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基于S-R和分解定理的几何非线性问题的数值计算分析

宋彦琦 郝亮钧 李向上

宋彦琦, 郝亮钧, 李向上. 基于S-R和分解定理的几何非线性问题的数值计算分析[J]. 应用数学和力学, 2017, 38(9): 1029-1040. doi: 10.21656/1000-0887.370229
引用本文: 宋彦琦, 郝亮钧, 李向上. 基于S-R和分解定理的几何非线性问题的数值计算分析[J]. 应用数学和力学, 2017, 38(9): 1029-1040. doi: 10.21656/1000-0887.370229
SONG Yan-qi, HAO Liang-jun, LI Xiang-shang. Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1029-1040. doi: 10.21656/1000-0887.370229
Citation: SONG Yan-qi, HAO Liang-jun, LI Xiang-shang. Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1029-1040. doi: 10.21656/1000-0887.370229

基于S-R和分解定理的几何非线性问题的数值计算分析

doi: 10.21656/1000-0887.370229
基金项目: 国家自然科学基金(41430640)
详细信息
    作者简介:

    宋彦琦(1969—),女,教授,博士,博士生导师(E-mail: yanqi_song@sina.com);郝亮钧(1990—),男,博士生 (通讯作者. E-mail: 276592704@qq.com).

  • 中图分类号: O241

Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem

Funds: The National Natural Science Foundation of China (41430640)
  • 摘要: 为了探究几何非线性问题的数值求解方法,采用理论推导、MATLAB编程计算、有限元模拟相结合的方法,基于S-R和分解定理及更新拖带坐标描述法,运用插值型无单元Galerkin方法对几何非线性问题的增量变分方程进行了推导,并通过四点Gauss积分法和不动点迭代法对其进行求解.最后以平面悬臂梁的大变形问题为例进行求解计算,发现与ANSYS的计算结果拟合相似度很高,说明了所采用的几何非线性力学理论及数值计算方法的正确性和合理性,为求解几何非线性问题提供了一种新的依据.
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出版历程
  • 收稿日期:  2016-07-22
  • 修回日期:  2016-09-01
  • 刊出日期:  2017-09-15

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