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辛求解体系下功能梯度材料平面梁的完整解析解

赵莉 陈伟球 吕朝锋

赵莉, 陈伟球, 吕朝锋. 辛求解体系下功能梯度材料平面梁的完整解析解[J]. 应用数学和力学, 2012, 33(10): 1143-1155. doi: 10.3879/j.issn.1000-0887.2012.10.001
引用本文: 赵莉, 陈伟球, 吕朝锋. 辛求解体系下功能梯度材料平面梁的完整解析解[J]. 应用数学和力学, 2012, 33(10): 1143-1155. doi: 10.3879/j.issn.1000-0887.2012.10.001
ZHAO Li, CHEN Wei-qiu, Lü Chao-feng. Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1143-1155. doi: 10.3879/j.issn.1000-0887.2012.10.001
Citation: ZHAO Li, CHEN Wei-qiu, Lü Chao-feng. Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1143-1155. doi: 10.3879/j.issn.1000-0887.2012.10.001

辛求解体系下功能梯度材料平面梁的完整解析解

doi: 10.3879/j.issn.1000-0887.2012.10.001
基金项目: 国家自然科学基金资助项目(11202111; 11090333; 10972193);宁波市自然科学基金资助项目(2011A610077)
详细信息
    通讯作者:

    赵莉(1982-),女,山东人,讲师,博士 (Tel:+86-574-87080435; E-mail: zhaoli06@zju.edu.cn);吕朝锋(1978-),浙江人, 副教授,博士生导师(联系人.Tel: +86-571-88208473; E-mail: lucf@zju.edu.cn).

  • 中图分类号: O343.1;O343.7

Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework

  • 摘要: 采用辛弹性力学解法,求取弹性模量沿轴向指数变化,而Poisson比保持不变的功能梯度材料平面梁的完整解析解.通过求解被Saint-Venant原理覆盖的一般本征解,建立起完整的解析分析过程,进而给出平面梁位移和应力的精确分布规律.传统的弹性力学分析方法常常忽略被Saint-Venant原理覆盖的解,但这些衰减的本征解对材料的局部效应起着较大的影响作用,可能导致材料或结构的突然失效.采用辛求解方法,充分利用本征向量之间的辛共轭正交关系,得到了功能梯度材料梁的完整解析解.两个数值算例分别将功能梯度材料平面梁的位移和应力分布与相应均匀材料情形的结果进行比较,研究了材料非均匀性对位移和应力解的影响.
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出版历程
  • 收稿日期:  2012-01-18
  • 修回日期:  2012-03-21
  • 刊出日期:  2012-10-15

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