复镜像法在平板导体涡流场计算中的应用

为了根据涡流检测中积分方程法(IEM)的理想裂缝模型,用矢量磁位推导出平板导体涡流场的并矢格林函数,将复镜像法用于涡流场并矢格林函数的计算,用Prony方法对矢量磁位中广义Sommerfeld积分(GSI)的被积函数进行指数逼近,使GSI转化为有限项级数之和,加速了无穷积分的计算,提高了涡流场的求解速度和计算精度。用涡流无损检测中的两组典型数据比较用复镜像法和直接数值积分法计算广义Sommerfeld积分的计算精度和求解速度,结果表明复镜像法在涡流场GSI积分计算中准确且高效。用复镜像法计算平板导体中含有平行裂缝和十字型裂缝的涡流场,其结果与有限元一边界元耦合法的计算结果对比表明求解方法正确和高效。

Application of Complex Image Method for Eddy Current Field Computation in a Conducting Plate

The ideal crack model of fatigue crack based on an integral equation method(IEM) is applied to a plate conductor.The dyadic Green's functions for the perturbed eddy current fields in the conductive plate are derived by employing magnetic vector potential.A discrete complex image method is used to calculate the Green's functions of the perturbed eddy current fields.The kernels of generalized Sommerfeld integrals(GSI) in vector potential are approximated by a short series of exponential functions with different complex coefficients.By use of the Prony method and the Sommerfeld equality,the generalized Sommerfeld integrals can be evaluated in terms of simple closed forms of spatial complex images.The accuracy and computing time of calculating the generalized Sommerfeld integrals by the complex image method are compared with those obtained by numerical integration.It is shown that the complex image method is more accurate and efficient.The perturbed eddy current fields of the plate conductor with two parallel cracks and a cross crack have been studied further.Numerical results computed by the presented integral equation method are compared with those obtained by the finite element-boundary element method(FE-BEM).Good agreement has been found between both solutions,and the integral equation method presented herein is correct and fast.