一种自适应影响域半径无网格Galerkin法的应用研究

Application of element-free Galerkin method in consideration of self-adaptive radius of influential domain

文章在背景积分网格积分方式的基础上,采用基于最小移动二乘近似的一种自适应影响域半径无网格Galerkin法,运用线弹性断裂力学理论,对有限板单边裂纹的应力强度因子进行了分析。由于该方法仅需节点信息,而不需要节点的连接信息,从而避免了有限元方法中的网格重构,大大简化了裂纹扩展的分析过程。数值计算结果表明了该方法的有效性。

An element-free Galerkin method （EFG） in consideration of the self-adaptive radius of the influential domain is presented based on the background finite element mesh used for quadrature. In the method, the radius of the influential domain is adjusted according to the density of nodes. By using the theory of linear elastic fracture mechanics, the stress intensity factors of finite plates with single edge crack are analyzed. Without the connectivity information of elements, the burdensome remesh- ing,which is used in the finite element method,is avoided in the present meshless method, and the a- nalysis of crack propagation is dramatically simplified. The examples reveal the effectiveness of the presented method.