic pull-in instability of nano-beams resting on elastic foundation based on the nonlocal elasticity theory.” Chin. J. Mech. Eng. 30 (2): 385–397. https://doi.org/10.1007/s10033-017-0079-3.
Jalaei, M. H., and H.-T. Thai. 2019. “Dynamic stability of viscoelastic porous FG nanoplate under longitudinal magnetic field via a nonlocal strain gradient quasi-3D theory.” Composites, Part B 175 (Jul): 107164. https://doi.org/10.1016/j.compositesb.2019.107164.
Javaheri, R., and M. R. Eslami. 2002. “Buckling of functionally graded plates under in-plane compressive loading.” Z. Angew. Math. Mech. 82 (4): 277–283. https://doi.org/10.1002/1521-4001(200204)82:4%3C277::AID-ZAMM277%3E3.0.CO;2-Y.
Khorshidi, K., and A. Fallah. 2016. “Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory.” Int. J. Mech. Sci. 113 (Jul): 94–104. https://doi.org/10.1016/j.ijmecsci.2016.04.014.
Kitipornchai, S., J. Yang, and K. M. Liew. 2004. “Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections.” Int. J. Solids Struct. 41 (9–10): 2235–2257. https://doi.org/10.1016/j.ijsolstr.2003.12.019.
Koizumi, M., and M. Niino. 1995. “Overview of FGM research in Japan.” MRS Bull. 20 (1): 19–21. https://doi.org/10.1557/S0883769400048867.
Lam, D. C. C., F. Yang, A. C. M. Chong, J. Wang, and P. Tong. 2003. “Experiments and theory in strain gradient elasticity.” J. Mech. Phys. Solids 51 (8): 1477–1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
Lanhe, W. 2004. “Thermal buckling of a simply supported moderately thick rectangular FGM plate.” Compos. Struct. 64 (2): 211–218. https://doi.org/10.1016/j.compstruct.2003.08.004.
Li, M., C. Guedes Soares, and R. Yan. 2021. “Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT.” Compos. Struct. 264 (Sep): 113643. https://doi.org/10.1016/j.compstruct.2021.113643.
Lore, S., S. Sarangan, and B. N. Singh. 2021. “Nonlinear free vibration analysis of laminated composite plates and shell panels using non-polynomial higher-order shear deformation theory.” Mech. Adv. Mater. Struct. 29 (26): 5608–5623. https://doi.org/10.1080/15376494.2021.1959971.
Mechab, I., B. Mechab, S. Benaissa, B. Serier, and B. B. Bachir Bouiadjra. 2016. “Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories.” J. Braz. Soc. Mech. Sci. Eng. 38 (8): 2193–2211. https://doi.org/10.1007/s40430-015-0482-6.
Mohammadi, M., A. R. Saidi, and E. Jomehzadeh. 2010. “A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 224 (9): 1831–1841. https://doi.org/10.1243/09544062JMES1804.
Naderi, A., and A. R. Saidi. 2014. “Modified nonlocal mindlin plate theory for buckling analysis of nanoplates.” J. Nanomech. Micromech. 4 (4): 1–8. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000068.
Naj, R., M. S. Boroujerdy, and M. R. Eslami. 2008. “Thermomechanical instability of functionally graded truncated conical shells with temperature-dependent material.” J. Strain Anal. Eng. Des. 43 (4): 259–272. https://doi.org/10.1243/03093247JSA316.
Rajput, M., and A. Gupta. 2021. “Microstructure/geometric imperfection sensitivity on the thermo-mechanical nonlinear stability behavior of functionally graded plates using four variable refined structural kinematics.” J. Strain Anal. Eng. Des. 56 (7): 500–516. https://doi.org/10.1177/0309324720972874.
Samsam Shariat, B. A., and M. R. Eslami. 2006a. “Thermal buckling of imperfect functionally graded plates.” Int. J. Solids Struct. 43 (14–15): 4082–4096. https://doi.org/10.1016/j.ijsolstr.2005.04.005.
Samsam Shariat, B. A., and M. R. Eslami. 2006b. “Thermomechanical stability of imperfect functionally graded plates based on the third-order theory.” AIAA J. 44 (12): 2929–2936. https://doi.org/10.2514/1.19492.
Samsam Shariat, B. A., and M. R. Eslami. 2007. “Buckling of thick functionally graded plates under mechanical and thermal loads.” Compos. Struct. 78 (3): 433–439. https://doi.org/10.1016/j.compstruct.2005.11.001.
Samsam Shariat, B. A., and S. Eslami. 2005. “Effect of initial imperfections on thermal buckling of functionally graded plates.” J. Therm. Stresses 28 (12): 1183–1198. https://doi.org/10.1080/014957390967884.
Samsam Shariat, B. A., R. Javaheri, and M. R. Eslami. 2005. “Buckling of imperfect functionally graded plates under in-plane compressive loading.” Thin-Walled Struct. 43 (7): 1020–1036. https://doi.org/10.1016/j.tws.2005.01.002.
Shahsavari, D., B. Karami, and L. Li. 2018a. “Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model.” C.R. Mec. 346 (12): 1216–1232. https://doi.org/10.1016/j.crme.2018.08.011.
Shahsavari, D., M. Shahsavari, L. Li, and B. Karami. 2018b. “A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation.” Aerosp. Sci. Technol. 72 (Jan): 134–149. https://doi.org/10.1016/j.ast.2017.11.004.
Shahverdi, H., and M. R. Barati. 2017. “Vibration analysis of porous functionally graded nanoplates.” Int. J. Eng. Sci. 120 (Nov): 82–99. https://doi.org/10.1016/j.ijengsci.2017.06.008.
Sobhy, M. 2013. “Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions.” Compos. Struct. 99 (May): 76–87. https://doi.org/10.1016/j.compstruct.2012.11.018.
Sobhy, M., and A. F. Radwan. 2017. “A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates.” Int. J. Appl. Mech. 9 (1): 1750008. https://doi.org/10.1142/S1758825117500089.
Thai, H.-T., and S.-E. Kim. 2013. “Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation.” Int. J. Mech. Sci. 75 (Oct): 34–44. https://doi.org/10.1016/j.ijmecsci.2013.06.007.
Thai, H.-T., T. P. Vo, T.-K. Nguyen, and J. Lee. 2014. “A nonlocal sinusoidal plate model for micro/nanoscale plates.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 228 (14): 2652–2660. https://doi.org/10.1177/0954406214521391.
Thai, S., H.-T. Thai, T. P. Vo, and S. Lee. 2018. “Postbuckling analysis of functionally graded nanoplates based on nonlocal theory and isogeometric analysis.” Compos. Struct. 201 (Oct): 13–20. https://doi.org/10.1016/j.compstruct.2018.05.116.
Tounsi, A., M. Bouazza, and E. Adda-Bedia. 2004. “Computation of transient hygroscopic stresses in unidirectional laminated composite plates with cyclic and asymmetrical environmental conditions.” Int. J. Mech. Mater. Des. 1 (3): 271–286. https://doi.org/10.1007/s10999-005-0222-7.
Tounsi, A., M. Bouazza, S. Meftah, and E. Adda-Bedia. 2005. “On the transient hygroscopic stresses in polymer matrix laminated composites plates with cyclic and unsymmetric environmental conditions.” Polym. Polym. Compos. 13 (5): 489–503. https://doi.org/10.1177/096739110501300506.
Van Thom, D., A. M. Zenkour, and D. Hong Doan. 2021. “Buckling of cracked FG plate resting on elastic foundation considering the effect of delamination phenomenon.” Compos. Struct. 273 (Oct): 114278. https://doi.org/10.1016/j.compstruct.2021.114278.
Xu, Y. P., and D. Zhou. 2009. “Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports.” J. Strain Anal. Eng. Des. 44 (4): 249–261. https://doi.org/10.1243/03093247JSA504.
Zargaripoor, A., A. Daneshmehr, I. I. Hosseini, and A. Rajabpoor. 2018. “Free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory using finite element method.” J. Comput. Appl. Mech. 49 (1): 86–101. https://doi.org/10.22059/jcamech.2018.248906.223.
Zenkour, A. M., and M. Sobhy. 2013. “Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium.” Physica E 53 (Sep): 251–259. https://doi.org/10.1016/j.physe.2013.04.022.
Zhang, J., S. Pan, and L. Chen. 2019. “Dynamic thermal buckling and postbuckling of clamped–clamped imperfect functionally graded annular plates.” Nonlinear Dyn. 95 (1): 565–577. https://doi.org/10.1007/s11071-018-4583-5.
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Journal of Engineering Mechanics
Volume 149 • Issue 7 • July 2023
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© 2023 American Society of Civil Engineers.
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Received: Aug 11, 2022
Accepted: Feb 18, 2023
Published online: Apr 26, 2023
Published in print: Jul 1, 2023
Discussion open until: Sep 26, 2023
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