The complex variable meshless local Petrov-Galerkin method for elasticity problems of functionally graded materials
The complex variable meshless local Petrov-Galerkin method for elasticity problems of functionally graded materials
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DOI：
10.1016/j.amc.2015.07.020
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发表时间：
2015-10
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影响因子：
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通讯作者：
Dandan Wei;Weiwei Zhang;Linghui Wang;Baodong Dai
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文献类型：
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作者：
Dandan Wei;Weiwei Zhang;Linghui Wang;Baodong Dai
本文提出了用于功能梯度材料（FGM）静态分析的复变量无网格局部 Petrov-Galerkin（CVMLPG）方法。该方法采用在移动最小二乘(MLS)近似的基础上引入复变量理论建立的复变量移动最小二乘(CVMLS)近似来构造场逼近函数。与传统的MLS方法相比，CVMLS方法的试探函数中的未知系数数量少于MLS近似，因此在相同的节点分布下可以获得更高的效率和精度。 FGM 的 CVMLPG 方法的优点之一是使用高斯点处的材料参数来模拟功能梯度材料属性的变化，因此它完全避免了 FGM 的有限元方法 (FEM) 中每个单元均匀假设的问题。考虑了一些选定的基准示例来确认所提出方法的有效性和准确性。
This paper proposed the complex variable meshless local Petrov–Galerkin (CVMLPG) method for the static analysis of functionally graded materials (FGMs). In the presented method, the complex variable moving least-square (CVMLS) approximation, which is established based on the moving least-square (MLS) approximation by introducing the complex variable theory, is adopted for construction of the field approximation function. Compared with the conventional MLS method, the number of the unknown coefficients in the trial function of the CVMLS method is less than that of the MLS approximation, thus higher efficiency and accuracy can be achieved under the same node distributions. One advantage of the CVMLPG method for the FGMs is that the variations of the functionally graded material properties are simulated by using material parameters at Gauss points, so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method (FEM) for the FGMs. Some of selected benchmark examples are considered to confirm the validity and accuracy of the proposed method.