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基于曲率插值的大变形梁单元

张志刚 齐朝晖 吴志刚

张志刚, 齐朝晖, 吴志刚. 基于曲率插值的大变形梁单元[J]. 应用数学和力学, 2013, 34(6): 620-629. doi: 10.3879/j.issn.1000-0887.2013.06.008
引用本文: 张志刚, 齐朝晖, 吴志刚. 基于曲率插值的大变形梁单元[J]. 应用数学和力学, 2013, 34(6): 620-629. doi: 10.3879/j.issn.1000-0887.2013.06.008
ZHANG Zhi-gang, QI Zhao-hui, WU Zhi-gang. Large Deformation Beam Element Based on Curvature Interpolation[J]. Applied Mathematics and Mechanics, 2013, 34(6): 620-629. doi: 10.3879/j.issn.1000-0887.2013.06.008
Citation: ZHANG Zhi-gang, QI Zhao-hui, WU Zhi-gang. Large Deformation Beam Element Based on Curvature Interpolation[J]. Applied Mathematics and Mechanics, 2013, 34(6): 620-629. doi: 10.3879/j.issn.1000-0887.2013.06.008

基于曲率插值的大变形梁单元

doi: 10.3879/j.issn.1000-0887.2013.06.008
基金项目: 国家自然科学基金资助项目(10972044)
详细信息
    作者简介:

    张志刚(1984—),男,河南开封人,博士生(E-mail:zhigangzhang@foxmail.com)

  • 中图分类号: O342

Large Deformation Beam Element Based on Curvature Interpolation

  • 摘要: 线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析.传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题.该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数.由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题.因而所提方法特别适用于梁的几何非线性分析.数值算例说明了所提方法的正确性和有效性.
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出版历程
  • 收稿日期:  2012-12-07
  • 修回日期:  2013-05-20
  • 刊出日期:  2013-06-15

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