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基于S-R和分解定理的三维几何非线性无网格法

宋彦琦 周涛

宋彦琦, 周涛. 基于S-R和分解定理的三维几何非线性无网格法[J]. 力学学报, 2018, 50(4): 853-862. doi: 10.6052/0459-1879-18-050
引用本文: 宋彦琦, 周涛. 基于S-R和分解定理的三维几何非线性无网格法[J]. 力学学报, 2018, 50(4): 853-862. doi: 10.6052/0459-1879-18-050
Song Yanqi, Zhou Tao. THREE-DIMENSIONAL GEOMETRIC NONLINEARITY ELEMENT-FREE METHOD BASED ON S-R DECOMPOSITION THEOREM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 853-862. doi: 10.6052/0459-1879-18-050
Citation: Song Yanqi, Zhou Tao. THREE-DIMENSIONAL GEOMETRIC NONLINEARITY ELEMENT-FREE METHOD BASED ON S-R DECOMPOSITION THEOREM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 853-862. doi: 10.6052/0459-1879-18-050

基于S-R和分解定理的三维几何非线性无网格法

doi: 10.6052/0459-1879-18-050
基金项目: 国家自然科学基金重点项目(41430640)和中国矿业大学(北京)深部岩土力学与地下工程国家重点实验室开放基金项目(SKLGDUEK1728)资助
详细信息
    作者简介:

    *宋彦琦, 教授, 主要研究方向: 固体力学理论及工程应用等方面的研究. E-mail:songyq@cumtb.edu.cn

    通讯作者:

    宋彦琦

  • 中图分类号: O331;

THREE-DIMENSIONAL GEOMETRIC NONLINEARITY ELEMENT-FREE METHOD BASED ON S-R DECOMPOSITION THEOREM

  • 摘要: S-R(strain-rotation)和分解定理克服了经典有限变形理论的一些缺点, 使其可以为几何非线性数值分析提供可靠的理论基础. 对于大变形问题, 由于无网格法(element-free method)避免了对单元网格的依赖, 从而从根本上避免了有限单元法(finite element method, FEM)的单元畸变问题, 保证了求解精度. 因此, 将无网格法和S-R和分解定理结合起来势必能建立一套更加合理可靠的几何非线性数值计算方法. 目前基于S-R 定理的无网格数值方法研究较少并且只能用于二维平面问题的求解, 但实际上绝大多数问题都必须以三维模型来进行处理, 因此建立适用于三维情况的S-R无网格法是非常有必要的. 本文给出了适用于三维情况的S-R 无网格法: 采用由更新拖带坐标法和势能率原理推导出来的增量变分方程, 利用基于全局弱式的无网格Galerkin 法(EFG)得到了用于求解三维空间问题的离散格式. 利用MATLAB编制三维S-R 无网格法程序, 对受均布载荷的三维悬臂梁和四边简支矩形板结构的非线性弯曲问题进行了计算. 最后将所得的数值结果与已有文献进行了比较, 验证了本文的三维S-R无网格数值算法的合理性、有效性和准确性. 本文的三维S-R无网格数值算法可以作为一种可靠的三维几何非线性数值分析方法.

     

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  • 收稿日期:  2018-03-05
  • 刊出日期:  2018-07-18

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