A high order local approximation free from linear dependency with quadrilateral mesh as mathematical cover and applications to linear elastic fractures
A high order local approximation free from linear dependency with quadrilateral mesh as mathematical cover and applications to linear elastic fractures
复制标题
以四边形网格为数学覆盖的无线性依赖性的高阶局部近似及其在线弹性裂缝的应用
DOI：
10.1016/j.compstruc.2016.10.001
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发表时间：
2017
影响因子：
4.7
通讯作者：
Wu Aiqing
中科院分区：
文献类型：
--
作者：
Xu Dongdong;Yang Yongtao;Zheng Hong;Wu Aiqing
数值流形方法福尔斯属于单位分解方法的范畴。为了提高精度，可以指定高阶多项式作为局部近似。然而，这将导致刚度矩阵的秩不足。在这项研究中，一个局部位移近似构造在一个物理补丁生成的四个四边形的数学网格。所有的自由度都是有物理意义的。应力在所有节点处都是连续的，这表明不需要应力抛光。所提出的近似具有相同的精度作为一阶多项式，但没有线性依赖于后者固有的。
The numerical manifold method falls into the category of the partition of unity methods. In order to enhance accuracy, high order polynomials can be specified as the local approximations. This, however, would incur rank deficiency of the stiffness matrix. In this study, a local displacement approximation is constructed over a physical patch generated from a four quadrilateral mathematical mesh. All the degrees of freedom are physically meaningful. The stresses are continuous at all nodes, suggesting that no stress polish is required. The proposed approximations have the same accuracy as the first-order polynomials, but no linear dependency inherent in the latter.