Stability of multi-cracked FG plate on elastic foundations
Email:
levinhan@utc.edu.vn
Từ khóa:
FG plate, multi-cracked plates, elastic foundation, Phase-Field theory, stability
Tóm tắt
Recently, the stability calculation of the functionally graded (FG) plate has attracted many scientists, especially when considering the FG plate with many cracks. In this work, the plate is made from a new generation composite material consisting of two components, ceramic and metal, with the law of continuous exponential material distribution. The plate is placed on a Winkler - Pasternak elastic foundation with two background parameters. Then, we used the third-order shear deformation plate theory to establish the dynamical equations. After applying Phase-Field theory to simulate the crack state, we applied the finite element method to solve the equations to find the critical force causing instability of the plate. Next, we investigated the influence of material index, number of cracks, crack length, crack shape as well as elastic foundation parameters on the plate stability. The results show that the crack length and elastic foundation parameter have the great influence on the stability of the FG plate. Especially, the elastic foundation with large shear coefficient, creating high stability for the plate. That is very meaningful in exploiting and using plate structure when the cracks appear.Tài liệu tham khảo
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[13]. P.M. Phuc, N.D. Duc, The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory, Composites Part B: Engineering, 175 (2019) 107086. https://doi.org/10.1016/j.compositesb.2019.107086
[14]. P.M. Phuc, N.D. Duc, The effect of cracks and thermal environment on free vibration of FGM plates, Thin–Walled Structures, 159 (2021) 107291. https://doi.org/10.1016/j.tws.2020.107291
[15]. N.D. Duc, P.M. Phuc, Free vibration analysis of cracked FG CNTRC plates using phase field theory, Aerospace Science and Technology, 112 (2021) 106654. https://doi.org/10.1016/j.ast.2021.106654
[16]. Pham Minh 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
[17]. 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
[18]. G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[19]. M.J. Borden, C.V. Verhoosel, M.A.Scott, T.J.R. Hughes, C.M. Landis, A phase-field description of dynamic brittle fracture, Comput Methods Appl Mech Eng, 217–220 (2012) 77–95. https://doi.org/10.1016/j.cma.2012.01.008
[2]. Takuya Morimoto, Yoshinobu Tanigawa, Elastic stability of inhomogeneous thin plates on an elastic foundation, Arch. Appl. Mech., 77 (2007) 653–674. https://doi.org/10.1007/s00419-007-0117-1
[3]. Mehdi Dehghan, Gholam Hosein Baradaran, Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method, Applied Mathematics and Computation, 218 (2011) 2772-2784. https://doi.org/10.1016/j.amc.2011.08.020
[4]. Huu-Tai Thai, Seung-Eock Kim, Closed-form solution for bucking analysis of thick functionally graded plates on elastic foundation, International Journal of Mechanical Sciences, 75 (2013) 34-44. http://dx.doi.org/10.1016/j.ijmecsci.2013.06.007
[5]. H. Foroughi, M. Azhari, Mechanical buckling and free vibration of thick functionally graded plates resting on elastic foundation using the higher order B-spline finite strip method, Meccanica, 49 (2014) 981–993. https://doi.org/10.1007/s11012-013-9844-2
[6]. A. Gupta, M. Talha, Static and Stability Characteristics of Geometrically Imperfect FGM Plates Resting on Pasternak Elastic Foundation with Microstructural Defect, Arab. J. Sci. Eng., 43 (2018) 4931-4947. https://doi.org/10.1007/s13369-018-3240-0
[7]. S. J. Singh, S. P. Harsha, Exact solution for Free Vibration and Buckling of sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions, International Journal of Structural Stability and Dynamics, 19 (2019) 1-35. https://doi.org/10.1142/S0219455419500287
[8]. J. Jędrysiak, M. Kaźmierczak-Sobińska, Theoretical Analysis of Buckling for Functionally Graded Thin Plates with Microstructure Resting on an Elastic Foundation, Materials, 13 (2020) 1-20. https://doi.org/10.3390/ma13184031
[9]. Nicolas Moës, John Dolbow, Ted Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Engng, 46 (1999) 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[10]. Amir Nasirmanesh, Soheil Mohammadi, XFEM buckling analysis of cracked composite plates, Composite Structures, 131 (2015) 333-343. https://doi.org/10.1016/j.compstruct.2015.05.013
[11]. C.S. Huang, O.G. McGee, M.J. Chang, Vibrations of cracked rectangular FGM thick plates, Composite Structures, 93 (2011) 1747-1764. https://doi.org/10.1016/j.compstruct.2011.01.005
[12]. P. Liu, T.Q. Bui, D. Zhu, T.T. Yu, J.W. Wang, S.H. Yin, S. Hirose, Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element, Composites Part B: Engineering, 77 (2015) 179-193. https://doi.org/10.1016/j.compositesb.2015.03.036
[13]. P.M. Phuc, N.D. Duc, The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory, Composites Part B: Engineering, 175 (2019) 107086. https://doi.org/10.1016/j.compositesb.2019.107086
[14]. P.M. Phuc, N.D. Duc, The effect of cracks and thermal environment on free vibration of FGM plates, Thin–Walled Structures, 159 (2021) 107291. https://doi.org/10.1016/j.tws.2020.107291
[15]. N.D. Duc, P.M. Phuc, Free vibration analysis of cracked FG CNTRC plates using phase field theory, Aerospace Science and Technology, 112 (2021) 106654. https://doi.org/10.1016/j.ast.2021.106654
[16]. Pham Minh 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
[17]. 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
[18]. G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[19]. M.J. Borden, C.V. Verhoosel, M.A.Scott, T.J.R. Hughes, C.M. Landis, A phase-field description of dynamic brittle fracture, Comput Methods Appl Mech Eng, 217–220 (2012) 77–95. https://doi.org/10.1016/j.cma.2012.01.008
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Nhận bài
20/03/2023
Nhận bài sửa
12/04/2023
Chấp nhận đăng
14/05/2023
Xuất bản
15/05/2023
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Kiểu trích dẫn
Pham Minh, P., & Le Vinh, A. (1684083600). Stability of multi-cracked FG plate on elastic foundations. Tạp Chí Khoa Học Giao Thông Vận Tải, 74(4), 544-556. https://doi.org/10.47869/tcsj.74.4.13
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