热电材料中共线不对称裂纹的圆形孔口问题

The problem of circular hole with collinear asymmetric cracks in thermoelectric material

基于复变函数方法,通过构造保角映射和解析延拓,研究了不可渗透型边界条件下热电材料中具有共线不对称裂纹的圆形孔口问题;给出了电场、温度场和应力场的精确解,获得了复应力函数ф(z)和φ(z)的解析解;根据Cauchy积分公式求解了共线裂纹的强度因子。数值算例讨论了电流密度强度因子和应力强度因子随孔口半径和裂纹长度变化的情形。结果表明:电流密度强度因子和应力强度因子都随着圆形孔口半径的增大而增大;当圆形孔口半径一定时,随着裂纹长度比的减小而减小。

Based on the complex function method,the problem of circular orifices with collinear asymmetric cracks in thermoelectric material with impermeable boundary conditions is studied by constructing the conformal mapping and analytical continuation.The exact solutions of electric field,temperature field and stress field are given,and the complex stress functionsф(z)andφ(z)are obtained.According to the Cauchy integral formula,the intensity factors of collinear crack are obtained.The numerical examples are given to discuss the change of electric flux density intensity factors and stress intensity factors with the radius of hole and the length of crack.Results show that both the current density intensity factor and the stress intensity factor increase with the increase of the radius of the circular hole.When the radius of the circular hole is fixed,it decreases with the decrease of the crack length ratio.