反平面断裂问题的无单元伽辽金比例边界法

摘要

Through incorporation of the element free Galerkin method into the scaled boundary method,an element-free Galerkin scaled boundary method (EFG-SBM) is developed for anti-plane fracture analysis.This is a boundary-type meshless method,in which the element-free Galerkin method is adopted for performing the circumferential discretization and therefore only nodes on the boundary are required.In addition,no fundamental solution is required in contrast with the boundary element method.In order to simplify the enforcement of the essential boundary conditions,the modified moving least squares shape functions are derived through the establishment of the relationship between the nodal values and the fictitious nodal values.In the radial direction,the solution is analytical so that this method is a semi-analytical numerical method.At last,numerical examples are presented to demonstrate that utilizing the proposed method to solve anti-plane crack problem has the advantages of simple postprocessing and higher accuracy.%将比例边界法与无单元伽辽金法相结合,建立了反平面断裂分析的无单元伽辽金比例边界法.这是一种边界型无网格法,在环向方向上采用无单元伽辽金法进行离散,因此计算时仅需要边界上的节点信息,不需要边界元所要求的基本解.为了便于施加本质边界条件,通过建立节点值和虚拟节点值之间的关系给出了修正的移动最小二乘形函数.在径向方向上,该方法利用解析的方法求解,因此是一种半解析的数值方法.最后,给出了数值算例,并验证了所提方法后处理简单和计算精度高的特点,适合于求解反平面断裂问题.