第05讲-应力强度因子的计算.ppt

1Shanghai University断裂力学Fracture Mechanics断裂力学第四讲断裂力学第四讲郭战胜******@:延长校区力学所317室平时答疑:每周一:5-6节晚修答疑:每周一:18:00-20:30地点:HE108或HE104b2应力强度因子计算预备知识:映射与广泛柯西积分公式)(Sz?(反射))(zf解析Sz?,求)(zf也解析)(Sz?定义)()(zfzf?Sz?设),(),()(yxiqyxpzf??定义),(),(),(),()()(11yxiqyxpyxiqyxpzfzf???????Sz?用1p,1q的柯西黎曼条件,易证)(zf也解析柯西黎曼条件Re ImImZ ZZy x? ???? ??? ?Im ReReZ ZZy x? ??? ??? ???/1???ire???ier1/1??若),(),()(?????iqpf??,????可导出:)/1()1()(???fff??,??????????1)(kkkcZ?????????0)(kkckcZ?????????kkkcZ1)(????????0/)(kkcRRZ????6)(/??在内不为零,上,本身可以是奇异的,它对应平面上的角点????)(??Zk?待定kknkieAZ???????????1)()((1950,Darwin).))(()(22mmiaZ?????????????????????????2)11(1ln)(?????—F(t)?F(z)L——闭曲线,方向逆时针?S——内有限域,?S——)(zF在?S内解析,在L??S上连续????????????S0S)()(21zzzFdtzttFiC?)(zF在内解析,(包括)-S??z??z0)(?zF?????????????S0S)()(21zzzFdtzttFiC?)(zF在内处为,有n阶极点,除此以外,在内解析?Saz???S)()()()()(001zFzgzFazAzFnsss????????则??????????????SS)()()()(21zzzgzFdtzttgtFiC?时,则10