完全变换法在无网格伽辽金方法中的应用

由于移动最小二乘形函数一般不具有常规有限元或边界元形函数所具有的插值特征，本质边界条件的处理成为无网格伽辽金法实施中的一个难点。本文通过建立节点位移和广义位移之间的关系对移动最小二乘形函数进行修正，给出了修正的移动最小二乘形函数；以二维问题为例，对完全交换法在无网格伽辽金方法中的应用进行了研究，实现了本质边界条件在节点处的精确施加。数值计算结果表明该方法不仅简单合理，而且具有较高的精度、收敛性和稳定性。

Application of full transformation method in element-free Galerkin method

Accurate imposition of essential boundary conditions is a main draw back in the use of element free Galerkin method (EFGM), because the Moving Least Squares (MLS), used in this method, lack the delta function property of the usual finite element or boundary element method shape functions. The modified MLS shape function, for alleviating the above problem, is given by establishing the relationship between the nodal value and the generalized displacement. As an application example, The full transformation method in EFGM is used in two|dimensional problem. Numerical examples show that the present method is not only simple and logical but also exhibits very high accuracy, convergency and stability.