Open Access
 Issue JNWPU Volume 39, Number 4, August 2021 747 - 752 https://doi.org/10.1051/jnwpu/20213940747 23 September 2021

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## 1 ES-FEM-Poly的基本理论

ES-FEM-Poly的形函数并不是关于相关结点位移的连续函数, 不需要导数, 针对这一特点使用线性插值法[15], 直接计算相关结点在积分面上高斯积分点处的形函数值, 将高斯积分点取为每个面的形心。以图 1所示的五面体为例, 表 1给出了对应的形函数值表。表中第i行第j列的值代表第i个结点在第j个相关结点处的形函数值。

ES-FEM-Poly的总体平衡方程可由光滑Garlerkin弱化形式[13]得到

 图1五面体单元光滑子域划分方法

## 2 算例分析

### 2.1 空心球模型

 图21/8空心球模型示意图
 图3球模型参考应力云图
 图4不同数量多面体单元的应力云图
 图5各算法的应力相对误差收敛曲线
 图6各算法的能量相对误差收敛曲线

### 2.2 梁模型

 图7梁模型示意图
 图8梁模型参考应力云图
 图9不同数量多面体单元的应力云图
 图10各算法的应力相对误差收敛曲线
 图11各算法的能量相对误差收敛曲线

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## All Figures

 图1五面体单元光滑子域划分方法 In the text
 图21/8空心球模型示意图 In the text
 图3球模型参考应力云图 In the text
 图4不同数量多面体单元的应力云图 In the text
 图5各算法的应力相对误差收敛曲线 In the text
 图6各算法的能量相对误差收敛曲线 In the text
 图7梁模型示意图 In the text
 图8梁模型参考应力云图 In the text
 图9不同数量多面体单元的应力云图 In the text
 图10各算法的应力相对误差收敛曲线 In the text
 图11各算法的能量相对误差收敛曲线 In the text

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