Non-Local Thermo-Elastic Buckling Analysis of Multi-Layer Annular/Circular Nano-Plates Based on First and Third Order Shear Deformation Theories Using DQ Method

Subject Areas : Engineering

Sh Dastjerdi ¹ , M Jabbarzadeh ²

1 - Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran
2 - Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Received: 2016-08-01 Accepted : 2016-10-07 Published : 2016-12-20

Keywords:

References:

[1] Boehm H.P., Setton R., Stumpp E., 1994, Nomenclature and terminology of graphite intercalation compounds, Pure and Applied Chemistry 66: 1893-1901.
[2] Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A., 2004, Electric field effect in atomically thin carbon films, Science 306: 666-669.
[3] Reddy J.N., 2011, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59(11): 2382-2399.
[4] Akgöz B., Civalek Ö., 2013, A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science 70: 1-14.
[5] Akgöz B., Civalek Ö., 2013, Buckling analysis of functionally graded micro beams based on the strain gradient theory, Acta Mechanica 224: 2185-2201.
[6] 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(8): 1477-1508.
[7] Ke L.L., Yang J., Kitipornchai S., 2011, Free vibration of size dependent Mindlin micro plates based on the modified couple stress theory, Journal of Sound and Vibration 331: 94-106.
[8] Akgöz B., Civalek Ö., 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.
[9] Akgöz B., Civalek Ö., 2013, Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory, Composite Structures 98: 314-322.
[10] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 2731-2743.
[11] Eringen A.C., Edelen D.G.B., 1972, On non-local elasticity, International Journal of Engineering Science 10: 233-248.
[12] Eringen A.C., 1983, On differential equations of non-local elasticity, solutions of screw dislocation, surface waves, Journal of Applied Physics 54: 4703-4710.
[13] Eringen A.C., 2002, Non-Local Continuum Field Theories, Springer-Verlag, New York.
[14] Eringen A.C., 2006, Non-local continuum mechanics based on distributions, International Journal of Engineering Science 44: 141-147.
[15] Wen C.C., Chang T.W., Kuo W.S., 2014, Experimental study on mechanism of buckling and Kink-band formation in graphene nanosheets, Applied Mechanics & Materials 710: 19-24.
[16] Ghorbanpour Arani A., Kolahchi R., Allahyari S.M.R., 2014, Non-local DQM for large amplitude vibration of annular boron nitride sheets on non-linear elastic medium, Journal of Solid Mechanics 6(4): 334-346.
[17] Mohammadi M., Goodarzi M., Ghayour M., AlivandS., 2012, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via non-local elasticity theory, Journal of Solid Mechanics 4(2): 128-143.
[18] Dastjerdi S., Jabbarzadeh M., Tahani M., Nonlinear bending analysis of sector graphene sheet embedded in elastic matrix based on nonlocal continuum mechanics, IJE Transaction B: Applications 28: 802-811.
[19] Anjomshoa A., Shahidi A.R., Shahidi S.H., Nahvi H., 2014, Frequency analysis of embedded orthotropic circular and elliptical micro/nano-plates using non-local variational principle, Journal of Solid Mechanics 7(1): 13-27.
[20] Pradhan S.C., 2009, Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory, Physics letters A 373: 4182-4188.
[21] He X.Q., Kitipornchai S., Liew K.M., 2005, Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, Journal of the Mechanics and Physics of Solids 53: 303-326.
[22] Scarpa F., Adhikari S., Gil A.J., Remillat C., 2010, The bending of single layer graphene sheets: The lattice versus continuum approach, Nanotechnology 21(12): 125702.
[23] Samaei A.T., Abbasian S., Mirsayar M.M., 2011, Buckling analysis of a single layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanics Research Communications 38: 481-485.
[24] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E 53: 251-259.
[25] Wang Y., Cui H.T., Li F.M., Kishimoto K., 2013, Thermal buckling of a nanoplate with small-scale effects, Acta Mechanica 224(6): 1299-1307.
[26] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A 373: 1062-1069.
[27] Bellman R.E., Casti J., 1971, Differential quadrature and long-term integration, Journal of Mathematical Analysis & Applications 34: 235-238.
[28] Bellman R.E., Kashef B.G., Casti J., 1972, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equation, Journal of Computational Physics 10: 40-52.
[29] Sepahi O., Forouzan M.R., Malekzadeh P., 2011, Thermal buckling and postbuckling analysis of functionally graded annular plates with temperature-dependent material properties, Materials and Design 32: 4030-4041.
[30] Wang C.M., Xiang Y., Kitipornchai S., Liew K.M., 1994, Buckling solutions for Mindlin plates of various shapes, Engineering Structures 16: 119-127.