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离散系统运动方程的Galerkin有限元EEP法自适应求解

邢沁妍 杨杏 袁驷

邢沁妍, 杨杏, 袁驷. 离散系统运动方程的Galerkin有限元EEP法自适应求解[J]. 应用数学和力学, 2017, 38(2): 133-143. doi: 10.21656/1000-0887.370288
引用本文: 邢沁妍, 杨杏, 袁驷. 离散系统运动方程的Galerkin有限元EEP法自适应求解[J]. 应用数学和力学, 2017, 38(2): 133-143. doi: 10.21656/1000-0887.370288
XING Qin-yan, YANG Xing, YUAN Si. An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems[J]. Applied Mathematics and Mechanics, 2017, 38(2): 133-143. doi: 10.21656/1000-0887.370288
Citation: XING Qin-yan, YANG Xing, YUAN Si. An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems[J]. Applied Mathematics and Mechanics, 2017, 38(2): 133-143. doi: 10.21656/1000-0887.370288

离散系统运动方程的Galerkin有限元EEP法自适应求解

doi: 10.21656/1000-0887.370288
基金项目: 国家自然科学基金(51508305;51378293;51078199)
详细信息
    作者简介:

    邢沁妍(1981—),女,讲师,博士(通讯作者. E-mail: xingqy@tsinghua.edu.cn);杨杏(1988—),男,硕士生(E-mail: xihuanyuye@126.com);袁驷(1953—),男,教授,博士(E-mail: yuans@tsinghua.edu.cn).

  • 中图分类号: O242.21

An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems

Funds: The National Natural Science Foundation of China(51508305;51378293;51078199)
  • 摘要: 对于结构动力分析中的离散系统运动方程,现有算法的计算精度和效率均依赖于时间步长的选取,这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法,以EEP超收敛解代替未知真解,估计常规有限元解的误差,并自动细分网格,目前已对诸类以空间坐标为自变量的边值问题取得成功.对离散系统运动方程建立弱型Galerkin有限元解,引入基于EEP法的自适应求解策略,在时间域上自动划分网格,最终得到所求时域内任一时刻均满足给定误差限的动位移解,进而建立了一种时间域上的新型自适应求解算法.
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出版历程
  • 收稿日期:  2016-09-21
  • 修回日期:  2016-11-17
  • 刊出日期:  2017-02-15

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