zbMATH — the first resource for mathematics

Strain gradient finite element analysis on the vibration of double-layered graphene sheets. (English) Zbl 1359.74450

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
82B05 Classical equilibrium statistical mechanics (general)
Full Text: DOI
[1] Ansari, R., Arash, B. and Rouhi, H. [2011] ” Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity,” Compos. Struct.93, 2419-2429. genRefLink(16, ’S0219876216500110BIB001’, ’10.1016%252Fj.compstruct.2011.04.006’); genRefLink(128, ’S0219876216500110BIB001’, ’000291511300029’);
[2] Ansari, R., Rajabiehfard, R. and Arash, B. [2010] ” Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets,” Comput. Mater. Sci.49, 831-838. genRefLink(16, ’S0219876216500110BIB002’, ’10.1016%252Fj.commatsci.2010.06.032’); genRefLink(128, ’S0219876216500110BIB002’, ’000281592900016’);
[3] Arash, B., Wang, Q. and Liew, K. M. [2012] ” Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation,” Comput. Methods Appl. Mech. Eng.223, 1-9. genRefLink(16, ’S0219876216500110BIB003’, ’10.1016%252Fj.cma.2012.02.002’); genRefLink(128, ’S0219876216500110BIB003’, ’000303699600001’); · Zbl 1253.74051
[4] Askes, H. A., Suiker, S. J. and Sluys, L. J. [2002] ” A classification of higher-order strain-gradient models-linear analysis,” Arch. Appl. Mech.72, 171-188. genRefLink(16, ’S0219876216500110BIB004’, ’10.1007%252Fs00419-002-0202-4’); genRefLink(128, ’S0219876216500110BIB004’, ’000175424800009’); · Zbl 1065.74004
[5] Behfar, K. and Naghdabadi, R. [2005] ” Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium,” Compos. Sci. Technol.65, 1159-1164. genRefLink(16, ’S0219876216500110BIB005’, ’10.1016%252Fj.compscitech.2004.11.011’); genRefLink(128, ’S0219876216500110BIB005’, ’000229533700016’);
[6] Fleck, N. A., Muller, G. M., Ashby, M. F. and Hutchinson, J. W. [1994] ” Strain gradient plasticity: Theory and experiment,” Acta Metall. Mater.42, 475-487. genRefLink(16, ’S0219876216500110BIB006’, ’10.1016%252F0956-7151%252894%252990502-9’); genRefLink(128, ’S0219876216500110BIB006’, ’A1994MV47900011’);
[7] Geim, A. K. and Novoselov, K. S. [2007] ” The rise of graphene,” Nat. Mater.6, 183-191. genRefLink(16, ’S0219876216500110BIB007’, ’10.1038%252Fnmat1849’); genRefLink(128, ’S0219876216500110BIB007’, ’000244570700015’);
[8] Grantab, R., Shenoy, V. B. and Ruoff, R. S. [2010] ” Anomalous strength characteristics of tilt grain boundaries of graphene,” Science330, 946-948. genRefLink(16, ’S0219876216500110BIB008’, ’10.1126%252Fscience.1196893’); genRefLink(128, ’S0219876216500110BIB008’, ’000284118000037’);
[9] He, X. Q., Kitipornchai, S. and Liew, K. M. [2005a] ” Resonance analysis of multi-layered graphene sheets used as nanoscale resonators,” Nanotechnology16, 2086-2091. genRefLink(16, ’S0219876216500110BIB009’, ’10.1088%252F0957-4484%252F16%252F10%252F018’); genRefLink(128, ’S0219876216500110BIB009’, ’000232906200019’);
[10] He, X. Q., Kitipornchai, S. and Liew, K. M. [2005b] ” Buckling analysis of multi-walls carbon nanotubes: A continuum model accounting for van der Waals interaction,” J. Mech. Phys. Solids53, 303-326. genRefLink(16, ’S0219876216500110BIB010’, ’10.1016%252Fj.jmps.2004.08.003’); genRefLink(128, ’S0219876216500110BIB010’, ’000226555700003’); · Zbl 1162.74354
[11] Koiter, W. T. [1964] ” Couple stresses in the theory of elasticity,” Proc. Koninklijke Nederlandse Akademie Wetenschappen67, 17-44. · Zbl 0124.17405
[12] Lee, C. G., Wei, X. D., Kysar, J. W. and Hone, J. [2008] ” Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science321, 385-388. genRefLink(16, ’S0219876216500110BIB012’, ’10.1126%252Fscience.1157996’); genRefLink(128, ’S0219876216500110BIB012’, ’000257713900044’);
[13] Liu, R. M. and Wang, L. F. [2013] ” Thermal vibrations of single-layered graphene sheets by molecular dynamics,” J. Nanosci. Nanotechnol.13, 1059-1062. genRefLink(16, ’S0219876216500110BIB013’, ’10.1166%252Fjnn.2013.6127’); genRefLink(128, ’S0219876216500110BIB013’, ’000318254500067’);
[14] Ma, Q. and Clarke, D. R. [1995] ” Size dependent hardness of silver single crystals,” J. Mater. Res.10, 853-863. genRefLink(16, ’S0219876216500110BIB014’, ’10.1557%252FJMR.1995.0853’); genRefLink(128, ’S0219876216500110BIB014’, ’A1995QN59100009’);
[15] Mindlin, R. D. [1964] ” Microstructure in linear elasticity,” Arch. Ration. Mech. Anal.16, 51-78. genRefLink(16, ’S0219876216500110BIB015’, ’10.1007%252FBF00248490’); genRefLink(128, ’S0219876216500110BIB015’, ’A1964XL64200003’);
[16] Mindlin, R. D. and Tiersten, H. F. [1962] ” Effects of couple-stresses in linear elasticity,” Arch. Ration. Mech. Anal.11, 415-448. genRefLink(16, ’S0219876216500110BIB016’, ’10.1007%252FBF00253946’); genRefLink(128, ’S0219876216500110BIB016’, ’A1963XL62100002’);
[17] Novoselov, K. S., Firsov, A. A. et al. [2004] ” Electric field effect in atomically thin carbon films,” Science306, 666-669. genRefLink(16, ’S0219876216500110BIB017’, ’10.1126%252Fscience.1102896’); genRefLink(128, ’S0219876216500110BIB017’, ’000224756700045’);
[18] Pradhan, S. C. and Phadikar, J. K. [2009a] ” Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models,” Phys. Lett. A373, 1662-1069. · Zbl 1236.74116
[19] Pradhan, S. C. and Phadikar, J. K. [2009b] ” Nonlocal elasticity theory for vibration of nanoplates,” J. Sound Vib.325, 206-223. genRefLink(16, ’S0219876216500110BIB019’, ’10.1016%252Fj.jsv.2009.03.007’); genRefLink(128, ’S0219876216500110BIB019’, ’000267679800013’);
[20] Rao, C. N. R., Sood, A. K., Subrahmanyam, K. S. and Govindaraj, A. [2009] ” Graphene: The new two-dimensional nanomaterial,” Angew. Chem. Int. Ed. Engl.48, 7752-7777. genRefLink(16, ’S0219876216500110BIB020’, ’10.1002%252Fanie.200901678’); genRefLink(128, ’S0219876216500110BIB020’, ’000270846600005’);
[21] Shi, J. X., Ni, Q. Q., Lei, X. W. and Natsuki, T. [2013] ” Nonlocal vibration analysis of nanomechanical systems resonators using circular double-layer graphene sheets,” Appl. Phys. A115, 213-219. genRefLink(16, ’S0219876216500110BIB021’, ’10.1007%252Fs00339-013-7963-1’); genRefLink(128, ’S0219876216500110BIB021’, ’000333612400032’);
[22] Shu, J. Y, Wayne, E. K. and Fleck, N. A. [1999] ” Finite elements for materiels with strain gradient effects,” Int. J. Numer. Methods Eng.44, 373-391. genRefLink(16, ’S0219876216500110BIB022’, ’10.1002%252F%2528SICI%25291097-0207%252819990130%252944%253A3%253C373%253A%253AAID-NME508%253E3.0.CO%253B2-7’); genRefLink(128, ’S0219876216500110BIB022’, ’000078092700004’); · Zbl 0943.74072
[23] Soh, A. and Chen, W. J. [2004] ” Finite element formulations of strain gradient theory for microstructures and the C0-1 patch test,” Int. J. Numer. Methods Eng.61, 433-454. genRefLink(16, ’S0219876216500110BIB023’, ’10.1002%252Fnme.1075’); genRefLink(128, ’S0219876216500110BIB023’, ’000223870900006’);
[24] Stolken, J. S. and Evans, A. G. [1998] ” A microbend test method for measuring the plasticity length scale,” Acta Metall. Mater.46, 5109-5115. genRefLink(16, ’S0219876216500110BIB024’, ’10.1016%252FS1359-6454%252898%252900153-0’); genRefLink(128, ’S0219876216500110BIB024’, ’000076014400026’);
[25] Timoshenko, S. and Woinowsky-Krieger, S. [1959] Theory of Plates and Shells, 2nd Edition (McGraw-Hill Book Company, New York). · Zbl 0114.40801
[26] Toupin, R. A. [1962] ” Elastic materials with couple-stresses,” Arch. Ration. Mech. Anal.11, 385-414. genRefLink(16, ’S0219876216500110BIB026’, ’10.1007%252FBF00253945’); genRefLink(128, ’S0219876216500110BIB026’, ’A1963XL62100001’);
[27] Wang, L. F., Han, D., Liu, G. R. and Cui, X. Y. [2011] ” Free vibration analysis of double-walled carbon nanotubes using the smoothed finite element method,” Int. J. Comput. Methods8(4), 879-890. [Abstract] genRefLink(128, ’S0219876216500110BIB027’, ’000296781200018’); · Zbl 1245.74023
[28] Wang, L. F. and He, X. Q [2010] ” Vibration of a multilayered graphene sheet with initial stress,” J. Nanotechnol. Eng. Med.1(4), 041004-1-5. genRefLink(16, ’S0219876216500110BIB028’, ’10.1115%252F1.4002402’);
[29] Wang, L. F. and Hu, H. Y. [2005] ” Flexural wave propagation in single-walled carbon nanotubes,” Phys. Rev. B71, 195412-1-7.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.