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自由单元法及其在结构分析中的应用

高效伟 徐兵兵 吕军 彭海峰

高效伟, 徐兵兵, 吕军, 彭海峰. 自由单元法及其在结构分析中的应用[J]. 力学学报, 2019, 51(3): 703-713. doi: 10.6052/0459-1879-19-011
引用本文: 高效伟, 徐兵兵, 吕军, 彭海峰. 自由单元法及其在结构分析中的应用[J]. 力学学报, 2019, 51(3): 703-713. doi: 10.6052/0459-1879-19-011
Xiaowei Gao, Bingbing Xu, Jun Lü, Haifeng Peng. FREE ELEMENT METHOD AND ITS APPLICATION IN STRUCTURAL ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 703-713. doi: 10.6052/0459-1879-19-011
Citation: Xiaowei Gao, Bingbing Xu, Jun Lü, Haifeng Peng. FREE ELEMENT METHOD AND ITS APPLICATION IN STRUCTURAL ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 703-713. doi: 10.6052/0459-1879-19-011

自由单元法及其在结构分析中的应用

doi: 10.6052/0459-1879-19-011
基金项目: 1)国家自然科学基金资助项目(11672061, 11772083).
详细信息
    通讯作者:

    高效伟

  • 中图分类号: O341;

FREE ELEMENT METHOD AND ITS APPLICATION IN STRUCTURAL ANALYSIS

  • 摘要: 通过吸收有限元与无网格法的优点,提出了一种新的数值方法------自由单元法.此方法在离散方面,采用有限元法中的等参单元,表征几何形状和进行物理量的插值;在算法方面,采用单元配点技术,逐点产生系统方程.主要特点是,在每个配置点只需要一个和周围自由选择的节点而形成的一个独立的等参单元,因而不需要考虑物理量在单元之间的相互连接关系与导数连续性问题. 本文介绍强形式与弱形式两种自由单元法,前者直接由控制方程和边界条件直接产生系统方程,后者通过在自由单元上建立控制方程的加权余量式产生弱形式积分式,并通过像传统有限元法中的积分过程建立系统方程组.本文提出的方法是一种单元配点法,对于域内点为了获得较高的导数精度,需要采用至少具有一个内部点的等参单元,为此除了可使用各阶次的拉格朗日四边形单元外, 还 给出了七节点三角形等参单元,用于模拟较为复杂的几何形状问题.

     

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出版历程
  • 收稿日期:  2019-01-07
  • 刊出日期:  2019-05-18

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