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薄板分析的线性基梯度光滑伽辽金无网格法

邓立克 王东东 王家睿 吴俊超

邓立克, 王东东, 王家睿, 吴俊超. 薄板分析的线性基梯度光滑伽辽金无网格法[J]. 力学学报, 2019, 51(3): 690-702. doi: 10.6052/0459-1879-19-004
引用本文: 邓立克, 王东东, 王家睿, 吴俊超. 薄板分析的线性基梯度光滑伽辽金无网格法[J]. 力学学报, 2019, 51(3): 690-702. doi: 10.6052/0459-1879-19-004
Like Deng, Dongdong Wang, Jiarui Wang, Junchao Wu. A GRADIENT SMOOTHING GALERKIN MESHFREE METHOD FOR THIN PLATE ANALYSIS WITH LINEAR BASIS FUNCTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 690-702. doi: 10.6052/0459-1879-19-004
Citation: Like Deng, Dongdong Wang, Jiarui Wang, Junchao Wu. A GRADIENT SMOOTHING GALERKIN MESHFREE METHOD FOR THIN PLATE ANALYSIS WITH LINEAR BASIS FUNCTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 690-702. doi: 10.6052/0459-1879-19-004

薄板分析的线性基梯度光滑伽辽金无网格法

doi: 10.6052/0459-1879-19-004
基金项目: 1) 国家自然科学基金资助项目(11772280, 11472233).
详细信息
    通讯作者:

    王东东

  • 中图分类号: O242.2;

A GRADIENT SMOOTHING GALERKIN MESHFREE METHOD FOR THIN PLATE ANALYSIS WITH LINEAR BASIS FUNCTION

  • 摘要: 薄板问题的控制方程为四阶微分方程,因而当采用伽辽金法进行分析时,形函数需要满足C$^{1}$连续性要求,且至少使用二次基函数才能保证方法的收敛性.无网格形函数虽然易于满足C$^{1}$连续性要求,但由于不是多项式,其二阶导数的计算较为复杂耗时,同时也对刚度矩阵的数值积分提出了更高的要求.本文提出了一种薄板分析的线性基梯度光滑伽辽金无网格法,该方法的基础是线性基无网格形函数的光滑梯度.在梯度光滑构造的理论框架内,无网格形函数的二阶光滑梯度可以表示为形函数一阶梯度的线性组合,因而可以提高形函数二阶梯度的计算效率.分析表明,线性基无网格形函数的光滑梯度不仅满足其固有的线性梯度一致性条件,还满足本属于二次基函数对应的额外高阶一致性条件,因此能够恰当地运用到薄板结构的伽辽金分析.此外,插值误差分析也很好地验证了线性基无网格光滑梯度的收敛特性.算例结果进一步表明,线性基梯度光滑伽辽金无网格法的收敛率与传统二次基伽辽金无网格法相当,但精度更高,同时刚度矩阵所需的高斯积分点数明显减少.

     

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出版历程
  • 收稿日期:  2019-01-02
  • 刊出日期:  2019-05-18

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