# Thermal-Structural Coupling Analysis of Subsea Connector Sealing Contact
## 5 Numerical Simulation of Thermal-Structural Coupling of the Subsea Connector
### Analysis of Coupling Stress Examples under a Steady-State Temperature Field  
The stress analysis of the lenticular sealing gasket of the subsea connector under the combined action of preload, internal pressure, and temperature load is carried out by using the composite stress expression of steady-state thermal structural coupling analyzed in Section 4.3.3, and the results are compared with the finite element simulation results. The coupling stress analysis model of the lenticular sealing gasket is shown in Figure 15a, and this analysis was carried out by using the core sealing structure of the 1/12 subsea connector. Table 1 shows the material parameters of each part. The inner side of the structure is subjected to an internal pressure of 34.5 MPa. Frictionless support is used on both sides of the radial direction. The bottom of the bottom hub is set as the fixed end, and 1/12 of the axial pre-tightening force [29], which is 856.8 kN, is applied to the top of the top hub. At the same time, the steady-state temperature field analysis results of 150 \({}^{\circ}\)C inside and 3 \({}^{\circ}\)C outside the connector are introduced to simulate the thermal-structural coupling stress of the connector, and the sealing characteristics of the lenticular sealing gasket under the thermal-structural coupling action are obtained. The finite element simulation analysis in the previous section shows that the temperature difference between the inside and outside of the lenticular sealing gasket is \(\tau\) = 10.17 \({}^{\circ}\)C, and the initial maximum contact stress is \(q_{\text{max}}\) = 458.03 MPa. These and other parameters are recorded in Table 1.  
Figure 14: Steady-state temperature field of the lens seal gasket. (**a**) Temperature field nephogram; (**b**) Path of the temperature field; (**c**) Temperature distribution along the path. Figure 15: Simulation and calculation model of the sealing structure. (**a**) Simulation model; (**b**) Location of stress calculation. As shown in Figure 15b, in order to study the sealing performance of the lenticular sealing gasket under the action of thermal-structural coupling, the contact position of the lenticular sealing gasket on any side can be used for analysis. From the analysis in Section 4.3.1, it can be seen that on the contact interface of the seal gasket, the principal stress is the contact stress, which cannot be superimposed with the structure thermal stress in Section 4.1. In the contact area of the sealing gasket, after the stress coordinate transformation in Section 4.3.2, the stress at any point has been given by Equation (77), which is the same as the calculation method of structure thermal stress, so thermal-structural coupling can be carried out. As shown in Figure 15b, in order to facilitate the finite element simulation analysis, the connecting line between the two endpoints on both sides of the sealing surface is taken as the analysis position, and the distance between the connecting line and the contact surface is 0.27 mm. Substituting the known parameters into Equation (78), the theoretical calculation results of the three-dimensional stress in the cylindrical coordinate system are obtained, and the comparison with the results obtained by the simulation analysis is shown in Figure 16. The change trend of the three-dimensional stress in the sealing width of the theoretical analysis is basically the same as the simulation result. Since the lenticular sealing gasket is under pressure, the three-dimensional stress is negative. As shown in Figure 16a, the theoretical maximum value of radial stress \(\sigma_{r}\) along the negative direction of \(r\)-axis is 477.94 MPa, and the simulation maximum value is 453.95 MPa, both of which occur at the contact center. The theoretical analysis is 5.28% higher than the simulation analysis. As shown in Figure 16b, the maximum value of circumferential stress \(\sigma_{\theta}\) occurs at the contact center.