| 复变量移动最小二乘法及其应用 |
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| 引用本文： | 程玉民,彭妙娟,李九红.复变量移动最小二乘法及其应用[J].力学学报,2005,37(6):719-723. |
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| 作者姓名： | 程玉民 彭妙娟 李九红 |
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| 作者单位： | 上海大学上海市应用数学和力学所，200072 |
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| 基金项目： | 国家自然科学基金(10571118)
上海市重点学科建设项目(Y0103)资助．~~ |
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| 摘 要： | 提出了复变量移动最小二乘法，并详细讨论了基于正交基函数的复变量移动最小二乘
法. 然后，将复变量移动最小二乘法和弹性力学的边界无单元法结合，提出了弹性力学的复
变量边界无单元法，推导了相应的公式，并给出了数值算例. 基于正交基函数的复变量移动
最小二乘法的优点是不形成病态方程组、精度高，所形成的无网格方法计算量小. 复变量边
界无单元法是边界积分方程的无网格方法的直接列式法，容易引入边界条件，且具有更高的
精度.
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| 关 键 词： | moving least-square approximation with complex variables 正交基函数 elasticity boundary integral equation boundary element-free method (BEFM) |
| 文章编号： | 0459-1879(2005)06-0719-05 |
| 收稿时间： | 2004-08-06 |
| 修稿时间： | 2005-03-03 |
THE MOVING LEAST-SQUARE APPROXIMATION WITH COMPLEX VARIABLES AND ITS APPLICATION IN BOUNDARY ELEMENT-FREE METHOD FOR ELASTICITY |
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| Cheng Yumin,Peng Miaojuan,Li Jiuhong.THE MOVING LEAST-SQUARE APPROXIMATION WITH COMPLEX VARIABLES AND ITS APPLICATION IN BOUNDARY ELEMENT-FREE METHOD FOR ELASTICITY[J].chinese journal of theoretical and applied mechanics,2005,37(6):719-723. |
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| Authors: | Cheng Yumin Peng Miaojuan Li Jiuhong |
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| Abstract: | Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is presented in this paper. And the complex variable moving least-square approximation based on the orthogonal basis function is discussed in detail. Then, combining the complex variable moving least-square approximation with the boundary element-free method (BEFM) for elasticity, the complex variable boundary element-free method (CVBEFM) for elasticity is presented, and the corresponding formulae are obtained. Some numerical examples are given at last. The complex variable moving least-square approximation can not form an ill-conditioned or singular equations. In the complex variable moving least-square approximation, the number of the constants is smaller than that in the moving least-square (MLS) approximation. Then the meshless method obtained from the complex variable moving least-square approximation has greater computational efficiency and precision. The complex variable boundary element-free method is a direct numerical method of the meshless method of boundary integral equation. And the boundary condition can be applied easily. The complex variable boundary element-free method has a greater precision. |
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| Keywords: | complex variable moving least-square approximation orthogonal basis function elasticity boundary integral equation boundary element-free method |
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