Browse > Article
http://dx.doi.org/10.12989/anr.2021.11.1.055

Mechanical analysis of bi-functionally graded sandwich nanobeams  

Luat, Doan Trac (Department of Solid Mechanics, Le Quy Don Technical University)
Van Thom, Do (Department of Solid Mechanics, Le Quy Don Technical University)
Thanh, Tran Trung (Department of Solid Mechanics, Le Quy Don Technical University)
Van Minh, Phung (Department of Solid Mechanics, Le Quy Don Technical University)
Van Ke, Tran (Department of Solid Mechanics, Le Quy Don Technical University)
Van Vinh, Pham (Department of Solid Mechanics, Le Quy Don Technical University)
Publication Information
Advances in nano research / v.11, no.1, 2021 , pp. 55-71 More about this Journal
Abstract
In this study, the bending, free vibration and buckling analysis of a novel bi-functionally graded sandwich nanobeam are investigated for the first time via a nonlocal refined simple shear deformation theory. The novel sandwich beam consists of one ceramic core and two different functionally graded face sheets, which has a significant potential application in various fields of practical engineering and industry. The Eringen's nonlocal elastic theory has been used in cooperation with a refined simple shear deformation theory as well as Hamilton's principle to derive the equations of motion. Closed-form solution based on Navier's technique is used to solve the equations of motion of simply supported nanobeams. The present numerical results are compared with the available solutions to demonstrate the accuracy of the present theory. The influence of some parameters such as the slender ratio, the power-law index, the skin-core-skin thicknesses and the small-scale parameter on the bending, free vibration and buckling behavior of bi-functionally graded sandwich nanobeams are carried out carefully.
Keywords
bi-functionally graded sandwich beams; nanobeams; nonlocal theory; refined simple shear deformation theory; sandwich beams;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Apetre, N.A., Sankar, B.V. and Ambur, D.R. (2008), "Analytical modeling of sandwich beams with functionally graded core", J. Sandw. Struct. Mater., 10(1), 53-74. https://doi.org/10.1177/1099636207081111.   DOI
2 Arefi, M. and Zenkour, A.M. (2016), "A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermoelectric environment", J. Sandw. Struct. Mater., 18(5), 624-651. https://doi.org/10.1177/1099636216652581.   DOI
3 Aria, A.I., Rabczuk, T. and Friswell, M.I. (2019), "A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams", Eur. J. Mech. A Solid, 77, 103767. https://doi.org/10.1016/j.euromechsol.2019.04.002.   DOI
4 Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/ANR.2019.7.5.351.   DOI
5 Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A,. Tounsi, A. and Tounsi, A. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 191-208. https://doi.org/10.12989/ANR.2019.7.3.191.   DOI
6 Hadj, B., Rabia, B. and Daouadji, T.H. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 61-70. https://doi.org/10.12989/SEM.2019.72.1.061.   DOI
7 Hana, B., Adda Bedia, E.A., Amina, B. and Abdelouahed, T. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/ANR.2019.7.5.351.   DOI
8 Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Bedia, E.A.A. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/SCS.2020.34.5.643,   DOI
9 Larbi, C.F., Abdelhakim, K., Ahmed, H.M.S., Abdelouahed, T., Anwar, B.O. and Samy, R.M. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/SCS.2015.18.2.425.   DOI
10 Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/ANR.2019.7.6.431.   DOI
11 Nguyen, T.K. and Nguyen, B.D. (2015), "A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams", J. Sandw. Struct. Mater., 17(6), 613-631. https://doi.org/10.1177/1099636215589237.   DOI
12 Gao, X.L. and Zhang, G.Y., (2015), "A microstructure- and surface energy-dependent third-order shear deformation beam model", J. Appl. Math. Phys., 66, 1871-1894. https://doi.org/10.1007/s00033-014-0455-0.   DOI
13 Trinh, L.C., Vo, T.P., Osofero, A.I. and Lee, J. (2016), "Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach", Compos. Struct., 156, 263-275. https://doi.org/10.1016/j.compstruct.2015.11.010.   DOI
14 Riadh, B., Ait, A.H. and Abdelouahed, T. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/SCS.2015.19.3.521.   DOI
15 Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/SEM.2015.54.4.693.   DOI
16 Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/SSS.2020.25.2.197.   DOI
17 Mama, A., Ahmed, H.M.S., Adda, B.E.A. and Abdelouahed, T. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/SCS.2016.20.5.963.   DOI
18 Bensaid, I., Daikh, A.A. and Drai, A. (2020), "Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234(18), 3667-3688.   DOI
19 Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/GAE.2020.21.5.471.   DOI
20 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(2), 115-126. https://doi.org/10.12989/SSS.2017.19.2.115.   DOI
21 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695.   DOI
22 Ahmed, H.M.S., Aicha, B., Fabrice, B., Abdelouahed, T. and Samy, R.M. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/SCS.2018.28.1.013.   DOI
23 Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/CAC.2019.24.6.579   DOI
24 Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009.   DOI
25 Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015a), "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct., 119, 1-12. https://doi.org/10.1016/j.compstruct.2014.08.006.   DOI
26 Yang, G., Wan Shen, X. and Haiping, Z. (2019), "Nonlinear thermal buckling of bi-directional functionally graded nanobeams", Struct. Eng. Mech., 71(6), 669-682. https://doi.org/10.12989/SEM.2019.71.6.669.   DOI
27 Zine, A, Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. https://doi.org/10.12989/CAC.2020.26.1.063.   DOI
28 Aria, A.I. and Friswell, M.I. (2019), "A nonlocal finite element model for buckling and vibration of functionally graded nanobeams", Compos. Part B Eng., 166, 233-246. https://doi.org/10.1016/j.compositesb.2018.11.071.   DOI
29 Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H, Tounsi, A, Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. http://dx.doi.org/10.12989/cac.2021.27.1.073.   DOI
30 Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E.A.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/ANR.2020.8.4.293.   DOI
31 Yarasca, J., Mantari, J.L. and Arciniega, R.A. (2016), "Hermite-Lagrangian finite element formulation to study functionally graded sandwich beams", Compos. Struct., 140, 567-581. https://doi.org/10.1016/j.compstruct.2016.01.015.   DOI
32 Nguyen, T.K., Truong-Phong Nguyen, T., 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", Compos. Part B Eng., 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032.   DOI
33 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", Compos. Struct., 156, 238-252. https://doi.org/10.1016/j.compstruct.2015.11.074.   DOI
34 Yang, T., Tang, Y., Li, Q. and Yang, X.D. (2018), "Nonlinear bending, buckling and vibration of bi-directional functionally graded nanobeams", Compos. Struct., 204, 313-319. https://doi.org/10.1016/j.compstruct.2018.07.045.   DOI
35 Zhang, G.Y. and Gao, X.L., (2020), "A new Bernoulli-Euler beam model based on a reformulated strain gradient elasticity theory", Math. Mech. Solids, 25, 630-643. https://doi.org/10.1177/1081286519886003.   DOI
36 Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015b), "Static behaviour of functionally graded sandwich beams using a quasi-3D theory", Compos. Part B Eng., 68, 59-74. https://doi.org/10.1016/j.compositesb.2014.08.030.   DOI
37 Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2020), "A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., 36(3), 355-367. https://doi.org/10.12989/SCS.2020.36.3.355.   DOI
38 Osofero, A.I., Vo, T.P., Nguyen, T.K. and Lee, J. (2015), "Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories", J. Sandw. Struct. Mater., 18(1), 3-29. https://doi.org/10.1177/1099636215582217.   DOI
39 Simsek, M. (2019), "Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory", Compos. Struct., 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041.   DOI
40 Simsek, M. and Al-shujairi, M. (2017), "Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads", Compos. Part B Eng., 108, 18-34. https://doi.org/10.1016/j.compositesb.2016.09.098.   DOI
41 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", Eng. Struct., 64, 12-22. https://doi.org/10.1016/j.engstruct.2014.01.029.   DOI
42 Songsuwan, W., Pimsarn, M. and Wattanasakulpong, N. (2018), "Dynamic responses of functionally graded sandwich beams resting on elastic foundation under harmonic moving loads", Int. J. Struct. Stabil. Dyn., 18(09), 1850112. https://doi.org/10.1142/S0219455418501122.   DOI
43 Tossapanon, P. and Wattanasakulpong, N. (2016), "Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation", Compos. Struct., 142, 215-225. https://doi.org/10.1016/j.compstruct.2016.01.085.   DOI
44 Vinh, P.V. (2021), "Deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak's elastic foundations via a hybrid quasi-3D theory", Mech. Based Des. Struct., 1, 1-32. https://doi.org/10.1080/15397734.2021.1894948.   DOI
45 Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Adda Bedia, E.A. Mahmoud, S.R. and Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., 22(2), 119-132. https://doi.org/10.12989/GAE.2020.22.2.119.   DOI
46 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.   DOI
47 Liu, H., Lv, Z. and Wu, H. (2019), "Nonlinear free vibration of geometrically imperfect functionally graded sandwich nanobeams based on nonlocal strain gradient theory" Compos. Struct., 214, 47-61. https://doi.org/10.1016/j.compstruct.2019.01.090.   DOI
48 Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0.   DOI
49 Karamanli, A. (2017), "Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory", Compos. Struct., 174, 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046.   DOI
50 Li, W., Ma, H. and Gao, W. (2019), "A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams", Compos. Struct., 221, 110830. https://doi.org/10.1016/j.compstruct.2019.04.002.   DOI