面内功能梯度矩形板的近似理论与解答

李尧臣; 聂国隽; 杨昌锦

doi:10.6052/0459-1879-12-318

面内功能梯度矩形板的近似理论与解答

1.
同济大学航空航天与力学学院, 上海 200092
2. 苏州大学城市轨道交通学院, 苏州 215006

基金项目: 国家自然科学基金资助项目(11072177).

详细信息

通讯作者:
李尧臣,教授,主要研究方向:断裂力学,岩土力学,压电材料.E-mail:yaochenli@tongji.edu.cn

中图分类号: O343.1
计量
- 文章访问数: 1796
- HTML全文浏览量: 125
- PDF下载量: 509
出版历程
- 收稿日期: 2012-11-11
- 修回日期: 2013-03-20
- 刊出日期: 2013-07-17

APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR RECTANGULAR PLATES WITH IN-PLANE STIFFNESS GRADIENT

1.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
2. School of Urban Rail Transportation, Soochow University, Suzhou 215006, China

Funds: The project was supported by the National Natural Science Foundation of China (11072177).

摘要

摘要: 提出了面内功能梯度矩形板在竖向载荷作用下的近似理论与解析解. 假设材料常数在面内x轴方向按指数规律变化.引入了板理论的Reissner-Mindlin假设, 并考虑了板中面上的剪切变形的影响.推导了板在平行于y轴的两边简支, 平行于x轴方向的两边简支或固支情况下中性层法线转角和挠度用Fourier级数表示的解.讨论了退化为Kirchhoff假设下经典薄板理论的解的情况.提供了经典薄板理论在和Reissner-Mindlin假设下的算例并与三维有限元的计算结果进行了比较, 说明了该方法在厚板情况下也是相当精确的.
- 面内变刚度 /
- Kirchhoff假设 /
- Reissner-Mindlin假设 /
- 近似理论 /
- 解析解
Abstract: Approximate theory for rectangular plates with in-plane stiffness gradient subjected to transverse loading is established. In this theory, Reissner-Mindlin assumption is introduced, and the shear deformation in the mid-surface of the plate is considered. Material properties of the plates vary exponentially in the direction parallel to one pair of edges. Analytical solution in the cases that one pair of edges of the plate is simply supported and the other pair is fixed or simply supported is obtained. It is indicated that this solution can degenerate into the classical solution of thin plates based on the well-known Kirchhoff assumption if the shear deformation in the mid-surface is ignored. The numerical results of this solution are given and compared with those from 3D finite element solution by means of PATRAN code. It shows that the precision of this solution is still high even for thick plates.
- in-plane variable stiffness /
- Kirchhoff presumption /
- Reissner-Mindlin presumption /
- approximate theory /
- analytical solution

HTML全文

参考文献(19)

吴瑞安,仲政,金波. 功能梯度压电材料矩形板的三维分析. 固体力学学报,2002, 23(特刊):43-49 (Wu Ruian, Zhong Zheng, Jin Bo. Three dimensional analysis of rectangular functionally graded piezoelectric plates. Acta Mechanica Solid Sinica, 2002, 23 (Special Issue): 43-49 (in Chinese))

仲政,尚尔涛. 功能梯度热释电材料矩形板的三维精确分析. 力学学报,2003,35(5):533-552 (Zhong Zheng, Shang Ertao. Three dimensional exact analysis of functionally gradient piezothermoelectric material rectangular plate. Acta Mechanica Sinica, 2003(5): 542-552 (in Chinese))

Chen WQ, Dong HJ. On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mechanica, 2002, 153: 207-216

伍晓红,沈亚鹏. 功能梯度压电板自由振动的三维解. 固体力学学报,2003,24(1):75-82 (Wu Xiaohong, Shen Yapeng. Three-dimensional free-vibration solution for functionally graded piezoelectric plates. Acta Mechnica Solida Sinica, 2003, 24(1): 75-82 (in Chinese))

Reddy JN. Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 2000, 47: 663-684 3.0.CO;2-8">

杨杰, 沈惠申. 热/机械载荷下功能梯度材料矩形厚板的弯曲行为. 固体力学学报, 2003, 24(1): 119-122 (Yang Jie, Shen Huishen. Bending behavior of functionally graded rectangular thick plates subjected to thermo-mechanical loading. Acta Mechnica Solida Sinica, 2003, 24(1): 119-122 (in Chinese))

Tanigawa Y, Matsumoto M, Akat T. Optimization problem of material composition for nonhomogeneous plate to minimize thermal stresses when subjected to unsteady heat supply. Transactions of the Japan Society of Mechanical Engineers, Series A, 1996, 62 (593): 115-122

Noda N, Tsuji T. Steady thermal stresses in a plate of functionally gradient material. Transactions of the Japan Society of Mechanical Engineers, Series A, 1991, 57(533): 98-103

Yang J, Kitipornchai S, Liew KM. Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates. Computational Methods Applied Mechanics Engineering, 2003, 192: 3861-3885

Croce LD, Venini P. Finite elements for functionally graded Reissner-Mindlin plates. Computational Methods Applied Mechanics Engineering, 2004, 193:705-725

朱昊文,李尧臣,杨昌锦.功能梯度压电材料板的有限元解. 力学季刊,2005,26(4):567-571 (Zhu Haowen, Li Yaochen, Yang Changjing. Finite element solution of functionally graded piezoelectric plates. Chnese Quarterly Mechanics, 2005, 26(4): 567-571 (in Chinese))

李尧臣,亓峰,仲政. 功能梯度压电材料圆板的简化理论与解析解. 力学学报,2008,40(5):636-645 (Li Yaochen, Qi Feng, Zhong Zheng. Simplified theory and analytical solutions for functionally graded piezoelectric circular plate. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 636-645 (in Chinese))

李尧臣,亓峰,仲政. 功能梯度矩形板的近似理论与解析解. 力学学报,2010,42(4):670-681 (Li Yaochen, Qi Feng, Zhong Zheng. Approximate theory and analytical solutions for functionally graded piezoelectric rectangular plates. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(4): 670-681 (in Chinese))

王锋,李道奎,唐国金.基于高阶位移模式的压电层合板动力有限元模型.计算力学学报, 2007, 24(6): 891-898 (Wang Feng, Li Daokui, Tang Guojin. Dynamic finite element model of piezoelectric laminated plates based on high-order displacement patterns. Chinese Journal of Computational Mechanics, 2007, 24(6): 891-898 (in Chinese))

尚新春.双向变刚度矩形板弯曲问题的精确解.兰州大学学报,1991, 27(2): 24-32 (Shang Xinchun. Exact solution of bending plates with variable stiffness in two directions. Journal of Lanzhou University, 1991, 27(2): 24-32 (in Chinese))

杨杰.单向变刚度板结构分析的伽辽金线法. 武汉化工学院学报,1996,18(1): 57-60 (Yang Jie. Galerkin line method for structural analysis of plates with variable stiffness in one direction. Journal of Wuhan College of Chemical Engineering, 1996, 18(1): 57-60 (in Chinese))

Liu DY, Wang CY, Chen WQ. Free vibration of FGM plates with in-plane material inhomogeneity. Composite Structures, 2010, 92: 1047-1051

于天崇,聂国隽,仲政. 变刚度矩形板弯曲问题的Levy解. 力学季刊,2012,33(1): 53-59 (Yu Tianchong, Nie Guojun, Zhong Zheng. Levy type solution for the bending of rectangular plates with variable stiffness. Chinese Quarterly of Mechanics, 2012,33(1): 53-59 (in Chinese))

Lü CF, Lim CW, Chen WQ. Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions. Int J Num Meth Eng, 2009, 79(1): 25-44