## 4 Parametric Analysis on Creep Deformation of PMMA Frustum Observation Windows
### Effect of Temperature on Creep of Frustum Observation Window  
Given the weak penetration of sunlight in the ocean, the intensity of sunlight rapidly diminishes after entering seawater. Typically, seawater temperature decreases by 1 to 2 \({}^{\circ}\)C for every 1000 m of seawater depth. In the depth range of 3500 to 11,000 m, the seawater temperature is approximately 2 \({}^{\circ}\)C, as depicted in Figure 10. Additionally, Table 5 indicates that the seawater temperature exhibits seasonal variations. In Section 4.2, the improved time-hardening creep model's good applicability is verified. To more realistically simulate the creep behavior of the observation window in a seawater environment, the model will be employed to analyze the creep behavior while accounting for temperature variations, particularly those occurring during the summer. The temperature range is set from 2 \({}^{\circ}\)C to 30 \({}^{\circ}\)C.  
Figure 8: Location of sensors in the observation window. Figure 9: Model test data and finite element simulation data. (**a**) Data of outer surface. (**b**) Data of inner surface. Utilizing the modified time-hardening creep model, finite element numerical calculations were employed to analyze the \(y\)-axis displacement of the center of the lower surface of the observation window in various temperature ranges. Among them, the temperature during the loading stages L1 and L2 changes linearly within the ranges of 2 \({}^{\circ}\)C to 30 \({}^{\circ}\)C and 30 \({}^{\circ}\)C to 2 \({}^{\circ}\)C, respectively. Meanwhile, the temperature during the holding stage remains consistent with the temperature at the end of the respective loading stage, specifically 30 \({}^{\circ}\)C and 2 \({}^{\circ}\)C. In addition, the temperature of the loading stage of L3 and L4 is 2 \({}^{\circ}\)C and 30 \({}^{\circ}\)C, respectively, while the temperature of the holding load stage changes linearly within 2\(\sim\)30 \({}^{\circ}\)C and 30\(\sim\)2 \({}^{\circ}\)C, respectively. As illustrated in Figure 11, the maximum axial displacements at the center of the inner surface of the observation window during the holding time for L1, L2, L3, and L4 are 7.1103 mm, 6.7667 mm, 6.7532 mm, and 6.5339 mm, respectively. The \(y\)-axis displacement at the center of the lower surface of the observation window is evidently influenced by temperature changes during both the loading and holding load stages. As the temperature increases, the displacement increases faster. As illustrated in Figures 12-15, the stress distribution across the observation window exhibits an initial increase followed by a decrease from the upper surface to the lower surface under four different temperature ranges. Notably, there is a significant stress concentration in the lower surface area, particularly at the position where the lower surface of the observation window and the window seat are in contact. The stress distribution of the observation window remains largely consistent before and after creep, with an overall reduction in stress after the creep process. The displacement distribution of the observation window remains generally consistent before and after creep, with an overall increase in displacement after creep. Along the central axis, the axial displacement of the observation window initially decreases and then increases from the upper surface to the lower surface. The maximum axial displacement is observed at the lower surface axis. L1 was 6.381 mm before creep and 7.146 mm after creep, with a creep of 0.765 mm. L2 was 6.381 mm before creep and 6.584 mm after creep, with a creep of 0.203 mm. L3 was 6.381 mm before creep and 6.811 after creep, with a creep of 0.430 mm. L4 was 6.381 mm before creep and 6.798 after creep, with a creep of 0.417 mm. The strain shows an upward trend as the loading time increases. The finite element numerical analysis indicates that the impact of temperature on the displacement and stress of the PMMA observation window, encompassing both creep deformation during the loading stage and the holding one, is substantial.