Surface Stress Effect on the Nonlocal Biaxial Buckling and Bending Analysis of Polymeric Piezoelectric Nanoplate Reinforced by CNT Using Eshelby-Mori-Tanaka Approach
الموضوعات :M Mohammadimehr 1 , B Rousta Navi 2 , A Ghorbanpour Arani 3
1 - Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
2 - Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
3 - Institute of Nanoscience & Nanotechnology, University of Kashan
الکلمات المفتاحية: Bending, Buckling, Polymeric piezoelectric nanoplate, Surface stress effect, Eshelby-Mori-Tanaka approach, SWCNT,
ملخص المقالة :
In this article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electro-magneto-mechanical loadings. Eshelby-Mori-Tanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed to obtain the critical buckling load of polymeric piezoelectric nanoplate for classical plate theory (CPT) and first order shear deformation theory (FSDT). The influences of various parameters on the biaxial nonlocal critical buckling load with respect to the local critical buckling load ratio () of nanoplate are examined. Surface stress effects on the surface biaxial critical buckling load to the non-surface biaxial critical buckling load ratio () can not be neglected. Moreover, the effect of residual surface stress constant on is higher than the other surface stress parameters on it. increases by applying the external voltage and magnetic fields. The nonlocal deflection to local deflection of piezoelectric nanocomposite plate ratio () decreases with an increase in the nonlocal parameter for both theories. And for FSDT, decreases with an increase in residual stress constant and vice versa for CPT.
[1] Schmidt D., Shah D., Giannelis EP., 2002, New advances in polymer/layered silicate nanocomposites, Current Opinion in Solid State and Material Science 6(3): 205-212.
[2] Thostenson E., Li C., Chou T., 2005, Review nanocomposites in context, Journal Composite Science Technology 65:491-516.
[3] Ghorbanpour Arani A., Hashemian M., Loghman A., Mohammadimehr M., 2011, Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method, Journal of applied mechanics and technical physics 52 (5): 815-824.
[4] Mohammadimehr M., Rahmati A. H., 2013, Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation, Turkish Journal of Engineering & Environmental Sciences 37: 1-15.
[5] Ghorbanpour Arani A., Rahnama Mobarakeh M., Shams Sh., Mohammadimehr M., 2012, The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder, Journal of Mechanical Science and Technology 26 (8): 2565-2572.
[6] Jaffe B., Cook W.R., Jaffe H., 1971, Piezoelectric Ceramics, New York, Academic.
[7] Xu S., Yeh Y.W., Poirier G., McAlpine M.C., Register R.A., Yao N., 2013, Flexible piezoelectric PMN-PT nanowire-based na nocomposite and device, Nano Letters 13: 2393-2398.
[8] Samaei A.T., Abbasion S., Mirsayar M.M., 2011, Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanical Resereach Communication 38: 481-485.
[9] Farajpour A., Shahidi A.R., Mohammadi M., Mahzoon M., 2013, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structure 94: 1605-1615.
[10] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954-959.
[11] Narendar S., 2011, Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects, Composite Structure 93: 3093-3103.
[12] Analooei H.R., Azhari M., Heidarpour A., 2013, Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method, Appllied Mathematical Modeling 37: 6703-6717.
[13] Murmu T., Sienz J., Adhikari S., Arnold C., 2013, Nonlocal buckling of double-nanoplate-systems under biaxial compression, Composite Part B 44: 84-94.
[14] Ansari R., Sahmani S., 2013, Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Appllied Mathematical Modeling 37: 7338-7351.
[15] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407: 4458-4465.
[16] Murmu T., Pradhan S.C., 2009, Buckling of biaxially compressed orthotropic plates at small scales, Mechanical Research Communication 36: 933-938.
[17] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E 44: 719-727.
[18] Gurtin M.E., Murdoch A.I., 1978, Surface stress in solids, International Journal of Solids Structure 14: 431-440.
[19] Tian L., Rajapakse R.K.N.D., 2007, Finite element modelling of nanoscale inhomogeneities in an elastic matrix, Computer Material Science 41: 44-53.
[20] Wang G.F., Feng X.Q., 2009, Timoshenko beam model for buckling and vibration of nanowires with surface effects, Physics D 42: 155-411.
[21] Wang K.F., Wang B.L., 2013, Effect of surface energy on the non-linear postbuckling behavior of nanoplates, International Journal of Nonlinear Mechanics 55: 19-24.
[22] Alzahrani E.O., Zenkour A.M., Sobhy M., 2013, Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium, Composite Structure 105: 163-172.
[23] Alibeigloo A., 2013, Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity, Composite Structure 95: 612-622.
[24] Zhu P., Lei Z.X., Liew K.M., 2012, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Composite Structure 94: 1450-1460.
[25] Lei Z.X., Liew K.M., Yu J.L., 2013, Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method, Composite Structure 98: 160-168.
[26] Jafari Mehrabadi S., Sobhani Aragh B., Khoshkhahesh V., Taherpour A., 2012, Mechanical buckling of rectangular nanocomposite plate reinforced by aligned and straight single-walled carbon nanotubes, Composite Part B 43: 2031-2040.
[27] Shi D.L., Feng X.Q., huang Y.Y., Hwang K.C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites, Journal of Engineering Material Technology 126: 250-257.
[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., 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.
[30] Ansari R., Sahmani S., 2011, Surface stress effects on the free vibration behavior of nanoplates, International Journal of Engineering Science 49: 1204-1215.
[31] Wang L., 2012, Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis, Physica E 44: 808-812.
[32] Kraus J., 1984, Electromagnetics, USA, McGrawHill Inc.
[33] Ghorbanpour Arani A., Amir S., Shajari A.R., Mozdianfard M.R., Khoddami Maraghi Z., Mohammadimehr M., 2012, Electro-thermal non-local vibration analysis of embedded DWBNNTs, Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 226: 1410-1422.
[34] Shen H.S., Zhu Z.H., 2012, Postbuckling of sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations, European Journal of Mechanical A/Solids 35: 10-21.
