## 5 Conclusions  
In this paper, the strength and fatigue life of a pipeline is checked by using the optimal transport meshless algorithm based on the strong fluid-structure coupled frame, and the pipeline life is predicted after the design of the pipeline. The most dangerous of the loads considered are the resonant excitation and the pulsating excitation of the fluid inside the line. Therefore, a method to obtain the resonance and pulsation excitation of the pipeline is proposed, and the compound excitation is added to the optimal transport meshless method of the strong fluid-structure coupling computational framework to calculate the stress of the pipeline. After stress is obtained, fatigue life is estimated based on the hazardous point method. The specific conclusions are as follows:  
1. A method for obtaining the resonant excitation of pipelines based on the load spectrum is proposed. The OTM method is an explicit integration algorithm whose boundary conditions can impose only time-domain signals. In this chapter, the load spectrum of the pipeline system is simulated in the time domain, and the random time-domain signal relative to the load spectrum is obtained. To obtain the time-domain maximum \begin{table}
\begin{tabular}{c c c c c c} \hline
**Material** & **0 Cr18 Ni9** & **1 Cr18 Ni9** & **LY12-M** & **2B06** & **30 CrMnSiA** \\ \hline Reliability correction factor C\({}_{R}\) & 0.8 & 0.8 & 0.8 & 0.8 & 0.8 \\ Strength limit \(\sigma_{0}\) (MPa) & 593 & 608 & 310 & 167.5 & 1080 \\ Fatigue strength \(S_{1000}\) (MPa) & 444.75 & 456 & 232.5 & 125.62 & 810 \\ Revised fatigue strength \(S_{1000,R}\) (MPa) & 355.8 & 364.8 & 186 & 100.5 & 648 \\ Stress concentration factor & 1 & 1 & 1 & 1 & 1 \\ Cyclic excitation stress ratio \(R\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) \\ Parameter \(a\) & 0.3270 & 0.3270 & 0.3270 & 0.3270 & 0.3270 \\ Parameter \(b\) & \(8.492\times 10^{-4}\) & \(8.492\times 10^{-4}\) & \(8.492\times 10^{-4}\) & \(8.492\times 10^{-4}\) & \(8.492\times 10^{-4}\) \\ Parameter c & \(-92\) & \(-92\) & \(-92\) & \(-92\) & \(-92\) \\ Fatigue limit \(\sigma_{-1}\) (MPa) & 138 & 226 & 55.8 & 28 & 342.4 \\ Young’s modulus \(E\) (GPa) & 199 & 184 & 72 & 69 & 190 \\ Material yield strength \(\sigma_{5}\) (MPa) & 226 & 235 & 265 & 46.4 & 835 \\ Airframe life \(AF\) (h) & 6000 & 6000 & 6000 & 6000 & 6000 \\ Max excitation \(f\) (Hz) & 2000 & 2000 & 2000 & 2000 & 2000 \\ Predicted S-N curve & \(\sigma^{20.50}\times N\) & \(\sigma^{18.50}\times N\) & \(\sigma^{14.6}\times N\) & \(\sigma^{9.285}\times N\) & \(\sigma^{27.56}\times N\) \\ \(=6.937\times 10^{54}\) & \(=9.62\times 10^{69}\) & \(=2.58\times 10^{55}\) & \(=2.58\times 10^{23}\) & \(=2.01\times 10^{60}\) \\ \hline \end{tabular}
\end{table} 
Table 4: S-N curve estimation parameters of several commonly used materials for pipelines. Figure 16: Line S-N curve. amplitude information of the acceleration of the random signal. The natural frequency of the pipeline is obtained via the mode analysis of the pipeline. Equation (6) incorporates the maximum amplitude of acceleration and the natural frequency of the pipeline to establish a resonance excitation in the pipeline. 2. The pressure on the inner wall of the pipeline caused by the fluid pulsating excitation is obtained, which is provided to the OTM to calculate the dynamic stress of the pipeline under the combined excitation. The pressure on the surface of the inner wall of the pipeline was extracted using CFX2021R2 software, and 1000 sample points were set on the surface of the inner wall of the pipeline. Due to the possibility of misalignment between the sampling points of the pipeline inner wall pressure and the OTM grid file, the nodes on the inner wall surface are clustered by the distance from the sampling points and are divided into 100 sets. A pressure sampling point load is applied to each set to achieve the addition of a fluid pulsation-excited pre-stress field in the OTM.