Analytical buckling and post-buckling characteristics of Mindlin micro composite plate with central opening by use of nonlocal elasticity theory
Document Type : Research Paper
Authors
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Abstract
The effect of central opening on the buckling and nonlinear post-buckling response of carbon nanotubes (CNTs) reinforced micro composite plate embedded in elastic medium is considered in this paper. It is assumed that the system is surrounded by elastic medium, therefore; the influence of Pasternak foundation on buckling and post-buckling behavior are analyzed. In order to derive the basic formulations of plate the Mindlin plate theory is applied. Furthermore, nonlocal elasticity theory is applied to consider the size-dependent effect. Analytical approach and Newton-Raphson iterative technique are utilized to calculate the impact of cut out on the buckling and nonlinear post-buckling response of micro composite plate. The variation of buckling and post-buckling of micro composite cut out plate based on some significant parameters such as volume fraction of CNTs, small scale parameter, aspect ratio, square cut out and elastic medium were discussed in details. According to the results, it is concluded that the aspect ratio and length of square cut out have negative effect on buckling and post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the buckling and post-buckling behavior of plate. Meanwhile, considering elastic medium increases the buckling and post-buckling load of system.
Keywords
[1] M. Shishesaz, M. Kharazi, P. Hosseini, M. Hosseini, Buckling Behavior of Composite Plates with a Pre-central Circular Delamination Defect under in-Plane Uniaxial Compression, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 111-122, 06/01, 2017. en
[2] A. Zargaripoor, M. Nikkhah bahrami, A wave-based computational method for free vibration and buckling analysis of rectangular Reddy nanoplates, Journal of Computational Applied Mechanics, 05/23, 2018. en
[3] H.-S. Shen, C.-L. Zhang, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Materials & Design, Vol. 31, No. 7, pp. 3403-3411, 2010/08/01/, 2010.
[4] S. Jafari Mehrabadi, B. Sobhani Aragh, V. Khoshkhahesh, A. Taherpour, Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes, Composites Part B: Engineering, Vol. 43, No. 4, pp. 2031-2040, 2012/06/01/, 2012.
[5] K. M. Liew, Z. X. Lei, J. L. Yu, L. W. Zhang, Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach, Computer Methods in Applied Mechanics and Engineering, Vol. 268, pp. 1-17, 2014/01/01/, 2014.
[6] M. Rafiee, X. Q. He, S. Mareishi, K. M. Liew, Nonlinear Response of Piezoelectric Nanocomposite Plates: Large Deflection, Post-Buckling and Large Amplitude Vibration, International Journal of Applied Mechanics, Vol. 07, No. 05, pp. 1550074, 2015/10/01, 2015.
[7] M. Jamali, T. Shojaee, R. Kolahchi, B. Mohammadi, Buckling analysis of nanocomposite cut out plate using domain decomposition method and orthogonal polynomials, Steel and Composite Structures, Vol. 22, pp. 691-712, 2016.
[8] M. Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016.
[9] M. Z. Nejad, A. Hadi, Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science, Vol. 105, pp. 1-11, 2016.
[10] R. Kolahchi, A. Cheraghbak, Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method, Nonlinear Dynamics, Vol. 90, No. 1, pp. 479-492, 2017/10/01, 2017.
[11] M. Z. Nejad, A. Hadi, A. Farajpour, Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials, Structural Engineering & Mechanics, Vol. 63(2), pp. 161-169, 07/25, 2017. En
[12] A. Hadi, M. Z. Nejad, A. Rastgoo, M. Hosseini, Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory, Steel and Composite Structures, Vol. 26(6), 03/25, 2018. En
[13] M. Z. Nejad, A. Hadi, A. Omidvari, A. Rastgoo, Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory, Structural Engineering and Mechanics, Vol. 67, No. 4, pp. 417-425, 2018.
[14] A. Farajpour, A. Arab Solghar, A. Shahidi, Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression, Physica E: Low-dimensional Systems and Nanostructures, Vol. 47, pp. 197-206, 2013/01/01/, 2013.
[15] K. F. Wang, B. L. Wang, Effect of surface energy on the non-linear postbuckling behavior of nanoplates, International Journal of Non-Linear Mechanics, Vol. 55, pp. 19-24, 2013/10/01/, 2013.
[16] A. Naderi, A. R. Saidi, Nonlocal postbuckling analysis of graphene sheets in a nonlinear polymer medium, International Journal of Engineering Science, Vol. 81, pp. 49-65, 2014/08/01/, 2014.
[17] M. Akbarzadeh Khorshidi, M. Shariati, S. A. Emam, Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory, International Journal of Mechanical Sciences, Vol. 110, pp. 160-169, 2016/05/01/, 2016.
[18] S. Sahmani, M. M. Aghdam, M. Bahrami, Size-dependent axial buckling and postbuckling characteristics of cylindrical nanoshells in different temperatures, International Journal of Mechanical Sciences, Vol. 107, pp. 170-179, 2016/03/01/, 2016.
[19] H. Wu, S. Kitipornchai, J. Yang, Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates, Materials & Design, Vol. 132, pp. 430-441, 2017/10/15/, 2017.
[20] S. Thai, H.-T. Thai, T. P. Vo, S. Lee, Postbuckling analysis of functionally graded nanoplates based on nonlocal theory and isogeometric analysis, Composite Structures, Vol. 201, pp. 13-20, 2018/10/01/, 2018.
[21] Y. M. Ghugal, A. S. Sayyad, A Static Flexure of Thick Isotropic Plates Using Trigonometric Shear Deformation Theory, Journal of Solid Mechanics, Vol. 2, No. 1, pp. 79-90, 03/30, 2010. en
[22] A. Ghorbanpour Arani, R. Kolahchi, H. Vossough, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B: Condensed Matter, Vol. 407, No. 22, pp. 4458-4465, 2012/11/15/, 2012.
[23] M. Bedroud, R. Nazemnezhad, S. Hosseini-Hashemi, M. Valixani, Buckling of FG circular/annular Mindlin nanoplates with an internal ring support using nonlocal elasticity, Applied Mathematical Modelling, Vol. 40, No. 4, pp. 3185-3210, 2016/02/15/, 2016.
[24] C. Liu, L.-L. Ke, J. Yang, S. Kitipornchai, Y.-S. Wang, Buckling and post-buckling analyses of size-dependent piezoelectric nanoplates, Theoretical and Applied Mechanics Letters, Vol. 6, No. 6, pp. 253-267, 2016/11/01/, 2016.
[25] A. Soleimani, M. H. Naei, M. M. Mashhadi, Nonlocal postbuckling analysis of graphene sheets with initial imperfection based on first order shear deformation theory, Results in Physics, Vol. 7, pp. 1299-1307, 2017/01/01/, 2017.
[26] A. Daneshmehr, A. Rajabpoor, A. Hadi, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, Vol. 95, pp. 23-35, 2015.
[27] A. Ghorbanpour Arani, M. Jamali, M. Mosayyebi, R. Kolahchi, Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory, Composites Part B: Engineering, Vol. 95, pp. 209-224, 2016/06/15/, 2016.
[28] H. Akhavan, S. Hosseini Hashemi, H. R. Damavandi Taher, A. Alibeigloo, S. Vahabi, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis, Computational Materials Science, Vol. 44, No. 3, pp. 968-978, 2009/01/01/, 2009.
[29] S. H. Hashemi, A. T. Samaei, Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 7, pp. 1400-1404, 2011/05/01/, 2011.
[30] A. T. Samaei, S. Abbasion, M. M. Mirsayar, Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanics Research Communications, Vol. 38, No. 7, pp. 481-485, 2011/10/01/, 2011.
[31] A. C. Eringen, 2002, Nonlocal Continuum Field Theories,
[32] A. Ghorbanpour Arani, M. Jamali, A. H. Ghorbanpour-Arani, R. Kolahchi, M. Mosayyebi, Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 231, No. 2, pp. 387-403, 2017/01/01, 2016.
[33] R. Ali, S. J. Atwal, Prediction of natural frequencies of vibration of rectangular plates with rectangular cutouts, Computers & Structures, Vol. 12, No. 6, pp. 819-823, 1980/12/01/, 1980.
[34] K. M. Liew, S. Kitipornchai, A. Y. T. Leung, C. W. Lim, Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method, International Journal of Mechanical Sciences, Vol. 45, No. 5, pp. 941-959, 2003/05/01/, 2003.
[35] Z. Pan, Y. Cheng, J. Liu, A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution, Thin-Walled Structures, Vol. 73, pp. 229-241, 2013/12/01/, 2013.
[36] K. Y. Lam, K. C. Hung, S. T. Chow, Vibration analysis of plates with cutouts by the modified Rayleigh-Ritz method, Applied Acoustics, Vol. 28, No. 1, pp. 49-60, 1989/01/01/, 1989.
[37] K. M. Liew, K. C. Hung, M. K. Lim, Method of domain decomposition in vibrations of mixed edge anisotropic plates, International Journal of Solids and Structures, Vol. 30, No. 23, pp. 3281-3301, 1993/01/01/, 1993.
[38] K. M. Liew, T. Y. Ng, S. Kitipornchai, A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation, International Journal of Solids and Structures, Vol. 38, No. 28, pp. 4937-4954, 2001/07/01/, 2001.
[39] K. M. El-Sawy, A. S. Nazmy, Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes, Thin-Walled Structures, Vol. 39, No. 12, pp. 983-998, 2001/12/01/, 2001.
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Volume 51, Issue 1
June 2020Pages 231-238
- Receive Date: 30 December 2018
- Revise Date: 12 March 2019
- Accept Date: 01 April 2019