含孔边裂纹板的弯曲断裂计算

FRACTURE CALCULATION OF BENDING PLATE WITH CRACKS AT HOLE

采用复变函数理论和边界配置方法 ,对含孔边裂纹板的弯曲断裂进行了分析计算。首先假设挠度的复变函数式 ,进而可以求板的内力。它们能满足一系列的基本方程和支配条件 ,仅板的边界条件需要考虑 ,并且可用边界配置法和最小二乘法近似满足。对孔双边裂纹问题进行了应力强度因子计算。数值算例表明 ,本文方法精度较高 ,计算量小 ,是一种有效的半解析。

Fracture of Kirchhoff plates with cracks emanating from holes is analyzed by the theory of complex variables and boundary collocation method. The deflection is assumed to be functions of complex variables, and then the moments and shearing forces of the plates can be obtained. The functions can satisfy a series of basic equations and governing conditions. Thus, it is only necessary to consider the boundary conditions on the hole boundary and the plate external boundaries, which can be approximately satisfied by the collocation method and least square technique. For two cracks emanating from a hole in the bending plate, the stress intensity factors have been calculated. The numerical examples show that the present method has many advantages such as good accuracy and less computer time. This is an effective semi analytical and semi numerical method.