含裂纹的直角域中凸起与衬砌的动态性能分析

摘要

To investigate the scattering of SH-wave caused by defects near a crack in a quarter space,the concentration of dynamic stress at the salient and lining near a crack in a quarter space was researched using the complex function method,mirror method,and crack incision method.The analytical expressions of dynamic stress concentration factor (DSCF) around the circular lining edge and dynamic stress intensity factor (DSIF) at the crack tip were obtained.Several calculations were plotted as examples to show the influences of the frequencies of incident wave,the physical constant of medium,and the geometry of structures on DSCF and DSIF.The calculations indicate that the influences of the frequencies of incident wave and length of crack on DSCF were obvious.When high frequency wave is incident,the maximum of DSCF will increase by 20% as compared with the case of low frequency wave.The increase in thickness of lining may not be able to decrease DSCF,and the frequency of incident wave exerts a great influence on surface displacement.Dynamic analysis of the quarter space with defects is critical.%为了研究直角域中裂纹附近缺陷对SH波的散射,采用复变函数法、镜像法和裂纹切割法研究直角域中裂纹附近凸起和衬砌的动应力集中问题,给出了圆形衬砌周边的动应力集中系数与裂纹尖端动应力强度因子的解析表达式,并给出了它们随入射波频率、材料的物理常数和结构几何参数变化的计算结果图.结果表明:入射频率、裂纹长度对动应力集中系数影响显著,高频入射时动应力集中系数最大值比低频入射时提高20%,增加衬砌厚度并不一定能使动应力集中系数减小,入射频率对地表位移影响较大.对含缺陷的直角域进行动力学分析非常必要.