摘要
数值流形方法通过数学和物理双重网格,分析连续和非连续问题,已应用于模拟节理岩体裂隙的开裂与闭合问题。但对于裂纹尖端的局部化问题,数值流形方法需要像有限元那样在裂纹尖端设置细密单元。本文利用裂纹尖端解析解将数值流形方法的基函数进行扩展,推导了相应的试函数。从最小势能原理出发提出了断裂力学的数值流形方法,推导了相应的求解方程,将其应用于建筑材料细观力学数值模拟。最后给出两个数值算例,将计算结果与解析解对比,说明该方法的正确性和可行性。
The mathematical mesh and physical mesh are unified to solve continuous and discontinuous problems in one system, and successfully simulate the open and close process of cracks in a fractured rock-mass.The basis function of the numerical manifold method (NMM) is expanded with the local analytical function at the tip of the cracks, and the corresponding trial function is obtained. Based on least potential energy principle, NMM for crack mechanics is presented, the corresponding formulae is given. The method is extended micro-mechanical simulation of architectural materials the validity and accuracy of this method are illustrated by two numerical examples.
出处
《应用力学学报》
EI
CAS
CSCD
北大核心
2008年第4期632-636,共5页
Chinese Journal of Applied Mechanics
关键词
数值流形方法
断裂力学
建筑材料
数值模拟
numerical manifold method, crack mechanics, architectural material, simulation.
