含孔边裂纹有限大单块板的解析变分解法

ANALYTICAL-VARIATIONAL METHOD OF SOLUTION FOR FINITE MONOLITHIC PLATE WITH HOLE EDGE CRACKS

本文利用复变函数方法导出含孔边双侧直线裂纹有限大板应力与位移的全场表达式,满足所有基本方程式、裂纹表面边界条件与复连通域位移单值条件。应用变分原理满足其余边界条件并求解应力强度因子。变分方程中只有线积分。故本方法计算效率较高。

Total field expressions of stress and displacement components in a finite monolithic plate with double linear hole edge crack are derived by means of method of functions of complex variables, and all of the basic equations, boundary conditions of crack surfaces and single-valued condition of displacements about multi-connected region are satisfied exactly. The stress intensity factors are solved by means of variational method to satisfy the other boundary conditions. In the variational equations there are only line integrals and no area integrals. The convergency is very rapid and the method is time-saving. Then, systematical results are presented by curves of nondimensional stress intensity factor versus nondimensional crack lengths with nondimensional hole radii and aspect ratios as parameters. Finally, the analytical-variational method is extended to the case without cracks, the convergency is nice also and systematical results are provided by-curves of stress concentration factors versus nondimensional hole radii with aspect ratios as parameters.