Numerical modelling of ultrasonic wave propagation using the efficient p-version finite element method

Abstract

In this paper, the new p-version of the finite element method has been used for the numerical modelling of ultrasonic wave propagation in solid media. The p-method involves increasing the polynomial order of the interpolation functions to achieve convergence. This is unlike the conventional h-version in which the number of elements is increased to achieve the same goal. Illustrative examples of wave propagation through an isotropic aluminium block, including a case with a built-in defect in the form of a crack, have been discussed. Also, a convergence criterion has been developed for dynamic problems. The potential to extend this model to other applications such as medical ultrasonics or to a more complex anisotropic medium is significant.