摘要
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。
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.
作者
景永强
彭妙娟
JING Yongqiang;PENG Miaojuan(Department of Civil Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China)
出处
《计算机辅助工程》
2021年第2期1-8,33,共9页
Computer Aided Engineering
基金
国家自然科学基金(11571223)。
关键词
弹性动力学
断裂力学
裂纹
改进的移动最小二乘法
形函数
隐式时间积分
elasto-dynamics
fracture mechanics
crack
improved moving least square method
shape function
implicit time integration
