动态松弛方法中虚密度与时间步长的选择

Choices of fictitious densities and time step in dynamic relaxation method

关键词:  动态松弛  虚密度  收敛速度

Key words:  dynamic relaxation  fictitious density  convergence rate

摘要:

动态松弛方法将静力问题转化成动力问题进行显式迭代求解,通过设置虚密度可加速收敛。针对虚密度影响收敛时步与计算结果的问题,提出影响收敛速度的时步比概念,从节点运动角度推导出时步计算公式,给出密度设定方法,并采用可变形离散单元法进行编程验证。结果表明:节点平衡位置与密度无关;虚密度加速收敛的关键在于不同单元设置不同密度,使得其拥有相同的收敛时步;按照新提出的密度、时步设定方案进行参数设定,加速收敛效果明显。

Abstract:

Using the dynamic relaxation method, the static problem can be converted into a dynamic one. It can be solved in an explicit iterative scheme. The convergence rate can be accelerated by setting fictitious densities. The problem that how fictitious densities affect the convergence time step and the final result was studied. The factor affecting convergence rate was defined as the ratio of time step. In consideration of node movement, the scheme to set effective densities and time step was proposed. A program using deformable discrete element method was coded to validate the conclusions. The results show that nodes positions are not related to their densities. It is important to keep different elements hold the same convergence time step by setting different densities in fictitious densities method. Setting time step and fictitious densities by the proposed scheme, the convergence rate can be largely accelerated.