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Original Articles

Static and dynamic response of sector-shaped graphene sheets

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Pages 432-442 | Received 27 Apr 2013, Accepted 26 Jul 2013, Published online: 17 Nov 2015

References

  • M.I. Katsnelson, Graphene: Carbon in Two Dimensions, Cambridge University Press, UK, pp. 1–30, 2012.
  • S.A. Hosseini Kordkheili and H. Moshrefzadeh-Sani, Mechanical properties of double-layered graphene sheets, Compos. Mater. Sci., vol. 69, pp. 335–343, 2013.
  • G. Van Lier, C. Van Alsenoy, and V. Van Doren, Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene, Chem. Phys. Lett., vol. 326, pp. 181–185, 2000.
  • Y. Liu, B. Xie, Z. Zhang, Q. Zheng, and Z. Xu, Mechanical properties of graphene papers, J. Mech. Phys. Solid., vol. 60, pp. 591–605, 2012.
  • L. Wang and Q. Zhang, Elastic behavior of bilayer graphene under in-plane loadings, Curr. Appl. Phys., vol. 12, pp. 1173–1177, 2012.
  • O.K. Kwo, J.H. Lee, J. Park, K.S. Kim, and J.W. Kang, Molecular dynamics simulation study on graphene-nanoribbon-resonators tuned by adjusting axial strain, Curr. Appl. Phys., vol. 13, pp. 360–365, 2013.
  • T. Ohta, A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, Controlling the electronic structure of bilayer graphene, Science, vol. 313, pp. 951–954, 2006.
  • A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54, pp. 4703–4710, 1983.
  • J.N. Reddy and S.D. Pang, Nonlocal continuum theories of beams for the analysis of carbon nanotubes, J. Appl. Phys., vol. 103, pp. 023511, 2008.
  • J.N. Reddy, Nonlocal theories for bending, buckling and vibration of beams, Int. J. Eng. Sci., vol. 45, pp. 288–307, 2007.
  • R. Aghababaei and J.N. Reddy, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, J. Sound Vib., vol. 326, pp. 277–289, 2009.
  • P. Lu, P.Q. Zhang, H.P. Lee, C.M. Wang, and J.N. Reddy, Non-local elastic plate theories, Proc. R. Soc. London, Ser. A, vol. 463, pp. 3225–3240, 2007.
  • K.M. Liew and Q. Wang, Analysis of wave propagation in carbon nanotubes via elastic shell theories, Int. J. Eng. Sci., vol. 45, pp. 227–241, 2007.
  • Q. Wang and K.M. Liew, Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures, Phys. Lett. A, vol. 363, pp. 236–242, 2007.
  • K.M. Liew, Y.G. Hu, and X.Q. He, Flexural wave propagation in single-walled carbon nanotubes, J. Comput. Theor. Nanosci., vol. 5, pp. 581–586, 2008.
  • Ö. Civalek and C. Demir, Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory, Appl. Math. Modell., vol. 35, pp. 2053–2067, 2011.
  • M. Şimşek, Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, J. Phys. E, vol. 43, pp. 182–191, 2010.
  • M. Şimşek and J.N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int. J. Eng. Sci., vol. 64, pp. 37–53, 2013.
  • C. Demir, Ö. Civalek, and B. Akgöz, Free vibration analysis of carbon nanotubes based on shear deformable beam theory by discrete singular convolution technique, Math. Comput. Appl., vol. 15, pp. 57–65, 2010.
  • Ö. Civalek, C. Demir, and B. Akgöz, Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model, Math. Comput. Appl., vol. 15, pp. 289–298, 2010.
  • C.L. Zhang and H.-S. Shen, Thermal buckling of initially compressed single-walled carbon nanotubes by molecular dynamics simulation, Carbon, vol. 45, pp. 2614–2620, 2007.
  • H.-S. Shen and C.L. Zhang, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Mater. Des., vol. 31, pp. 3403–3411, 2010.
  • L. Shen, H.-S. Shen, and C.L. Zhang, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Comput. Mater. Sci., vol. 48, pp. 680–685, 2010.
  • B. Akgöz and Ö. Civalek, Application of strain gradient elasticity theory for buckling analysis of protein microtubules, Curr. Appl. Phys., vol. 11, pp. 1133–1138, 2011.
  • B. Akgöz and Ö. Civalek, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, Int. J. Eng. Sci., vol. 49, pp. 1268–1280, 2011.
  • A.N. Alizada and A.H. Sofiyev, Modified Young's moduli of nano-materials taking into account the scale effects and vacancies, Meccanica, vol. 46, pp. 915–920, 2011.
  • G.W. Wei, Discrete singular convolution for the solution of the Fokker-Planck equations, J. Chem. Phys., vol. 110, pp. 8930–8942, 1999.
  • G.W. Wei, Solving quantum eigenvalue problems by discrete singular convolution, J. Phys. B, vol. 20, pp. 343–352, 2000.
  • G.W. Wei, A new algorithm for solving some mechanical problems, Comput. Methods Appl. Mech. Eng., vol. 190, pp. 2017–2030, 2001.
  • G.W. Wei, Y.B. Zhao, and Y. Xiang, A novel approach for the analysis of high-frequency vibrations, J. Sound Vib., vol. 257, pp. 207–246, 2002.
  • G.W. Wei, Vibration analysis by discrete singular convolution, J. Sound Vib., vol. 244, pp. 535–553, 2001.
  • G.W. Wei, Discrete singular convolution for beam analysis, Eng. Struct., vol. 23, pp. 1045–1053, 2001.
  • G.W. Wei, Y.B. Zhao, and Y. Xiang, Discrete singular convolution and its application to the analysis of plates with internal supports, Part 1: Theory and algorithm, Int. J. Numer. Methods Eng., vol. 55, pp. 913–946, 2002.
  • G.W. Wei, Y.B. Zhao, and Y. Xiang, The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution, Int. J. Mech. Sci., vol. 43, pp. 1731–1746, 2001.
  • Y.B. Zhao, G.W. Wei, and Y. Xiang, Discrete singular convolution for the prediction of high frequency vibration of plates, Int. J. Solids Struct., vol. 39, pp. 65–88, 2002.
  • Y.B. Zhao and G.W. Wei, DSC analysis of rectangular plates with non-uniform boundary conditions, J. Sound Vib., vol. 255, pp. 203–228, 2002.
  • S. Zhao and G.W. Wei, Comparison of the discrete singular convolution and three other numerical schemes for solving Fisher's equation, SIAM J. Sci. Comput., vol. 25, pp. 127–147, 2003.
  • Ö. Civalek, Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach, Finite Elem. Anal. Des., vol. 43, pp. 1013–1022, 2007.
  • Ö. Civalek, A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution, Thin Walled Struct., vol. 45, pp. 692–698, 2007.
  • Ö. Civalek, Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC), Struct. Eng. Mech., vol. 25, pp. 127–130, 2007.
  • Ö. Civalek, Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach, J. Comput. Appl. Math., vol. 205, pp. 251–271, 2007.
  • Ö. Civalek and M. Ulker, Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates, Struct. Eng. Mech., vol. 17, pp. 1–14, 2004.
  • Ö. Civalek, Free vibration analysis of composite conical shells using the discrete singular convolution algorithm, Steel Compos. Struct., vol. 6, pp. 353–366, 2006.
  • A. Seçkin and A.S. Sarıgül, Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: Algorithm and verification, J. Sound Vib., vol. 315, pp. 197–211, 2009.
  • J.B. Han and K.M. Liew, An eight-node curvilinear differential quadrature formulation for Reissner/Mindlin plates, Comput. Methods Appl. Mech. Eng., vol. 141, pp. 265–280, 1997.
  • C.M. Wang, J.N. Reddy, and K.H. Lee, Shear Deformable Beams and Plates—Relationship with Classical Solutions, Elsevier, pp. 177–192, 2000.
  • S. Zhao, G.W. Wei, and Y. Xiang, DSC analysis of free-edged beams by an iteratively matched boundary method, J. Sound Vib., vol. 284, pp. 487–493, 2005.

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