참고문헌
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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,
- 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.
- 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. https://doi.org/10.1177/0954406220916481
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.