多个共面任意分布表面裂纹的应力强度因子

The Stress Intensity Factors of Multitudinous Arbitraily Distributed Coplanar Surface Cracks

采用线弹簧模型求解多个共面任意分布表面裂纹的应力强度因子。基于Reissner板理论和连续分布位错思想,通过积分变换方法,将含有多个共面任意分布表面裂纹的无限平板问题归结为一组Cauchy型奇异积分方程。利用Gauss-Chebyshev方法获得了奇异积分方程的数值解。为验证本文方法的正确性,文中最后给出了有关应力强度因子或P-V曲线的数值结果并与现有的理论结果或实验结果进行了对比。结果表明了连续位错理论是描述裂纹问题的一种有效的数学手段,将其与线弹簧模型结合求解多个共面任意分布表面裂纹问题是可行的,具有足够的精度。

The stress intensity factors of multitudinous arbitrarily distributed coplanar surface cracks are solved by using the line - spring model. Based on the Reissner' s plate theory along with continuously distributed dislocation thought, the problem of a infinite plate containing multitudinous arbitraily distributed coplanar surface cracks is came down to a set of Cauchy - type singular integral equations, which is resolved by using Gauss - Ghebyshev method. In the end, in order to verify the validity of the method in the paper, the numerical results are given and compared with the concerned theoretical or experimental results. The comparison shows that the continuously distributed dislocation thought combined with the line - spring model is a available and accurate mathematical means which solved the problem of multitudinous arbitraily distributed coplanar surface cracks.