Abstract
The present investigation involved the modeling and analysis of the thermomechanical buckling behavior of sandwich nanoplates with foam core layers. The study employed the utilization of the new higher order deformation theory and nonlocal strain gradient elasticity theory. The modeling of foam core involves separate consideration of uniform and symmetric open cell foam distribution types, while the face plates are predicted to exhibit FGM and isotropic layers. A total of six sandwich plate types were modeled and analyzed. The thermomechanical buckling behavior of sandwich nanoplates is significantly influenced by the sandwich type, volumetric foam ratio of the core layer, and its distribution along the foam core height, as demonstrated in prior analyses. The study revealed that the incorporation of foam structure resulted in an elevation of the buckling temperature during the thermo-mechanical response of the nanoplate. At low temperatures, the uniform foam model had lesser thermal buckling than the symmetrical foam model. However, this trend changed after reaching ΔT = 350–360 K levels. The study is expected to yield significant insights into the development and application of nanosensors, transducers, and nanoelectro mechanical systems that are designed to operate in high-temperature settings.
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References
Sobczak, J.J., Drenchev, L.: Metallic functionally graded materials: a specific class of advanced composites. J. Mater. Sci. Technol. 29, 297–316 (2013). https://doi.org/10.1016/j.jmst.2013.02.006
Swaminathan, K., Sangeetha, D.M.: Thermal analysis of fgm plates—a critical review of various modelling techniques and solution methods. Compos. Struct. (2016). https://doi.org/10.1016/j.compstruct.2016.10.047
Garg, A., Belarbi, M.O., Chalak, H.D., Chakrabarti, A.: A review of the analysis of sandwich FGM structures. Compos. Struct. 258, 113427 (2021). https://doi.org/10.1016/j.compstruct.2020.113427
Naebe, M., Shirvanimoghaddam, K.: Functionally graded materials: a review of fabrication and properties. Appl. Mater. Today 5, 223–245 (2016). https://doi.org/10.1016/j.apmt.2016.10.001
Li, Y., Feng, Z., Hao, L., Huang, L., Xin, C., Wang, Y., Bilotti, E., Essa, K., Zhang, H., Li, Z., Yan, F., Peijs, T.: A review on functionally graded materials and structures via additive manufacturing: from multi-scale design to versatile functional properties. Adv. Mater. Technol. (2020). https://doi.org/10.1002/admt.201900981
Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A., Mahmoud, S.: Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory. J. Sandw. Struct. Mater. 23, 814–851 (2021). https://doi.org/10.1177/1099636219845841
Kawasaki, A., Watanabe, R.: Concept and P/M fabrication of functionally gradient materials. Ceram. Int. 23, 73–83 (1997). https://doi.org/10.1016/0272-8842(95)00143-3
Barretta, R., Feo, L., Luciano, R., Marotti de Sciarra, F., Penna, R.: Functionally graded Timoshenko nanobeams: a novel nonlocal gradient formulation. Compos. Part B Eng. 100, 208–219 (2016). https://doi.org/10.1016/j.compositesb.2016.05.052
Li, Y., Li, D., Huang, B.-Z.: Effects of parameters on postbuckling failure of composite sandwich panels loaded axially: function form and applications. J. Sandw. Struct. Mater. (2023). https://doi.org/10.1177/10996362231181530
Journal, A.I., Akbari, H., Azadi, M., Fahham, H.: Free vibration analysis of thick sandwich cylindrical panels with saturated FG-porous core. Mech. Based Des. Struct. Mach. 50, 1268–1286 (2022). https://doi.org/10.1080/15397734.2020.1748051
Kumar, R., Lal, A., Sutaria, B.M.: Free vibration of porous functionally graded sandwich plates with hole. J. Vib. Eng. Technol. (2022). https://doi.org/10.1007/s42417-022-00810-7
Ke, L.L., Wang, Y.S., Wang, Z.D.: Thermal effect on free vibration and buckling of size-dependent microbeams. Phys. E Low-Dimens. Syst. Nanostruct. 43, 1387–1393 (2011). https://doi.org/10.1016/j.physe.2011.03.009
Esen, I.: Dynamics of size-dependant Timoshenko micro beams subjected to moving loads. Int. J. Mech. Sci. 175, 105501 (2020). https://doi.org/10.1016/j.ijmecsci.2020.105501
Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal. (1962). https://doi.org/10.1007/BF00253946
Eringen, A.C., Edelen, D.G.B.: On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248 (1972). https://doi.org/10.1016/0020-7225(72)90039-0
Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. (1983). https://doi.org/10.1063/1.332803
Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972). https://doi.org/10.1016/0020-7225(72)90070-5
Mechab, B., Mechab, I., Benaissa, S., Ameri, M., Serier, B.: Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations. Appl. Math. Model. 40, 738–749 (2016). https://doi.org/10.1016/j.apm.2015.09.093
Li, L., Hu, Y., Ling, L.: Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos. Struct. 133, 1079–1092 (2015). https://doi.org/10.1016/j.compstruct.2015.08.014
Esen, I., Daikh, A.A., Eltaher, M.A.: Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load. Eur. Phys. J. Plus (2021). https://doi.org/10.1140/epjp/s13360-021-01419-7
Arefi, M., Zenkour, A.M.: Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation. Mech. Res. Commun. 79, 51–62 (2017). https://doi.org/10.1016/j.mechrescom.2017.01.004
Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. (2002). https://doi.org/10.1016/S0020-7683(02)00152-X
Eltaher, M.A., Abdelrahman, A.A., Esen, I.: Dynamic analysis of nanoscale Timoshenko CNTs based on doublet mechanics under moving load. Eur. Phys. J. Plus 136, 1–21 (2021). https://doi.org/10.1140/epjp/s13360-021-01682-8
Eringen, A.C.: Theories of nonlocal plasticity. Int. J. Eng. Sci. (1983). https://doi.org/10.1016/0020-7225(83)90058-7
Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A., Mahmoud, S.: A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations. J. Sandw. Struct. Mater. 21, 1906–1929 (2019). https://doi.org/10.1177/1099636217727577
Lal, R., Dangi, C.: Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen’s nonlocal theory incorporating the surface effect. Appl. Math. Comput. 395, 125857 (2021). https://doi.org/10.1016/j.amc.2020.125857
Liu, H., Lyu, Z.: Modeling of novel nanoscale mass sensor made of smart FG magneto-electro-elastic nanofilm integrated with graphene layers. Thin-Walled Struct. 151, 106749 (2020). https://doi.org/10.1016/j.tws.2020.106749
Qi, Y.N., Dai, H.L., Deng, S.T.: Thermoelastic analysis of stiffened sandwich doubly curved plate with FGM core under low velocity impact. Compos. Struct. 253, 112826 (2020). https://doi.org/10.1016/j.compstruct.2020.112826
Adhikari, B., Dash, P., Singh, B.N.: Buckling analysis of porous FGM sandwich plates under various types nonuniform edge compression based on higher order shear deformation theory. Compos. Struct. 251, 112597 (2020). https://doi.org/10.1016/j.compstruct.2020.112597
Singh, S.J., Harsha, S.P.: Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov’s method: a semi-analytical approach. Thin-Walled Struct. 150, 106668 (2020). https://doi.org/10.1016/j.tws.2020.106668
Van Long, N., Thinh, T.I., Bich, D.H., Tu, T.M.: Nonlinear dynamic responses of sandwich-FGM doubly curved shallow shells subjected to underwater explosions using first-order shear deformation theory. Ocean Eng. 260, 111886 (2022). https://doi.org/10.1016/j.oceaneng.2022.111886
Liang, C., Wang, Y.Q.: A quasi-3D trigonometric shear deformation theory for wave propagation analysis of FGM sandwich plates with porosities resting on viscoelastic foundation. Compos. Struct. 247, 112478 (2020). https://doi.org/10.1016/j.compstruct.2020.112478
Shinde, B.M., Sayyad, A.S.: A new higher order shear and normal deformation theory for FGM sandwich shells. Compos. Struct. 280, 114865 (2022). https://doi.org/10.1016/j.compstruct.2021.114865
Liang, C., Yaw, Z., Lim, C.W.: Thermal strain energy induced wave propagation for imperfect FGM sandwich cylindrical shells. Compos. Struct. 303, 116295 (2023). https://doi.org/10.1016/j.compstruct.2022.116295
Belkhodja, Y., El Amine Belkhodja, M., Fekirini, H., Ouinas, D.: New quasi-three-, and two-dimensional trigonometric-cubic monomial HSDT for thermal buckling and thermo-mechanical bending analyses of FGM symmetrical/non-symmetrical sandwich plates with hard/soft core. Compos. Struct. 304, 116402 (2023). https://doi.org/10.1016/j.compstruct.2022.116402
Katili, I., Batoz, J.L., Bouabdallah, S., Maknun, I.J., Katili, A.M.: Discrete shear projection method for mechanical buckling analysis of FGM sandwich plates. Compos. Struct. 312, 116825 (2023). https://doi.org/10.1016/j.compstruct.2023.116825
Karakoti, A., Pandey, S., Kar, V.R.: Nonlinear transient analysis of porous P-FGM and S-FGM sandwich plates and shell panels under blast loading and thermal environment. Thin-Walled Struct. 173, 108985 (2022). https://doi.org/10.1016/j.tws.2022.108985
Sayyad, A.S., Ghugal, Y.M., Kant, T.: Higher-order static and free vibration analysis of doubly-curved FGM sandwich shallow shells. Forces Mech. 11, 100194 (2023). https://doi.org/10.1016/j.finmec.2023.100194
Singh, S.J., Harsha, S.P.: Nonlinear dynamic analysis of sandwich S-FGM plate resting on Pasternak foundation under thermal environment. Eur. J. Mech. A/Solids 76, 155–179 (2019). https://doi.org/10.1016/j.euromechsol.2019.04.005
Liu, B.L., Li, S., Li, Y.S.: Bending of FGM sandwich plates with tunable auxetic core using DQM. Eur. J. Mech. A/Solids (2023). https://doi.org/10.1016/j.euromechsol.2022.104838
Zhao, W., Guo, D., Gong, X., Li, C.: Nonlinear axisymmetric buckling analysis of the FGM sandwich shallow spherical shells under thermomechanical loads. Eur. J. Mech. A/Solids 97, 104841 (2023). https://doi.org/10.1016/j.euromechsol.2022.104841
Tomar, S.S., Talha, M.: Influence of material uncertainties on vibration and bending behaviour of skewed sandwich FGM plates. Compos. Part B Eng. 163, 779–793 (2019). https://doi.org/10.1016/j.compositesb.2019.01.035
Singh, D., Gupta, A.: Influence of geometric imperfections on the free vibrational response of the functionally graded material sandwich plates with circular cut-outs. Mater. Today Proc. 62, 1496–1499 (2022). https://doi.org/10.1016/j.matpr.2022.02.187
Sahoo, B., Sharma, N., Sahoo, B., Malhari Ramteke, P., Kumar Panda, S., Mahmoud, S.R.: Nonlinear vibration analysis of FGM sandwich structure under thermal loadings. Structures 44, 1392–1402 (2022). https://doi.org/10.1016/j.istruc.2022.08.081
Al-Osta, M.A.: An efficient model for wave propagation of temperature-dependent E-FGM plates resting on viscoelastic foundation. Mater. Today Commun. 35, 105784 (2023). https://doi.org/10.1016/j.mtcomm.2023.105784
Alipour, M.M., Shariyat, M.: Nonlocal zigzag analytical solution for Laplacian hygrothermal stress analysis of annular sandwich macro/nanoplates with poor adhesions and 2D-FGM porous cores. Arch. Civ. Mech. Eng. 19, 1211–1234 (2019). https://doi.org/10.1016/j.acme.2019.06.008
Ebrahimi, F., Farazmandnia, N., Kokaba, M.R., Mahesh, V.: Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory. Eng. Comput. 37, 921–936 (2021). https://doi.org/10.1007/s00366-019-00864-4
Hirane, H., Belarbi, M.O., Houari, M.S.A., Tounsi, A.: On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Eng. Comput. 38, 3871–3899 (2022). https://doi.org/10.1007/s00366-020-01250-1
Zaitoun, M.W., Chikh, A., Tounsi, A., Sharif, A., Al-Osta, M.A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01498-1
Sahoo, B., Mehar, K., Sahoo, B., Sharma, N., Panda, S.K.: Thermal post-buckling analysis of graded sandwich curved structures under variable thermal loadings. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01514-4
Abdoun, F., Azrar, L.: Nonlinear thermal analysis of multilayered composite and FGM plates with temperature-dependent properties based on an asymptotic numerical method. Arch. Appl. Mech. 91, 4361–4387 (2021). https://doi.org/10.1007/s00419-021-01999-x
Singh, B.N., Ranjan, V., Hota, R.N.: Vibroacoustic response from thin exponential functionally graded plates. Arch. Appl. Mech. 92, 2095–2118 (2022). https://doi.org/10.1007/s00419-022-02163-9
Joseph, S.V., Mohanty, S.C.: Free vibration and parametric instability of viscoelastic sandwich plates with functionally graded material constraining layer. Acta Mech. 230, 2783–2798 (2019). https://doi.org/10.1007/s00707-019-02433-8
Chan, D.Q., Quan, T.Q., Phi, B.G., Van Hieu, D., Duc, N.D.: Buckling analysis and dynamic response of FGM sandwich cylindrical panels in thermal environments using nonlocal strain gradient theory. Acta Mech. 233, 2213–2235 (2022). https://doi.org/10.1007/s00707-022-03212-8
Chaabani, H., Mesmoudi, S., Boutahar, L., El Bikri, K.: A high-order continuation for bifurcation analysis of functionally graded material sandwich plates. Acta Mech. 233, 2125–2147 (2022). https://doi.org/10.1007/s00707-022-03216-4
Mirzavand Borojeni, B., Shams, S., Kazemi, M.R., Rokn-Abadi, M.: Effect of temperature and magnetoelastic loads on the free vibration of a sandwich beam with magnetorheological core and functionally graded material constraining layer. Acta Mech. 233, 4939–4959 (2022). https://doi.org/10.1007/s00707-022-03316-1
Chaabani, H., Mesmoudi, S., Boutahar, L., Bikri, K.E.: Buckling of porous FG sandwich plates subjected to various non-uniform compressions and resting on Winkler-Pasternak elastic foundation using a finite element model based on the high-order shear deformation theory. Acta Mech. 233, 5359–5376 (2022). https://doi.org/10.1007/s00707-022-03388-z
Xiao, J., Wang, J.: Nonlinear vibration of FGM sandwich nanoplates with surface effects. Acta Mech. Solida Sin. (2022). https://doi.org/10.1007/s10338-022-00371-y
Karroubi, R., Irani-Rahaghi, M.: Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis. Appl. Math. Mech. 40, 563–578 (2019). https://doi.org/10.1007/s10483-019-2469-8
Liu, Y., Qin, Z., Chu, F.: Nonlinear forced vibrations of functionally graded piezoelectric cylindrical shells under electric-thermo-mechanical loads. Int. J. Mech. Sci. 201, 106474 (2021). https://doi.org/10.1016/j.ijmecsci.2021.106474
Liu, Y., Qin, Z., Chu, F.: Nonlinear forced vibrations of FGM sandwich cylindrical shells with porosities on an elastic substrate. Nonlinear Dyn. 104, 1007–1021 (2021). https://doi.org/10.1007/s11071-021-06358-7
Li, H., Liu, Y., Zhang, H., Qin, Z., Wang, Z., Deng, Y., Xiong, J., Wang, X., Kyu Ha, S.: Amplitude-dependent damping characteristics of all-composite sandwich plates with a foam-filled hexagon honeycomb core. Mech. Syst. Signal Process. 186, 109845 (2023). https://doi.org/10.1016/j.ymssp.2022.109845
Singh, S.J., Harsha, S.P.: Thermal buckling of porous symmetric and non-symmetric sandwich plate with homogenous core and S-FGM face sheets resting on Pasternak foundation. Int. J. Mech. Mater. Des. 16, 707–731 (2020). https://doi.org/10.1007/s10999-020-09498-7
Chedad, A., Elmeiche, N., Hamzi, S., Abbad, H.: Effect of porosity on the thermal buckling of functionally graded material (FGM) sandwich plates under different boundary conditions. Mech. Based Des. Struct. Mach. (2022). https://doi.org/10.1080/15397734.2022.2148691
Mahdavi, S., Shaterzadeh, A., Jafari, M.: Determination of optimum effective parameters on thermal buckling of hybrid composite plates with quasi-square cut-out using a genetic algorithm. Eng. Optim. (2020). https://doi.org/10.1080/0305215X.2019.1575965
Journal, A.I., Mehditabar, A., Sadrabadi, S.A., Walker, J.: Thermal buckling analysis of a functionally graded microshell based on higher-order shear deformation and modified couple stress theories. Mech. Based Des. Struct. Mach. (2023). https://doi.org/10.1080/15397734.2021.1908145
Shaterzadeh, A.R., Rezaei, R., Abolghasemi, S.: Thermal buckling analysis of perforated functionally graded plates. J. Therm. Stress. 38(11), 1248–1266 (2015). https://doi.org/10.1080/01495739.2015.1073525
Hu, X., Yuan, W., Song, H.: Theoretical analysis on the thermal buckling behavior of material-filled truss-core sandwich plates with various boundary conditions. J. Therm. Stress. 45, 81–99 (2022). https://doi.org/10.1080/01495739.2021.2006102
Huang, H., Rao, D.: Thermal buckling of functionally graded cylindrical shells with temperature-dependent elastoplastic properties. Contin. Mech. Thermodyn. 32, 1403–1415 (2020). https://doi.org/10.1007/s00161-019-00854-3
Li, Y.S., Liu, B.L.: Thermal buckling and free vibration of viscoelastic functionally graded sandwich shells with tunable auxetic honeycomb core. Appl. Math. Modell. 108, 685–700 (2022). https://doi.org/10.1016/j.apm.2022.04.019
Markworth, A.J., Ramesh, K.S., JW, P.: Modelling studies applied to functionally graded materials. J. Mater. Sci. 30, 2183–2193 (1995)
Mahmoudi, A., Bachir Bouiadjra, R., Benyoucef, S., Selim, M.M., Tounsi, A., Hussain, M.: Analytical investigation of wave propagation in bidirectional FG sandwich porous plates lying on an elastic substrate. Waves Random Complex Media 33, 202–224 (2023). https://doi.org/10.1080/17455030.2022.2038814
Özmen, R., Kılıç, R., Esen, I.: Thermomechanical vibration and buckling response of nonlocal strain gradient porous FG nanobeams subjected to magnetic and thermal. Mech. Adv. Mater. Struct. (2022). https://doi.org/10.1080/15376494.2022.2124000
Abdelmola, F., Carlsson, L.A.: State of water in void-free and void-containing epoxy specimens. J. Reinf. Plast. Compos. 38, 556–566 (2019). https://doi.org/10.1177/0731684419833469
Touloukian, Y.S.: Thermophysical Properties of High Temperature Solid Materials. Macmillan, New York (1967)
Touloukian, Y.S.: Thermophysical Properties of High Temperature Solid Materials 4 Oxides and Their Solutions and Mixtures. Macmillan, New York (1966)
Kiani, Y., Eslami, M.R.: An exact solution for thermal buckling of annular FGM plates on an elastic medium. Compos. Part B Eng. 45, 101–110 (2013). https://doi.org/10.1016/j.compositesb.2012.09.034
Zhang, D.G.: Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Meccanica 49, 283–293 (2014). https://doi.org/10.1007/s11012-013-9793-9
Lim, C.W., Zhang, G., Reddy, J.N.: A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids (2015). https://doi.org/10.1016/j.jmps.2015.02.001
Saseendran, V., Carlsson, L.A., Berggreen, C.: Shear and foundation effects on crack root rotation and mode-mixity in moment- and force-loaded single cantilever beam sandwich specimen. J. Compos. Mater. 52, 2537–2547 (2018). https://doi.org/10.1177/0021998317749714
Bouhadra, A., Benyoucef, S., Tounsi, A., Bernard, F., Bouiadjra, R.B., Houari, M.S.A.: Thermal buckling response of functionally graded plates with clamped boundary conditions. J. Therm. Stress. 38, 630–650 (2015). https://doi.org/10.1080/01495739.2015.1015900
Zenkour, A.M., Sobhy, M.: Thermal buckling of various types of FGM sandwich plates. Compos. Struct. 93, 93–102 (2010). https://doi.org/10.1016/j.compstruct.2010.06.012
Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000). https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3%3c663::AID-NME787%3e3.0.CO;2-8
Mouthanna, A., Bakhy, S.H., Al-Waily, M.: Analytical investigation of nonlinear free vibration of porous eccentrically stiffened functionally graded sandwich cylindrical shell panels. Iran. J. Sci. Technol. Trans. Mech. Eng. (2022). https://doi.org/10.1007/s40997-022-00555-4
Liu, Y., Wang, J., Hu, J., Qin, Z., Chu, F.: Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields. Appl. Math. Mech. 43, 1543–1554 (2022). https://doi.org/10.1007/s10483-022-2904-9
Mekerbi, M., Benyoucef, S., Mahmoudi, A., Tounsi, A., Bousahla, A.A., Mahmoud, S.R.: Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions. J. Sandw. Struct. Mater. 23, 1028–1057 (2021). https://doi.org/10.1177/1099636219851281
Sobhy, M.: Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Compos. Struct. 99, 76–87 (2013). https://doi.org/10.1016/j.compstruct.2012.11.018
Duc, N.D., Lee, J., Nguyen-Thoi, T., Thang, P.T.: Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations. Aerosp. Sci. Technol. 68, 391–402 (2017). https://doi.org/10.1016/j.ast.2017.05.032
Radwan, A.F.: Effects of non-linear hygrothermal conditions on the buckling of FG sandwich plates resting on elastic foundations using a hyperbolic shear deformation theory. J. Sandw. Struct. Mater. 21, 289–319 (2019). https://doi.org/10.1177/1099636217693557
Esen, I., Abdelrhmaan, A.A., Eltaher, M.A.: Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields. Eng. Comput. 38, 3463–3482 (2022). https://doi.org/10.1007/s00366-021-01389-5
Daikh, A.A., Houari, M.S.A., Tounsi, A.: Buckling analysis of porous FGM sandwich nanoplates due to heat conduction via nonlocal strain gradient theory. Eng. Res. Express (2019). https://doi.org/10.1088/2631-8695/ab38f9
Esen, I., Özmen, R.: Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity. Compos. Struct. (2022). https://doi.org/10.1016/j.compstruct.2022.115878
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Yıldız, T., Esen, I. Effect of foam structure on thermo-mechanical buckling of foam core sandwich nanoplates with layered face plates made of functionally graded material (FGM). Acta Mech 234, 6407–6437 (2023). https://doi.org/10.1007/s00707-023-03722-z
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DOI: https://doi.org/10.1007/s00707-023-03722-z