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 to a fictitious domain approach to represent complex geometrical features through singed 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 SHM-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method.

A Parametrized Reduced Order Model for Rapid Evaluation of Flaws in Guided Wave Testing

“…The employed model can significantly speed up simulations, rendering the approach attractive for more realistic applications, such as the detection of cracks or delaminations in aluminum or composite plates, using advanced numerical models [13]. As a potential drawback of the approach, the interpolation model requires extensive calculations in the offline phase for different notch locations, as a full grid of parameters is needed.…”

Comparison of Plate and Solid Spectral Element Modeling of Composite Delamination for Guided Wave Simulations

“…To overcome this, we adopt a novel moment fitting procedure similar to Ref. [17], which is under ongoing study, to restore the diagonal property of the mass matrix.…”