과제정보
Authors would like to appreciate the faculty members of Faculty of Civil Engineering in Babol Noshirvani Univeresity of Technology of Iran who kindly examined the research and suggested useful comments and modifications.
참고문헌
- Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326(1-2), 277-289. https://doi.org/10.1016/j.jsv.2009.04.044
- Alwar, R.S. and Reddy, B.S. (1979), "Large deflection static and dynamic analysis of isotropic and orthotropic annular plates", Int. J. Non-Linear Mech., 14(5-6), 347-359. https://doi.org/10.1016/0020-7462(79)90008-8
- Alzahrani, E.O., Zenkour, A.M. and Sobhy, M. (2013), "Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium", Compos. Struct., 105, 163-172. https://doi.org/10.1016/j.compstruct.2013.04.045
- Analooei, H.R., Azhari, M. and Heidarpour, A. (2013), "Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method", Appl. Mathe. Model., 37(10-11), 6703-6717. https://doi.org/10.1016/j.apm.2013.01.051
- Ansari, R., Rajabiehfard, R. and Arash, B. (2010a), "Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets", Computat. Mater. Sci., 49(4), 831-838. https://doi.org/10.1016/j.commatsci.2010.06.032
- Ansari, R., Sahmani, S. and Arash, B. (2010b), "Nonlocal plate model for free vibrations of single-layered graphene sheets", Phys. Lett. A, 375(1), 53-62. https://doi.org/10.1016/j.physleta.2010.10.028
- Arash, B. and Wang, Q. (2011), "Vibration of single-and double-layered graphene sheets", J. Nanotech. Eng. Med., 2(1). https://doi.org/10.1115/1.4003353
- Babaei, H. and Shahidi, A.R. (2011), "Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method", Arch. Appl. Mech., 81(8), 1051-1062. https://doi.org/10.1007/s00419-010-0469-9
- Behfar, K., Seifi, P., Naghdabadi, R. and Ghanbari, J. (2006), "An analytical approach to determination of bending modulus of a multi-layered graphene sheet", Thin Solid Films, 496(2), 475-480. https://doi.org/10.1016/j.tsf.2005.08.317
- Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
- Chen, J.H., Jang, C., Xiao, S., Ishigami, M. and Fuhrer, M.S. (2008), "Intrinsic and extrinsic performance limits of graphene devices on SiO2", Nature Nanotech., 3(4), 206-209. https://doi.org/10.1038/nnano.2008.58
- Choi, W., Lahiri, I., Seelaboyina, R. and Kang, Y.S. (2010), "Synthesis of graphene and its applications: a review", Critical Rev. Solid State Mater. Sci., 35(1), 52-71. https://doi.org/10.1080/10408430903505036
- Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., Int. J., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115
- Duan, W.H. and Wang, C.M. (2009), "Nonlinear bending and stretching of a circular graphene sheet under a central point load", Nanotechnology, 20(7), 075702. https://doi.org/10.1088/0957-4484/20/7/075702
- Erami, F.E. and Firoozjaee, A.R. (2020), "Numerical solution of bed load transport equations using discrete least squares meshless (DLSM) method", Appl. Mathe. Model., 77, 1095-1109. https://doi.org/10.1016/j.apm.2019.08.016
- 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
- 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
- Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science & Business Media.
- Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
- Farajpour, A., Shahidi, A.R., Mohammadi, M. and Mahzoon, M. (2012), "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Compos. Struct., 94(5), 1605-1615. https://doi.org/10.1016/j.compstruct.2011.12.032
- Fattahi, A.M., Safaei, B. and Moaddab, E. (2019), "The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates", Steel Compos. Struct., Int. J., 32(2), 281-292. https://doi.org/10.12989/scs.2019.32.2.281
- Firoozjaee, A.R. and Afshar, M.H. (2009), "Discrete least squares meshless method with sampling points for the solution of elliptic partial differential equations", Eng. Anal. Boundary Elem., 33(1), 83-92. https://doi.org/10.1016/j.enganabound.2008.03.004
- Geim, A.K. (2009), "Graphene: status and prospects", Science, 324(5934), 1530-1534. https://doi.org/10.1126/science.1158877
- Geim, A.K. and Kim, P. (2008), "Carbon wonderland", Scientific American, 298(4), 90-97. https://doi.org/10.1038/scientificamerican0408-90
- Geim, A.K. and Novoselov, K.S. (2007), "The rise of graphene", Naturematerials, 6, 183-191. https://doi.org/10.1142/9789814287005_0002
- Ghannadpour, S.A.M. and Moradi, F. (2019), "Nonlocal nonlinear analysis of nano-graphene sheets under compression using semi-Galerkin technique", Adv. Nano Res., Int. J., 7(5), 311-324. https://doi.org/10.12989/anr.2019.7.5.311
- GR, L. (2003, November), "1013 Mesh Free Methods: Moving beyond the Finite Element Method", Proceedings of The Computational Mechanics Conference, The Japan Society of Mechanical Engineers, pp. 937-938. https://doi.org/10.1299/jsmecmd.2003.16.937
- Heyrovska, R. (2008), "Atomic structures of graphene, benzene and methane with bond lengths as sums of the single, double and resonance bond radii of carbon", arXiv preprint arXiv:0804.4086.
- Hutchinson, J.W. and Fleck, N. (1997), "Strain gradient plasticity", In: Advances in Applied Meechanics, 33, 295-361. https://doi.org/10.1016/S0065-2156(08)70388-0
- Jomehzadeh, E. and Saidi, A.R. (2011), "Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates", Compos. Struct., 93(2), 1015-1020. https://doi.org/10.1016/j.compstruct.2010.06.017
- Katsnelson, M.I. (2007), "Graphene: carbon in two dimensions", Mater. Today, 10(1-2), 20-27. https://doi.org/10.1016/S1369-7021(06)71788-6
- Kuzmenko, A.B., Van Heumen, E., Carbone, F. and Van Der Marel, D. (2008), "Universal optical conductance of graphite", Phys. Rev. Lett., 100(11), 117401. https://doi.org/10.1103/PhysRevLett.100.117401
- Liu, J., Chen, L., Xie, F., Fan, X. and Li, C. (2016), "On bending, buckling and vibration of graphene nanosheets based on the nonlocal theory", Smart Struct. Syst., Int. J., 17(2), 257-274. https://doi.org/10.12989/sss.2016.17.2.257
- Love, A.E.H. (1888), "XVI. The small free vibrations and deformation of a thin elastic shell", Philosophical Transactions of the Royal Society of London.(A.), 179, 491-546. https://doi.org/10.1098/rsta.1888.0016
- Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M. and Reddy, J.N. (2007), "Non-local elastic plate theories", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463(2088), 3225-3240. https://doi.org/10.1098/rspa.2007.1903
- Malekzadeh, P., Setoodeh, A.R. and Beni, A.A. (2011a), "Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium", Compos. Struct., 93(8), 2083-2089. https://doi.org/10.1016/j.compstruct.2011.02.013
- Malekzadeh, P., Setoodeh, A. and Beni, A.A. (2011b), "Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates", Compos. Struct., 93(7), 1631-1639. https://doi.org/10.1016/j.compstruct.2011.01.008
- Martel, R., Schmidt, T., Shea, H.R., Hertel, T. and Avouris, P. (1998), "Single-and multi-wall carbon nanotube field-effect transistors", Appl. Phys. Lett., 73(17), 2447-2449. https://doi.org/10.1063/1.122477
- 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: Low-dimensional Systems and Nanostructures, 41(7), 1232-1239. https://doi.org/10.1016/j.physe.2009.02.004
- Murmu, T. and Pradhan, S.C. (2009b), "Buckling of biaxially compressed orthotropic plates at small scales", Mech. Res. Commun., 36(8), 933-938. https://doi.org/10.1016/j.mechrescom.2009.08.006
- Naderi, A. and Baradaran, G. (2013), "Element free Galerkin method for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory", Int. J. Eng., 26(7), 795-806.
- Nowacki, W. (1974), "The Micropolar Thermoelasticity", In: Micropolar Elasticity, Springer, Vienna, pp. 105-168.
- 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
- Pouresmaeeli, S., Fazelzadeh, S.A. and Ghavanloo, E. (2012), "Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium", Compos. Part B: Eng., 43(8), 3384-3390. https://doi.org/10.1016/j.compositesb.2012.01.046
- Pradhan, S.C. and Phadikar, J.K. (2009), "Nonlocal elasticity theory for vibration of nanoplates", J. Sound Vib., 325(1-2), 206-223. https://doi.org/10.1016/j.jsv.2009.03.007
- Pumera, M., Ambrosi, A., Bonanni, A., Chng, E.L.K. and Poh, H.L. (2010), "Graphene for electrochemical sensing and biosensing", TrAC Trends Anal. Chem., 29(9), 954-965. https://doi.org/10.1016/j.trac.2010.05.011
- Rao, C.N.R., Biswas, K., Subrahmanyam, K.S. and Govindaraj, A. (2009), "Graphene, the new nanocarbon", J. Mater. Chem., 19(17), 2457-2469. https://doi.org/10.1039/B815239J
- Reddy, J.N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48(11), 1507-1518. https://doi.org/10.1016/j.ijengsci.2010.09.020
- Rouhi, H., Ansari, R. and Darvizeh, M. (2016), "Size-dependent free vibration analysis of nanoshells based on the surface stress elasticity", Appl. Mathe. Model., 40(4), 3128-3140. https://doi.org/10.1016/j.apm.2015.09.094
- Sakhaee-Pour, A. (2009), "Elastic properties of single-layered graphene sheet", Solid State Commun., 149(1-2), 91-95. https://doi.org/10.1016/j.ssc.2008.09.050
- Sakhaee-Pour, A., Ahmadian, M.T. and Vafai, A. (2008), "Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors", Solid State Commun., 145(4), 168-172. https://doi.org/10.1115/IMECE2007-43238
- Shen, H.S. (2011), "Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments", Compos. Struct., 93(3), 1143-1152. https://doi.org/10.1016/j.compstruct.2010.10.009
- Shen, L.E., Shen, H.S. and Zhang, C.L. (2010), "Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments", Computat. Mater. Sci., 48(3), 680-685. https://doi.org/10.1016/j.commatsci.2010.03.006
- Sobhy, M. (2014a), "Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium", Physica E: Low-dimens. Syst. Nanostruct., 56, 400-409. https://doi.org/10.1016/j.physe.2013.10.017
- Sobhy, M. (2014b), "Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions", Acta Mechanica. 225(9), 2521. https://doi.org/10.1007/s00707-014-1093-5
- Wang, Q. and Varadan, V.K. (2006), "Wave characteristics of carbon nanotubes", Int. J. Solids Struct., 43(2), 254-265. https://doi.org/10.1016/j.ijsolstr.2005.02.047
- Wang, C.M., Tan, V.B.C. and Zhang, Y.Y. (2006), "Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes", J. Sound Vib., 294(4-5), 1060-1072. https://doi.org/10.1016/j.jsv.2006.01.005
- Wang, Y., Li, F., Jing, X. and Wang, Y. (2015a), "Nonlinear vibration analysis of double-layered nanoplates with different boundary conditions", Phys. Lett. A, 379(24-25), 1532-1537. https://doi.org/10.1016/j.physleta.2015.04.002
- Wang, Y., Li, F.M. and Wang, Y.Z. (2015b), "Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method", Chaos: An Interdiscipl. J. Nonlinear Sci., 25(6), 063108. https://doi.org/10.1063/1.4922299
- Wang, Y., Li, F.M. and Wang, Y.Z. (2016), "Nonlocal effect on the nonlinear dynamic characteristics of buckled parametric double-layered nanoplates", Nonlinear Dyn., 85(3), 1719-1733. https://doi.org/10.1007/s11071-016-2789-y
- Wang, Y., Li, F. and Shu, H. (2019), "Nonlocal nonlinear chaotic and homoclinic analysis of double layered forced viscoelastic nanoplates", Mech. Syst. Signal Process., 122, 537-554. https://doi.org/10.1016/j.ymssp.2018.12.041
- Wu, C.P. and Li, W.C. (2017), "Free vibration analysis of embedded single-layered nanoplates and graphene sheets by using the multiple time scale method", Comput. Mathe. Appl., 73(5), 838-854. https://doi.org/10.1016/j.camwa.2017.01.014
- Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
- Zenkour, A.M. and Sobhy, M. (2013), "Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler-Pasternak elastic substrate medium", Physica E: Low-dimens. Syst. Nanostruct., 53, 251-259. https://doi.org/10.1016/j.physe.2013.04.022
- Zhang, Y., Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2015), "Nonlocal continuum model for vibration of single-layered graphene sheets based on the element-free kp-Ritz method", Eng. Anal. Bound. Elem., 56, 90-97. https://doi.org/10.1016/j.enganabound.2015.01.020