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对偶变量块体混合元及其位移元的收敛性和精度分析

卿光辉 刘艳红

卿光辉, 刘艳红. 对偶变量块体混合元及其位移元的收敛性和精度分析[J]. 应用数学和力学, 2017, 38(2): 153-162. doi: 10.21656/1000-0887.370089
引用本文: 卿光辉, 刘艳红. 对偶变量块体混合元及其位移元的收敛性和精度分析[J]. 应用数学和力学, 2017, 38(2): 153-162. doi: 10.21656/1000-0887.370089
QING Guang-hui, LIU Yan-hong. Convergence and Precision of the Dual-Variable Brick Mixed Element and Its Displacement Element[J]. Applied Mathematics and Mechanics, 2017, 38(2): 153-162. doi: 10.21656/1000-0887.370089
Citation: QING Guang-hui, LIU Yan-hong. Convergence and Precision of the Dual-Variable Brick Mixed Element and Its Displacement Element[J]. Applied Mathematics and Mechanics, 2017, 38(2): 153-162. doi: 10.21656/1000-0887.370089

对偶变量块体混合元及其位移元的收敛性和精度分析

doi: 10.21656/1000-0887.370089
基金项目: 国家自然科学基金青年科学基金(11502286)
详细信息
    作者简介:

    卿光辉(1968—),男,教授,博士,硕士生导师(通讯作者. E-mail: qingluke@126.com).

  • 中图分类号: O342; O343

Convergence and Precision of the Dual-Variable Brick Mixed Element and Its Displacement Element

Funds: The National Science Fund for Young Scholars of China(11502286)
  • 摘要: 弹性力学Hamilton正则方程和Hamilton混合元的等效刚度系数矩阵,均具有直观的辛特性.基于HR变分原理和弹性力学保辛理论建立的对偶变量块体混合元,其等效刚度系数矩阵同样具有直观的辛特性.根据对偶变量块体混合元列式,可直接建立问题的控制方程,进行混合法求解.同时,通过对偶变量块体混合元列式可以导出对偶变量块体位移元列式,建立问题的控制方程后,可先求位移的解.数值实例表明:线性8结点对偶变量块体位移减缩积分元的各力学量的收敛速度均衡、收敛过程稳定、结果精度高,其应力变量的收敛速度与传统的20结点位移协调减缩积分元接近.对偶变量块体位移元具有普适性.
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出版历程
  • 收稿日期:  2016-03-28
  • 修回日期:  2016-10-19
  • 刊出日期:  2017-02-15

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