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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.
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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

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