无网格法中一种处理本质边界的新方法

A new method of essential boundary conditions treatment for element-free Galerkin method

无网格伽辽金法中形函数一般不具有插值函数的特征,本质边界条件需特殊处理.在通过拉格朗日乘子识别法强加本质边界条件的基础上,为提高计算精度,再对修正泛函使用罚函数法来强加本质边界条件.该方法不仅没有增加未知量的数目,刚度矩阵仍然正定带状,而且计算精度较高,对罚因子依赖性降低,能较好的模拟位移边界条件.以弹性力学问题为例进行了数值试验,计算结果表明,该方法不仅简单合理,而且具有较高的计算精度和数值稳定性.

Element-flee Galerkin method is a new numerical method developed recently. But the approximate form of field variations was expressed by moving least square theory, which are not interpolate. Thus, it is a notorious problem to treat essential boundary conditions for element-free Galerkin method. In this paper, a new implementation of using penalty methods is developed based on a modified variational principle . The present method has the folloving several advantage, smaller condition number, less sersitvity to penalty factor, higher computing accuracy,and it makes the stiffness matrix to be positive definite. The application examples reveal that the present method is not only simple and logical but also exhibit high accuracy and stability.