留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

梯度材料平板弯拉耦合力学的精确化支配方程

胡超 郑日恒 孙旭峰 周传平

胡超, 郑日恒, 孙旭峰, 周传平. 梯度材料平板弯拉耦合力学的精确化支配方程[J]. 应用数学和力学, 2016, 37(7): 756-765. doi: 10.21656/1000-0887.370097
引用本文: 胡超, 郑日恒, 孙旭峰, 周传平. 梯度材料平板弯拉耦合力学的精确化支配方程[J]. 应用数学和力学, 2016, 37(7): 756-765. doi: 10.21656/1000-0887.370097
HU Chao, ZHENG Ri-heng, SUN Xu-feng, ZHOU Chuan-ping. Refined Equations for Functionally Graded Material Plates Under Bending-Tension Coupling[J]. Applied Mathematics and Mechanics, 2016, 37(7): 756-765. doi: 10.21656/1000-0887.370097
Citation: HU Chao, ZHENG Ri-heng, SUN Xu-feng, ZHOU Chuan-ping. Refined Equations for Functionally Graded Material Plates Under Bending-Tension Coupling[J]. Applied Mathematics and Mechanics, 2016, 37(7): 756-765. doi: 10.21656/1000-0887.370097

梯度材料平板弯拉耦合力学的精确化支配方程

doi: 10.21656/1000-0887.370097
基金项目: 国家自然科学基金(51378451;51276129);高超声速发动机技术国家重点实验室开放基金(20130103007)
详细信息
    作者简介:

    胡超(1961—),男,教授,博士,博士生导师(通讯作者. E-mail: chaohu@yzu.edu.cn).

  • 中图分类号: O302

Refined Equations for Functionally Graded Material Plates Under Bending-Tension Coupling

Funds: The National Natural Science Foundation of China(51378451;51276129)
  • 摘要: 基于非均匀材料弹性力学理论,采用算子谱分解和算子代数方法,对梯度材料平板结构弯曲与拉伸问题进行了研究.首次给出了指数梯度材料平板弯曲与拉伸的力学方程.研究结果表明:与各向同性平板结构弯曲和拉伸问题不同,在功能梯度平板中描述弯曲应力状态与描述拉伸应力状态的广义位移函数以及剪切函数都是耦合的.没有采用工程假设,推导得到的梯度材料平板结构力学方程是精确化的.通过分析可以认识和理解,分别对应于弯曲状态与拉伸状态的应力场耦合机理以及力学响应的构成等.给出的方程及其分析过程可望能够用于类平板形式热防护材料结构的应力分析与强度设计,推进热防护材料结构的轻型化.
  • [1] Mian M A, Spencer A J M. Exact solutions for functionally graded and laminated elastic materials[J]. Journal of the Mechanics and Physics of Solids,1998,46(12): 2283-2295.
    [2] 沈惠申. 功能梯度复合材料板壳结构的弯曲、屈曲和振动[J]. 力学进展, 2004,34(1): 53-60.(SHEN Hui-shen. Bending, buckling and vibration of functionally graded plates and shells[J]. Advances in Mechanics,2004,34(1): 53-60.(in Chinese))
    [3] Birman V, Byrd L W. Modeling and analysis of functionally graded materials and structures[J]. Applied Mechanics Reviews,2007,60(5): 195-216.
    [4] HU Chao, FANG Xue-qian, DU Shan-yi. Multiple scattering of thermal waves from a subsurface spheroid in exponentially graded materials based on non-Fourier’s model[J].Infrared Physics & Technology,2007,50(1): 70-77.
    [5] 孟宇鹏, 郑日恒. 超声速进气道与飞航导弹一体化发展概述[J]. 飞航导弹, 2008(1): 47-52.(MENG Yu-peng, ZHENG Ri-heng. Brief review on inlet of the supersonic flow and integrated development of winged missiles[J]. Winged Missiles Journal,2008(1): 47-52.(in Chinese))
    [6] Benachour A, Tahar H D, Atmane H A, Tounsi A, Ahmed A S. A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient[J]. Composites Part B: Engineering,2011,42(6): 1386-1394.
    [7] Woodward B, Kashtalyan M. Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates[J]. European Journal of Mechanics—A/Solids,2011,30(5): 705-718.
    [8] THAI Huu-tai, CHOI Dong-ho. A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation[J]. Composites Part B: Engineering,2012,43(5): 2335-2347.
    [9] Zenkour A M. Bending of FGM plates by a simplified four-unknown shear and normal deformations theory[J]. International Journal of Applied Mechanics,2013,5(2): 1350020-1-1350020-15.
    [10] 胡超, M·A Fai, 马兴瑞, 黄文虎. 厚板弯曲与拉伸振动精化理论及其求解新途径[J]. 中国科学:物理、力学、天文学, 2012,42(5): 522-530.(HU Chao, Fai M A, MA Xing-rui, HUNG Wen-hu. Refined dynamic theory of thick plates in extension-bending and its new formulism[J]. Scientia Sinica: Physica, Mechanica & Astronomica,2012,42(5): 522-530.(in Chinese))
    [11] Sanchez-Palencia E. Non-Homogeneous Media and Vibration Theory [M]. Springer-Verlag, 1980.
    [12] ZHANG Da-guang, ZHOU You-he. A theoretical analysis of FGM thin plates based on physical neutral surface[J]. Computational Materials Science,2008,44(2): 716-720.
    [13] 张贤科, 许甫华. 高等代数学[M]. 北京: 清华大学出版社, 2008.(ZHANG Xian-ke, XU Fu-hua.Higher Algebra [M]. Beijing: Tsinghua University Press, 2008.(in Chinese))
    [14] 胡海昌. 弹性力学的变分原理及其应用[M]. 北京: 科学出版社, 1981.(HU Hai-chang. Variational Principle in Elasticity and Its Applications [M]. Beijing: Science Press, 1981.(in Chinese))
    [15] 张鸿庆. 线性算子方程组一般解的代数构造[J]. 大连工学院学报, 1979,18(3): 23-47.(ZHANG Hong-qing. Algebraic construction of general solutions of linear operational systems[J].Journal of Dalian Institute of Technology,1979,18(3): 23-47.(in Chinese))
  • 加载中
计量
  • 文章访问数:  595
  • HTML全文浏览量:  43
  • PDF下载量:  653
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-04-06
  • 修回日期:  2016-05-23
  • 刊出日期:  2016-07-15

目录

    /

    返回文章
    返回