Abstract
In this work, analytical solutions are presented for the thermodynamic behavior of bidirectional functionally graded (BDFG) porous beam lying on different supports by the mean of a quasi-3D shear deformation theory. The beams are composed of two distinct materials, and the material properties are expected to be smooth varying in both length and thickness direction according to a simple power law. The beams are supposed to be simply supported and lying on various types of foundations such Winkler, Pasternak, Variable, Kerr, and viscoelastic. The governing equations are found analytically by the mean of the presented quasi-3D model, and then, Navier’s method is used to obtain the different solutions. The impact of the characteristics of various factors like the grading indexes and type of foundation, porosity on the displacements, and stresses of the BDFG beam lying on elastic foundation is discussed in detail.
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References
Abouelregal AE, Mohammad-Sedighi H, Faghidian SA, Shirazi AH (2021) Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load. Facta Univ Series: Mech Eng 19(4):633–56. https://doi.org/10.22190/FUME201222024A
Akbaş ŞD (2017) Post-buckling responses of functionally graded beams with porosities. Steel Comp Struct 24(5):579–589. https://doi.org/10.12989/scs.2017.24.5.579
Akbaş ŞD (2018) Forced vibration analysis of functionally graded porous deep beams. Compos Struct 186:293–302. https://doi.org/10.1016/j.compstruct.2017.12.013
Attia A, Bousahla AA, Tounsi A, Mahmoud SR, Alwabli S (2018) A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundation. Struct Eng Mech 65(4):453–464. https://doi.org/10.12989/sem.2018.65.4.453
Avcar M (2019) Free vibration of imperfect sigmoid and power law functionally graded beams. Steel Comp Struct 30(6):603–615. https://doi.org/10.12989/scs.2019.30.6.603
Avcar M, Mohammed WKM (2018) Free vibration of functionally graded beams resting on Winkler-Pasternak foundation. Arab J Geosci 11:232. https://doi.org/10.1007/s12517-018-3579-2
Babaei H, Eslami MR, Khorshidvand AR (2020) Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane. J Therm Stress 43(1):109–131. https://doi.org/10.1080/01495739.2019.1660600
Chen D, Yang J, Kitipornchai S (2016a) Free and forced vibrations of shear deformable functionally graded porous beams. Int J Mech Sci 108:14–22. https://doi.org/10.1016/j.ijmecsci.2016.01.025
Chen D, Kitipornchai S, Yang J (2016b) Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Struct 107:39–48. https://doi.org/10.1016/j.tws.2016.05.025
Ebrahimi F, Mahmoodi F, Reza Barati M (2017) Thermo-mechanical vibration analysis of functionally graded micro/nanoscale beams with porosities based on modified couple stress theory. Adv Mater Res 6(3):279–301. https://doi.org/10.12989/amr.2017.6.3.279
Ebrahimi F, Jafari A, Selvamani R (2020) Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment. Adv Nano Res 8(1):83. https://doi.org/10.12989/anr.2020.8.1.083
Ebrahimi F and Jafari A (2016) A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities. J Eng 2016.https://doi.org/10.1155/2016/9561504
Eltaher MA, Fouda N, El-midany T, Sadoun AM (2018) Modified porosity model in analysis of functionally graded porous nanobeams. J Braz Soc Mech Sci Eng 40(3):141. https://doi.org/10.1007/s40430-018-1065-0
Fazzolari FA (2018) Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations. Compos B Eng 136:254–271. https://doi.org/10.1016/j.compositesb.2017.10.022
Gafour Y, Hamidi A, Benahmed A, Zidour M, Bensattalah T (2020) Porosity-dependent free analysis of FG non-local shear deformation and energy principal. Adv Nano Res 8(1):49–58. https://doi.org/10.12989/anr.2020.8.1.04
Gao K, Huang Q, Kitipornchai S, Yang J (2021) Nonlinear dynamic buckling of functionally graded porous beams. Mech Adv Mater Struct 28(4):418–429. https://doi.org/10.1080/15376494.2019.1567888
Ghayesh MH (2019) Resonant dynamics of axially functionally graded imperfect tapered Timoshenko beam. J Vib Control 25(2):336–350. https://doi.org/10.1177/1077546318777591
Hadji L, Avcar M (2021) Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory. Adv Nano Res 10(3):281–293. https://doi.org/10.12989/anr.2021.10.3.281
Hamed MA, Abo-bakr RM, Mohamed SA, Eltaher MA (2020) Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core. Eng Comp 36:1929–1946. https://doi.org/10.1007/s00366-020-01023-w
Hashemi SH, Mehrabani H, Savadkoohi AA (2015) Exact solution for free vibration of coupled double viscoelastic graphene sheets by visco Pasternak medium. Compos Part B 78:377–383. https://doi.org/10.1016/j.compositesb.2015.04.008
He CH, Liu C, He JH, Mohammad-Sedighi H, Shokri A, Gepreel KA (2022) A fractal model for the internal temperature response of a porous concrete. Appl Comput Math 21(1):71–77. https://doi.org/10.30546/1683-6154.21.1.2022.71
Hieu DV, Chan DQ, Mohammad-Sedighi H (2021) Nonlinear bending, buckling and vibration of functionally graded nonlocal strain gradient nanobeams resting on an elastic foundation. J Mech Mater Struct 16(3):327–346. https://doi.org/10.2140/jomms.2021.16.327
Jena SK, Chakraverty S, Malikan M, Mohammad-Sedighi H (2020) Implementation of Hermite-Ritz method and Navier’s technique for vibration of functionally graded porous nanobeam embedded in Winkler-Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity. J Mech Mater Struct 15(3):405–434. https://doi.org/10.2140/jomms.2020.15.405
Jouneghani FZ, Dimitri R, Tornabene F (2018) Structural response of porous FG nanobeams under hygro-thermomechanical loadings. Compos B Eng 152:71–78. https://doi.org/10.1016/j.compositesb.2018.06.023
Liu Y, Su S, Huang H, Liang Y (2019) Thermal mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Compos B 168:236–242. https://doi.org/10.1016/j.compositesb.2018.12.063
Meksi A, Benyoucef S, Sekkal M, BachirBouiadjra R, Selim MM, Tounsi A, Muzamal H (2021) Influence of micromechanical models on the bending response of bidirectional FG beams under linear, uniform, exponential and sinusoidal distributed loading. Steel Comp Struct 39(2):215–228. https://doi.org/10.12989/scs.2021.39.2.215
Merzoug M, Bourada M, Sekkal M, Ali Chaibdra A, Belmokhtar C, Benyoucef S, Benachour A (2020) 2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models. Geomech Eng 22(4):361–374. https://doi.org/10.12989/gae.2020.22.4.361
Nebbab M, Ait Atmane H, Bennai R, Tounsi A (2019) Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation. Arab J Geosci 12:809. https://doi.org/10.1007/s12517-019-4871-5
Penna R, Feo L, Lovisi G (2021) Hygro-thermal bending behavior of porous FG nano-beams via local/nonlocal strain and stress gradient theories of elasticity. Compos Struct 263:113627. https://doi.org/10.1016/j.compstruct.2021.113627
Pradhan SC, Murmu T (2009) Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method. J Sound Vibr 321:342–362. https://doi.org/10.1016/j.jsv.2008.09.018
Shahsavari D, Shahsavari M, Li L, Karami B (2018) A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerosp Sci Tech 72:134–149. https://doi.org/10.1016/j.ast.2017.11.004
She G-L, Liu H-B, Karami B (2020) On resonance behavior of porous FG curved nanobeams. Steel Comp Struct 36(2):179–186. https://doi.org/10.12989/scs.2020.36.2.179
Sobhy M (2015) Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations. J Appl Mech 7(6):1550082. https://doi.org/10.1142/S1758825115500829
Tang H, Li L, Hu Y (2018) Buckling analysis of two-directionally porous beam. Aerosp Sci Technol 78:471–479. https://doi.org/10.1016/j.ast.2018.04.045
Tlidji Y, Benferhat R, HassaineDaouadji T (2021) Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity. Struct Eng Mech 77(2):217–229. https://doi.org/10.12989/sem.2021.77.2.217
Trinh LC, Vo TP, Thai HT, Nguyen TK (2018) Size-dependent vibration of bi-directional functionally graded micro-beams with arbitrary boundary conditions. Compos Part B Eng 134:225–245. https://doi.org/10.1016/j.compositesb.2017.09.054
Winkler E (1867) Die Lehre von Elastizitat und Festigkeit (on Elasticity and Fixity). Dominicus, Prague
Wu D, Liu A, Huang Y, Huang Y, Pi Y, Gao W (2018) Dynamic analysis of functionally graded porous structures through finite element analysis. Eng Struct 165:287–301. https://doi.org/10.1016/j.engstruct.2018.03.023
Younesian D, Hosseinkhani A, Askari E, E, (2019) Elastic and viscoelastic foundations: review on linear and nonlinear vibration modeling and applications. Nonlinear Dyn 97:853–895. https://doi.org/10.1007/s11071-019-04977-9
Zghal S and Dammak F (2020) Vibrational behavior of beams made of functionally graded materials by using a mixed formulation. Proc I Mech E Part C: J Mechanical Engineering Science.https://doi.org/10.1177/0954406220916533 In press
Zghal S, Ataoui D and Dammak F (2020) Static bending analysis of beams made of functionally graded porous materials. Mech Based Des Struct Mach 1-18. https://doi.org/10.1080/15397734.2020.1748053
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Charef, T., Bachir Bouiadjra, R., Sekkal, M. et al. Assessing the impact of different foundations on the thermodynamic response of bidirectional FG porous beams. Arab J Geosci 16, 48 (2023). https://doi.org/10.1007/s12517-022-11138-7
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DOI: https://doi.org/10.1007/s12517-022-11138-7