混合变换法在无网格伽辽金方法中的应用

移动最小二乘近似的非插值特征给无网格伽辽金方法的应用带来了一定的的困难，本文将再生核质点法中的混合变换法与无网格伽辽金方法相结合，通过对移动最小二乘近似进行局部修正，实现了无网格伽辽金方法中本质边界条件的精确施加。对权函数、影响半径、积分阶等对计算精度的影响进行了有益的探讨。数值计算结果表明了方法的可行性。

Application of Mixed Transformation Method in Element-free Galerkin method

The application of element-free Galerkin method often presents difficulties because the Moving Least Squares (MLS) approximation, used in this method, lacks the interpolation property. In this paper, the mixed transformation method, proposed in Reproducing Kernel Particle Method, is utilized for the implementation of essential boundary conditions in element-free Galerkin method by modifying MLS approximation locally. As a consequence, the essential boundary conditions can be imposed directly at nodes. The proposed method eliminates the shortcomings of Lagrange multipliers and penalty functions typically used in element-free Galerkin method fomulations. A comprehensive study is given including the influence of weight function, influence domain and integration order on precision of the present method. The application examples reveal that the present method is not only simple and logical but also exhibit very high accuracy, convergency and stability.