-
In the present paper, the kinematic equation of a monolayer graphene is proposed based on a plate theory, and the nonlinear elasticity stress-strain relations are obtained from experiments. The equation includes cubic and quintic nonlinearities. The bending produced when subjected to a concentrated force at the center of the plate and the static buckling arising from edge in-plane axial uniform loads are investigated using Ritz methods for a simply-supported rectangular plate. Results suggest that the plate theory with nonlinear constitutive equation may characterize the mechanical property of a monolayer graphene appropriately, and the quintic nonlinearities have a significant effect on the bending deformations of the graphene.
-
Keywords:
- monolayer graphene /
- nonlinear constitutive equation /
- plate theory /
- Ritz methods
[1] Singh V, Joung D, Zhai L, Das S, Khondaker S I, Seal S 2011 Progress in Materials Science 56 1178
[2] Geim A K, Novoselov K S 2007 Nature Materials 6 183
[3] [4] Han T W, He P F 2010 Acta Phys. Sin. 59 3408 (in Chinese) [韩同伟, 贺鹏飞 2010 59 3408]
[5] [6] [7] Ouyang Y, Peng J C, Wang H, Yi S P 2008 Acta Phys. Sin. 57 615 (in Chinese) [欧阳玉, 彭景翠, 王慧, 易双萍 2008 57 615]
[8] Zhu G B, Zhang P 2013 Chin. Phys. B 22 017303
[9] [10] Sun L F, Dong L M, Fang C 2013 Chin. Phys. B 22 047203
[11] [12] Yakobson B I, Brabec C J, Bernholc J 1996 Phys. Rev. Lett. 76 2511
[13] [14] [15] Ouyang Z C, Su Z B, Wang C L 1997 Phys. Rev. Lett. 78 4055
[16] [17] Tu Z, Ouyang Z C 2002 Phy. Rev. B 65 233407
[18] Zhou X, Zhou J J, Ouyang Z C 2000 Phys. Rev. B 62 13692
[19] [20] [21] Dong J I, Gao X, Kong X Y, Li J M 2007 Chin. Phys. Lett. 24 165
[22] Kong Y, Li F S, Yang S J K 2007 Chin. Phys. Lett. 24 2036
[23] [24] Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385
[25] [26] [27] Cadelano E, Palla P L, Giordano S, Colombo L 2009 Phys. Rev. Lett. 102 235502
[28] Wu J, Hwang K C, Huang Y 2008 J. Mech. Phys. Solids 56 279
[29] [30] [31] Pradhan S C, Phadikar J K 2009 Phys. Lett. A 373 1062
[32] [33] Hwang K C, Xia Z X 1987 Theory of plate and shell (Beijing: Tsinghua University Press) p6 (in Chinese) [黄克智, 夏之熙1987板壳理论(北京: 清华大学出版社)第6页]
[34] [35] Washizu K 1975 Variational methods in elasticity and plasticity (Oxford: Pergamon Press) p5
[36] [37] Nayfeh A H, Mook D T 2008 Nonlinear oscillations (New York: Wiley. Com) p1
[38] Wu L Y 1989 Theory of plate and shell (Shanghai: Shanghai Jiaotong University Press) p5 (in Chinese) [吴连元1989板壳理论(上海: 上海交通大学出版社)第5页]
[39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] -
[1] Singh V, Joung D, Zhai L, Das S, Khondaker S I, Seal S 2011 Progress in Materials Science 56 1178
[2] Geim A K, Novoselov K S 2007 Nature Materials 6 183
[3] [4] Han T W, He P F 2010 Acta Phys. Sin. 59 3408 (in Chinese) [韩同伟, 贺鹏飞 2010 59 3408]
[5] [6] [7] Ouyang Y, Peng J C, Wang H, Yi S P 2008 Acta Phys. Sin. 57 615 (in Chinese) [欧阳玉, 彭景翠, 王慧, 易双萍 2008 57 615]
[8] Zhu G B, Zhang P 2013 Chin. Phys. B 22 017303
[9] [10] Sun L F, Dong L M, Fang C 2013 Chin. Phys. B 22 047203
[11] [12] Yakobson B I, Brabec C J, Bernholc J 1996 Phys. Rev. Lett. 76 2511
[13] [14] [15] Ouyang Z C, Su Z B, Wang C L 1997 Phys. Rev. Lett. 78 4055
[16] [17] Tu Z, Ouyang Z C 2002 Phy. Rev. B 65 233407
[18] Zhou X, Zhou J J, Ouyang Z C 2000 Phys. Rev. B 62 13692
[19] [20] [21] Dong J I, Gao X, Kong X Y, Li J M 2007 Chin. Phys. Lett. 24 165
[22] Kong Y, Li F S, Yang S J K 2007 Chin. Phys. Lett. 24 2036
[23] [24] Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385
[25] [26] [27] Cadelano E, Palla P L, Giordano S, Colombo L 2009 Phys. Rev. Lett. 102 235502
[28] Wu J, Hwang K C, Huang Y 2008 J. Mech. Phys. Solids 56 279
[29] [30] [31] Pradhan S C, Phadikar J K 2009 Phys. Lett. A 373 1062
[32] [33] Hwang K C, Xia Z X 1987 Theory of plate and shell (Beijing: Tsinghua University Press) p6 (in Chinese) [黄克智, 夏之熙1987板壳理论(北京: 清华大学出版社)第6页]
[34] [35] Washizu K 1975 Variational methods in elasticity and plasticity (Oxford: Pergamon Press) p5
[36] [37] Nayfeh A H, Mook D T 2008 Nonlinear oscillations (New York: Wiley. Com) p1
[38] Wu L Y 1989 Theory of plate and shell (Shanghai: Shanghai Jiaotong University Press) p5 (in Chinese) [吴连元1989板壳理论(上海: 上海交通大学出版社)第5页]
[39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77]
Catalog
Metrics
- Abstract views: 6528
- PDF Downloads: 453
- Cited By: 0
下载:
