[1] B. Arash, R. Ansari, Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain, Physica E, Vol. 42, pp. 2058 –2064, 2010.
[2] S. Sahmani, R. Ansari, On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Composite Structures, Vol. 95, pp. 430–442, 2013.
[3] B. Zhang, Y. He, D. Liu, Z. Gan, L. Shen, Non-classical Timoshenko beam element based on the strain gradient elasticity theory, Finite Elements in Analysis and Design, Vol. 79, pp. 22 – 39, 2014.
[4] M. Şimşek, Nonlinear Static and Free Vibration Analysis of Microbeams Based on the Non-linear Elastic Foundation Using Modified Couple Stress Theory and He’s Variational Method,
Composite Structures,
Vol. 112, , pp. 264-272, 2014.
[5] M. H. Ghayesh, H. Farokhi, M. Amabili, Nonlinear dynamics of a microscale beam based on the modified couple stress theory, Composites: Part B: Engineering, Vol. 50, pp. 318–324, 2013.
[6] M. Mohammadimehr, M. Mohandes, The Effect of Modified Couple Stress Theory on Buckling and Vibration Analysis of Functionally Graded Double-Layer Boron Nitride Piezoelectric Plate Based on CPT, Journal of Solid Mechanics, Vol. 7, No. 3, pp. 281-298, 2015.
[7] A. Ghorbanpour Arani, M. Abdollahian, R. Kolahchi, Nonlinear vibration of embedded smart composite microtube conveying fluid based on modified couple stress theory, Polymer Composites, Vol. 36, No. 7, pp. 1314-1324, 2015.
[8] R. A. Toupin, Elastic materials with couple stresses, Arch.Rational Mech.Anal, Vol. 11, pp. 385–414, 1962.
[9] R. D. Mindlin, H. F. Tiersten, Effects of couple-stresses in linear elasticity, Arch. Rational Mech. Anal, Vol. 11, pp. 415–448, 1962.
[10] W. T. Koiter, Couple stresses in the theory of elasticity, I and II.Proc.K.Ned.Akad.Wet.(B), Vol. 67, pp. 17–44, 1964.
[11] R. D. Mindlin, Micro-structure in linear elasticity, Arch.Rational Mech.Anal.Vol. 16, pp. 51–78, 1964.
[12] F. Yang, A. C. M. Chong, D. C. C. Lam, P. Tong, Couple stress Based Strain gradient theory for elasticity, Int.J.Solids Struct, Vol. 39, pp. 2731–2743, 2002.
[13] K. Shengli, Z. Shenjie, Z. Nie, K. Wang, The size-dependent natural frequency of Bernoulli–Euler micro-beams, J Eng Sci, Vol. 46, pp. 427–37, 2008.
[14] J. N. Reddy, J. Berry, Nonlinear theories of axisymmetric bending of functionally graded circular plates with modified couple stress, Compos Struct,Vol. 94, pp. 3664-3668, 2012.
[15] A. Ghorbanpour Arani, M. R. Bagheri, R. Kolahchi, Z. Khoddami Maraghi, Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory, Journal of Mechanical Science and Technology, Vol. 27, No. 9, pp. 2645-2658, 2013.
[16] F. Pampaloni, E. L. Florin, Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials, Trends Biotechnol, Vol. 26, pp. 302–310, 2008.
[17] H. G. Craighead, Nanoelectromechanical systems, Science, Vol. 290, pp. 1532–1535, 2000.
[18] M. Li, H. X. Tang, M. L. Roukes, Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications, Nat. Nanotech-nol. Vol. 2, pp. 114–120, 2007.
[19]M. Rahaeifard, M. H. Kahrobaiyan, M. T. Ahmadian, Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials, ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, San Diego, California, USA, August 30–September 2, 2009.
[20] Y. Tadi Beni, A. Koochi, M. Abadyan, Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS, Phys E,Vol. 43, pp. 979-988, 2011.
[21] M. Şimşek, J. N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int J of Eng Sci, Vol. 64, pp. 37–53, 2013.
[22] J. Abdi, A. Koochi, A.S. Kazemi, M. Abadyan, Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory, Smart Mater and Struct, Vol. 20, pp. 11-55, 2011.
[23] M. Şimşek, Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, Int J of Eng Sci, Vol. 48 No. 12, pp. 1721-1732, 2010.
[24] B. Akgöz, Ö. Civalek, Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory, Composite Structures, Vol. 98, pp. 314-322, 2013.
[25] M. Mohammad-Abadi, A. R. Daneshmehr, 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, Vol. 74, pp. 1-14, 2014.
[26] Y. G. Wang, W. H. Lin, N. Liu, Nonlinear free vibration of a microscale beam based on modified couple stress theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 47, pp. 80-85, 2013.
[27] Y. Tadi Beni, A. Koochi, M. R. Abadyan, Using modified couple stress theory for modeling the size dependent pull-in instability of torsional nano-mirror under Casimir force, Int J of Optomechatronics, Vol. 8, pp. 47-71, 2014.
[28] R. Li, G. A. Kardomateas, Vibration characteristics of multiwalled carbon nanotubes embedded in elastic media by a nonlocal elastic shell model, Journal of Applied Mechanics, Vol. 74, No. 6, pp. 1087-1094, 2007.
[29] H. Zeighampour, Y. Tadi Beni, Cylindrical thin-shell model based on modified strain gradient theory, International Journal of Engineering Science, Vol. 78, pp. 27–47, 2014.
[30] H. Zeighampour, Y. Tadi Beni, Analysis of conical shells in the framework of coupled stresses theory, International Journal of Engineering Science, Vol. 81, pp. 107-122, 2014.
[31] F. Mehralian, Y. Tadi Beni, Size-dependent torsional buckling analysis of functionally graded cylindrical shell, Composites, Part B, Vol. 94, pp. 11-25, 2016.
[33]S. Sahmani, R. Ansari, R. Gholami, A. Darvizeh, Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory, Composites: Part B, Vol. 51, pp. 44–53, 2013.
[34]
A. Ghorbanpour Arani,
S. Amir, A. R. Shajari,
M. R. Mozdianfard, Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory,
Composites Part B: Engineering, Vol. 43, No. 2, pp. 195-203, 2012.
[35] H. Zeighampour, Y. Tadi Beni, Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 61, pp. 28-39, 2014.
[36] D. H. Wu, W. T. Chien, C. J. Yang, Y. T. Yen, Coupled- field analysis of piezoelectric beam actuator using FEM, Sens Actuators A, Vol. 118, pp. 171–176, 2005.
[37] R. A. Coutu, P. E. Kladitis, L. A. Starman, J. R. Reid, A comparison of micro-switch analytic, finite element, and experimental results, Sens Actuators A,Vol. 115, pp. 252–258, 2004.
[38] F. Chapuis, F. Bastien, J. F. Manceau, F. Casset, P. L. Charvet, FEM modelling of Piezo-actuated microswitches, In: Seventh international conference on thermal, mechanical and multiphysics simulation and experiments in micro-electronics and micro-systems, EuroSime 2006, IEEE; April 24-26, 2006.
[39] B. Zhang, Y. He, D. Liu , Z. Gan, L. Shen, A non-classical Mindlin plate finite element based on a modified couple stress theory, European Journal of Mechanics A/Solids, Vol. 42, pp. 63-80, 2013.
[40] M. H. Kahrobaiyan, M. Asghari , M. T. Ahmadian, A Timoshenko beam element based on the modi fied couple stress theory, International Journal of Mechanical Sciences, Vol. 79, pp. 75–83, 2014.
[41] P. Metz, G. Alici, G. M. Spinks, A finite element model for bending behaviour of conducting polymer electromechanical actuators, Sens Actuators A, Vol. 130, pp. 1–11, 2006.
[42]S. A. Tajalli, M. Moghimi Zand, M.T. Ahmadian, Effect of geometric nonlinearity on dynamic pull-in behavior of coupled-domain microstructures based on classical and shear deformation plate theories, Eur J Mech A Solids, Vol. 28, pp. 916 –9 25, 2009.
[43] J. Jiang, M. D. Olson, Nonlinear analysis of orthogonally stiffened cylindrical shells by a super element approach, Finite elements in Analysis and Design, Vol. 18, No. 1, pp. 99-110, 1994.
[44] S. A. Lukasiewicz, Geometrical super-elements for elasto-plastic shells with large deformation, Finite Elements in Analysis and design, Vol. 3, No. 3, pp. 199-211, 1987.
[45] T. S. Koko, M. D. Olson, Vibration analysis of stiffened plates by super elements, Journal of Sound and Vibration, Vol. 158, No.1, pp. 149-167, 1992.
[46] M. T. Ahmadian, M. Sherafati Zangeneh, Vibration analysis of orthotropic rectangular plates using superelements, Computer methods in applied mechanics and engineering, Vol. 191, No. 19, pp. 2097-2103, 2002.
[47] M.T. Ahmadian, M. Bonakdar, A new cylindrical element formulation and its application to structural analysis of laminated hollow cylinders, Finite Elements in Analysis and Design, Vol. 44, pp. 617–630, 2008.
[48] A.W. Leissa, Vibration of shells, published for the Acoustical Society of America through the American Institute of Physics, 1993.
[49] R. Gholami, R. Ansari, A. Darvizeh, S. Sahmani, Axial Buckling and Dynamic Stability of Functionally Graded Microshells Based on the Modifed Couple Stress Theory, International Journal of Structural Stability and Dynamics, Vol. 15, No. 4, pp. 1450070-94 2014.
)