Tính toán ổn định của tấm nano chiều dày biến đổi có vết nứt và có xét đến ảnh hưởng của hiệu ứng flexo
Email:
phamminhphuc@utc.edu.vn
Từ khóa:
Chiều dày biến đổi, flexo, tấm nano, phương pháp phần tử hữu hạn
Tóm tắt
Việc tính toán ổn định của tấm nano có vết nứt đã nhận được rất nhiều sự quan tâm trong thời gian gần đây, đặc biệt là xét đến tấm có chiều dày biến đổi và hiệu ứng flexo. Công thức phần tử hữu hạn được thiết lập dựa vào lý thuyết biến dạng cắt bậc nhất của Mindlin, vết nứt được mô phỏng dựa trên lý thuyết phase-field thông qua tham số phase-field, đây là cách tiếp cận kết cấu có vết nứt rất linh hoạt và có nhiều ưu điểm so với các phương pháp khác. Độ tin cậy của lý thuyết tính toán được kiểm chứng thông qua các so sánh với các kết quả đã công bố. Trên cơ sở đó, bài báo tiến hành khảo sát ảnh hưởng của một vài tham số vật liệu, hình học đến đáp ứng ổn định của tấm, trong đó chiều dày của tấm biến đổi theo cả quy luật tuyến tính và phi tuyến, đây là các kết quả nghiên cứu thú vị, thể hiện rõ sự ảnh hưởng đồng thời của hiệu ứng flexo, quy luật biến đổi của chiều dày tấm đến tải tới hạn mất ổn định của tấm nano cũng như các dạng mất ổn định của tấm nano. Kết quả số chỉ ra rằng, khi tấm nano xuất hiện vết nứt thì nó nhanh bị mất ổn định hơn, ngược lại khi tăng hệ số flexo thì tấm cứng hơn và chịu lực tốt hơn. Nghiên cứu này tạo cơ sở khoa học giúp các nhà thiết kế, chế tạo tấm nano đưa ra các khuyến cáo sử dụng khi tấm xuất hiện các vết nứtTài liệu tham khảo
[1] Z. Zhang, Z. Yan, L. Jiang L, Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate, Journal of Applied Physics, 116 (2014) 014307. https://doi.org/10.1063/1.4886315
[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
[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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Kiểu trích dẫn
Đoàn Hồng, Đức, Đỗ Văn, T., & Phạm Minh, P. (1655226000). Tính toán ổn định của tấm nano chiều dày biến đổi có vết nứt và có xét đến ảnh hưởng của hiệu ứng flexo. Tạp Chí Khoa Học Giao Thông Vận Tải, 73(5), 470-485. https://doi.org/10.47869/tcsj.73.5.3
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