Malikan, M. (2019). On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory. Journal of Applied and Computational Mechanics, 5(1), 103-112. doi: 10.22055/jacm.2018.25507.1274

Mohammad Malikan. "On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory". Journal of Applied and Computational Mechanics, 5, 1, 2019, 103-112. doi: 10.22055/jacm.2018.25507.1274

Malikan, M. (2019). 'On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory', Journal of Applied and Computational Mechanics, 5(1), pp. 103-112. doi: 10.22055/jacm.2018.25507.1274

Malikan, M. On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory. Journal of Applied and Computational Mechanics, 2019; 5(1): 103-112. doi: 10.22055/jacm.2018.25507.1274

On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory

^{}Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Mashhad Branch, Iran

Abstract

In the present study, the buckling analysis of single-walled carbon nanotubes (SWCNT) on the basis of a new refined beam theory is analyzed. The SWCNT is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new proposed beam theory has only one unknown variable which leads to one equation similar to Euler beam theory and is also free from any shear correction factors. The equilibrium equation is formulated by the nonlocal elasticity theory in order to predict small-scale effects. The equation is solved by Navier’s approach by which critical buckling loads are obtained for simple boundary conditions. Finally, to approve the results of the new beam theory, some available well-known references are compared.

[1] M. Pacios Pujadó, Carbon Nanotubes as Platforms for Biosensors with Electrochemical and Electronic Transduction, Springer Heidelberg, (2012), DOI: 10.1007/978-3-642-31421-6.

[2] F. Liu, R. M. Wagterveld, B. Gebben, M. J. Otto, P. M. Biesheuvel, H. V. M. Hamelers, Carbon nanotube yarns as strong flexible conductive capacitive electrodes, Colloids and Interface Science Communications, 3 (2014) 9–12.

[3] Ch. B. Parker, S. A. Raut, B. Brown, B. R. Stoner, J. T. Glass, Three-dimensional arrays of graphenated carbon nanotubes, Journal of Materials Research, 27 (2012) 1046–1053.

[4] S. Iijima, Helical microtubules of graphitic carbon, Nature, 354 (1991) 56–58.

[5] M.-F.Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F. Kelly, R. S. Ruoff, Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load, Science, 287 (2000) 637–640.

[6] E. Pop, D. Mann, Q. Wang, K. Goodson, H. Dai, Thermal conductance of an individual single-wall carbon nanotube above room temperature, Nano Letters, 6 (2005) 96–100.

[7] S. Sinha, S. Barjami, G. Iannacchione, A. Schwab, G. Muench, Off-axis thermal properties of carbon nanotube films, Journal of Nanoparticle Research, 7 (2005) 651–657.

[8] K. K. Koziol, D. Janas, E. Brown, L. Hao, Thermal properties of continuously spun carbon nanotube fibres, Physica E: Low-dimensional Systems and Nanostructures, 88 (2017) 104–108.

[9] J. W. Mintmire, B. I. Dunlap, C. T. White, Are Fullerene Tubules Metallic?, Physical Review Letters, 68 (1992) 631–634.

[10] X. Lu, Z. Chen, Curved Pi-Conjugation, Aromaticity, and the Related Chemistry of Small Fullerenes (C60) and Single-Walled Carbon Nanotubes, Chemical Reviews, 105 (2005) 3643–3696.

[11] T. A. Hilder, J. M. Hill, Modeling the Loading and Unloading of Drugs into Nanotubes, Small, 5 (2009) 300–308.

[12] G. Pastorin, Crucial Functionalizations of Carbon Nanotubes for Improved Drug Delivery: A Valuable Option?, Pharmaceutical Research, 26 (2009) 746–769.

[13] A. A. Bhirde, V. Patel, J. Gavard, G. Zhang, A. A. Sousa, A. Masedunskas, R. D. Leapman, R. Weigert, J. S. Gutkind, J. F. Rusling, Targeted Killing of Cancer Cells in Vivo and in Vitro with EGF-Directed Carbon Nanotube-Based Drug Delivery, ACS Nano, 3 (2009) 307–316.

[14] M. Malikan, M. Jabbarzadeh, Sh. Dastjerdi, Non-linear Static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum, Microsystem Technologies, 23 (2017) 2973-2991.

[15] M. Malikan, Buckling analysis of a micro composite plate with nano coating based on the modified couple stress theory, Journal of Applied and Computational Mechanics, 4 (2018) 1–15.

[16] M. Malikan, Analytical predictions for the buckling of a nanoplate subjected to nonuniform compression based on the four-variable plate theory, Journal of Applied and Computational Mechanics, 3 (2017) 218–228.

[17] X. Yao, Q. Han, The thermal effect on axially compressed buckling of a double-walled carbon nanotube, European Journal of Mechanics A/Solids, 26 (2007) 298–312.

[18] R. Ansari , R. Gholami , M. Faghih Shojaei , V. Mohammadi , M.A. Darabi, Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin′s strain gradient theory, Applied Mathematical Modelling, 40(23–24) (2016) 9872-9891.

[19] H. L. Dai , S. Ceballes , A. Abdelkefi , Y. Z. Hong , L. Wang , Exact modes for post-buckling characteristics of nonlocal nanobeams in a longitudinal magnetic field, Applied Mathematical Modelling, 55 (2018) 758-775.

[20] B. L. Wang, M. Hoffman, A. B. Yu, Buckling analysis of embedded nanotubes using gradient continuum theory, Mechanics of Materials, 45 (2012) 52–60.

[21] L. L. Ke, Y. Xiang, J. Yang, S. Kitipornchai, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Computational Materials Science, 47 (2009) 409–417.

[22] R. Ansari, S. Sahmani, H. Rouhi, Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh–Ritz technique, Computational Materials Science, 50 (2011) 3050–3055.

[23] R. Ansari, M. Faghih Shojaei, V. Mohammadi, R. Gholami, H. Rouhi, Buckling and postbuckling of single-walled carbon nanotubes based on a nonlocal Timoshenko beam model, Z. Angew. Math. Mech., 95(9) (2015) 939-951.

[24] R. Ansari, A. Arjangpay, Nanoscale vibration and buckling of single-walled carbon nanotubes using the meshless local Petrov–Galerkin method, Physica E, 63 (2014) 283–292.

[25] H.-Sh. Shen, X.-Q. He, D.-Q. Yang, Vibration of thermally postbuckled carbon nanotube-reinforced composite beams resting on elastic foundations, International Journal of Non-Linear Mechanics, 91 (2017) 69-75.

[26] F. Mehralian, Y. Tadi Beni, M. Karimi Zeverdejani, Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes, Physica B: Condensed Matter, 514 (2017) 61-69.

[27] Y.-Z. Wang, Y.-S. Wang, L.-L. Ke, Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory, Physica E: Low-dimensional Systems and Nanostructures, 83 (2016) 195-200.

[28] R. Ansari, R. Gholami, S. Sahmani, Prediction of compressive post-buckling behavior of single-walled carbon nanotubes in thermal environments, Applied Physics A, 113 (2013) 145-153.

[29] R. Ansari, R. Gholami, S. Ajori, Torsional vibration analysis of carbon nanotubes based on the strain gradient theory and molecular dynamic simulations, Journal of Vibration and Acoustics, 135 (2013) 051016.

[30] R. Ansari, R. Gholami, Dynamic stability analysis of embedded single walled carbon nanotubes including thermal effects, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 39(M1+) (2015) 153.

[31] R. Ansari, R. Gholami, S. Sahmani, A. Norouzzadeh, M. Bazdid-Vahdati, Dynamic stability analysis of embedded multi-walled carbon nanotubes in thermal environment, Acta Mechanica Solida Sinica, 28 (2015) 659-667.

[32] R. Ansari, R. Gholami, A. Norouzzadeh, M. A. Darabi, Wave characteristics of nanotubes conveying fluid based on the non-classical Timoshenko beam model incorporating surface energies, Arabian Journal for Science and Engineering, 41 (2016) 4359-4369.

[33] Z. J. Zhang, Y. S. Liu, H. L. Zhao, W. Liu, Acoustic nanowave absorption through clustered carbon nanotubes conveying fluid, Acta Mechanica Solida Sinica, 29 (2016) 257–270.

[34] L. Wang, Y. Z. Hong, H. L. Dai, Q. Ni, Natural frequency and stability tuning of cantilevered CNTs conveying fluid in magnetic field, Acta Mechanica Solida Sinica, 29 (2016) 567–576.

[35] R. Ansari, R. Gholami, Dynamic stability analysis of multi-walled carbon nanotubes with arbitrary boundary conditions based on the nonlocal elasticity theory, Mechanics of Advanced Materials and Structures, 24 (2017) 1180-1188.

[36] Y. W. Zhang, L. Zhou, B. Fang, T. Z. Yang, Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid, Acta Mechanica Solida Sinica, 30 (2017) 550–556.

[37] J. Jiang, L. Wang, Analytical solutions for thermal vibration of nanobeams with elastic boundary conditions, Acta Mechanica Solida Sinica, 30 (2017) 474-483.

[38] M. Malikan, Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory, Applied Mathematical Modelling, 48 (2017) 196–207.

[39] R. P. Shimpi, Refined Plate Theory and Its Variants, AIAA Journal, 40 (2002) 137-146.

[40] M. Malikan, Temperature influences on shear stability a nanosize plate with piezoelectricity effect, Multidiscipline Modeling in Materials and Structures, 14 (2017) 125-142.

[41] M. Malikan, M. N. Sadraee Far, (2018), Differential quadrature method for dynamic buckling of graphene sheet coupled by a viscoelastic medium using neperian frequency based on nonlocal elasticity theory, Journal of Applied and Computational Mechanics, 4(3) (2018) 147-160.

[42] M. Malikan, V. B. Nguyen, Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 102 (2018) 8-28.

[43] C. M. Wang, Y. Y. Zhang, S. S. Ramesh, S. Kitipornchai, Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics, 39 (2006) 3904-3909.

[44] S. C. Pradhan, G. K. Reddy, Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM, Computational Materials Science, 50 (2011) 1052–1056.

[45] E. Ghavanloo, S.A. Fazelzadeh, Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect, Applied Mathematical Modelling, 36 (2012) 4988-5000.

[46] D. H. Robertson, D. W. Brenner, J. W. Mintmire, Energetics of nanoscale graphitic tubules, Physical Review B, 45 (1992) 12592.

[47] A. Benzair, A. Tounsi, A. Besseghier, H. Heireche, N. Moulay, L. Boumia, The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics, 41 (2008) 2254041.

[48] T. Murmu, S. Adhikari, Nonlocal transverse vibration of double-nanobeam-systems, Journal of Applied Physics, 108 (2010) 083514.

[49] P. Ponnusamy, A. Amuthalakshmi, Influence of thermal and magnetic field on vibration of double walled carbon nanotubes using nonlocal Timoshenko beam theory, Procedia Materials Science, 10 (2015) 243-253.