Nondestructive ultrasonic testing in rod structure with a novel numerical Laplace based wavelet finite element method

Abstract Rod structure has been widely used in aerospace engineering and civil engineering. Nondestructive testing is a very important method applied to detect unseen flaws in structures, ultrasonic wave nondestructive testing has been used in many areas. Finite Element Method is one of the most widely used numerical methods but would have a high cost when doing simulation on ultrasonic wave due to the requirement of small time interval and element size. Wavelet based finite element method could improve the spatial resolution with fewer elements needed but still needs very small time interval. Laplace transform could easily convert the time domain into frequency and then inverse to time domain. This paper presents an innovative method combining Laplace transform and B-spline wavelet on interval (BSWI) finite element method, which could not only decrease the element number but also increase the time integration interval. Moreover, this innovative method is applied to simulate the ultrasonic wave propagation in 1D rod structure as well as used for nondestructive testing of damages in rod structures.

摘要：杆结构已广泛应用于航空航天工程与土木工程领域。无损检测（Nondestructive testing）是检测结构内部隐蔽缺陷的重要手段，超声无损检测已在诸多领域得到应用。有限元法（Finite Element Method）是目前应用最广泛的数值方法之一，但由于需要极小的时间步长与单元尺寸，在开展超声仿真时往往计算成本高昂。基于小波的有限元法可在减少单元使用量的前提下提升空间分辨率，但仍需采用极小的时间步长。拉普拉斯变换（Laplace transform）可便捷地将时域信号转换至频域，再通过逆变换还原为时域。本文提出一种创新性方法，将拉普拉斯变换与区间B样条小波有限元法（B-spline wavelet on interval, BSWI）相结合，该方法不仅能够减少所需单元数量，还可增大时间积分步长。此外，本文将该创新性方法应用于一维杆结构中的超声传播仿真，并用于杆结构的损伤无损检测。