Z形与曲线形裂纹的不连续位移解法

The Displacement Discontinuity Method Applied to Solve problems of Z-shaped and Curve-shaped Cracks

本文采用Fourier变换方法,导出了无限平面不连续位移的弹性解,并利用应力(或位移)边界条件建立了一组求解裂隙表面间断位移的线性代数方程。证明了Z形与曲线形裂纹应力强度因子K_Ⅰ、K_Ⅱ与无限平面单直裂纹问题的等价性,进而获得了Z形与曲线形裂纹尖端应力强度因子的数值结果。和现有数值方法比较,本方法具有未知量少、精确度高以及收敛性强的优点。

By the Fourier transformation method, the elastic solutions of displacement discontinuity in infinite plane have been derived in this paper and one set of linear algebraic equations for solving the value of discontinuous displacement on the crack surface has been established according to stress or displacement boundary conditions. This paper proved the equivalence relation of stress intensity factors K_Ⅰand K_Ⅱ between Z-shaped or curveshaped crack and single straight crack, and then the numerical results of stress intensity factor at the tips of complex cracks are obtained. Compared with the present numerical method. this method introduced in this paper has got the advantages of less unknowns, high accuracy and very strong convergency.