任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法

A new method for computing SIF of the infinite anisotropic plates containing multiple elliptical holes and cracks

采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。

Based on the complex potential method in the plane theory of elasticity of an anisotropic body, the stress and displacement distributions in the infinite anisotropic plate with multiple elliptical holes and cracks subjected to remote loads are obtained with the aid of the conformal mappings and the Faber series expansion. The stress intensity factors （SIF） of crack tips are also performed in this paper using the linear elastic fracture mechanical method. The effects of material parameters and the size of holes and cracks on the stress intensity factors are also studied in detail. Several conclusions valuable to practice are drawn. Numerical results indicate that the present method has many advantages such as high accuracy, good convergence and convenience in use, and is convenient to investigate effects of various parameters on fracture capabilities of the structures.