无网格局部Petrov-Galerkin方法在弹塑性断裂力学问题中的应用

AN APPLICATION OF THE MESHLESS LOCAL PETROV-GALERKIN METHOD IN THE ELASTO-PLASTIC FRACTURE PROBLEM

采用无网格局部Petrov-Galerkin方法来分析弹塑性断裂力学问题.这种无网格方法采用移动最小二乘法(MLS)来构造近似试函数和采用Heaviside函数作为加权残值法中的权函数,由于近似函数不满足Kronecker Delta条件,因此采用直接插值法来施加本质边界条件.如果不考虑体力,所形成的整体刚度矩阵只包含局部边界积分,而不包含局部域积分和奇异积分.采用增量Newton-Raphson迭代法来求解弹塑性增量形式的局部Petrov-Galerkin方程.数值算例结果表明,该文方法对于弹塑性断裂力学问题的求解是可行的和有效的,并且所得到的结果具有较好的精度.

A meshless local Petrov-Galerkin method for the analysis of the elasto-plastic fracture problem is presented. The meshless method uses the moving least squares （MLS） to approximate the field variables, and uses the Heaviside function as a test function of the weighted residual method. Because the MLS approximation is without the Kronecker Delta function property, a direct interpolation method is adopted to impose essential boundary conditions. The method is not involved any sub-domain integrals and singular integrals in forming the global stiffness matrix if body force is ignored; it only involves local boundary integrations. An incremental Newton-Raphson iterative algorithm is employed to solve incremental nonlinear local Petrov-Galerkin equations. Numerical results show that the present method possesses not only feasibility and validity, but also high accuracy for the elasto-plastic fracture problem.