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Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept

  • Ahouel, Mama (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bedia, E.A. Adda (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2014.12.21
  • Accepted : 2015.12.28
  • Published : 2016.04.10
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Abstract

A nonlocal trigonometric shear deformation beam theory based on neutral surface position is developed for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The present model is capable of capturing both small scale effect and transverse shear deformation effects of FG nanobeams, and does not require shear correction factors. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived by employing Hamilton's principle, and the physical neutral surface concept. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

Keywords

References

  1. Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Braz. J. Phys., 45(2), 225-233. https://doi.org/10.1007/s13538-015-0306-2
  2. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  3. Aissani, K., Bachir Bouiadjra, M., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., Int. J., 55(4), 743-762. https://doi.org/10.12989/sem.2015.55.4.743
  4. 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. https://doi.org/10.1177/1099636214526852
  5. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  6. Al-Basyouni, K.S., Tounsi, A. 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. https://doi.org/10.1016/j.compstruct.2014.12.070
  7. 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. https://doi.org/10.1016/j.apm.2010.03.029
  8. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  9. Bagdatli, S.M. (2015), "Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory", Struct. Eng. Mech., Int. J., 55(2), 281-298. https://doi.org/10.12989/sem.2015.55.2.281
  10. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  11. 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. https://doi.org/10.1016/j.compositesb.2013.12.057
  12. 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. https://doi.org/10.12989/scs.2015.18.4.1063
  13. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  14. 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. https://doi.org/10.1016/j.compositesb.2013.08.020
  15. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  16. 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(22), 225404. https://doi.org/10.1088/0022-3727/41/22/225404
  17. 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. https://doi.org/10.12989/sem.2013.48.3.351
  18. Bessaim, A., Houari, M.S.A., Bernard, F. and Tounsi, A. (2015), "A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates", Struct. Eng. Mech., Int. J., 56(2), 223-240. https://doi.org/10.12989/sem.2015.56.2.223
  19. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  20. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  21. 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. https://doi.org/10.12989/scs.2013.14.1.085
  22. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Struct. Eng. Mech., Int. J. (SEM52581C: Submitted)
  23. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  24. 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. https://doi.org/10.12989/scs.2015.18.2.409
  25. 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. Computat. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  26. Chong, A.C.M., Yang, F., Lam, D.C.C. and Tong, P. (2001), "Torsion and bending of micron-scaled structures", J. Mater. Res., 16(4), 1052-1058. https://doi.org/10.1557/JMR.2001.0146
  27. Dai, H., Hafner, J.H., Rinzler, A.G., Colbert, D.T. and Smalley, R.E. (1996), "Nanotubes as nanoprobes in scanning probe microscopy", Nature, 384(6605), 147-150. https://doi.org/10.1038/384147a0
  28. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., Int. J., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  29. 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. https://doi.org/10.12989/scs.2014.17.1.069
  30. Ebrahimi, F. and Dashti, S. (2015), "Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., Int. J., 19(5), 1279-1298. https://doi.org/10.12989/scs.2015.19.5.1279
  31. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  32. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  33. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  34. 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. https://doi.org/10.1007/s11012-013-9827-3
  35. Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W. (1994), "Strain gradient plasticity: theory and experiment", Acta Metall. Mater., 42(2), 475-487. https://doi.org/10.1016/0956-7151(94)90502-9
  36. Fu, Y., Du, H. and Zhang, S. (2003), "Functionally graded TiN/TiNi shape memory alloy films", Mater Lett., 57(20), 2995-2999. https://doi.org/10.1016/S0167-577X(02)01419-2
  37. Hajnayeb, A. and Khadem, S.E. (2015), "An analytical study on the nonlinear vibration of a double walled carbon nanotube", Struct. Eng. Mech., Int. J., 54(5), 987-998. https://doi.org/10.12989/sem.2015.54.5.987
  38. 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. https://doi.org/10.12989/scs.2015.18.1.235
  39. Harik, V.M. (2001), "Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods", Solid. State. Commun., 120(7-8), 331-335. https://doi.org/10.1016/S0038-1098(01)00383-0
  40. Harik, V.M. (2002), "Mechanics of carbon nanotubes: Applicability of the continuum-beam models", Comput. Mater. Sci., 24(3), 328-342. https://doi.org/10.1016/S0927-0256(01)00255-5
  41. Hasanyan, D.J., Batra, R.C. and Harutyunyan, S. (2008), "Pull-in instabilities in functionally graded microthermoelectromechanical systems", J. Therm. Stress., 31(10), 1006-1021. https://doi.org/10.1080/01495730802250714
  42. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "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. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  43. Heireche, H., Tounsi, A., Benzair, A. and Adda Bedia, E.A. (2008), "Sound wave propagation in singlewalled carbon nanotubes using nonlocal elasticity", Physica E, 40(8), 2791-2799. https://doi.org/10.1016/j.physe.2007.12.021
  44. Janghorban, M. and Zare, A. (2011), „Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method", Physica E., 43(9), 1602-1604. https://doi.org/10.1016/j.physe.2011.05.002
  45. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  46. 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. Computat. Method., 11(5), 135007.
  47. Kolahchi, R., Bidgoli, A.M.M. and Mehdi Heydari, M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., Int. J., 55(5), 1001-1014. https://doi.org/10.12989/sem.2015.55.5.1001
  48. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  49. 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. https://doi.org/10.12989/scs.2015.18.2.425
  50. Lee, Z., Ophus, C., Fischer, L., Nelson-Fitzpatrick, N., Westra, K.L., Evoy, S., Radmilovic, V., Dahmen, U. and Mitlin, D. (2006), "Metallic NEMS components fabricated from nanocomposite Al-Mo films", Nanotechnol., 17(12), 3063-3070. https://doi.org/10.1088/0957-4484/17/12/042
  51. Lourie, O., Cox, D.M. and Wagner, H.D. (1998), "Buckling and collapse of embedded carbon nanotubes", Phys. Rev. Lett., 81(8), 1638. https://doi.org/10.1103/PhysRevLett.81.1638
  52. Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2006), "Dynamic properties of flexural beams using a nonlocal elasticity model", J. Appl. Phys., 99(7), 073510. https://doi.org/10.1063/1.2189213
  53. Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2007), "Application of nonlocal beam models for carbon nanotubes", Int. J. Solids Struct., 44(16), 5289-5300. https://doi.org/10.1016/j.ijsolstr.2006.12.034
  54. Lu, C., Wu, D. and Chen, W. (2011), "Non-linear responses of nano-scale FGM films including the effects of surface energies", IEEE Trans. Nanotechnol., 10(6), 1321-1327. https://doi.org/10.1109/TNANO.2011.2139223
  55. 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. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  56. Mohammadi-Alasti, B., Rezazadeh, G., Borgheei, A.M., Minaei, S. and Habibifar, R. (2011), "On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure", Compos. Struct., 93(6), 1516-1525. https://doi.org/10.1016/j.compstruct.2010.11.013
  57. Murmu, T. and Pradhan, S.C. (2009a), "Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM", Physica E, 41(7), 1232-1239. https://doi.org/10.1016/j.physe.2009.02.004
  58. Murmu, T. and Pradhan, S.C. (2009b), "Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory", Physica E, 41(8), 1451-1456. https://doi.org/10.1016/j.physe.2009.04.015
  59. Murmu, T. and Pradhan, S.C. (2009c), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comp. Mater. Sci., 46(4), 854-869. https://doi.org/10.1016/j.commatsci.2009.04.019
  60. Nami, M.R. and Janghorban, M. (2013), "Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory", Beilstein J. Nanotechnol., 4(1), 968-973. https://doi.org/10.3762/bjnano.4.109
  61. 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. https://doi.org/10.1080/15397734.2013.763713
  62. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3-5), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  63. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method", Struct. Eng. Mech., Int. J., 54(6), 1061-1073. https://doi.org/10.12989/sem.2015.54.6.1061
  64. Rahaeifard, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the 3rd International Conference on Micro-and Nanosystems, San Diego, CA, USA, September, pp. 539-544.
  65. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  66. Reddy, J.N. and Pang, S.D. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511. https://doi.org/10.1063/1.2833431
  67. Roque, C.M.C., Ferreira, A.J.M. and Reddy, J.N. (2011), "Analysis of timoshenko nanobeams with a nonlocal formulation and meshless method", Int. J. Eng. Sci., 49(9), 976-984. https://doi.org/10.1016/j.ijengsci.2011.05.010
  68. Salima, A., Fekrar, A., Heireche, H., Saidi, H., Tounsi, A. and Adda Bedia, E.A. (2016), "An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations", Wind Struct., Int. J., 22(3), 329-348. https://doi.org/10.12989/was.2016.22.3.329
  69. Stolken, J.S. and Evans, A.G. (1998), "A microbend test method for measuring the plasticity length scale", Acta Mater., 46(14), 5109-5115. https://doi.org/10.1016/S1359-6454(98)00153-0
  70. Semmah, A., Tounsi, A., Zidour, M., Heireche, H. and Naceri, M. (2015), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Fuller. Nanotub. Carb. Nanostruct., 23(6), 518-522. https://doi.org/10.1080/1536383X.2012.749457
  71. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  72. Sobhy, M. (2015), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980. https://doi.org/10.1016/j.compstruct.2015.08.102
  73. Sudak, L.J. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94(11), 7281-7287. https://doi.org/10.1063/1.1625437
  74. Tagrara, S.H., Benachour, A., Bachir Bouiadjra, M. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., Int. J., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  75. Tounsi, A., Houari, M.S.A., Benyoucef, S., 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. https://doi.org/10.1016/j.ast.2011.11.009
  76. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  77. Tounsi, A, Semmah, A. and Bousahla, A.A. (2013c), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", ASCE J. Nanomech. Micromech., 3(3), 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  78. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301. https://doi.org/10.1063/1.2141648
  79. Wang, L.F. and Hu, H.Y. (2005), "Flexural wave propagation in single-walled carbon nanotubes", Phys. Rev. B., 71(19), 195412. https://doi.org/10.1103/PhysRevB.71.195412
  80. Wang, Q. and Varadan, V.K. (2006), "Vibration of carbon nanotubes studied using nonlocal continuum mechanics", Smart Mater. Struct., 15(2), 659. https://doi.org/10.1088/0964-1726/15/2/050
  81. Witvrouw, A. and Mehta, A. (2005), "The use of functionally graded poly-SiGe layers for MEMS applications", Mater. Sci. Forum., 492, 255-260.
  82. Yahoobi, H. and Feraidoon, A. (2010), "Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load", World Appl. Sci. J., 10(3), 337-341.
  83. 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., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  84. Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Compos. Struct., Int. J., 18(4), 909-924. https://doi.org/10.12989/scs.2015.18.4.909
  85. Zhang, J. and Fu, Y. (2012), "Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory", Meccanica, 47(7), 1649-1658. https://doi.org/10.1007/s11012-012-9545-2
  86. 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. Technolgy, 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  87. Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. https://doi.org/10.1007/s11029-014-9396-0

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  3. Dynamic modeling of porous heterogeneous micro/nanobeams vol.132, pp.12, 2017, https://doi.org/10.1140/epjp/i2017-11754-7
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  5. Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam vol.123, pp.1, 2017, https://doi.org/10.1007/s00339-016-0712-5
  6. Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory vol.30, pp.6, 2017, https://doi.org/10.1016/j.camss.2017.09.007
  7. Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects vol.120, 2017, https://doi.org/10.1016/j.ijmecsci.2016.11.025
  8. Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium vol.18, pp.6, 2016, https://doi.org/10.12989/sss.2016.18.6.1125
  9. A review of continuum mechanics models for size-dependent analysis of beams and plates vol.177, 2017, https://doi.org/10.1016/j.compstruct.2017.06.040
  10. Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams vol.40, pp.5, 2017, https://doi.org/10.1080/01495739.2016.1230483
  11. Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method 2018, https://doi.org/10.1016/j.aej.2017.06.001
  12. Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution vol.122, pp.12, 2016, https://doi.org/10.1007/s00339-016-0542-5
  13. Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium vol.47, pp.6, 2017, https://doi.org/10.1007/s13538-017-0524-x
  14. Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes vol.514, 2017, https://doi.org/10.1016/j.physb.2017.03.030
  15. Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium 2018, https://doi.org/10.1177/0954406217713518
  16. Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects vol.123, pp.3, 2017, https://doi.org/10.1007/s00339-017-0784-x
  17. Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0922-5
  18. Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams vol.28, pp.15, 2017, https://doi.org/10.1177/1045389X16682850
  19. Free vibration of symmetric and sigmoid functionally graded nanobeams vol.122, pp.9, 2016, https://doi.org/10.1007/s00339-016-0324-0
  20. Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties vol.123, pp.1, 2017, https://doi.org/10.1007/s00339-016-0591-9
  21. Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory 2019, https://doi.org/10.1177/0954406218756451
  22. A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations vol.11, pp.2, 2016, https://doi.org/10.12989/gae.2016.11.2.289
  23. A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams vol.159, 2017, https://doi.org/10.1016/j.compstruct.2016.09.058
  24. Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory 2017, https://doi.org/10.1016/j.aej.2017.07.003
  25. Thermo-elastic effects on shear correction factors for functionally graded beam vol.123, 2017, https://doi.org/10.1016/j.compositesb.2017.05.031
  26. Forced Vibration Analysis of Functionally Graded Nanobeams vol.09, pp.07, 2017, https://doi.org/10.1142/S1758825117501009
  27. Vibration analysis of functionally graded piezoelectric nanoscale plates by nonlocal elasticity theory: An analytical solution vol.100, 2016, https://doi.org/10.1016/j.spmi.2016.08.046
  28. Free vibration investigation of nano mass sensor using differential transformation method vol.123, pp.3, 2017, https://doi.org/10.1007/s00339-017-0796-6
  29. Investigating post-buckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions vol.182, 2017, https://doi.org/10.1016/j.compstruct.2017.09.008
  30. Size-dependent thermoelastic analysis of a functionally graded nanoshell vol.32, pp.03, 2018, https://doi.org/10.1142/S0217984918500331
  31. Nonlinear bending of a two-dimensionally functionally graded beam vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.087
  32. Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory vol.159, 2017, https://doi.org/10.1016/j.compstruct.2016.09.092
  33. A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams vol.4, pp.4, 2016, https://doi.org/10.12989/anr.2016.4.4.251
  34. Magneto-hygro-thermal vibration behavior of elastically coupled nanoplate systems incorporating nonlocal and strain gradient effects vol.39, pp.11, 2017, https://doi.org/10.1007/s40430-017-0890-x
  35. On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory vol.162, 2017, https://doi.org/10.1016/j.compstruct.2016.11.058
  36. Small-scale effects on the dynamic response of inhomogeneous nanobeams on elastic substrate under uniform dynamic load vol.132, pp.4, 2017, https://doi.org/10.1140/epjp/i2017-11441-9
  37. Nonlocal stress-strain gradient vibration analysis of heterogeneous double-layered plates under hygro-thermal and linearly varying in-plane loads 2018, https://doi.org/10.1177/1077546317731672
  38. Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0955-9
  39. A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate vol.168, 2017, https://doi.org/10.1016/j.compstruct.2017.02.090
  40. Investigating dynamic response of porous inhomogeneous nanobeams on hybrid Kerr foundation under hygro-thermal loading vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0908-3
  41. Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality vol.36, pp.3, 2017, https://doi.org/10.1177/0263092317700153
  42. A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment vol.122, pp.9, 2016, https://doi.org/10.1007/s00339-016-0322-2
  43. Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects vol.123, pp.1, 2017, https://doi.org/10.1007/s00339-016-0511-z
  44. Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory vol.133, pp.2, 2018, https://doi.org/10.1140/epjp/i2018-11868-4
  45. Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.052
  46. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM 2017, https://doi.org/10.1080/19475411.2017.1377312
  47. Parametric excitation analysis of a piezoelectric-nanotube conveying fluid under multi-physics field 2017, https://doi.org/10.1007/s00542-017-3670-8
  48. Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams vol.322, 2017, https://doi.org/10.1016/j.cma.2017.05.007
  49. Effects of neutral surface deviation on nonlinear resonance of embedded temperature-dependent functionally graded nanobeams vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.058
  50. Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates vol.132, pp.10, 2017, https://doi.org/10.1140/epjp/i2017-11666-6
  51. Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams vol.122, pp.11, 2016, https://doi.org/10.1007/s00339-016-0465-1
  52. On thermal stability of plates with functionally graded coefficient of thermal expansion vol.60, pp.2, 2016, https://doi.org/10.12989/sem.2016.60.2.313
  53. A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate vol.60, pp.4, 2016, https://doi.org/10.12989/sem.2016.60.4.547
  54. Dynamic characteristics of temperature-dependent viscoelastic FG nanobeams subjected to 2D-magnetic field under periodic loading vol.123, pp.4, 2017, https://doi.org/10.1007/s00339-017-0829-1
  55. Bending analysis of FGM plates using a sinusoidal shear deformation theory vol.23, pp.6, 2016, https://doi.org/10.12989/was.2016.23.6.543
  56. Dynamic modeling of smart shear-deformable heterogeneous piezoelectric nanobeams resting on Winkler–Pasternak foundation vol.122, pp.11, 2016, https://doi.org/10.1007/s00339-016-0466-0
  57. Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments 2017, https://doi.org/10.1080/15376494.2017.1308603
  58. Testing specimen effect on shrinkage of lightweight concrete vol.171, pp.3, 2018, https://doi.org/10.1680/jstbu.16.00125
  59. On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell pp.1435-5663, 2019, https://doi.org/10.1007/s00366-018-0669-4
  60. Vibration Analysis of Nano Beam Using Differential Transform Method Including Thermal Effect vol.54, pp.1661-9897, 2018, https://doi.org/10.4028/www.scientific.net/JNanoR.54.1
  61. Stabilities and electronic properties of nanowires made of single atomic sulfur chains encapsulated in zigzag carbon nanotubes vol.29, pp.41, 2018, https://doi.org/10.1088/1361-6528/aad67a
  62. Forced vibration analysis of cracked nanobeams vol.40, pp.8, 2018, https://doi.org/10.1007/s40430-018-1315-1
  63. Axial magnetic field effects on dynamic characteristics of embedded multiphase nanocrystalline nanobeams vol.24, pp.8, 2018, https://doi.org/10.1007/s00542-018-3771-z
  64. Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media vol.29, pp.11, 2018, https://doi.org/10.1177/1045389X18770856
  65. Modelling of thermally affected elastic wave propagation within rotating Mori–Tanaka-based heterogeneous nanostructures vol.24, pp.6, 2018, https://doi.org/10.1007/s00542-018-3800-y
  66. Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection pp.1432-1858, 2019, https://doi.org/10.1007/s00542-018-4277-4
  67. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529
  68. Modal participation of fixed–fixed single-walled carbon nanotube with vacancies pp.2008-6695, 2019, https://doi.org/10.1007/s40091-019-0222-8
  69. A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams vol.19, pp.2, 2017, https://doi.org/10.12989/sss.2017.19.2.115
  70. Non-linear study of mode II delamination fracture in functionally graded beams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.263
  71. Assessment of various nonlocal higher order theories for the bending and buckling behavior of functionally graded nanobeams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.339
  72. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2016, https://doi.org/10.12989/sss.2017.19.3.289
  73. Wave propagation in functionally graded beams using various higher-order shear deformation beams theories vol.62, pp.2, 2016, https://doi.org/10.12989/sem.2017.62.2.143
  74. Analysis of functionally graded plates using a sinusoidal shear deformation theory vol.19, pp.4, 2017, https://doi.org/10.12989/sss.2017.19.4.441
  75. A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams vol.62, pp.6, 2017, https://doi.org/10.12989/sem.2017.62.6.695
  76. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2016, https://doi.org/10.12989/sss.2017.19.6.601
  77. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2016, https://doi.org/10.12989/cac.2017.20.2.229
  78. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2016, https://doi.org/10.12989/eas.2017.13.3.255
  79. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  80. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  81. Damping and vibration analysis of viscoelastic curved microbeam reinforced with FG-CNTs resting on viscoelastic medium using strain gradient theory and DQM vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.141
  82. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  83. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  84. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  85. An analytical solution for bending and vibration responses of functionally graded beams with porosities vol.25, pp.4, 2016, https://doi.org/10.12989/was.2017.25.4.329
  86. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  87. Effects of triaxial magnetic field on the anisotropic nanoplates vol.25, pp.3, 2017, https://doi.org/10.12989/scs.2017.25.3.361
  88. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  89. Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams vol.25, pp.4, 2016, https://doi.org/10.12989/scs.2017.25.4.415
  90. A simple quasi-3D sinusoidal shear deformation theory with stretching effect for carbon nanotube-reinforced composite beams resting on elastic foundation vol.13, pp.5, 2016, https://doi.org/10.12989/eas.2017.13.5.509
  91. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2016, https://doi.org/10.12989/sem.2017.64.4.391
  92. Coupled effects of electrical polarization-strain gradient on vibration behavior of double-layered flexoelectric nanoplates vol.20, pp.5, 2017, https://doi.org/10.12989/sss.2017.20.5.573
  93. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  94. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  95. A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.717
  96. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  97. Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory vol.16, pp.2, 2016, https://doi.org/10.12989/gae.2018.16.2.141
  98. A nonlocal strain gradient theory for nonlinear free and forced vibration of embedded thick FG double layered nanoplates vol.68, pp.1, 2018, https://doi.org/10.12989/sem.2018.68.1.103
  99. Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory vol.65, pp.5, 2016, https://doi.org/10.12989/sem.2018.65.5.621
  100. Wave dispersion analysis of rotating heterogeneous nanobeams in thermal environment vol.6, pp.1, 2016, https://doi.org/10.12989/anr.2018.6.1.021
  101. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2016, https://doi.org/10.12989/anr.2018.6.1.039
  102. Post-buckling responses of a laminated composite beam vol.26, pp.6, 2016, https://doi.org/10.12989/scs.2018.26.6.733
  103. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  104. A novel four variable refined plate theory for wave propagation in functionally graded material plates vol.27, pp.1, 2018, https://doi.org/10.12989/scs.2018.27.1.109
  105. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.061
  106. Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects vol.21, pp.4, 2018, https://doi.org/10.12989/cac.2018.21.4.431
  107. Three dimensional dynamic response of functionally graded nanoplates under a moving load vol.66, pp.2, 2016, https://doi.org/10.12989/sem.2018.66.2.249
  108. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2016, https://doi.org/10.12989/sss.2018.21.4.397
  109. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  110. Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory vol.27, pp.3, 2018, https://doi.org/10.12989/scs.2018.27.3.311
  111. Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory vol.27, pp.3, 2018, https://doi.org/10.12989/scs.2018.27.3.371
  112. Free vibration of FGM plates with porosity by a shear deformation theory with four variables vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.353
  113. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2016, https://doi.org/10.12989/gae.2018.15.1.711
  114. Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation vol.21, pp.5, 2018, https://doi.org/10.12989/cac.2018.21.5.569
  115. Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis vol.27, pp.4, 2016, https://doi.org/10.12989/scs.2018.27.4.465
  116. Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell vol.27, pp.4, 2018, https://doi.org/10.12989/scs.2018.27.4.479
  117. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.599
  118. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2016, https://doi.org/10.12989/anr.2018.6.2.147
  119. Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.761
  120. A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.771
  121. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2016, https://doi.org/10.12989/scs.2018.28.1.013
  122. Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field vol.67, pp.1, 2016, https://doi.org/10.12989/sem.2018.67.1.021
  123. Size effect and age factor in mechanical properties of BST Light Weight Concrete vol.177, pp.None, 2018, https://doi.org/10.1016/j.conbuildmat.2018.05.115
  124. Technical and economical assessment of applying silica nanoparticles for construction of concrete structures vol.22, pp.1, 2018, https://doi.org/10.12989/cac.2018.22.1.117
  125. Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory vol.22, pp.1, 2016, https://doi.org/10.12989/sss.2018.22.1.027
  126. Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory vol.28, pp.3, 2016, https://doi.org/10.12989/scs.2018.28.3.381
  127. Single variable shear deformation model for bending analysis of thick beams vol.67, pp.3, 2016, https://doi.org/10.12989/sem.2018.67.3.291
  128. Numerical study for vibration response of concrete beams reinforced by nanoparticles vol.67, pp.3, 2018, https://doi.org/10.12989/sem.2018.67.3.311
  129. A nonlocal strain gradient theory for scale-dependent wave dispersion analysis of rotating nanobeams considering physical field effects vol.7, pp.4, 2016, https://doi.org/10.12989/csm.2018.7.4.373
  130. Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix vol.67, pp.5, 2016, https://doi.org/10.12989/sem.2018.67.5.517
  131. Effect of homogenization models on stress analysis of functionally graded plates vol.67, pp.5, 2018, https://doi.org/10.12989/sem.2018.67.5.527
  132. Elastic wave dispersion modelling within rotating functionally graded nanobeams in thermal environment vol.6, pp.3, 2016, https://doi.org/10.12989/anr.2018.6.3.201
  133. Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory vol.6, pp.3, 2018, https://doi.org/10.12989/anr.2018.6.3.279
  134. Seismic analysis of AL2O3 nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory vol.15, pp.3, 2016, https://doi.org/10.12989/eas.2018.15.3.285
  135. A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates vol.22, pp.3, 2016, https://doi.org/10.12989/sss.2018.22.3.303
  136. Dynamic analysis of immersion concrete pipes in water subjected to earthquake load using mathematical methods vol.15, pp.4, 2016, https://doi.org/10.12989/eas.2018.15.4.361
  137. Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory vol.15, pp.4, 2018, https://doi.org/10.12989/eas.2018.15.4.369
  138. An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.247
  139. A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.269
  140. Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory vol.22, pp.5, 2016, https://doi.org/10.12989/sss.2018.22.5.527
  141. Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation vol.27, pp.5, 2018, https://doi.org/10.12989/was.2018.27.5.311
  142. A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment vol.6, pp.4, 2018, https://doi.org/10.12989/anr.2018.6.4.299
  143. Critical buckling loads of carbon nanotube embedded in Kerr's medium vol.6, pp.4, 2016, https://doi.org/10.12989/anr.2018.6.4.339
  144. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2016, https://doi.org/10.12989/scs.2019.30.1.013
  145. Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory vol.6, pp.1, 2019, https://doi.org/10.12989/aas.2019.6.1.001
  146. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2016, https://doi.org/10.12989/sem.2019.69.2.205
  147. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.019
  148. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  149. A novel refined shear deformation theory for the buckling analysis of thick isotropic plates vol.69, pp.3, 2019, https://doi.org/10.12989/sem.2019.69.3.335
  150. Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load vol.7, pp.1, 2016, https://doi.org/10.12989/acc.2019.7.1.051
  151. Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory vol.16, pp.2, 2019, https://doi.org/10.12989/eas.2019.16.2.177
  152. Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress vol.23, pp.2, 2016, https://doi.org/10.12989/sss.2019.23.2.141
  153. Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams vol.134, pp.3, 2016, https://doi.org/10.1140/epjp/i2019-12464-x
  154. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2016, https://doi.org/10.12989/sem.2019.69.5.511
  155. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.089
  156. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.109
  157. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2016, https://doi.org/10.12989/sem.2019.69.6.637
  158. Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  159. Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.136
  160. Participation Factor and Vibration of Carbon Nanotube with Vacancies vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.158
  161. A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.325
  162. Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.157
  163. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.191
  164. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2016, https://doi.org/10.12989/sem.2019.70.4.407
  165. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2016, https://doi.org/10.12989/gae.2019.18.2.161
  166. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2016, https://doi.org/10.12989/scs.2019.31.5.503
  167. Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems vol.31, pp.6, 2016, https://doi.org/10.12989/scs.2019.31.6.641
  168. Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities vol.6, pp.2, 2016, https://doi.org/10.12989/smm.2019.6.2.147
  169. Chaotic dynamics of a non-autonomous nonlinear system for a smart composite shell subjected to the hygro-thermal environment vol.25, pp.7, 2019, https://doi.org/10.1007/s00542-018-4206-6
  170. Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment vol.134, pp.7, 2019, https://doi.org/10.1140/epjp/i2019-12581-6
  171. Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports vol.233, pp.16, 2016, https://doi.org/10.1177/0954406219855095
  172. Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method vol.9, pp.17, 2016, https://doi.org/10.3390/app9173517
  173. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  174. Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets vol.134, pp.10, 2019, https://doi.org/10.1140/epjp/i2019-12806-8
  175. Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model vol.72, pp.1, 2016, https://doi.org/10.12989/sem.2019.72.1.071
  176. A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes vol.60, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.60.21
  177. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.443
  178. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2016, https://doi.org/10.1140/epjp/i2019-12662-6
  179. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  180. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2016, https://doi.org/10.12989/was.2019.29.6.371
  181. Exact solution for dynamic response of size dependent torsional vibration of CNT subjected to linear and harmonic loadings vol.8, pp.1, 2016, https://doi.org/10.12989/anr.2020.8.1.025
  182. Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures vol.73, pp.2, 2020, https://doi.org/10.12989/sem.2020.73.2.109
  183. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-020-00137-w
  184. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates vol.25, pp.2, 2020, https://doi.org/10.12989/sss.2020.25.2.197
  185. Parametrically excited nonlinear dynamics and instability of double-walled nanobeams under thermo-magneto-mechanical loads vol.26, pp.4, 2016, https://doi.org/10.1007/s00542-019-04638-2
  186. Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.147
  187. Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading vol.8, pp.3, 2016, https://doi.org/10.12989/anr.2020.8.3.203
  188. Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories vol.74, pp.2, 2020, https://doi.org/10.12989/sem.2020.74.2.175
  189. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2016, https://doi.org/10.12989/sss.2020.25.4.409
  190. Stability of perforated nanobeams incorporating surface energy effects vol.35, pp.4, 2020, https://doi.org/10.12989/scs.2020.35.4.555
  191. A comprehensive review on the modeling of smart piezoelectric nanostructures vol.74, pp.5, 2016, https://doi.org/10.12989/sem.2020.74.5.611
  192. Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles vol.9, pp.3, 2016, https://doi.org/10.12989/csm.2020.9.3.281
  193. Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00737-w
  194. Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00742-z
  195. Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory vol.48, pp.4, 2016, https://doi.org/10.1080/15397734.2019.1642766
  196. Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula vol.8, pp.7, 2020, https://doi.org/10.3390/math8071162
  197. Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models vol.36, pp.3, 2016, https://doi.org/10.12989/scs.2020.36.3.293
  198. Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes vol.36, pp.6, 2016, https://doi.org/10.12989/scs.2020.36.6.643
  199. Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes vol.36, pp.4, 2016, https://doi.org/10.1007/s00366-019-00790-5
  200. Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment vol.11, pp.7, 2016, https://doi.org/10.3390/app11073250
  201. Mechanical analysis of bi-functionally graded sandwich nanobeams vol.11, pp.1, 2016, https://doi.org/10.12989/anr.2021.11.1.055
  202. On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations vol.40, pp.3, 2021, https://doi.org/10.12989/scs.2021.40.3.389