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

TL;DR

This paper introduces a novel spectral element method using moment fitting for explicit simulation of guided wave propagation in complex geometries, improving accuracy and efficiency for structural health monitoring applications.

Contribution

It presents a new moment fitting approach that restores diagonal mass matrices in intersected elements, enabling explicit time integration in complex geometries.

Findings

Enhanced accuracy over existing methods

Maintains computational efficiency with minimal overhead

Effective for SHM component analysis

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.