无网格方法中本质边界条件的处理

Treatment of Essential Boundary Conditions for Element-free Galerkin method

基于新的离散模定义,采用移动最小二乘近似方法,给出了场变量的近似表达形式;从约束变分原理出发,给出了无网格方法中新的本质边界条件的处理方案——罚函数法;对权函数、罚函数的选择对计算精度的影响进行了研究。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和稳定性。

Based on a new definition of discrete norm, the approximate form of field variations was expressed by moving least square theory. By using constrained variational principle, the penalty method was given to implement essential boundary conditions in meshless method . On the choice of weight functions and penalty functions a comprehensive study was presented. The application examples reveal that the present method is not only simple and logical but also exhibit high accuracy and stability.