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一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究

袁学刚 朱正佑

袁学刚, 朱正佑. 一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究[J]. 应用数学和力学, 2005, 26(2): 169-177.
引用本文: 袁学刚, 朱正佑. 一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究[J]. 应用数学和力学, 2005, 26(2): 169-177.
YUAN Xue-gang, ZHU Zheng-you. Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres[J]. Applied Mathematics and Mechanics, 2005, 26(2): 169-177.
Citation: YUAN Xue-gang, ZHU Zheng-you. Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres[J]. Applied Mathematics and Mechanics, 2005, 26(2): 169-177.

一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究

基金项目: 国家自然科学基金资助项目(10272069);上海市重点学科基金资助项目
详细信息
    作者简介:

    袁学刚(1971- ),男,吉林市人,副教授,博士(E-mail:mengjn@ytu.edu.cn);朱正佑,男,教授,博士生导师(联系人.Tel:+86-21-56331454;E-mail:chjcheng@mail.shu.edu.cn)

  • 中图分类号: O175;O343

Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres

  • 摘要: 研究了一类不可压的广义neo-Hookean材料组成的球体的空穴分岔问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压的neo-Hookean材料,得到了球体内部空穴生成的条件.与均匀各向同性的neo-Hookean球体的情况相比,证明了当摄动参数属于某些区域时,从平凡解局部向左分岔的空穴分岔解上存在一个二次转向分岔点,空穴生成时的临界载荷会比无摄动的材料的临界载荷小.用奇点理论证明了,空穴分岔方程在临界点附近等价于具有单边约束条件的正规形.用最小势能原理分别讨论了空穴分岔解的稳定性和实际稳定的平衡状态.
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出版历程
  • 收稿日期:  2002-12-20
  • 修回日期:  2004-06-25
  • 刊出日期:  2005-02-15

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