带双裂纹的椭圆孔口问题的应力分析

利用复变方法,通过构造新的保角映射,研究了带双裂纹椭圆孔口的平面弹性问 题,得到了I型与II型裂纹问题应力强度因子的解析解.在极限情形下, 不仅可以还原经典的Griffith裂纹的结果,而且可模拟出十字裂纹和带双裂纹的圆 形孔口问题.

STRESS ANALYSIS FOR AN ELLIPTICAL HOLE WITH TWO STRAIGHT CRACKS

Using the complex variable function method and the technique of conformal mapping which transforms the complicated region in physical plane onto the interior of the unit circle in $\zeta$ plane, then based on Cauchy integral theory, the plane elasticity problem of an elliptical hole with two straight cracks is solved, and the analytic solutions of the stress intensity factors for mode I and mode II problems are obtained. Under the limiting conditions, the present results are reduced to the results of the well-known Griffith cracks. Moreover, they include the cross crack and the circular hole with two straight cracks. Analytic solutions obtained in this paper are useful in materials science and engineering.