A Finite Element Formulation for Ultrasonic NDT Modeling

Numerical analysis techniques have been successfully applied to the modeling of electromagnetic field/defect interactions1 Studies of magnetostatic leakage field and eddy current NDT phenomena have clearly shown that finite element codes can be used effectively for probe design2 and the simulation of test geometries difficult to replicate in the laboratory3. In extending these codes to three dimensional geometries4 and pulsed eddy current phenomena5, it was realized that the required computing capability should also be sufficient to model ultrasound/defect interactions directly in the time domain. Increasing availability of powerful vector computers6 bodes well for the ultimate solution of the generic NDT problem in which it is desired to predict the probe response to any arbitrarily shaped defect. As a first step in this direction, the NDT research group at Colorado State University, following the pioneering numerical efforts of Bond7 and Dewey8, has developed a finite element code for direct time domain solution of the elastic wave equation (Figure 1 shows the relationship between numerical and analytical approaches). The following sections describe the finite element formulation and the application of the code to the prediction of 2-D displacements in a rectangular bar excited at one end by a step input of force.