Moment fitted cut spectral elements for explicit analysis of guided wave propagation

Abstract

In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination with a fictitious domain approach to represent complex geometrical features through signed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a “leap-frog” algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for structural health monitoring-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method.