多块体接触有限元法及其对不连续面围岩的模拟

A finite element solution for multi-block contact problems and its application to simulating rock discontinuities

给出了一种求解多块体接触的有限元解法,即将接触面条件精确引入并以节点接触力为基本未知量,把高度接触非线性问题凝缩在可能接触面上进行。首先从两块体三维接触力学模型着手,从整体有限元方程导出增量形式的协调方程,在此基础上详细讨论了多块体接触协调方程的建立方法。随后以广义Mohr-Coulomb准则为摩擦力条件,给出了增量形式的定解和判定条件。程序实施时,针对三维接触问题滑动方向无穷的问题,同时对接触状态及滑动摩擦力分量进行判定,使得迭代收敛快速准确;对于多块体常见的非光滑接触,即角点问题,将角点分类,并根据角点实际的接触状态分情况给出了更为合理的处理方法。通过算例验证后的程序应用于不连续面地下洞室开挖模拟,取得了满意的结果。

A finite element solution for multibody contact problems is presented.Contact conditions being exactly introduced,this solution takes nodal contact forces as primary variable and limits contact highly nonlinear problem in potential contact surfaces to iterate,so it is an accurate and high efficient approach.The paper begins with 3D mechanical model for two bodies contact and compatibility equation in incremental form is educed from global finite element equation.On this basis how to obtain compatibility equation on multibody contact problems is discussed in detail.Subsequently,solvable and judged conditions in incremental form of contact problems are presented in which generalized Mohr-Coulomb criterion is used as friction condition.For the characteristics of any slipping direction of contact nodes on the contact interface in 3D case,contact states and friction force components are judged simultaneously in the program by which iteration and convergence are fast and accurate.For the common non-smooth contact namely corner problems in the more contacting bodies,more reasonable techniques are proposed by classification and real contact state of corners.Finally,after being verified by several numerical examples the program is employed to model rock discontinuities;and the results are satisfactory.