边界奇异权方法在无网格伽辽金方法中的应用

Application of boundary singular kernel method in elementfree Galerkin method

根据变分原理 ,采用边界奇异权方法满足本质边界条件 ,推导出二维弹性问题的无网格伽辽金方法的离散方程 ;通过在求解应力应变的过程中使用非奇异权函数 ,解决了奇异点上应力应变的计算问题 .数值计算结果表明该方法不仅形式简单、易于实施 。

Based on variational principle for which bou ndary singular kernel met hod is proposed to impose essential boundary conditions, the 2D elastic stiffnes s equation of element free Galerkin method is obtained. In order to calculate th e stresses and strains at singular nodes, a strategy is presented and its validi ty is justified by the following numerical example. Numerical examples also show that the presented method is not only simple and logical but also exhibits very high stability and accuracy.