###### Abstract  
This study presents a fatigue analysis procedure for inclined structures operated in level ice fields. Three methods for calculating the local ice load causing fatigue damage, namely the direct method, simplified method, and semi-analytical method, were introduced and compared. The direct method uses finite element analysis to simulate the continuous breaking of ice, while the simplified method and the semi-analytical method estimate the probability distribution of local ice loads based on theoretical equations and empirical data. The fatigue damage ratio at the target location was calculated by applying the ice load calculated by each method to a deformable finite element model of the structure. The results obtained from each method indicate that they provide a reasonable estimation of the local ice load causing fatigue damage in level ice fields. The direct method offers high accuracy but requires significant computational time, while the simplified method and semi-analytical method offer a faster analysis time and are more suitable for long-term time domain analysis. The semi-analytical method requires empirical data to supplement theoretical formulas due to the complex natural phenomena involving various environmental conditions that must be modeled. The findings of this study provide valuable insights into the prediction of fatigue damage in ice-going ships due to long-term ice impacts. The methods proposed in this study can aid in the design of Arctic ships exposed to various conditions and provide a more cost-effective and time-efficient approach to evaluating fatigue damage compared to field measurement. Future research in this field could investigate the application of these methods to other types of structures and further refine the methodology to improve accuracy and reduce computational costs. ice induced fatigue; sloped structure; level ice; ice breaking; semi-analytical method; simplified method; finite element method +
Footnote †: journal: Applied Sciences  
based on numerical simulation is scarce. [PERSON] et al. [2] and [PERSON] et al. [5] defined the fatigue load in ice-covered water through a probabilistic method and evaluated fatigue damage based on the probability model of fatigue stress and impact frequency; however, these methods calculated fatigue damage from results measured during ship operation. To be applied in the initial design of offshore structures operating in ice-covered seas, it is necessary to utilize efficient computational techniques such as numerical analysis or analytical methods to evaluate the fatigue life under various environmental conditions. By incorporating ice failure models developed based on fracture mechanics, it becomes possible to efficiently simulate the interaction between ships and ice, as well as the resulting ice fractures [4; 6; 7]. In this paper, we introduce fatigue analysis procedures for inclined structures operated in level ice fields. We consider the 'Direct Method', 'Simplified Method', and 'Semi-analytical Method' to calculate the local ice load causing fatigue damage. The 'Direct Method' uses finite element (FE) analysis to simulate the continuous breaking of ice for different conditions of ice thickness and velocity. The interaction between ice and structures is simulated using a damage-based erosion model ([PERSON] and [PERSON] [8]). This method has high accuracy, but also requires a large amount of computational time due to the fine element size and the short time increments characteristic of FE analysis. The 'Simplified Method' is a method for estimating the probability distribution of local ice loads based on theoretical equations for various structure shapes and types of ice. Assuming an ice plate as an elastic beam, the peak of the ice-breaking load in the form of impact can be calculated from beam bending theory (ISO 19906 [9], [PERSON] [10]). The ice load calculated from the beam theory is used as the average of a 2-parameter Weibull distribution, derived for each panel on the ship's outer hull.