Buckling analysis of variable thickness cracked nanoplates considerting the flexoelectric effect
Email:
phamminhphuc@utc.edu.vn
Keywords:
Variable thickness, flexo, nanoplates, FEM
Abstract
The buckling response calculation of cracked nanoplates has received a lot of attention recently, especially considering the variable thickness plate and flexoelectric effect. The finite element formulations are derived from Mindlin's first-order shear deformation theory, and the crack is simulated using phase-field parameters in accordance with phase-field theory. This is a very adaptable crack structural approach that has a number of benefits over other solutions. The computational theory's dependability is established by comparisons to published findings. On that premise, this study captures the effect of various material and geometrical parameters on the buckling response of a plate with varying thickness according to both linear and nonlinear principles. These are fascinating study findings, which clearly show the simultaneous influence of the flexoelectric effect, the variation law of plate thickness on the critical buckling load as well as the critical buckling mode shape of the structure. Numerical results show that, when cracks appear, the nanoplates become destabilized earlier, but conversely, when the flexoelectric coefficient increases, the plates have greater stiffness and can withstand stronger forces. This study creates a scientific basis to help designers and manufacturers of nanoplates give recommendations to users when cracks appear.References
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[22] V.D. Thom, H.D. Duc, N.D. Duc, Q.B. Tinh, Phase-field thermal buckling analysis for cracked functionally graded composite plates considering neutral surface, Composite Structures, 182 (2017) 524-548. https://doi.org/10.1016/j.compstruct.2017.09.059
[23] H.D. Duc, Q.B. Tinh, Thom, Duc, A rate-dependent hybrid phase field model for dynamic crack propagation, Journal of applied Physics, 122 (2017) 1-4. https://doi.org/10.1063/1.4990073
[24] H.D. Duc, V.D. Thom, P.M. Phuc, N.D. Duc, Validation simulation for free vibration and buckling of cracked Mindlin plates using phase-field method, Mechanics of Advanced Materials and Structures, 0 (2018) 1-10. https://doi.org/10.1080/15376494.2018.1430262
[25] N.D. Duc, T.D. Truong, V.D. Thom, H.D. Duc, On the Buckling Behavior of Multi-cracked FGM Plates, Procceeding of the International Conference on Advances in Computational Mechanics, Lecture Notes in Mechanical Engineering, 2017, Springer, 29-45. https://doi.org/10.1007/978-981-10-7149-2_3
[26] V.H. Nam, H.D. Duc, M.K. Nguyen, V.D. Thom, T.T. Hong, Phase-field buckling analysis of cracked stiffened functionally graded plates, Composite Structures, 217 (2019) 50-59. https://doi.org/10.1016/j.compstruct.2019.03.014
[27] P.M. Phuc, Analysis free vibration of the functionally grade material cracked plates with varying thickness using the Phase-field theory, Transport and Communications Science Journal, 70 (2019) 122-131. https://doi.org/10.25073/tcsj.70.2.35.
[28] Pham Minh Phuc, Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness, Transport and Communications Science Journal, 71 (2020) 853-867. https://doi.org/10.47869/tcsj.71.7.10
[29] R. Seifi, K.Y. Nafiseh, Experimental and numerical studies on buckling of cracked thin plates under full and partial compression edge loading, Thin-Walled Structures, 19 (2011) 1504-1516. https://doi.org/10.1016/j.tws.2011.07.010
[30] I.E. Harik, X. Liu, R. Ekambaram, Elastic stability of plates with varying rigidities, Computers & Structures, 38 (1991) 161-168. https://doi.org/10.1016/0045-7949(91)90094-3
[31] W.H. Wittrik, C.H. Ellen, Buckling of tapered rectangular plates in compression, Aeronautical Quarterly, 13 (1962) 308-326. https://doi.org/10.1017/S0001925900002547
[32] M.S. Nerantzaki, J.T. Katsikadelis, Buckling of plates with variable thickness-an analog equation solution, Engineering Analysis with Boundary Elements, 18 (1996) 149-154. https://doi.org/10.1016/S0955-7997(96)00045-8
[33] L.M. Thai, D.T. Luat, V.B. Phung, P.V. Minh, D.V. Thom, Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects, Archive of Applied Mechanics, 92 (2022) 163–182. https://doi.org/10.1007/s00419-021-02048-3.
[34] D.H. Doan, A.M. Zenkour, D.V. Thom, Finite element modeling of free vibration of cracked nanoplates with flexoelectric effects, The European Physical Journal Plus, 137 (2022) 447. https://doi.org/10.1140/epjp/s13360-022-02631-9
[2] W. Yang, X. Liang, S. Shen, Electromechanical responses of piezoelectric nanoplates with flexoelectricity, Acta Mechanica, 226 (2015) 3097–3110. https://doi.org/10.1007/s00707-015-1373-8
[3] K.B. Shingare, S.I. Kundalwal, Static and dynamic response of graphene nanocomposite plates with flexoelectric effect, Mechanics of Materials, 134 (2019) 69-84. https://doi.org/10.1016/j.mechmat.2019.04.006
[4] S. Amir, H.B.A. Zarei, M. Khorasani, Flexoelectric vibration analysis of nanocomposite sandwich plates, Mechanics Based Design of Structures and Machines: An International Journal, 48 (2020) 146-163. https://doi.org/10.1080/15397734.2019.1624175
[5] A. Ghobadi, Y.T. Beni, H. Golestanian, Nonlinear thermo-electromechanical vibration analysis of size-dependent functionally graded flexoelectric nano-plate exposed magnetic field, Archive of Applied Mechanics, 90 (2020) 2025–2070. https://doi.org/10.1007/s00419-020-01708-0
[6] A.G. Arani, A.H.S. Arani, E. Haghparast, Flexoelectric and surface effects on vibration frequencies of annular nanoplate, Indian Journal of Physics, 95 (2021) 2063-2083. https://doi.org/10.1007/s12648-020-01854-9
[7] Y. Yue, Nonlinear Vibration of the Flexoelectric Nanoplate with Surface Elastic Electrodes Under Active Electric Loading, Acta Mechanica Solida Sinica, 33 (2020) 864–878. https://doi.org/10.1007/s10338-020-00169-w
[8] B. Wang, L. Xian-Fang, Flexoelectric effects on the natural frequencies for free vibration of piezoelectric nanoplates, Journal of Applied Physics, 129 (2021) 034102. https://doi.org/10.1063/5.0032343
[9] A. Ghobadi, Y.T. Beni, K.K. Zurd, Porosity distribution effect on stress, electric field and nonlinear vibration of functionally graded nanostructures with direct and inverse flexoelectric phenomenon, Composite Structures, 259 (2021) 113220. https://doi.org/10.1016/j.compstruct.2020.113220
[10] Z. Yan, L.Y. Jiang, Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468 (2012) 3458-3475. https://doi.org/10.1098/rspa.2012.0214
[11] A. Reza, G. Raheb, Size-Dependent Nonlinear Vibrations of First-Order Shear Deformable Magneto-Electro-Thermo Elastic Nanoplates Based on the Nonlocal Elasticity Theory, International Journal of Applied Mechanics, 08 (2016) 1650053. https://doi.org/10.1142/S1758825116500538
[12] X. Liang, W. Yang, S. Hu, S. Shen, Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads, Journal of Physics D: Applied Physic, 49 (2016) 115307. https://doi.org/10.1088/0022-3727/49/11/115307
[13] S. Amir, M. Khorasani, H.B. Zarei, Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory, Journal of Sandwich Structures & Materials, 22 (2018) 1-24. https://doi.org/10.1177/1099636218795385
[14] F. Ebrahimi, M. Karimiasl, Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams, Mechanics of Advanced Materials and Structures, 25 (2018) 943-952. https://doi.org/10.1080/15376494.2017.1329468
[15] S. Zeng, B.L. Wang, K. F. Wang, Nonlinear vibration of piezoelectric sandwich nanoplates with functionally graded porous core with consideration of flexoelectric effect, Composite Structures, 207 (2019) 340-351. https://doi.org/10.1016/j.compstruct.2018.09.040
[16] K.K. Zur, M. Arefi, J. Kim, J.N. Reddy, Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory, Composites Part B: Engineering, 182 (2020) 107601. https://doi.org/10.1016/j.compositesb.2019.107601
[17] L.L. Shu, X.Y. Wei, T. Pang, X. Yao, C.L. Wang, Symmetry of flexoelectric coefficients in crystalline medium. Journal of Applied Physics, 110 (2011) 104106. https://doi.org/10.1063/1.3662196
[18] B. Zaouagui, S.A. Belalia, A. Boukhalfa, h-p finite element vibration analysis of side cracked rectangular nano-plates based on nonlocal elasticity theory, The European Physical Journal Plus, 134 (2019). https://doi.org/10.1140/epjp/i2019-12724-9
[19] K. Josef, A. Marreddy, L.D. Lorenzis, G. Hector, R. Alessandro, Phase-field description of brittle fracture in plates and shells, Computer Methods in Applied Mechanics and Engineering, 312 (2016) 374-394. https://doi.org/10.1016/j.cma.2016.09.011
[20] B. Bourdin, G.A. Francfort, J.J. Marigo, The variational approach to fracture, Journal of Elasticity, 91 (2008) 5–148. https://doi.org/10.1007/s10659-007-9107-3
[21] J.B. Michael, V.V. Clemens, A.S. Michael, J.R.H. Thomas, M.L. Chad, A phase-field description of dynamic brittle fracture, Computer Methods in Applied Mechanics Engineering, 217-220 (2012) 77–95. https://doi.org/10.1016/j.cma.2012.01.008
[22] V.D. Thom, H.D. Duc, N.D. Duc, Q.B. Tinh, Phase-field thermal buckling analysis for cracked functionally graded composite plates considering neutral surface, Composite Structures, 182 (2017) 524-548. https://doi.org/10.1016/j.compstruct.2017.09.059
[23] H.D. Duc, Q.B. Tinh, Thom, Duc, A rate-dependent hybrid phase field model for dynamic crack propagation, Journal of applied Physics, 122 (2017) 1-4. https://doi.org/10.1063/1.4990073
[24] H.D. Duc, V.D. Thom, P.M. Phuc, N.D. Duc, Validation simulation for free vibration and buckling of cracked Mindlin plates using phase-field method, Mechanics of Advanced Materials and Structures, 0 (2018) 1-10. https://doi.org/10.1080/15376494.2018.1430262
[25] N.D. Duc, T.D. Truong, V.D. Thom, H.D. Duc, On the Buckling Behavior of Multi-cracked FGM Plates, Procceeding of the International Conference on Advances in Computational Mechanics, Lecture Notes in Mechanical Engineering, 2017, Springer, 29-45. https://doi.org/10.1007/978-981-10-7149-2_3
[26] V.H. Nam, H.D. Duc, M.K. Nguyen, V.D. Thom, T.T. Hong, Phase-field buckling analysis of cracked stiffened functionally graded plates, Composite Structures, 217 (2019) 50-59. https://doi.org/10.1016/j.compstruct.2019.03.014
[27] P.M. Phuc, Analysis free vibration of the functionally grade material cracked plates with varying thickness using the Phase-field theory, Transport and Communications Science Journal, 70 (2019) 122-131. https://doi.org/10.25073/tcsj.70.2.35.
[28] Pham Minh Phuc, Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness, Transport and Communications Science Journal, 71 (2020) 853-867. https://doi.org/10.47869/tcsj.71.7.10
[29] R. Seifi, K.Y. Nafiseh, Experimental and numerical studies on buckling of cracked thin plates under full and partial compression edge loading, Thin-Walled Structures, 19 (2011) 1504-1516. https://doi.org/10.1016/j.tws.2011.07.010
[30] I.E. Harik, X. Liu, R. Ekambaram, Elastic stability of plates with varying rigidities, Computers & Structures, 38 (1991) 161-168. https://doi.org/10.1016/0045-7949(91)90094-3
[31] W.H. Wittrik, C.H. Ellen, Buckling of tapered rectangular plates in compression, Aeronautical Quarterly, 13 (1962) 308-326. https://doi.org/10.1017/S0001925900002547
[32] M.S. Nerantzaki, J.T. Katsikadelis, Buckling of plates with variable thickness-an analog equation solution, Engineering Analysis with Boundary Elements, 18 (1996) 149-154. https://doi.org/10.1016/S0955-7997(96)00045-8
[33] L.M. Thai, D.T. Luat, V.B. Phung, P.V. Minh, D.V. Thom, Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects, Archive of Applied Mechanics, 92 (2022) 163–182. https://doi.org/10.1007/s00419-021-02048-3.
[34] D.H. Doan, A.M. Zenkour, D.V. Thom, Finite element modeling of free vibration of cracked nanoplates with flexoelectric effects, The European Physical Journal Plus, 137 (2022) 447. https://doi.org/10.1140/epjp/s13360-022-02631-9
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Received
22/02/2022
Revised
23/05/2022
Accepted
08/06/2022
Published
15/06/2022
Type
Research Article
How to Cite
Đoàn Hồng, Đức, Đỗ Văn, T., & Phạm Minh, P. (1655226000). Buckling analysis of variable thickness cracked nanoplates considerting the flexoelectric effect. Transport and Communications Science Journal, 73(5), 470-485. https://doi.org/10.47869/tcsj.73.5.3
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