爆炸荷载下岩石破坏的数值流形方法模拟

为了更好地利用数值流形方法对动力学问题进行分析，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三个明显的优势:（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得多的时间步长；（3）充分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 rock failure by numerical manifold method under blasting load

In order to perfectly analyze the dynamics problem by numerical manifold method (NMM), adopts the Newmark method of dynamic finite element method to improve the algorithm in original NMM on the basis of analyzing the solution idea of dynamics problem in NMM. The improved method has three evident advantages over the original one: (1) The solution of this method is convergent without any condition, when selecting suitable parameters; (2) The time step that can be adopted in this method is much longer than that in the original one; (3) The damp effect in the dynamics problem is fully considered. In the end, a calculation example is adopted to illustrate that the improved numerical manifold method can perfectly simulate the whole process of rock failure under impact load, which overcomes the deficiency of FEM in simulating the block movement of rock after failure.