Boundary element‐free method (BEFM) and its application to two‐dimensional elasticity problems
Boundary element‐free method (BEFM) and its application to two‐dimensional elasticity problems
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DOI：
10.1002/nme.1489
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发表时间：
2006-02
影响因子：
2.9
通讯作者：
K. Liew;Yumin Cheng;S. Kitipornchai
中科院分区：
文献类型：
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作者：
K. Liew;Yumin Cheng;S. Kitipornchai
在本研究中，我们首先讨论移动最小二乘近似（MLS）方法。在某些情况下，MLS可能会形成病态方程组，从而无法正确获得解。因此，在本文中，我们提出了一种改进的移动最小二乘近似（IMLS）方法。在IMLS方法中，使用具有权函数的正交函数系统作为基函数。 IMLS比MLS具有更高的计算效率和精度，并且不会导致病态方程组。结合边界积分方程（BIE）方法和 IMLS 近似方法，提出了一种直接无网格 BIE 方法，即无边界元方法（BEFM），用于二维弹性分析。与其他无网格BIE方法相比，BEFM是一种直接数值方法，其基本未知量是节点变量的实解，且边界条件易于应用；因此，它具有更高的计算精度。出于演示目的，给出了选定的数值示例。版权所有 © 2005 约翰·威利父子有限公司
In this study, we first discuss the moving least‐square approximation (MLS) method. In some cases, the MLS may form an ill‐conditioned system of equations so that the solution cannot be correctly obtained. Hence, in this paper, we propose an improved moving least‐square approximation (IMLS) method. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill‐conditioned system of equations. Combining the boundary integral equation (BIE) method and the IMLS approximation method, a direct meshless BIE method, the boundary element‐free method (BEFM), for two‐dimensional elasticity is presented. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied easily; hence, it has higher computational precision. For demonstration purpose, selected numerical examples are given. Copyright © 2005 John Wiley & Sons, Ltd.