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Mechanical nature of a single walled carbon nanotube using Legendre’s polynomials

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Języki publikacji
EN
Abstrakty
EN
This paper is concerned with the mechanical response of a single-walled carbon nanotube. Euler-Bernoulli’s beam theory and Hamilton’s principle are employed to derive the set of governing differential equations. An efficient variational method is used to determine the solution of the problem and Legendre’s polynomials are used to define basis functions. Significance of using these polynomials is their orthonormal property as these shape functions convert mass and stiffness matrices either to zero or one. The impact of various parameters such as length, temperature and elastic medium on the buckling load is observed and the results are furnished in a uniform manner. The degree of accuracy of the obtained results is verified with the available literature, hence illustrates the validity of the applied method. Current findings show the usage of nanostructures in vast range of engineering applications. It is worth mentioning that completely new results are obtained that are in validation with the existing results reported in literature.
Rocznik
Strony
1153--1162
Opis fizyczny
Bibliogr. 25 poz., rys., tab.
Twórcy
autor
  • Centre for Advanced Computational Solutions, Lincoln University, New Zealand, parultiwari8922@gmail.com
  • Jaypee Institute of Information Technology, Noida, Uttar Pradesh, India
autor
  • Jaypee Institute of Information Technology, Noida-201309, Uttar Pradesh, India
Bibliografia
  • 1. Ansari R., Gholami R., Darabi M.A., 2011, Thermal buckling analysis of embedded singlewalled carbon nanotubes with arbitrary boundary conditions using the nonlocal Timoshenko beam theory, Journal of Thermal Stresses, 34, 12, 1271-1281
  • 2. Benzair A., Tounsi A., Besseghier A., Heireche H., Moulay N., Boumia L., 2008, The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics, 41, 22, 225404
  • 3. Chakraverty S., Behera L., 2015, Vibration and buckling analyses of nanobeams embedded in an elastic medium, Chinese Physics B, 24, 9, 097305
  • 4. Challamel N., 2011, Higher-order shear beam theories and enriched continuum, Mechanics Research Communications, 38, 5, 388-392
  • 5. Dai H., Hafner J.H., Rinzler A.G., Colbert D.T., Smalley R.E., 1996, Nanotubes as nanoprobes in scanning probe microscopy, Nature, 384, 6605, 147-150
  • 6. Eringen A.C., 1972, Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science, 10, 5, 425-435
  • 7. Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 9, 4703
  • 8. Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer Science & Business Media
  • 9. Iijima S., 1991, Helical microtubules of graphitic carbon, Nature, 354, 6348, 56-58
  • 10. Kim P., Lieber C.M., 1999, Nanotube nanotweezers, Science, 286, 5447, 2148-2150
  • 11. Li X., Bhushan B., Takashima K., Baek C.W., Kim Y.K., 2003, Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques, Ultramicroscopy, 97, 1-4, 481-494
  • 12. Lu Q., Bhattacharya B., 2005, The role of atomistic simulations in probing the small-scale aspects of fracture – a case study on a single-walled carbon nanotube, Engineering Fracture Mechanics, 72, 13, 2037-2071
  • 13. Murmu T., Pradhan S.C., 2009, Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E: Low-Dimensional Systems and Nanostructures, 41, 7, 1232-1239
  • 14. Murmu T., Pradhan S.C., 2010, Thermal effects on the stability of embedded carbon nanotubes, Computational Materials Science, 47, 3, 721-726
  • 15. Nagar P., Tiwari P., 2017, Recursive differentiation method to study the nature of carbon nanobeams: A numerical approach, AIP Conference Proceedings, 1897, 1, 020009, AIP Publishing
  • 16. Nejad Z.M., Hadi A., 2016, Eringen’s non-local elasticity theory for bending analysis of bidirectional functionally graded Euler-Bernoulli nano-beams, International Journal of Engineering Science, 106, 1-9
  • 17. Norouzzadeh A., Ansari R., 2017, Finite element analysis of nano-scale Timoshenko beams using the integral model of nonlocal elasticity, Physica E: Low-Dimensional Systems and Nanostructures, 88, 194-200
  • 18. Peddieson J., Buchanan G.R., McNitt R.P., 2003, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 3, 305-312
  • 19. Pradhan S.C., Reddy G.K., 2011, Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM, Computational Materials Science, 50, 3, 1052-1056
  • 20. Rafiee R., Moghadam R.M., 2014, On the modeling of carbon nanotubes: A critical review, Composites Part B: Engineering, 56, 435-449
  • 21. Reddy J.N., El-Borgi S., 2014, Eringen’s nonlocal theories of beams accounting for moderate rotations, International Journal of Engineering Science, 82, 159-177
  • 22. Sakharova N.A., Antunes J.M., Pereira A.F.G., Fernandes J.V., 2017, Developments in the evaluation of elastic properties of carbon nanotubes and their heterojunctions by numerical simulation, AIMS Materials Science, 4, 3, 706-737
  • 23. Semmah A., Tounsi A., Zidour M., Heireche H., Naceri M., 2015, Effect of the chirality on critical buckling temperature of zigzag single-walled carbon nanotubes using the nonlocal continuum theory, Fullerenes, Nanotubes and Carbon Nanostructures, 23, 6, 518-522
  • 24. Wang C.M., Zhang Y.Y., Ramesh S.S., Kitipornchai S., 2006, Buckling analysis of microand nano-rods/tubes based on nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics, 39, 17, 3904
  • 25. Wang Q., Varadan V.K., Quek S.T., 2006, Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models, Physics Letters A, 357, 2, 130-135
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f328c86a-67fc-4665-aa86-33ab8552a7e5
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