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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.
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.
 Citation: 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.

## THE MOVING LEAST-SQUARE APPROXIMATION WITH COMPLEX VARIABLES AND ITS APPLICATION IN BOUNDARY ELEMENT-FREE METHOD FOR ELASTICITY

• 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.

Abstract: Based on the moving least-square (MLS) approximation, the moving least-square approximation with complex variables (MLSCV) is presented in this paper. And the moving least-square approximation with complex variables based on the orthogonal basis function is discussed in detail. The method can not form an ill-conditioned system of equations. The meshless method obtained from the moving least-square approximation with complex variables has greater computational efficiency. Then, combining the moving least-square approximation with complex variables and the boundary element-free method (BEFM) for elasticity, the boundary element-free method with complex variables (BEFMCV) for elasticity is presented, and the corresponding formulae are obtained. The boundary element-free method with complex variables is a direct numerical method of the meshless method of boundary integral equation. And the boundary condition can be applied easily. The boundary element-free method with complex variables has a greater precision. Some numerical examples are given at last.

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