Dynamic analysis of nanoscale beams including surface stress effects |
Youcef, Djamel Ould
(Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes)
Kaci, Abdelhakim (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique) Benzair, Abdelnour (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) Tounsi, Abdelouahed (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) |
1 | Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. DOI |
2 | Ahouel, M., Houari, M.S.A., AddaBedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. DOI |
3 | 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 |
4 | AitYahia, S., AitAtmane, 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., 53(6), 1143-1165. DOI |
5 | Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos.: Part B, 96, 136-152. DOI |
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. DOI |
7 | Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. DOI |
8 | 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, 671-703. DOI |
9 | Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. DOI |
10 | 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. DOI |
11 | 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., 14(1), 85-104. DOI |
12 | Boukhari, A., AitAtmane, H., Tounsi, A., AddaBedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. DOI |
13 | Baseri, V., Jafari, G.S. and Kolahchi, R. (2016), "Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory", Steel Compos. Struct., 21(4), 883-919. DOI |
14 | Ansari, R., Hosseini, K., Darvizeh, A. and Daneshian, B. (2013), "A sixth-order compact finite difference method for nonclassical vibration analysis of nanobeams including surface stress effects", Appl. Math. Comput., 219, 4977-4991. |
15 | Attia, A., Tounsi, A., AddaBedia, 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., 18(1), 187-212. DOI |
16 | Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. DOI |
17 | Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Compos. Struct., 21(6), 1347 - 1368. DOI |
18 | 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 |
19 | Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "Anew simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. DOI |
20 | 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", Steel Compos. Struct., 20(2), 227-249. DOI |
21 | Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. DOI |
22 | Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. DOI |
23 | 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. Meth., 11(6), 1350082. DOI |
24 | Chen, C.Q., Shi, Y., Zhang, Y.S., Zhu, J. and Yan, Y.J. (2006), "Size dependence of Young's modulus in ZnO nanowires", Phys. Rev. Lett., 96(7), 075505. DOI |
25 | Gibbs, J.W. (1906), "The scientific papers of J. Willard Gibbs", Dover Publications, Inc, New York. |
26 | Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786. DOI |
27 | Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. DOI |
28 | El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. DOI |
29 | Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocalnanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51-64. DOI |
30 | Gao, X.L. and Zhang, G.Y. (2015), "A microstructure- and surface energy-dependent third-order shear deformation beam model", ZAMP, 66(4), 1871-1894. |
31 | Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. Anal., 57(4), 291-323. DOI |
32 | Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38, 265-275. DOI |
33 | Belkorissat, I., Houari, M.S.A., Tounsi, A., AddaBedia, 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., 18(4), 1063-1081. DOI |
34 | Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017b), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. DOI |
35 | Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017a), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695 -702. DOI |
36 | Benachour, A, Tahar, H.D., Atmane, H.A., 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, 1386-1394. DOI |
37 | Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. DOI |
38 | 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. DOI |
39 | 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., 18(1), 235-253. DOI |
40 | Hadji, L., Atmane, H.A., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four variable refined plate theory", Appl. Math. Mech., 32(7), 925-942. DOI |
41 | Hanifi Hachemi Amar, L., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. DOI |
42 | He, J. and Lilley, C.M. (2008), "Surface effect on the elastic behavior of static bending nanowires", Nano Lett., 8, 1798-1802. DOI |
43 | He, J., and Lilley, C. M., (2008), "Surface Stress Effect on Bending Resonance of Nanowires With Different Boundary Conditions," Appl. Phys. Lett., 93,263108. DOI |
44 | Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and AddaBedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. - ASCE, 140(2), 374-383. DOI |
45 | Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257 - 276. DOI |
46 | Kar, V.R. and Panda, S.K. (2015), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. DOI |
47 | Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. DOI |
48 | 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., 18(2), 425-442. DOI |
49 | Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct., 14(6), 431-440. DOI |
50 | Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. DOI |
51 | Liu, C., Rajapakse, R.K.N.D. and Phani, A.S. (2011), "Finite element modelling of beams with surface energy effects", ASME J. Appl. Mech., 78, 031014, see also Erratum, (2012), ASME J. Appl. Mech., 79, 017001. |
52 | Liu, L. and Zhang, Y. (2004), "Multi-wall carbon nanotube as a new infrared detected material", Sensors Actuat., 116, 394-397. DOI |
53 | Maede, R.D. and Vanderbilt, D. (1989), "Origins of stress on elemental and chemisorbed semiconductor surfaces", Phys. Rev. Lett., 63(13), 1404-1407. DOI |
54 | Mahi, A., AddaBedia, 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. DOI |
55 | Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. DOI |
56 | Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11(3), 139-147. DOI |
57 | Qin, C., Shen, J., Hu, Y. and Ye, M. (2009), "Facile attachment of magnetic nanoparticles to carbon nanotubes via robust linkages and its fabrication of magneticnanocomposites", Compos. Sci. Technol., 69, 427-431. DOI |
58 | Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. DOI |
59 | Needs, R.J. (1987), "Calculations of the surface stress tensor at aluminum (111) and (110) surfaces", Phys. Rev. Lett., 58(1),. 53-56. DOI |
60 | Ould Youcef, D., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., 3(3), 177-191. DOI |
61 | Reddy, J.N. (2002), "Energy principles and variational methods in applied mechanics", Wiley, NewYork. |
62 | Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J Appl. Mech., 51(4), 745-752. DOI |
63 | Saidi, H., Tounsi, A. and Bousahla, A.A. (2016), "A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations", Geomech. Eng., 11(2), 289-307. DOI |
64 | Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. DOI |
65 | Shenoy, V.B. (2005), "Atomistic calculations of elastic properties of metallic Fcc crystal surfaces", Phys. Rev. B, 71(9), 094104. DOI |
66 | Wang, G.F. and Feng, X.Q. (2009a), "Surface effects on buckling of nanowiresunder uniaxial compression", Appl. Phys. Lett., 94, 141913. DOI |
67 | Song, F., Huang, G.L., Park, H.S. and Liu, X.N. (2011), "A continuum model for the mechanical behavior of nanowires including surface and surface induced initial stresses", Int. J. Solids Struct., 48, 2154-2163. DOI |
68 | Taibi, F.Z., Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17(2), 99-129. DOI |
69 | Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. DOI |
70 | Wang, G.F. and Feng, X.Q. (2009b), "Timoshenko beam model for bucklingand vibration of nanowires with surface effects," J. Phys. D: Appl. Phys., 42,155411. DOI |
71 | Wang, G.F. and Feng, X.Q. (2007), "Effects of Surface elasticity and residualsurface tension on the natural frequency of microbeams," Appl. Phys. Lett., 90, 231904. DOI |
72 | Wong, E.W., Sheehan, P.E. and Lieber, C.M. (1997), "Nanobeam mechanics: elasticity,strength, and toughness of nanorods and nanotubes", Science, 277, 1971-1975. DOI |
73 | Xu, F., Qin, Q., Mishra, A., Gu, Y. and Zhu, Y. (2010), "Mechanical properties of ZnO nanowires under different loading modes", Nano Res., 3, 271-280. DOI |
74 | Yan, X.B., Chen, X.J., Tay, B.K. and Khor, K.A. (2007), "Transparent and flexible glucose via layer-by-layerassembly of multi-wall carbon nanotubes and glucoseoxidase", Electrochem. Commun., 9, 1269-1275. DOI |
75 | Zhao, C., Song, Y., Ren, J. and Qu, X. (2009), "A DNA nanomachine induced by single-walled carbon nanotubes on gold surface", Biomaterials, 30, 1739-1745. DOI |
76 | Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., (In press). |
77 | 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. DOI |
78 | Zhang, W.D., Wen, Y., Liu, S.M., Tjiu, W.C., Xu, G.Q. and Gan. L.M. (2002), "Synthesis of vertically alignedcarbon nanotubes on metal deposited quartz plates", Carbon, 40, 1981-1989. DOI |
79 | Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153. |
80 | Zidi, M., Tounsi, A., Houari M.S.A., AddaBedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygrothermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. DOI |
81 | Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. DOI |