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考虑前屈曲耦合变形时功能梯度圆板的稳定性分析
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Abstract:
功能梯度材料(FGM)结构的非均匀性来自于材料组份沿某一方向梯度变化，因此会存在拉弯耦合效应。在周边简支边界条件下，只要有面内载荷就会产生挠度。本文基于经典板理论，研究了机械载荷和热载荷作用下FGM简支圆板的非线性变形及稳定性问题。假设FGM圆板的材料性质只沿厚度方向进行变化，利用能量原理推导出FGM圆板的平衡方程，得到了包含前屈曲耦合变形影响的控制方程，并用打靶法进行求解。讨论了外载荷、前屈曲耦合变形以及材料的温度依赖性质等因素对FGM圆板非线性变形和稳定性的影响。
The inhomogeneity of functionally graded materials (FGM) structure comes from the gradient change of material components along a certain direction, so there will be stretch bending coupling effect. As long as the in-plane load is applied, deflection will occur, in the case of simply supported boundary conditions. Based on the classical plate theory, the nonlinear deformation and stability of FGM simply supported circular plates under mechanical and thermal loads are studied in this paper. Assuming that the material properties of FGM circular plate only change along the thickness direction, the equilibrium equation of FGM circular plate is derived by using the energy principle, and the governing equation including the influence of pre-buckling coupling deformation is obtained, which is solved by shooting method. The effects of external loads, pre-buckling coupling deformation and temperature dependence of material properties on the nonlinear deformation and stability of FGM circular plate are discussed.
| [1] | Najafizadeh, M.M. and Eslami, M.R. (2002) Buckling Analysis of Circular Plates of Functionally Graded Materials under Uniform Radial Compression. International Journal of Mechanical Sciences, 44, 2479-2493.
https://doi.org/10.1016/S0020-7403(02)00186-8 |
| [2] | Najafizadeh, M.M. and Heydari, H.R. (2008) An Exact Solution for Buckling of Functionally Graded Circular Plates Based on Higher Order Shear Deformation Plate Theory under Uniform Radial Compression. International Journal of Mechanical Sciences, 50, 603-612. https://doi.org/10.1016/j.ijmecsci.2007.07.010 |
| [3] | Ma, L.S. and Wang, T.J. (2003) Nonlinear Bending and Post-Buckling of a Functionally Graded Circular Plate under Mechanical and Thermal Loadings. International Journal of Solids and Structures, 40, 3311-3330.
https://doi.org/10.1016/S0020-7683(03)00118-5 |
| [4] | Ma, L.S. and Wang, T.J. (2002) Axisymmetric Post-Buckling of a Functionally Graded Circular Plate Subjected to Uniformly Distributed Radial Compression. Mate-rials Science Forum, 423-425, 719-724. |
| [5] | Lal, A., Jagtap, K.R. and Singh, B.N. (2013) Post Buckling Response of Functionally Graded Materials Plate Subjected to Mechanical and Thermal Loadings with Random Material Properties. Applied Mathematical Modelling, 37, 2900-2920.
https://doi.org/10.1016/j.apm.2012.06.013 |
| [6] | Li, S.R., Zhang, J.H. and Zhao, Y.G. (2007) Nonlinear Thermo-mechanical Post-Buckling of Circular FGM Plate with Geometric Imperfection. Thin-Walled Structures, 45, 528-536. https://doi.org/10.1016/j.tws.2007.04.002 |
| [7] | Samsam Shariata, B.A. and Eslami, M.R. (2007) Buckling of Thick Functionally Graded Plates under Mechanical and Thermal Loads. Composite Structures, 78, 433-439. https://doi.org/10.1016/j.compstruct.2005.11.001 |
| [8] | Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010) Levy Solution for Buckling Analysis of Functionally Graded Rectangular Plates. Applied Composite Materials, 17, 81-93. https://doi.org/10.1007/s10443-009-9100-z |
| [9] | Ghomshei, M.M. and Abbasi, V. (2013) Thermal Buckling Analysis of Annular FGM Plate Having Variable Thickness under Thermal Load of Arbitrary Distribution by Finite Element Method. Journal of Mechanical Science and Technology, 27, 1031-1039. https://doi.org/10.1007/s12206-013-0211-y |
| [10] | 李清禄, 段鹏飞, 张靖华. 陶瓷基 FGM 材料线形变厚度圆板的热后屈[J]. 航空材料学报, 2019, 39(1): 102-107. |
| [11] | Zhao, W.D. (2020) Nonlinear Axisymmetric Thermome-chanical Response of FGM Circular Plates. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42, Article No. 360.
https://doi.org/10.1007/s40430-020-02440-0 |
| [12] | Trinh, M.C., Mukhopadhyay, T. and Kim, S.E. (2020) A Semi-Analytical Stochastic Buckling Quantification of Porous Functionally Graded Plates. Aerospace Science and Technology, 105, Article ID: 105928.
https://doi.org/10.1016/j.ast.2020.105928 |
| [13] | Minh, P.P. and Duc, N.D. (2019) 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, Article ID: 107086.
https://doi.org/10.1016/j.compositesb.2019.107086 |
| [14] | Ghannadpour, S.A.M, Karimi, M. and Tornabene, F. (2019) Application of Plate Decomposition Technique in Nonlinear and Post-Buckling Analysis of Functionally Graded Plates Containing Crack. Composite Structures, 220, 158-167.
https://doi.org/10.1016/j.compstruct.2019.03.025 |
| [15] | Qatu, M.S. and Leissa, A.W. (1993) Buckling or Trans-verse Deflections of Unsymmetrically Laminated Plates Subjected to In-Plane Loads. AIAA Journal, 31, 189-194. https://doi.org/10.2514/3.11336 |
| [16] | Laissa, A.W. (1986) Condition for Laminated Plates to Remain Flat under in Plane Loading. Composite Structure, 6, 261-270. https://doi.org/10.1016/0263-8223(86)90022-X |
| [17] | 周履, 范赋群. 复合材料力学[M]. 北京: 高等教育出版社, 1991. |
| [18] | 杨帆, 马连生. 前屈曲耦合变形对FGM圆板稳定性的影响[J]. 工程力学, 2010, 27(4): 68-72, 89. |
| [19] | Liew, K.M., Yang, J. and Kitipornchai, S. (2003) Postbuckling of Piezoelectric FGM Plates Subject to Thermo-Electro-Mechanical Loading. International Journal of Solids and Structures, 40, 3869-3892.
https://doi.org/10.1016/S0020-7683(03)00096-9 |
| [20] | Shen, H.S. (2005) Postbuckling of FGM Plates with Piezo-electric Actuators under Thermo-Electro-Mechanical Loadings. International Journal of Solids and Structures, 42, 6101-6121. https://doi.org/10.1016/j.ijsolstr.2005.03.042 |
| [21] | Shen, H.S. and Li, S.R. (2008) Postbuckling of Sandwich Plates with FGM Face Sheets and Temperature-Dependent Properties. Composites Part B: Engineering, 39, 332-344. https://doi.org/10.1016/j.compositesb.2007.01.004 |
| [22] | Ma, L.S. and Lee, D.W. (2011) A Further Dis-cussion of Nonlinear Mechanical Behavior for FGM Beams under In-Plane Thermal Loading. Composite Structures, 93, 831-842. https://doi.org/10.1016/j.compstruct.2010.07.011 |
| [23] | Fallah, F., Vahidipoor, M.K. and Nosier, A. (2015) Post-Buckling Behavior of Functionally Graded Circular Plates under Asymmetric Transverse and In-Plane Loadings. Composite Structures, 125, 477-488.
https://doi.org/10.1016/j.compstruct.2015.02.018 |
| [24] | Ma, L.S. and Wang, T.J. (2004) Relationships between Axisymmetric Bending and Buckling Solutions of FGM Circular Plates Based on Third-Order Plate Theory and Classical Plate Theory. International Journal of Solids and Structures, 41, 85-101. https://doi.org/10.1016/j.ijsolstr.2003.09.008 |
| [25] | Li, Q.L. and Zhang, J.H. (2016) Vibration and Post-Buckling of a Functionally Graded Beam Subjected to Non-Conservative Forces. Journal of Vibroengineering, 8, 4901-4913. https://doi.org/10.21595/jve.2016.16824 |
