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Analytical and numerical investigations on buckling behavior of nanotube structures

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Abstract

One of the significant issues in the nanotube research community is buckling behavior. In the present work, the buckling of single-walled nanotubes (SWNTs), double-walled nanotubes (DWNTs) and multi-walled nanotubes (MWNTs) under axial compression is investigated. Buckling analysis for nanotube composite structures is performed by using layer-wise theory based on the nonlocal constitutive relations of Eringen. The governing equations of SWNTs, DWNTs and MWNTs are developed. Then analytical solutions are obtained using the state-space method. The effects of nanotube length, diameter and nonlocal parameter on the buckling loads are studied. The numerical results indicate that the nonlocal parameter is important for the buckling analysis of nanotube composite structures.

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References

  1. Iijima, S.: Helical Microtubules of Graphitic Carbon. Nature Publishing Group, London (1991)

  2. Naghashpour A., Hoa S.V.: A technique for real-time detecting, locating, and quantifying damage in large polymer composite structures made of carbon fibers and carbon nanotube networks. J. Struct. Health Monit. (SHM) 14(1), 34–45 (2015)

    Google Scholar 

  3. Naghashpour A., Hoa S.V.: In-situ monitoring of through-thickness strain in composite laminates using carbon nanotube sensors. J. Compos. Sci. Technol. 78, 41–47 (2013)

    Article  Google Scholar 

  4. Naghashpour A., Hoa S.V.: A technique for real-time detection, location and quantification of damages in large polymer composite structures made of electrically non-conductive fibers and carbon nanotube networks. J. Nanotechnol. 24, 455–502 (2013)

    Google Scholar 

  5. Thostenson E.T., Chou T.W.: Carbon nanotube networks: sensing of distributed strain and damage for life prediction and self-healing. Adv. Mater. 18, 2837–2841 (2006)

    Article  Google Scholar 

  6. Arash B., Wang Q.: A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput. Mater. Sci. 51(1), 303–313 (2012)

    Article  Google Scholar 

  7. Yazdani Sarvestani, H., Naghashpour, A.: Investigation of through-thickness stresses in composite laminates using layerwise theory. Int. J. Eng. Math. 2013, 1–11, Art. ID 676743 (2013). doi:10.1155/2013/676743

  8. Yazdani Sarvestani H., Naghashpour A., Heidari-Rarani M.: Prediction of interlaminar stresses of an unsymmetric cross-ply laminate using layerwise and higher-order equivalent single-layer theories. Int. J. Aerosp. Lightweight Struct. 3(4), 419–444 (2013)

    Article  Google Scholar 

  9. Yazdani Sarvestani, H., Naghashpour, A.: Analysis of free edge stresses in composite laminates using higher order theories. Indian J. Mater. Sci. 2014, 1–15, Art. ID 253018 (2014). doi:10.1155/2014/253018

  10. Yazdani Sarvestani, H., Naghashpour, A., Heidari-Rarani, M.: Bending analysis of a general cross-ply laminate using 3D elasticity solution and layerwise theory. Int. J. Comput. Methods (submitted)

  11. Eringen A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  12. Eringen A.C.: Continuum Physics Volume IV: Polar and Nonlocal Field Theories. Academic Press, New York (1976)

    Google Scholar 

  13. Eringen A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)

    Article  Google Scholar 

  14. Eringen A.C., Edelen D.G.B.: On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  15. Peddieson J., Buchanan G.R., McNitt R.P.: Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci. 41, 305–312 (2003)

    Article  Google Scholar 

  16. Sudak L.J.: Column buckling of multi-walled carbon nanotubes using nonlocal continuum mechanics. J. Appl. Phys. 94, 7281–7287 (2003)

    Article  Google Scholar 

  17. Zhang Y.Q., Liu G.R., Wang J.S.: Small-scale effects on buckling of multi-walled carbon nanotubes under axial compression. Phys. Rev. B 70, 205430 (2004)

    Article  Google Scholar 

  18. Wang Q., Varadan V.K., Quek S.T.: Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models. Phys. Lett. A 357, 130–135 (2006)

    Article  Google Scholar 

  19. Reddy J.N.: Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007)

    Article  MATH  Google Scholar 

  20. Reddy J.N., Pang S.D.: Nonlocal continuum theories of beams for the analysis of carbon nanotubes. J. Appl. Phys. 103, 023511 (2008)

    Article  Google Scholar 

  21. Kumar D., Heinrich C., Waas A.M.: Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories. J. Appl. Phys. 103, 073521 (2008)

    Article  Google Scholar 

  22. Ma H.M., Gao X.-L., Reddy J.N.: A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. J. Mech. Phys. Solids 56, 3379–3391 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  23. Wang C.M., Zhang Y.Y., Xiang Y., Reddy J.N.: Recent studies on buckling of carbon nanotubes. Appl. Mech. Rev. 63, 030804 (2010)

    Article  Google Scholar 

  24. Silvestre N., Wang C.M., Zhang Y.Y., Xiang Y.: Sanders shell model for buckling of single-walled carbon nanotubes with small aspect ratio. Compos. Struct. 93, 1683–1691 (2011)

    Article  Google Scholar 

  25. Aydogdu M.: A general nonlocal beam theory: its application to nanobeams bending buckling and vibration. Physica E 41, 1651–1655 (2009)

    Article  Google Scholar 

  26. Feliciano J., Tang C., Zhang Y., Chen C.: Aspect ratio dependent buckling mode transition in single-walled carbon nanotubes under compression. J. Appl. Phys. 109, 084323 (2011)

    Article  Google Scholar 

  27. Treacy M.M.J., Ebbesen T.W., Gibson J.M.: Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381, 678–680 (1996)

    Article  Google Scholar 

  28. Wei X.L., Chen Q., Peng L.M., Cui R.L., Li Y.: Tensile loading of double-walled and triple-walled carbon nanotubes and their mechanical properties. J. Phys. Chem. C 39(113), 17002–17005 (2009)

    Article  Google Scholar 

  29. Yu M.F., Lourie O., Dyer M.J., Moloni K., Kelly T.F., Ruoff R.S.: Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science 287(5453), 637–640 (2000)

    Article  Google Scholar 

  30. Wang X., Yang H.K.: Bending stability of multiwalled carbon nanotubes. Phys. Rev. B 73, 5401–5409 (2006)

    Google Scholar 

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Authors and Affiliations

  1. Concordia Centre for Composites (CONCOM), Department of Mechanical and Industrial Engineering, Concordia University, Montreal, H3G1M8, Canada

    Hamidreza Yazdani Sarvestani & Ali Naghashpour

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  1. Hamidreza Yazdani Sarvestani
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  2. Ali Naghashpour
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Correspondence to Hamidreza Yazdani Sarvestani.

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Yazdani Sarvestani, H., Naghashpour, A. Analytical and numerical investigations on buckling behavior of nanotube structures. Acta Mech 226, 3695–3705 (2015). https://doi.org/10.1007/s00707-015-1434-z

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  • DOI: https://doi.org/10.1007/s00707-015-1434-z

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