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Volumn 52, Issue 2, 2016, Pages 73-103

Three-dimensional static analysis of nanoplates and graphene sheets by using Eringen's nonlocal elasticity theory and the perturbation method

Author keywords

Eringen's nonlocal elasticity theory; Graphene sheets; Nanoplates; Static; The perturbation method; Three dimensional nonlocal elasticity

Indexed keywords

ASYMPTOTIC ANALYSIS; BENCHMARKING; FOURIER SERIES; GRAPHENE; MATHEMATICAL OPERATORS; NANOSTRUCTURES; PERTURBATION TECHNIQUES; STATIC ANALYSIS;

EID: 85031127496     PISSN: 15462218     EISSN: 15462226     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (6)

References (53)
  • 1
    • 67651171206 scopus 로고    scopus 로고
    • Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates
    • Aghababaei, R.; Reddy, J. N. (2009): Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. Journal of Sound and Vibration, vol. 326, pp. 277-289.
    • (2009) Journal of Sound and Vibration , vol.326 , pp. 277-289
    • Aghababaei, R.1    Reddy, J.N.2
  • 2
    • 83055181420 scopus 로고    scopus 로고
    • Free vibration analysis of nano-plate using threedimensional theory of elasticity
    • Alibeigloo, A. (2011): Free vibration analysis of nano-plate using threedimensional theory of elasticity. Acta Mechanica, vol. 222, pp. 149-159.
    • (2011) Acta Mechanica , vol.222 , pp. 149-159
    • Alibeigloo, A.1
  • 3
    • 84887169248 scopus 로고    scopus 로고
    • Three-dimensional free vibration analysis of multilayered graphene sheets embedded in elastic matrix
    • Alibeigloo, A. (2012): Three-dimensional free vibration analysis of multilayered graphene sheets embedded in elastic matrix. Journal of Vibration and Control, vol. 19, pp. 2357-2371.
    • (2012) Journal of Vibration and Control , vol.19 , pp. 2357-2371
    • Alibeigloo, A.1
  • 4
    • 84878197540 scopus 로고    scopus 로고
    • Static analysis of rectangular nano-plate using three-dimensional theory of elasticity
    • Alibeigloo, A.; Zanoosi, A. A. P. (2013): Static analysis of rectangular nano-plate using three-dimensional theory of elasticity. Apply Mathematical Modelling, vol. 37, pp. 7016-7026.
    • (2013) Apply Mathematical Modelling , vol.37 , pp. 7016-7026
    • Alibeigloo, A.1    Zanoosi, A.A.P.2
  • 5
    • 84880806172 scopus 로고    scopus 로고
    • Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium
    • Alzahrani, E. O.; Zenkour, A. M.; Sobhy, M. (2013): Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium. Composite Structures, vol. 105, pp. 163-172.
    • (2013) Composite Structures , vol.105 , pp. 163-172
    • Alzahrani, E.O.1    Zenkour, A.M.2    Sobhy, M.3
  • 6
    • 84934344009 scopus 로고    scopus 로고
    • Threedimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach
    • Ansari, R.; Shojaei, M. F.; Shahabodini, A.; Bazdid-Vahdati, M. (2015): Threedimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach. Composite Structures, vol. 131, pp. 753-764.
    • (2015) Composite Structures , vol.131 , pp. 753-764
    • Ansari, R.1    Shojaei, M.F.2    Shahabodini, A.3    Bazdid-Vahdati, M.4
  • 7
    • 84939233406 scopus 로고    scopus 로고
    • Nonlocal dynamic response of embedded single-layered graphene sheet via analytical approach
    • Arani, A. G.; Jalaei, M. H. (2015): Nonlocal dynamic response of embedded single-layered graphene sheet via analytical approach. Journal of Engineering Mathematics, doi: 10.1007/s10665-015-9814-x.
    • (2015) Journal of Engineering Mathematics
    • Arani, A.G.1    Jalaei, M.H.2
  • 8
    • 80052033169 scopus 로고    scopus 로고
    • A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes
    • Arash, B.;Wang Q. (2012): A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Computational Materials Science, vol. 51, pp. 303-313.
    • (2012) Computational Materials Science , vol.51 , pp. 303-313
    • Arash, B.1    Wang, Q.2
  • 9
    • 84894517089 scopus 로고    scopus 로고
    • A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes
    • Brischetto, S. (2014): A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes. Composites Part B-Engineering, vol. 61, pp. 222-228.
    • (2014) Composites Part B-Engineering , vol.61 , pp. 222-228
    • Brischetto, S.1
  • 10
    • 84858335619 scopus 로고    scopus 로고
    • Classical and refined shell models for the analysis of nano-reinforced structures
    • Brischetto, S.; Carrera, E. (2012a): Classical and refined shell models for the analysis of nano-reinforced structures. International Journal of Mechanical Sciences, vol. 55, pp. 104-117.
    • (2012) International Journal of Mechanical Sciences , vol.55 , pp. 104-117
    • Brischetto, S.1    Carrera, E.2
  • 11
    • 84863840556 scopus 로고    scopus 로고
    • Analysis of nano-reinforced layered plates via classical and refined two-dimensional theories
    • Brischetto, S.; Carrera, E. (2012b): Analysis of nano-reinforced layered plates via classical and refined two-dimensional theories. Multidiscipline Modeling in Materials and Structures, vol. 8, pp. 4-31.
    • (2012) Multidiscipline Modeling in Materials and Structures , vol.8 , pp. 4-31
    • Brischetto, S.1    Carrera, E.2
  • 12
    • 84975687245 scopus 로고    scopus 로고
    • Refined 2D and exact 3D shell models for the free vibration analysis of single- and doublewalled carbon nanotubes
    • Brischetto, S.; Tornabene, F.; Fantuzzi, N.; Bacciocchi, M. (2015): Refined 2D and exact 3D shell models for the free vibration analysis of single- and doublewalled carbon nanotubes. Technologies, vol. 3, pp. 259-284.
    • (2015) Technologies , vol.3 , pp. 259-284
    • Brischetto, S.1    Tornabene, F.2    Fantuzzi, N.3    Bacciocchi, M.4
  • 13
    • 33646446022 scopus 로고    scopus 로고
    • Small but strong: A review of the mechanical properties of carbon nanotube-polymer composites
    • Coleman, J. N.; Khan, U.; Blau,W. J.; Gun'ko, Y. K. (2006): Small but strong: a review of the mechanical properties of carbon nanotube-polymer composites. Carbon, vol. 44, pp. 1624-1652.
    • (2006) Carbon , vol.44 , pp. 1624-1652
    • Coleman, J.N.1    Khan, U.2    Blau, W.J.3    Gun'ko, Y.K.4
  • 14
    • 34848825910 scopus 로고    scopus 로고
    • Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory
    • Duan, W. H.; Wang, C. M. (2007): Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory. Nanotechnology, vol. 18, pp. 385704.
    • (2007) Nanotechnology , vol.18 , pp. 385704
    • Duan, W.H.1    Wang, C.M.2
  • 18
    • 34250752881 scopus 로고    scopus 로고
    • Carbon nanotube reinforced composites: Potential and current challenges
    • Esawi, A. M. K.; Farag, M. M. (2007): Carbon nanotube reinforced composites: potential and current challenges. Materials & Design, vol. 28, pp. 2394-2401.
    • (2007) Materials & Design , vol.28 , pp. 2394-2401
    • Esawi, A.M.K.1    Farag, M.M.2
  • 19
    • 84875860746 scopus 로고    scopus 로고
    • Nonlocal elasticity theory for radial vibration of nanoscale spherical shells
    • Ghavanloo, E.; Fazelzadeh, S. A. (2013): Nonlocal elasticity theory for radial vibration of nanoscale spherical shells. European Journal of Mechanics A-Solids, vol. 41, pp. 37-42.
    • (2013) European Journal of Mechanics A-Solids , vol.41 , pp. 37-42
    • Ghavanloo, E.1    Fazelzadeh, S.A.2
  • 20
    • 84919776386 scopus 로고    scopus 로고
    • An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory
    • Hosseini-Hashemi, S.; Kermajani, M.; Nazemnezhad, R. (2015): An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory. European Journal of Mechanics A-Solids, vol. 51, pp. 29-43.
    • (2015) European Journal of Mechanics A-Solids , vol.51 , pp. 29-43
    • Hosseini-Hashemi, S.1    Kermajani, M.2    Nazemnezhad, R.3
  • 21
    • 0342819025 scopus 로고
    • Helical microtubules of graphitic carbon
    • Iijima, S. (1991): Helical microtubules of graphitic carbon. Nature, vol. 354, pp. 56-58.
    • (1991) Nature , vol.354 , pp. 56-58
    • Iijima, S.1
  • 23
    • 40649101140 scopus 로고    scopus 로고
    • Sensors and actuators based on carbon nanotubes and their composites: A review
    • Li, C.; Thostenson, E. T.; Chou, T. W. (2008): Sensors and actuators based on carbon nanotubes and their composites: a review. Composites Science and Technology, vol. 68, pp. 1227-1249.
    • (2008) Composites Science and Technology , vol.68 , pp. 1227-1249
    • Li, C.1    Thostenson, E.T.2    Chou, T.W.3
  • 24
    • 84944463361 scopus 로고    scopus 로고
    • Bending of a sinusoidal piezoelectric nanoplate with surface effect
    • Li, Y. S.; Pan, E. (2016): Bending of a sinusoidal piezoelectric nanoplate with surface effect. Composite Structures, vol. 136, pp. 45-55.
    • (2016) Composite Structures , vol.136 , pp. 45-55
    • Li, Y.S.1    Pan, E.2
  • 25
    • 33747361653 scopus 로고    scopus 로고
    • Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix
    • Liew, K. M.; He, X. Q.; Kitipornchai, S. (2006): Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix. Acta Materialia, vol. 54, pp. 4229-4236.
    • (2006) Acta Materialia , vol.54 , pp. 4229-4236
    • Liew, K.M.1    He, X.Q.2    Kitipornchai, S.3
  • 26
    • 84908307699 scopus 로고    scopus 로고
    • Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review
    • Liew, K. M.; Lei, Z. X.; Zhang, L.W. (2015): Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review. Composite Structures, vol. 120, pp. 90-97.
    • (2015) Composite Structures , vol.120 , pp. 90-97
    • Liew, K.M.1    Lei, Z.X.2    Zhang, L.W.3
  • 29
    • 79951517665 scopus 로고    scopus 로고
    • Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method
    • Pradhan, S. C.; Kumar, A. (2011): Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method. Composite Structures, vol. 93, pp. 774-779.
    • (2011) Composite Structures , vol.93 , pp. 774-779
    • Pradhan, S.C.1    Kumar, A.2
  • 30
    • 67349168181 scopus 로고    scopus 로고
    • Nonlocal elasticity theory for vibration of nanoplates
    • Pradhan, S. C.; Phadikar, J. K. (2009): Nonlocal elasticity theory for vibration of nanoplates. Journal of Sound and Vibration, vol. 325, pp. 206-223.
    • (2009) Journal of Sound and Vibration , vol.325 , pp. 206-223
    • Pradhan, S.C.1    Phadikar, J.K.2
  • 31
    • 33645664001 scopus 로고    scopus 로고
    • Reinforcement of piezoelectric polymers with carbon nanotubes: Pathway to next-generation sensors
    • Ramaratnam, A.; Jalili, N. (2006): Reinforcement of piezoelectric polymers with carbon nanotubes: pathway to next-generation sensors. Journal of Intelligent Material Systems and Structures, vol. 17, pp. 199-208.
    • (2006) Journal of Intelligent Material Systems and Structures , vol.17 , pp. 199-208
    • Ramaratnam, A.1    Jalili, N.2
  • 32
    • 0021580001 scopus 로고
    • A refined nonlinear theory of plates with transverse shear deformation
    • Reddy, J. N. (1984): A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures, vol. 20, pp. 881-896.
    • (1984) International Journal of Solids and Structures , vol.20 , pp. 881-896
    • Reddy, J.N.1
  • 34
    • 78649635423 scopus 로고    scopus 로고
    • Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates
    • Reddy, J. N. (2010): Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, vol. 48, pp. 1507-1518.
    • (2010) International Journal of Engineering Science , vol.48 , pp. 1507-1518
    • Reddy, J.N.1
  • 35
    • 0021857259 scopus 로고
    • Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory
    • Reddy, J. N.; Phan, N. D. (1985): Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. Journal of Sound and Vibration, vol. 98, pp. 157-170.
    • (1985) Journal of Sound and Vibration , vol.98 , pp. 157-170
    • Reddy, J.N.1    Phan, N.D.2
  • 36
    • 77950929047 scopus 로고    scopus 로고
    • Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments
    • Shen, L.; Shen, H. S.; Zhang, C. L. (2010): Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments. Computational Materials Science, vol. 48, pp. 680-685.
    • (2010) Computational Materials Science , vol.48 , pp. 680-685
    • Shen, L.1    Shen, H.S.2    Zhang, C.L.3
  • 37
    • 84855896366 scopus 로고    scopus 로고
    • A nonlocal beam theory for bending, buckling, and vibration of nanobeams
    • Thai, H. T. (2012): A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, vol. 52, pp. 56-64.
    • (2012) International Journal of Engineering Science , vol.52 , pp. 56-64
    • Thai, H.T.1
  • 38
    • 84858016932 scopus 로고    scopus 로고
    • A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams
    • Thai, H. T.; Vo, T.P. (2012): A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, vol. 54, pp. 58-66.
    • (2012) International Journal of Engineering Science , vol.54 , pp. 58-66
    • Thai, H.T.1    Vo, T.P.2
  • 40
    • 3943077884 scopus 로고    scopus 로고
    • Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes
    • Wang, Q. (2004): Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes. International Journal of Solids and Structures, vol. 41, pp. 5451-5461.
    • (2004) International Journal of Solids and Structures , vol.41 , pp. 5451-5461
    • Wang, Q.1
  • 41
    • 29744459272 scopus 로고    scopus 로고
    • Wave propagation in carbon nanotubes via nonlocal continuum mechanics
    • Wang, Q. (2005): Wave propagation in carbon nanotubes via nonlocal continuum mechanics. Journal of Applied Physics, vol. 98, 124301.
    • (2005) Journal of Applied Physics , vol.98 , pp. 124301
    • Wang, Q.1
  • 42
    • 40149087006 scopus 로고    scopus 로고
    • Molecular mechanics modeling for properties of carbon nanotubes
    • Wang, Q.; Liew, K. M. (2008): Molecular mechanics modeling for properties of carbon nanotubes. Journal of Applied Physics, vol. 103, 046103.
    • (2008) Journal of Applied Physics , vol.103 , pp. 046103
    • Wang, Q.1    Liew, K.M.2
  • 43
    • 84862784988 scopus 로고    scopus 로고
    • Static bending behaviors of nanoplate embedded in elastic matrix with small scale effects
    • Wang, Y. Z.; Li, F. M. (2012): Static bending behaviors of nanoplate embedded in elastic matrix with small scale effects. Mechanics Research Communications, vol. 41, pp. 44-48.
    • (2012) Mechanics Research Communications , vol.41 , pp. 44-48
    • Wang, Y.Z.1    Li, F.M.2
  • 44
    • 33947547136 scopus 로고    scopus 로고
    • The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes
    • Wang, Q.; Wang, C. M. (2007): The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology, vol. 18, 075702.
    • (2007) Nanotechnology , vol.18 , pp. 075702
    • Wang, Q.1    Wang, C.M.2
  • 46
    • 0037076804 scopus 로고    scopus 로고
    • Thermally induced dynamic instability of laminated composite conical shells
    • Wu, C. P.; Chiu, S. J. (2002): Thermally induced dynamic instability of laminated composite conical shells. International Journal of Solids and Structures, vol. 39, pp. 3001-3021.
    • (2002) International Journal of Solids and Structures , vol.39 , pp. 3001-3021
    • Wu, C.P.1    Chiu, S.J.2
  • 47
    • 58149380326 scopus 로고    scopus 로고
    • A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells
    • Wu, C. P.; Chiu, K. H.; Wang, Y. M. (2008): A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. CMC-Computers, Materials, & Continua, vol. 8, pp. 93-132.
    • (2008) CMC-Computers, Materials, & Continua , vol.8 , pp. 93-132
    • Wu, C.P.1    Chiu, K.H.2    Wang, Y.M.3
  • 48
    • 34547769781 scopus 로고    scopus 로고
    • Exact solutions of functionally graded piezoelectric shells under cylindrical bending
    • Wu, C. P.; Syu, Y. S. (2007): Exact solutions of functionally graded piezoelectric shells under cylindrical bending. International Journal of Solids and Structures, vol. 44, pp. 6450-6472.
    • (2007) International Journal of Solids and Structures , vol.44 , pp. 6450-6472
    • Wu, C.P.1    Syu, Y.S.2
  • 49
    • 0005133784 scopus 로고    scopus 로고
    • Three-dimensional analysis of doubly curved laminated shells
    • Wu, C. P.; Tarn, J.Q.; Chi, S.M. (1996a): Three-dimensional analysis of doubly curved laminated shells. Journal of Engineering Mechanics, vol. 122, pp. 391-401.
    • (1996) Journal of Engineering Mechanics , vol.122 , pp. 391-401
    • Wu, C.P.1    Tarn, J.Q.2    Chi, S.M.3
  • 50
    • 0030296064 scopus 로고    scopus 로고
    • An asymptotic theory for dynamic response of doubly curved laminated shells
    • Wu, C. P.; Tarn, J. Q.; Chi, S. M. (1996b): An asymptotic theory for dynamic response of doubly curved laminated shells. International Journal of Solids and Structures, vol. 33, pp. 3813-3841.
    • (1996) International Journal of Solids and Structures , vol.33 , pp. 3813-3841
    • Wu, C.P.1    Tarn, J.Q.2    Chi, S.M.3
  • 51
    • 0005174857 scopus 로고    scopus 로고
    • Refined asymptotic theory of doubly curved laminated shells
    • Wu, C. P.; Tarn, J. Q.; Chen, P. Y. (1997): Refined asymptotic theory of doubly curved laminated shells. Journal of Engineering Mechanics, vol. 123, pp. 1238- 1246.
    • (1997) Journal of Engineering Mechanics , vol.123 , pp. 1238-1246
    • Wu, C.P.1    Tarn, J.Q.2    Chen, P.Y.3
  • 52
    • 2942612743 scopus 로고    scopus 로고
    • Asymptotic DQ solutions of functionally graded annular spherical shells
    • Wu, C. P.; Tsai, Y. H. (2004): Asymptotic DQ solutions of functionally graded annular spherical shells. European Journal of Mechanics A-Solids, vol. 23, pp. 283-299.
    • (2004) European Journal of Mechanics A-Solids , vol.23 , pp. 283-299
    • Wu, C.P.1    Tsai, Y.H.2
  • 53
    • 84879122590 scopus 로고    scopus 로고
    • Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler-Pasternak elastic substrate medium
    • Zenkour, A. M.; Sobhy, M. (2013): Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler-Pasternak elastic substrate medium. Physica E-Low-Dimensional Systems & Nanostructures, vol. 53, pp. 251-259.
    • (2013) Physica E-Low-Dimensional Systems & Nanostructures , vol.53 , pp. 251-259
    • Zenkour, A.M.1    Sobhy, M.2


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