等参数平面裂纹问题的二级分形有限元分析

Fractal two-level finite element analysis of plane crack problem with equal-parameter

针对正交各向异性板的平面裂纹问题,应用二级分形有限元的办法研究了裂纹尖端应力强度因子的计算方法.与各向同性平面裂纹问题比拟,获得正交各向异性平面裂纹问题的一般解,并将它作为整体插值函数;利用二级分形有限元对平面裂纹板进行离散,使得求解的自由度极大地减少.结果表明,只需有限粗略的网格划分和简单的插值单元就可以有效地获得较精确的裂纹尖端应力强度因子.

The stress intensity factor （SIF） of plane crack on ormotropic plate equal-parameter was evaluated by using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem was obtained by assimilating the problem with isotropic crack problem, and employed as the global interpolation function in F2LFEM. The plane crack plate was discredited by F2LFEM, reducing degrees of freedom to be determined greatly. The numerical exampled showed that the method was efficient and accurate in solving the stress intensity factor by using finite coarse mesh and simple interpolating element.