正六边形孔角裂纹应力强度因子复变函数解

Complex variable function solutions of stress intensity factors for cracks emanating from a hexagonal hole in an infinite plate

针对工程结构中的正六边形孔角双裂纹问题,利用复分析方法,构造了带孔角双裂纹的正六边形孔到单位圆的共形映射,获得了正六边形孔角双裂纹应力强度因子问题的解析解。采用Mathematica数学软件编程,计算了内部含正六边形孔角对称和非对称双裂纹无限大板的裂尖应力强度因子值。通过与ABAQUS有限元仿真模拟结果进行对比,结果表明,采用复势法和本文引入的共形映射函数推导获得的解析解,不仅适用于无限大板内正六边形孔角对称裂纹的情况,也适用于非对称裂纹。

For the hexagonal hole edge crack problems of engineering structure, using the method of complex analysis, the conformal mapping of hexagonal hole with double side cracks to the unit circle is constructed. Theanalytical solutions of stress intensity factor for cracks emanating from a hexagonal hole in an infinite plate are obtained. Using the mathematical software Mathematica, stress intensity factor for cracks emanating from a hexagonal hole in an infinite plate is calculated and the result is compared with the one via the finite element method. The results show that, the complex variable analysis method and conformal mapping function introduced in this paper are not only applicable to the hexagonal hole angle of symmetric cracks in infinite plate, but also to asymmetric cracks.