Development of Post Processing for Wave Propagation Problem: Response Filtering Method

Abstract

This study develops a new response filtering approach for recovering dynamic mechanical stresses under impact loading. For structural safety, it is important to consider the propagation of transient mechanical stresses inside structures under impact loads. Commonly, mechanical stress waves can be obtained by solving Newton’s second law using explicit or implicit finite element procedures. Regardless of the numerical approach, large discrepancies called the Gibb’s phenomenon are observed between the numerical solution and the analytical solution. To reduce these discrepancies and enhance the accuracy of the numerical solution, this study develops a response filtering method (RFM). The RFM averages the transient responses within split time domains. By solving several benchmark problems and analyzing the stresses in the frequency domain, it was possible to verify that the RFM can provide an improved solution that converges toward the analytical solution. A mathematical theory is also presented to correlate the relationship between the filtering length and the frequency components of the filtered stress values.

Keywords

• stress wave propagation
• finite element
• numerical dispersion
• Gibbs phenomenon
• response filtering method
• post-processing