Buckling analysis of axially functionally graded carbon nanotubes-reinforced columns using the meshless method

Document Type : Research

Authors

1 Master, Department of Civil Engineering, Quchan University of Technology, Quchan, Iran.

2 Assistant Professor, Department of Civil Engineering, Quchan University of Technology, Quchan, Iran.

Abstract

The spread of different material processing technologies has led to the novel methods developed for reinforcing structural members. One of these approaches is to add the carbon nanotubes (CNTs) with different distributions through the matrix phase of composite materials to improve its properties. Due to superior properties such as lightweight and high values of elastic modulus, elastic strain, and failure strain, CNTs can be used to reinforce structures and elements. The present paper aims to investigate the effect of adding CNTs as reinforcement of matrix on the buckling capacity of columns. The meshless local Petrov-Galerkin (MLPG) method is applied for buckling analysis of CNT-reinforced columns. Since the MLPG method uses some scattered nodes through the domain and boundaries for discretization (rather than the meshing), the functionally graded (FG) variation of material properties can be conveniently modeled under the influence of reinforcing elements (CNTs). Four types of volume fraction exponent functions are considered for modeling the FG variation of the CNT volume fraction to examine the effect of CNTs distribution on the buckling capacity of the column and determine the most optimal distribution of CNTs. Effective mechanical properties of the CNT-reinforced column are estimated based on the extended rule of mixture. Results show that reinforcing the polymer matrix with a low volume fraction of CNTs with appropriate distribution can significantly increase its buckling capacity. Using the obtained results, one can determine the best distribution pattern of CNTs in the longitudinal direction of the column at various boundary conditions. 

Keywords


[1] Chen, W. F., and Lui, E. M., "Structural stability; theory and implementation", Elsevier, New York, 1987.
[2] Timoshenko, S. P., and Gere, J. M., "Theory of elastic stability", Courier Corporation, United States, 2009.
[3] Fiedler, B., Gojny, F.H., Wichmann, M.H.G., Nolte, M.C.M., and Schulte, K., "Fundamental aspects of nano-reinforced composites", Composites Science and Technology, 2006, Vol. 66, pp. 3115-3125.
[4] Rahai, A.R., and Kazemi, S., "Buckling analysis of non-prismatic columns based on modified vibration modes", Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 8, 2008, pp. 1721-1735.
[5] Wang, C. M., and Wang C. Y., "Exact solutions for buckling of structural members". CRC press, 2004.
[6] O'Rourke, M., and Zebrowski, T., "Buckling load for nonuniform columns", Computers & Structures, Vol. 7, No. 6, 1977, pp. 717-720.
[7] Dube, G.P., and Dumir, P.C., "Tapered thin open section beams on elastic foundation -I. Buckling analysis", Computers & structures, Vol. 61, No. 5, 1996, pp. 845-857.
[8] Sapountzakis, E. J., and Tsiatas, G. C., "Elastic flexural buckling analysis of composite beams of variable cross-section by BEM", Engineering Structures, Vol. 29, No. 5, 2007,pp. 675-681.
[9] Elfelsoufi, Z., and Azrar, L., "Buckling, flutter and vibration analyses of beams by integral equation formulations", Computers & Structures, Vol. 83, No. 31-32, 2005, pp. 2623-2649.
[10] Huang, Y., and Li, X.F., "Buckling analysis of nonuniform and axially graded columns with varying flexural rigidity", Journal of engineering mechanics, Vol. 137, No. 1, 2011, pp. 73-81.
[11] Bazeos, N., and Karabalis, D.L., "Efficient computation of buckling loads for plane steel frames with tapered members", Engineering Structures, Vol. 28, No. 5, 2006, pp. 771-775.
[12] Soltani, M., Asgarian, B., and Mohri, F., "Improved finite element model for lateral stability analysis of axially functionally graded nonprismatic I-beams", International Journal of Structural Stability and Dynamics, Vol. 19, No. 9, 2019, pp. 1950108.
[13] Liu, G.R., and Gu, Y.T., "An introduction to meshfree methods and their programming", Springer Science & Business Media, Netherlands, 2005.
[14] Heidargheitaghi, F., Ghadiri Rad, M.H., and Kazemi, M., "Buckling Analysis of Non-Prismatic Columns Subjected to Non-Uniform Loading Using the Meshless Local Petrov-Galerkin Method". Computational Methods in Engineering, Vol. 40, No. 2, 2022, pp.39-56.
[15] Soltani, M., "Flexural-torsional stability of sandwich tapered I-beams with a functionally graded porous core", Journal of Numerical Methods in Civil Engineering, Vol. 4, No. 3, 2020, pp. 8-20.
[16] Soltani, M., and Asgarian, B., "Finite element formulation for linear stability analysis of axially functionally graded nonprismatic timoshenko beam", International Journal of Structural Stability and dynamics, Vol. 19, No. 2, 2019, p.1950002.
[17] Soltani, M., Asgarian, B., and Jafarzadeh, F., "Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material", AUT Journal of Civil Engineering, Vol. 4, No. 1, 2020, pp.91-102.
[18] Soltani, M., "Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation", Mechanics of Advanced Composite Structures‎, Vol. 7, No. 2, 2020, pp.203-218.
[19] Soltani, M., and Asgarian, B., "Exact stiffness matrices for lateral-torsional buckling of doubly symmetric tapered beams with axially varying material properties", Iranian Journal of Science and Technology, Transactions of Civil Engineering, Vol. 45, No. 2, 2021, pp.589-609.
[20] Soltani, M., Atoufi, F., Mohri, F., Dimitri, R., and Tornabene, F., "Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials", Thin-Walled Structures, Vol. 159, 2021, p.107268.
[21] Soltani, M., Atoufi, F., Mohri, F., Dimitri, R., and Tornabene, F., "Nonlocal Analysis of the Flexural-Torsional Stability for FG Tapered Thin-Walled Beam Columns", Nanomaterials, Vol. 11, No. 8, 2021, p.1936.
[22] Rad, M.H.G., Shahabian, F., and Hosseini, S.M., "Geometrically nonlinear dynamic analysis of FG graphene platelets-reinforced nanocomposite cylinder: MLPG method based on a modified nonlinear micromechanical model", Steel and Composite Structures, Vol. 35, No. 1, 2020, pp. 77-92.
[23] Lee, C., Wei, X., Kysar, J.W., and Hone, J., "Measurement of the elastic properties and intrinsic strength of monolayer graphene", science, Vol. 321, No. 5887, 2008, pp. 385-388.
[24] Kazemi, M., Rad, M.H.G., and Hosseini, S.M., "Nonlinear dynamic analysis of FG carbon nanotube/epoxy nanocomposite cylinder with large strains assuming particle/matrix interphase using MLPG method", Engineering Analysis with Boundary Elements, Vol. 132, 2021, pp.126-145.
[25] Sudak, L., "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", Journal of applied physics, Vol. 94, No. 11, 2003, pp. 7281-7287.
[26] Goudah, G., Suliman, S.M.A., and Elfaki, E.A., "Carbon Nanotubes and Their Composites: A Review", Sudan Eng. Society Journals, Vol. 58, No. 1, 2019.
[27] Zhang, W., Suhr, J., and Koratkar, N.A., "Observation of high buckling stability in carbon nanotube polymer composites", Advanced Materials, Vol. 18, No. 4, 2006, pp. 452-456.
[28] Han, Y., and Elliott, J., "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Computational Materials Science, Vol. 39, No. 2, 2006, pp. 315-323.
[29] Yas, M., and N. Samadi, "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", International Journal of Pressure Vessels and Piping, Vol. 98, 2012, pp. 119-128.
[30] Lei, Z.X., Liew, K.M., and Yu, J.L., "Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment", Composite Structures, Vol. 106, 2013, pp. 128-138.
[31] Li, Q., Liu, J., and Xu, S., "Progress in research on carbon nanotubes reinforced cementitious composites", Advances in Materials Science and Engineering, 2015.
[32] Mirzaei, M., and Kiani, Y., "Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels", Composite Structures, Vol. 142, 2016, pp. 45-56.
[33] Arani, A.J., and Kolahchi, R., "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Computers and Concrete, Vol. 17, No. 5, 2016, pp. 567-578.
[34] Wang, Q., Qin, B., Shi, D., and Liang, Q., "A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution", Composite Structures, Vol. 174, 2017, pp. 87-109.
[35] Karami, B., Janghorban, M., Shahsavari, D., Dimitri, R., and Tornabene, F., "Nonlocal buckling analysis of composite curved beams reinforced with functionally graded carbon nanotubes", Molecules, Vol. 24, No. 15, 2019, p. 2750.
[36] Civalek, O., and Jalaei, M.H., "Shear buckling analysis of functionally graded (FG) carbon nanotube reinforced skew plates with different boundary conditions", Aerospace Science and Technology, Vol. 99, 2020, p. 105753.
[37] Liew, K.M., Lei, Z.X., and Zhang, L.W., "Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review", Composite Structures, Vol. 120, 2015, pp. 90-97.
[38] Ghayoumizadeh, H., Shahabian, F., and Hosseini, S.M., "Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs)", Engineering Analysis with Boundary Elements, Vol. 37, No. 11, 2013, pp. 1524-1531.
[39] Ghoohestani, S., Shahabian Moghadam, F., and Hosseini, S.M., "Dynamic analysis of a layered cylinder reinforced by functionally graded carbon nanotubes distributions subjected to shock loading using MLPG method", Computer Modeling in Engineering and Sciences-CMES, Vol. 100, No. 4, 2014, pp. 295-321.
[40] Rad, M.H.G., Shahabian, F., and Hosseini, S.M., "Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken FG cylinder subjected to shock loading using MLPG method", Engineering Analysis with Boundary Elements, Vol. 50, 2015, pp. 83-96.
[41] Hosseini, S.M., and Zhang, C., "Elastodynamic and wave propagation analysis in a FG graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model", Steel and Composite Structures, Vol. 27, No. 3, 2018, pp. 255-271.
[42] Hosseini, S.M., and Zhang, C., "Coupled thermoelastic analysis of an FG multilayer graphene platelets-reinforced nanocomposite cylinder using meshless GFD method: A modified micromechanical model", Engineering Analysis with Boundary Elements, Vol. 88, 2018, pp. 80-92.
[43] Nguyen, T.N., Thai, C.H., Luu, A.T., Nguyen-Xuan, H., and Lee, J., "NURBS-based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells", Computer Methods in Applied Mechanics and Engineering, Vol. 347, 2019, pp. 983-1003.
[44] Zhou, T., and Song, Y., "Three-dimensional nonlinear bending analysis of FG-CNTs reinforced composite plates using the element-free Galerkin method based on the SR decomposition theorem", Composite Structures, Vol. 207, 2019, pp. 519-530.
[45] Rad, M.H.G., Shahabian, F., and Hosseini, S.M., "A meshless local Petrov-Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping", Acta Mechanica, Vol. 226, No. 5, 2015, pp. 1497-1513.
[46] Raju, I.S., Phillips, D.R., and Krishnamurthy, T., "A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems", Computational Mechanics, Vol. 34, No. 6, 2004, pp. 464-474.
[47] Raju, I.S., and Phillips, D.R., "Further developments in the MLPG method for beam problems", Computer Modeling in Engineering and Sciences, Vol. 4, No. 1, 2003, pp.141-160.