三维断裂弹性动力学的改进无单元Galerkin法

为提高断裂弹性动力学问题数值计算的精度,避免出现病态或奇异方程组,基于改进的移动最小二乘法建立三维弹性动力学问题的积分弱形式,采用罚函数法施加位移边界条件,引入隐式时间积分并且结合三维断裂力学的形函数考虑裂纹尖端的奇异性,探究将改进的无单元Galerkin(improved element-free Galerkin,IEFG)法用于断裂弹性动力学问题的数值计算.通过悬臂梁、柱和矩形板等3个算例,讨论节点分布、影响域比例参数、罚因子和时间步长等参数对计算精度的影响,证明IEFG法用于求解三维断裂弹性动力学问题的正确性和有效性.

Improved element free Galerkin method for three dimensional fracture elasto dynamics

To improve the accuracy of the numerical calculation of fracture elasto dynamics, and to avoid the ill conditioned or singular equations, the improved element free Galerkin(IEFG) method is applied to the numerical calculation of fracture elasto dynamics. Based on the improved moving least square method, the integral weak form of the three dimensional elasto dynamics problem is established. The penalty function method is used to set the displacement boundary conditions. The singularity of crack tip is considered by introducing the implicit time integration and the shape function of three dimensional fracture mechanics. Three examples(include the cantilever beam, the column and the square plate) are selected to analyze the influence of computing parameters(include the node distribution, the influence domain scale parameter, the penalty factor and the time step) on the calculation accuracy. It is proved that the IEFG method is correct and effective for solving three dimensional fracture elasto dynamics problems.