| 基于紧支径向基函数的点插值无网格方法 |
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| 引用本文： | 孔亮,高学军,王燕昌.基于紧支径向基函数的点插值无网格方法[J].岩土力学,2004,25(Z2):117-120. |
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| 作者姓名： | 孔亮 高学军 王燕昌 |
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| 作者单位： | 1. 宁夏大学,物电学院固体力学研究所,宁夏,银川,750021
2. 宁夏大学,校长办公室,宁夏,银川750021 |
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| 基金项目： | 教育部科学技术研究重点项目(204151)与宁夏大学科研基金资助项目(032106). |
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| 摘 要： | 紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性.
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| 关 键 词： | 无网格法 紧支径向基函数 点插值 |
| 文章编号： | 1000-7598-(2004)增-0117-05 |
| 修稿时间： | 2004年4月27日 |
Point interpolation meshless method based on compactly supported radial basis functions |
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| KONG Liang,GAO Xue-jun,WANG Yan-chang.Point interpolation meshless method based on compactly supported radial basis functions[J].Rock and Soil Mechanics,2004,25(Z2):117-120. |
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| Authors: | KONG Liang GAO Xue-jun WANG Yan-chang |
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| Institution: | KONG Liang1,GAO Xue-jun1,WANG Yan-chang2 |
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| Abstract: | The local characteristic of compactly supported radial basis functions (RBFs), which makes the stiffness matrix of governing equations sparse and banded, is well adopted in meshless methods. However, its accuracy is not much high in interpolation. Interpolation functions in the point interpolation method (PIM) have delta function property, which is convenient to implement essential boundary conditions. The limitation of the PIM is that the matrix may be singular. In order to improve the accuracy and avoid the limitation of PIM, this paper proposes a technique to modify the compactly supported RBFs based on the completeness. These modified compactly supported RBFs are used to construct interpolation functions, thus a compactly supported radial point interpolation method is obtained. With this modified PIM, the governing equations of two-dimensional elastic mechanics are discretized. This modification overcomes possible singularities associated with polynomial basis only. Furthermore, its shape functions have the property of delta function and the essential boundary conditions can be applied as easy as in conventional finite element method (FEM). In addition, the method is applied to two-dimensional static problems, and a cantilever beam problem is analyzed. The numerical results show that the proposed method is accurate, convenient and efficient. |
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| Keywords: | meshless method compactly supported radial basis functions point interpolation |
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