不同积分路径对动态有限差分法计算精度的影响效应研究

动态有限差分法作为解决冲击动力学问题的有效方法而被广泛应用。但目前还鲜有学者给出该方法实现细节中的积分路径的形状和网格单元类型对计算结果影响效应的系统研究。针对这一问题，本文基于拉格朗日动态有限差分法求解框架，使用JAVA语言编写计算程序，模拟了应力波在长柱模型中的传播，利用理论解，对比了多种积分路径下模拟结果。然后模拟了应力波在无限大介质中的传播，从能量误差的角度，指出了四边形网格的沙漏效应缺陷。最后得出结论：对于常应力单元，由积分路径围成的控制体集合必须完全覆盖计算区域，才能得到正确的解。并且三角形网格能够避免四边形网格因为沙漏变形效应引起的能量误差而产生的计算错误。

EFFECT OF INTEGRAL PATHS ON THE ACCURACY OF FINITE DIFFERENCE METHOD

Dynamic finite-difference scheme was widely used in dynamics simulations. However, there are few reports about the effect of integral paths and element types on the calculation accuracy of such algorithm. For such problem, A finite-difference scheme based on Lagrangian solver was developed by using arbitrary elements. The wave propagation in a thin rod model was simulated using a dynamics code developed by JAVA, and a comparison of several types of integration paths was carried out. And the wave propagation in infinite medium was also simulated. From the point of energy error, the weakness of quadrilateral meshes results from Hourglass mode was revealed. The results showed that the computational domain must be completely covered by the control volume, and the triangular meshes are more applicable as compared to quadrilateral meshes because they can avoid the energy error induced by Hourglass mode.