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.
Highlights
This study develops a new response filtering approach for recovering dynamic mechanical stress under impact loads
The transient solutions of Newton’s second law obtained through either the implicit or explicit method inevitably exhibit undershooting or overshooting phenomena. Both the stability and accuracy of the numerical methods are important, it is rare to investigate the accuracy of the time integration scheme compared with the stability issue
These numerical discrepancies are often neglected through the safety factor in mechanical or civil engineering
Summary
This study develops a new response filtering approach for recovering dynamic mechanical stress under impact loads. From a structural engineering point of view, a mechanical stress wave, due to structural impacts such as an impact force, explosion, or collision, that propagates through a structural medium is important. Some efforts have been undertaken to reduce the differences and the numerical errors between the numerical solutions and analytical solutions [3,5,6]. To this end, this study develops a new post-processing approach for transient stress waves named the response filtering method (RFM) with an average operator
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