Journal of Applied and Computational Mechanics

Buckling Analysis of Embedded Nanosize FG Beams Based on a Refined Hyperbolic Shear Deformation Theory

Document Type : Research Paper

Authors

1 Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie

2 Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie

3 Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie

4 Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria

5 Centre Universitaire de Relizane, Algérie

6 Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria

Abstract

In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the power-law model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FG nanobeams embedded in the elastic foundation are obtained. To predict the buckling behavior of embedded FG nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, power-law index, nonlocal parameter, and slenderness ratio on the critical buckling loads of size dependent FG nanobeams.

Keywords

Main Subjects

[1] Bedjilili, Y., Tounsi, A., Berrabah, H.M., Mechab, I., Adda Bedia, E.A., Benaissa, S., Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation, Applied Mathematics and Mechanics, 30(6), 2009, 717-726.
[2] Ghugal, Y.M., Shimpi, R.P., A review of refined shear deformation theories for isotropic and anisotropic laminated beams, Journal of Reinforced Plastics and Composites, 20(3), 2001, 255-272.
[3] Sayyad, A.S., Ghugal, Y.M., A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates, International Journal of Applied Mechanics, 9(1), 2017, 1750007.
[4] Peddieson, J., Buchanan, G.R., Mc Nitt, R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 2003, 305–312.
[5] Ebrahimi, F., Barati, M.R., Electromechanical buckling behavior of smart piezoelectrically actuated higher order size-dependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials, 7, 2016, 69–90.
[6] Eringen, A.C., Nonlocal polar elastic continua, International Journal of Engineering Science, 10(1), 1972, 1-16.
[7] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54(9), 1983, 4703-4710.
[8] Yang, F.A.C.M., Chong, A.C.M., Lam, D.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10), 2002, 2731-2743.
[9] Zemri, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A., A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory, Structural Engineering and Mechanics, 54(4), 2015, 693-710.
[10] Ebrahimi, F., Barati, M.R., Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(3), 2017, 937-952.
[11] Aydogdu, M., A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, 41, 2009, 1651–1655.
[12] Rahmani ,O., Jandaghian ,A.A., Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory, Applied Physics A, 119(3), 2015, 1019–1032.
[13] Tounsi, A, Semmah, A., Bousahla, A.A., Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory, Journal of Nanomechanics and Micromechanics, 3, 2013, 37–42.
[14] Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Bég, O., Mahmoud, S.R., Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18(2), 2015, 425-442.
[15] Pisano, A.A., Sofi, A., Fuschi, P., Finite element solutions for nonhomogeneous nonlocal elastic problems, Mechanics Research Communications, 36, 2009, 755–761.
[16] Pisano, A.A., Sofi, A., Fuschi, P., Nonlocal integral elasticity: 2D finite element based solutions, International Journal of Solids and Structures, 46, 2009, 3836–3849.
[17] Janghorban, M., Zare, A., Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method, Physica E: Low-dimensional Systems and Nanostructures, 43, 2011, 1602–1604.
[18] Eltaher, M.A., Emam, S.A., Mahmoud, F.F., Free vibration analysis of functionally graded size-dependent nanobeams, Applied Mathematics and Computation, 218, 2012, 7406-7420.
[19] Lim, C.W., Zhang, G., Reddy, J.N., A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78, 2015, 298–313.
[20] Ebrahimi, F, Barati, M.R, Dabbagh, A., A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, International Journal of Engineering Science, 107, 2016, 169–182.
[21] Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A., Tounsi, A., A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems, 19(2), 2017, 115-126.
[22] Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics, 62(6), 2017, 695-702.
Journal of Applied and Computational Mechanics
Volume 4, Issue 3
July 2018
Pages 140-146