考虑裂纹尖端场的数值流形方法

数值流形方法起源于不连续变形分析,主要用于统一求解连续和非连续问题,其核心技术是在分析时采用了双重网格:数学网格提供的节点形成求解域的有限覆盖和权函数;而物理网格为求解的积分域。由于该方法考虑了块体运动学,因此就可以模拟节理岩体裂隙的开裂与闭合过程。但对于裂纹尖端的局部化现象,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。本文在单位分解法的理论基础上,应用裂纹尖端局部函数来扩展原有的数值流形方法的基函数,提出考虑裂纹尖端场的数值流形方法。本文方法扩展了原有数值流形方法对裂纹尖端问题的求解能力,同时对非连续问题也比原有数值流形方法的求解精度高。

NUMERICAL MANIFOLD METHOD FOR CRACK TIP FIELDS

The Numerical Manifold Method(NMM)comes from discontinuous deformation analysis,and unifies continuous and discontinuous mechanics into one system.Two meshes are employed in the method:the mathematical mesh provides the nodes to build a finite cover system of the solution domain and the weighted functions,while the physical mesh provides the sub-domains of integration.The NMM can simulate the open and close process of cracks in a fractured rockmass due to the kinematics theory for the blocks.However,the NMM needs lots of elements at the tip of a crack when employed in solving the local problems with cracks.In this paper,based on the unit partition method,the basis functions of the NMM are expanded by using the local functions at the tip of the cracks,to formulate a numerical manifold method for crack tip fields.The proposed method extends the capability of NMM in solving crack problems and is more accurate than the conventional NMM.