[1] Eltaher M. A., Khater M. E., Emam S. A., (2016), Review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model. 40: 4109–4128.
[2] Farajpour A., Ghayesh M. H., Farokhi H., (2018), A review on the mechanics of nanostructures. Int. J. Eng. Sci. 133: 231–263.
[3] Chandel V. S., Wang G., Talha M., (2020), Advances in modelling and analysis of nano structures: A review. Nanotechnol. Rev. 9: 230–258.
[4] Eringen A. C., (1983), On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54: 4703-4710.
[5] Bernoulli J., (1694), Curvatura laminae elasticae. Acta Eruditorum Lipsiae. 3: 262–276.
[6] Timoshenko S. P., (1921), On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philos. Mag. 41: 742–746.
[7] Sayyad A. S., Ghugal Y. M., (2015), On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results. Compos. Struct. 129: 177–201.
[8] Sayyad A. S., Ghugal Y. M., (2017), Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature. Compos. Struct. 171: 486–504.
[9] Sayyad A. S., Ghugal Y. M., (2018), Modeling and analysis of functionally graded sandwich beams: A review. Mech. Adv. Mater. Struct. 26: 1776-1795.
[10] Reddy J. N., (2007), Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45: 288-307.
[11] Nikam R. D., Sayyad A. S., (2020), A unified nonlocal formulation for bending, buckling and free vibration analysis of nanobeams. Mech. Adv. Mater. Struct. 27: 807-815.
[12] Thai H., (2012), A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int. J. Eng. Sci. 52: 56–64.
[13] Thai H., Vo T. P., (2012), A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. Int. J. Eng. Sci. 54: 58–66.
[14] Thai S., Thai H-T., Vo T. P., Patel, V. I., (2018), A simple shear deformation theory for nonlocal beams. Compos. Struct. 183: 262–270.
[15] Darjani H., Mohammadabadi H., (2014), A new deformation beam theory for static and dynamic analysis of microbeams. Int. J. Mech. Sci. 89: 31–39.
[16] Hashemi S. H., Khaniki H. B., (2017), Vibration analysis of a timoshenko non-uniform nanobeam based on nonlocal theory: An analytical solution. Int. J. Nano Dimens. 8: 70-81.
[17] Arefi M., (2019), Magneto-electro-mechanical size-dependent vibration analysis of three-layered nanobeam with initial curvature considering thickness stretching. Int. J. Nano Dimens. 10: 48-61.
[18] Aydogdu M., (2009), A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration. Physica E: Low Dimens. Syst. Nanostruct. 41: 1651-1655.
[19] Bouazza M., Amara K., Zidour M., Tounsi A., Bedia E. A. A., (2015), Postbuckling analysis of nanobeams using trigonometric shear deformation theory. App. Sci. Report 10: 112-121.
[20] Mahmoud F. F., Eltaher M. A., Alshorbagy A. E., Meletis E. I., (2012), Static analysis of nanobeams including surface effects by nonlocal finite element. J. Mech. Sci. Technol. 26: 3555-3563.
[21] Roque C. M. C., Ferreira A. J. M., Reddy J. N., (2011), Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method. Int. J. Eng. Sci. 49: 976–984.
[22] Tounsi A., Semmah A., Bousahla A. A., (2013), Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory. J. Nanomech. Micromech. 3: 37-42.
[23] Akgoz B., Civalek O., (2014), A new trigonometric beam model for buckling of strain gradient microbeams. Int. J. Mech. Sci. 81: 88–94.
[24] Akgoz B., Civalek O., (2012), Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory. Arch. Appl. Mech. 82: 423–443.
[25] Bedia W. A., Houari M. S. A., Bessaim A., Bousahla A. A., Tounsi A., Saeed T., Alhodaly M. S., (2019), New hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams. J. Nano Res. 57: 175-191.
[26] Simsek M., Yurtcu H. H., (2013), Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos. Struct. 97: 378–386.
[27] Simsek M., Reddy J. N., (2013), Bending and vibration of functionally graded micro beams using a new higher order beam theory and the modified couple stress theory. Int. J. Eng. Sci. 64: 37-53.
[28] Akgoz B., Civalek O., (2015), Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Compos. Struct. 134: 294-301.
[29] Lei J., He Y., Zhang B., Gan Z., Zeng P., (2013), Bending and vibration of functionally graded sinusoidal micro beams based on the strain gradient elasticity theory. Int. J. Eng. Sci. 72: 36-52.
[30] Ebrahimi F., Barati M. R., (2015), A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams. Arab. J. Sci. Eng. 115: 41-50.
[31] Ansari R., Gholami R., Shojaei M. F., Mohammadi V., Sahmani S., (2013), Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory. Compos. Struct. 100: 385–397.
[32] Yu T., Hu H., Zhang J., Bui T. Q., (2019), Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory. Thin Walled Struct. 138: 1–14.
[33] Aria A. I., Friswell M. I., (2019), A nonlocal finite element model for buckling and vibration of functionally graded nanobeams. Compos. Part B- Eng. 166: 233–246.
[34] Reddy J. N., (2011), Microstructure-dependent couple stress theories of functionally graded beams. J. Mech. Phys. Solids. 59: 2382–2399.
[35] Eltaher M. A., Emam S. A., Mahmoud F. F., (2013), Static and stability analysis of nonlocal functionally graded nanobeams. Compos. Struct. 96: 82–88.
[36] Khaniki H. B., (2019), On vibrations of FG nanobeams. Int. J. Eng. Sci. 135: 23–36.
[37] 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. Int. J. Mech. Sci. 57: 63–73.
[38] Zenkour A., Ebrahimi F., Barati M. R., (2019), Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations. Int. J. Nano Dimens. 10: 141-153.
[39] Sayyad A. S., Ghugal Y. M., (2020), Bending, buckling and free vibration analysis of size-dependent nanoscale FG beams using refined models and Eringen’s nonlocal theory. Int. J. Appl. Mech. 12: 1-34.
[40] Nguyen T. K., Vo T. P., Nguyen B. D., Lee J., (2016), An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Compos. Struct. 156:238–252.
[41] Sayyad A. S., Ghugal Y. M., (2018), An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation. Adv. Aircr. Spacecr. Sci. Int. J. 5: 671-689.
[42] Wakashima K., Hirano T., Niino M., (1990), Space applications of advanced structural materials. ESP. SP-303:397.