Analytical solution for bending analysis of functionally graded beam |
Sallai, Benoumrane
(Laboratoire des Materiaux & Hydrologie, Universite de Sidi Bel Abbes)
Hadji, Lazreg (Laboratoire des Materiaux & Hydrologie, Universite de Sidi Bel Abbes) Daouadji, T. Hassaine (Laboratoire des Materiaux & Hydrologie, Universite de Sidi Bel Abbes) Adda Bedia, E.A. (Laboratoire des Materiaux & Hydrologie, Universite de Sidi Bel Abbes) |
1 | Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., Int. J., 48(3), 351-365. DOI |
2 | Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. DOI |
3 | Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013) "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. DOI ScienceOn |
4 | Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. DOI |
5 | Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Method., 11(6), 1350082. DOI |
6 | Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81. DOI |
7 | El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. DOI ScienceOn |
8 | Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. DOI |
9 | Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., Int. J., 16(5), 507-519. DOI |
10 | Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253. DOI |
11 | Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. DOI |
12 | Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E., 40(8), 2791-2799. DOI |
13 | Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci, 76, 102-111. DOI |
14 | Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. DOI ScienceOn |
15 | Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Method., 11(5), 135007. |
16 | Li, X.F., Wang, B.L. and Han, J.C., (2010), "A higher-order theory for static and dynamic analyses of functionally graded beams", Arch. Appl. Mech., 80(10), 1197-1212. DOI |
17 | Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B., 28(1-2), 1-4. DOI |
18 | Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. DOI |
19 | Li, X.-F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4-5), 1210-1229. DOI |
20 | Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Modelling, 39(9), 2489-2508. DOI |
21 | Mantari, J.L. and Guedes Soares, C. (2014), "Four-unknown quasi-3D shear deformation theory for advanced composite plates", Compos. Struct., 109, 231-239. DOI |
22 | Mantari, J.L. and Granados, E.V. (2015), "Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns", Compos.: Part B, 69, 317-334. DOI |
23 | Marur, P.R. (1999), "Fracture behaviour of functionally graded materials", Ph.D. Dissertation; Auburn University, Auburn, AL, USA. |
24 | Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650. DOI |
25 | Sina, S.A., Navazi, H.M. and Haddadpour H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. DOI |
26 | Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433. DOI ScienceOn |
27 | Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15(2), 221-245. DOI ScienceOn |
28 | Semmah, A., Tounsi, A., Zidour, M., Heireche, H. and Naceri, M. (2014), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Fuller. Nanotub. Car. Nanostruct., 23(6), 518-522. DOI |
29 | Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. DOI |
30 | Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., 99, 172-180. DOI |
31 | Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013a), A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. DOI |
32 | Tounsi, A, Semmah, A. and Bousahla, A.A. (2013b), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", ASCE J. Nanomech. Micromech., 3(3), 37-42. DOI |
33 | Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. DOI |
34 | Tounsi, A, Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013c), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. DOI ScienceOn |
35 | Tounsi, A., Benguediab, S., Houari, M.S.A. and Semmah, A. (2013d), "A new nonlocal beam theory with thickness stretching effect for nanobeams", Int. J. Nanosci., 12(4), 1350025. DOI |
36 | Tounsi, A., Al-Basyouni, K.S. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. DOI |
37 | Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. DOI |
38 | Amara, K., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Math. Model., 34(12), 3933-3942. DOI ScienceOn |
39 | Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. DOI |
40 | Allahverdizadeh, A, Eshraghi, I., Mahjoob, M.J. and Nasrollahzadeh, N. (2014), "Nonlinear vibration analysis of FGER sandwich beams", Int. J. Mech. Sci., 78, 167-176. DOI |
41 | Aydogdu, M. (2008), "Vibration of multi-walled carbon nanotubes by generalized shear deformation theory", Int. J. Mech. Sci., 50(4), 837-844. DOI |
42 | Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. DOI |
43 | Aydogdu, M. (2007), "Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions", Compos. Sci. Technol., 67(6), 1096-1104. DOI ScienceOn |
44 | Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567. DOI |
45 | Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. DOI |
46 | Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42(6), 1386-1394. DOI |
47 | Benatta, M.A, Tounsi, A., Mechab, I. and Bachir Bouiadjra, M., (2009), "Mathematical solution for bending of short hybrid composite beams with variable fibers spacing", Appl. Math. Comput., 212(2), 337-348. DOI |
48 | Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24. DOI |
49 | Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41, 225404. DOI |