第一类不适定积分方程在裂纹反演中的应用

THE APPLICATION OF THE FIRST KIND ILL-POSED INTEGRAL EQUATION IN CRACK DETECTION

本文研究了第一类不适定积分方程在裂纹反演中的应用.从Green公式出发,结合正散射问题和逆散射问题,得到第一类Fredholm积分方程,通过正则化方法求解积分方程的正则解,利用正则解的模指示存在于结构和材料中的裂纹形状与位置.数值例子验证了方法的有效性.

In this paper, we study the application of the first kind ill-posed integral equation in crack detection. From Green＇s formulation, combining direct and inverse scattering, the first kind of Fredholm＇s integral equation is obtained. We get regularized solution of the integral equation by the regularization method, and use the norm of the regularized solution to indicate shape and location of the crack in materials and structures. Finally, numerical experiments are given to confirm effectiveness of the method.