A Modified Couple Stress Theory for Postbuckling Analysis of Timoshenko and Reddy-Levinson Single-Walled Carbon Nanobeams
Subject Areas : EngineeringM Akbarzadeh Khorshidi 1 , M Shariati 2
1 - Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
2 - Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
Keywords:
Abstract :
[1] Singha M.K., Lamachandra L.S., Bandyopadhyay J.N., 2001, Thermal postbuckling analysis of laminated composite plates, Composite Structures 54: 453-458.
[2] Yang J., Liew K.M., Wu Y.F., Kitipornchai S., 2006, Thermo-mechanical postbuckling of FGM cylindrical panels with temperature-dependant properties, International Journal of Solids and Structures 43: 307-324.
[3] Shariati M., Allahbakhsh H.R., 2010, Numerical and experimental investigations on the buckling of steel semi- spherical shells under various loadings, Thin-Walled Structures 48: 620-628.
[4] Shariati M., Rokhi M.M., 2010, Buckling of steel cylindrical shells with an elliptical cutout, International Journal of Steel Structures 10(2): 193-205.
[5] Shariati M., Sedighi M., Saemi J., Poorfar A.K., 2011, Numerical analysis and experimental study of buckling behavior of steel cylindrical panels, Steel Research International 82(3): 202-212.
[6] Yuan Zh., Wang X., 2011, Buckling and postbuckling analysis of extensible beam-columns by using the differential quadrature method, Computer and Mathematics with Applications 62: 4499-4513.
[7] Emam S.A., 2011, Analysis of shear-deformable composite beams in postbuckling, Composite Structures 94: 24-30.
[8] Daneshmehr A., Heydari M., Akbarzadeh Khorshidi M., 2013, Post-buckling analysis of FGM beams according to different shear deformation theories, International Journal of Multidisciplinary and Current Research 1: 37-49.
[9] Levinson M., 1981, A new rectangular beam theory, Journal of Sound and Vibration 74: 81-87.
[10] Reddy J.N., 1984, A simple higher-order theory for laminated composite plate, ASME Journal of Application Mechanics 51: 745-752.
[11] Yang F., Chong A.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory of elasticity, International Journal of Solids and Structures 39: 2731-2743.
[12] Ma H.M., Gao X.L., Reddy J.N., 2008, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids 56: 3379-3391.
[13] Asghari M., Kahrobaiyan M.H., Ahmadian M.T., 2010, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science 48: 1749-1761.
[14] Ma H.M., Gao X.L., Reddy J.N., 2010, A nonclassical Reddy-Levinson beam model based on a modified couple stress theory, Journal of Multiscale Computational Engineering 8(2): 167-180.
[15] Ke L.L., Wang Y., 2011, Size effect on dynamic stability of functionally graded microbeams based on modified couple stress theory, Composite Structures 93: 342-350.
[16] Akgoz B., Civalek O., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science 49: 1268-1280.
[17] Salamat-Talab M., Nateghi A., Torabi J., 2012, Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory, International Journal of Mechanical Sciences 57: 63-73.
[18] Roque C.M.C., Fidalgo D.S., Ferreira A.J.M., Reddy J.N., 2013, A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method, Composite Structures 96: 532-537.
[19] Mohammad-Abadi M., Daneshmehr A.R., 2014, Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions, International Journal of Engineering Science 74: 1-14.
[20] Shen H., Zhang Ch., 2006, Postbuckling prediction of axially loaded double-walled carbon nanotubes with temperature dependent properties and initial defects, Physical Review B 74: 035410.
[21] Wang C.M., Xiang Y., Kitipornchai S., 2009, Postbuckling of nano rods/tubes based on nonlocal beam theory, International Journal of Applied Mechanics 1(2): 259-266.
[22] Setoodeh A.R., Khosrownejad M., Malekzadeh P., 2011, Exact nonlocal solution for postbuckling of single-walled carbon nanotubes, Physica E 43:1730-1737.
[23] Li Y, Chen Ch., Fang B., Zhang J., Song J., 2012, Postbuckling of piezoelectric nanobeams with surface effects, International Journal of Applied Mechanics 4(2): 12500181-12500191.
[24] Ansari R., Mohammadi V., Faghih Shojaei M., Gholami R., Sahmani S., 2014, Postbuckling analysis of Timoshenko nanobeams including surface stress effect, International Journal of Engineering Science 75: 1-10.
[25] Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2011, Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225: 498-506.
[26] Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Han Q., 2011, Postbuckling equilibrium path of a long thin-walled cylindrical shell (single-walled carbon nanotubes) under axial compression using energy method, International Journal of Engineering 24(1): 79-86.
[27] Yao X., Han Q., 2007, Postbuckling prediction of double-walled carbon nanotubes under axial compression, European Journal of Mechanics A/Solids 26: 20-32.
[28] Rahmati A.H., Mohammadimehr M., 2014, Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM, Physica B: Condensed Matter 440: 88-98.
[29] Mohammadimehr M., Mohandes M., Moradi M., 2014, Size dependent effect on the buckling and vibration analysis of double bonded nanocomposite piezoelectric plate reinforced by BNNT based on modified couple stress theory, Journal of Vibration and Control doi: 10.1177/1077546314544513.
[30] Mindlin R.D., 1963, Influence of couple-stresses on stress concentrations, Experimental Mechanics 3: 1-7.
[31] Chong A.C.M., Yang F., Lam D.C.C., Tong, P., 2001, Torsion and bending of micron-scaled structures, Journal of Material Research 16: 1052-1058.
[32] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51: 1477-1508.