Biaxial Buckling of Single Layer Graphene Sheet Based on Nonlocal Plate Model and Molecular Dynamics Simulation
References:
[1] Ma, Q. and Clarke, D. R. (1995), “Size dependent Hardness of Silver Single Crystals”, Materials Research, Vol. 10, pp. 853-63.
[2] Ebrahimi, F. Salari, E. (2015), “Thermal buckling and free vibration analysis of size dependent Timoshenko FG”, Composite Structures, vol. 128, pp. 363-380.
[3] Murmu, T. and Pradhan, S.C. (2009), “Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model”, Physica E, Volume 41, Issue 8, pp. 1628-1633.
[4] R, Ansari, S., Sahmani, (2013), “Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations”, Applied Mathematical Modelling, Volume 37, Issues 12–13, Pages 7338–7351.
[5] S. Kitipornchai, X.Q. He, K.M. Liew (2005), “Continuum model for the vibration of multilayered graphene sheets,” Phys. Rev. B 72 075443.
[6] K.M. Liew, X.Q. He, S. Kitipornchai (2006), “Continuum model for the vibration of multilayered graphene sheets,” Acta Mater. 54 4229.
[7] R, Ansari, R, Rajabiehfard, B., Arash, B. (2010),“Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets”, Computational Materials Science, Volume 49, Issue 4, pp. 831-838..
[8] L. Shen, H.S. Shen, C.L. Zhang (2010), “Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments,” Comput. Mater. Sci. 48 680.
[9] S.C. Pradhan, J.K. Phadikar, (2009), “Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models,” Phys. Lett. A 373 1062.
[10] T S. Narendar, S. Gopalakrishnan, (2009), “Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes”, Comput. Mater. Sci. 47 - 526...
[11] B. Arash, R. Ansari, (2010), “Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain,” Physica E 42 - 2058.
[12] M.J. Hao, X.M. Guo, Q. Wang, Eur. J. (2010), “Small-scale effect on torsional buckling of multi-walled carbon nanotubes,” Mech. A/Solids 29 (2010) 49.
[13] T. Natsuki, X.W. Lei, Q.Q. Ni, M. Endo, (2010), “Free vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium,” Phys. Lett. A 374 -2670.
[14] A.C. Eringen, J. Appl. (1983), “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” Phys. 54, 4703.
[15] S.K. Jang, C.W. Bert, A.G. Striz, (1989), “Application of differential quadrature to static analysis of structural components,” Int J. Num. Methods Eng. 28, 561
[16] R. Bellman, B.G. Kashef, J. Casti, J. (1972), “Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations”, Comput. Phys. 10, 40
[17] A.N. Sherbourne, M.D. Pandey, (1991), “Differential quadrature method in the buckling analysis of beams and composite plates,” Comput. Struct. 40, 903
[18] C. Shu, (2000), “Differential quadrature and its application in engineering,” Springer, Berlin.
[19] H.-S. Shen, C.-L. Zhang (2006), “Postbuckling prediction of axially loaded double-walledcarbon nanotubes with temperature dependent properties and initial defects”, Phys. Rev. B 74 035410.
[20] H.-S. Shen, C.-L. Zhang (2007), “Postbuckling of double-walled carbon nanotubes with temperature dependent properties and initial defects under combined axialand radial mechanical loads,” Int. J. Solids Struct. 44 1461–1487.
[21] S. Plimpton (1995), “Fast parallel algorithms for short-range molecular dynamics,” J.Comput. Phys. 117 1–19.
[22] W. Humphrey, A. Dalke, K. Schulten, (1996) “VMD: visual molecular dynamics” J. Mole. Graph. 14 33–38.
[23] S.J. Stuart, A.B. Tutein, J.A. Harrison, (2000) “A reactive potential for hydrocarbons with intermolecular interactions”, J. Chem. Phys. 112 6472.
[24] P.M. Agrawal, B.S. Sudalayandi, L.M. Raff, R. Komanduri, (2006) “A comparison of different methods of Young's modulus determination for single-wall carbon nanotubes (SWCNT) using molecular dynamics (MD) simulations” Comput. Mater. Sci. 38, 271.
[25] K. Mylvaganam, L. Zhang (2004), “Important issues in a molecular dynamics simulation for characterising the mechanical properties of carbon nanotubes”, Carbon 42, 2025.
