# Transient Response of Dynamic Stress Concentration around a Circular Opening: Incident SH Wave
## 5 Numerical Examples and Discussion
This observation highlights the influence of the size of the aperture on the stress concentration phenomenon during shockwave impact. Figure 5 illustrates the distribution of the position peak stress coefficient (PSPC) at the edge of the opening with changes in position. From the observations in Figure 5, it can be seen that as the aperture size increases, the distribution of PSPC gradually shifts toward the shaded region, and the range of PSPC also narrows. These findings further support the conclusion that smaller apertures correspond to greater dynamic stress concentrations. As the aperture size increases, the restrictions on the shockwave passing through the opening diminish. This restriction reduction decreases the stress concentration area near the aperture edge, causing the PSPC distribution to shift progressively toward the shaded region. Additionally, the range of PSPC also gradually narrows as the aperture size increases. This narrowing range may be attributed to the larger aperture, resulting in a more uniform stress distribution. Overall, these observations highlight the influence of aperture size on the distribution of PSPC and provide further insights into the dynamic stress concentration phenomenon. Figure 6 shows the peak value of the DSCC and its occurrence as the \(r_{0}\) changes. It can be observed that the peak value of the DSCC displays continuous variations in its numerical value and limits toward a constant. In terms of location, the peak is primarily concentrated at the upper and lower ends of the circular opening, specifically at \(\theta=\pi/2\) and \(3\pi/2\). The discontinuity of the DSCC peak at the opening edge may be attributed to changes in sidelobes. However, as the radius increases, the location of the peak gradually stabilizes. Figure 4: Opening edge DSCC corresponding to peak time with \(r=1,2,3\). Figures 7 and 8 depict the variations of the DSCC under different aperture sizes and angles. When the aperture size is small (\(r=1\)), the range of DSCC variation is also limited as the detection position transitions from the shaded region to the illuminated region, and the curve representing the change in DSCC shifts toward the left in the figure. This indicates that the DSCC decreases as the detection position moves from the shaded region to the illuminated region. However, in the case of a large aperture, the initial value of the shaded region is opposite to that of the illuminated region. This means the DSCC increases as the detection position moves from the shaded region to the illuminated region. This behavior differs from a small aperture, where the DSCC decreases as the detection position moves from the shaded region to the illuminated region. These observations highlight the influence of both aperture size and detection position on the variation of DSCC. Figure 5: The distribution of the PSPC at the edge of the opening with changes in position with \(r=1,2,3\). Figure 6: The peak value of the DSCC and its occurrence as the \(r_{0}\) changes. Figure 9 shows the nephogram of DSCC over time along the edge in the range 0 to \(\pi\). In the figure, the radius of the aperture of the circle is 1. At each moment, the distribution of DSCC is mainly concentrated around the \(\pi/2\) position. In terms of position change, DSCC increases first and then decreases. In terms of time, the change of DSCC is consistent with the change of incident wave. These observations provide insights into the temporal and positional dynamics of the DSCC. Figure 10 shows the distribution of stress peak coefficients in time and space. It can be observed that the stress peak coefficient exhibits spatial symmetry concerning the circular aperture and is mainly concentrated in the light region. Regarding time, stress peak coefficient is concentrated in the 0-4.61 ms range. The higher stress peak coefficient (SPC) values are concentrated in two regions: \(\pi/4\)-\(\pi/2\) and \(3\pi/2\)-\(7\pi/4\). Figure 8: Change of DSCC over time at different positions with \(r=1\).