A Moment-Fitted Extended Spectral Cell Method for Structural Health Monitoring Applications

Abstract

The spectral cell method has been shown as an efficient tool for performing dynamic analyses over complex domains. Its good performance can be attributed to the combination of the spectral element method with mesh-independent geometrical descriptions and the adoption of customized mass lumping procedures for elements intersected by a boundary, which enable it to exploit highly efficient, explicit solvers. In this contribution, we introduce the use of partition-of-unity enrichment functions, so that additional domain features, such as cracks or material interfaces, can be seamlessly added to the modeling process. By virtue of the optimal lumping paradigm, explicit time integration algorithms can be readily applied to the non-enriched portion of a domain, which allows one to maintain fast computing simulations. However, the handling of enriched elements remains an open issue, particularly with respect to stability and accuracy concerns. In addressing this, we propose a novel mass lumping method for enriched spectral elements in the form of a customized moment-fitting procedure and study its accuracy and stability. While the moment-fitting equations are deployed in an effort to minimize the lumping error, stability issues are alleviated by deploying a leap-frog algorithm for the solution of the equations of motion. This approach is numerically benchmarked in the 2D and 3D modeling of damaged aluminium components and validated in comparison with experimental scanning laser Doppler vibrometer data of a composite panel under piezo-electric excitation.

Keywords

• spectral cell method
• spectral element method
• partition-of-unity enrichment
• mass matrix lumping
• moment-fitting