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.

An approximate theoretical analysis is presented for a rigid, perfectly plastic clamped beam struck transversely at the mid-span by a mass which produces Finite transverse displacements. An alternative quasi-static procedure is proposed for estimating the dynamic plastic response of a beam when struck by a heavy mass that travels at a low speed. The theoretical basis of this method is explained and the accuracy is examined by an error analysis. Finally, it is suggested that this quasi-static procedure could be used for estimating the dynamic plastic response of other structures that are struck by a heavy mass traveling at a low speed,