岩石冲击破坏的数值流形方法模拟(英文)

岩石冲击破坏是一种典型的动力学问题。为了更好地利用数值流形方法对动力学问题进行分析,本文在对原数值流形方法中的动力学问题求解思想进行分析的基础上,采用动力有限元方法中的Newmark法对该算法进行了改进。改进后的数值流形方法与原来相比具有3个明显的优势:①当选择合适的参数后,该方法能够保证解的无条件收敛;②可以采用比原算法大的多的时间步长;③充分地考虑了动力学问题中的阻尼效应。最后通过一个算例说明了改进后的数值流形方法能够很好地模拟岩石在冲击载荷作用下破坏的全过程,克服了有限元法不能模拟岩石破坏后块体运动情况的不足。

Simulation of impact failure of rock by numerical manifold method

Impact failure of rock is a kind of typical dynamic problem. In order to perfectly analyze the dynamic problem by use of numerical manifold method (NMM), the Newmark method of dynamic finite element method was adopted to improve the algorithm in original NMM on the basis of analyzing the solution idea of dynamics problem in NMM. There were three obvious advantages in the improved method over the original one: ①The solution of this method was convergent without any condition when suitable parameters were selected; ②The time step adopted in this method was much longer than that in the original one;③The damping effect in the dynamic problem was fully considered. In the end, a calculation example was used to illustrate the application of this method in simulation of the whole process of impact failure of rock, which overcame the shortcomings of FEM in simulating the block movement after rock failure.