A partition-of-unity based ‘FE-Meshfree’ QUAD4 element with radial-polynomial basis functions for static analyses
A partition-of-unity based ‘FE-Meshfree’ QUAD4 element with radial-polynomial basis functions for static analyses
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DOI：
10.1016/j.cma.2011.08.005
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发表时间：
2011-11
影响因子：
7.2
通讯作者：
Jiangping Xu;S. Rajendran
中科院分区：
文献类型：
--
作者：
Jiangping Xu;S. Rajendran
最近，一种基于单位剖分(PU)的有限元--无网格QUAD4单元问世。该单元采用多项式基函数进行局部逼近(LA)。本文采用径向多项式混合基函数构造了一种新的无网格QUAD4单元。径向多项式基的一个优点是避免了矩矩阵可能出现的奇异性，这种奇异性有时会导致多项式基函数的选择不当。另一个优点是提高了有限元解的精度。新单元已被应用于几个线性和非线性测试问题。结果表明，新单元的计算性能明显优于基于纯多项式基的无网格QUAD4单元。即使具有较低阶基，即只有三或四个多项式项，本单元也能够给出比采用六项多项式基的前一单元更精确的解。与已知的二次单元相比，新单元对网格变形的容忍度也要高得多。此外，与许多基于单位分割法(PU)的单元相关的线性相关性问题从本单元中完全消除。
Recently, a partition-of-unity (PU) based finite element called ‘FE-Meshfree’ QUAD4 element has been published. That element employed polynomial basis functions for the local approximation (LA). In the present paper, a new FE-Meshfree QUAD4 element employing hybrid radial-polynomial basis functions for the LA is proposed. An advantage of radial-polynomial basis is the freedom from the possible singularity of the moment matrix that could sometimes result with an inappropriate choice of polynomial basis functions. Another advantage is the improved accuracy of finite element solution. The new element has been applied to several linear and nonlinear test problems. The results demonstrate that the new element gives much better performance as compared to the previous FE-Meshfree QUAD4 element with pure polynomial basis. Even with a lower order basis, viz., with just three or four polynomial terms, the present element is capable of giving more accurate solution than the previous element which employs a six-term polynomial basis. The new element also exhibits a much higher degree of tolerance to mesh distortion than the known quadratic elements. Moreover, the linear dependence problem, otherwise associated with many of the partition-of-unity (PU) based elements, is completely eliminated from the present element.