## 1 Introduction
Given the global loads endured by container ships, specific attention is directed to a localized structure termed the upper wing torsional box, situated on both the port and starboard sides at the main deck's height. This region manifests the highest stress concentrations, predominantly around the midship section, prompting multiple investigations into the structural evaluation of this area. [PERSON] et al. [14] scrutinized the influence of various geometric configurations resulting from different cut-out designs on the optimal weight of the torsional box. Meanwhile, [PERSON] et al. [15] directed their study toward the variations in warping stresses near the torsional box by comparing different formulations of hydrodynamic torsion moments. The concept of hydroelasticity, especially concerning permanent and transient springing and whipping phenomena, assumes significance due to its impact on fatigue. This influence is particularly accentuated in the torsion box area due to its heightened stress levels. [PERSON] et al. [16] introduced a design methodology to predict wave-induced vibrations (springing and whipping) and their role in estimating fatigue damage for a 16,000 TEU container ship. [PERSON] and [PERSON] [17] ascertained how the whipping effect contributes to  
Figure 1: Laura Maersk methanol-powered feeder container ship [7]. fatigue phenomena in both hogging and sagging conditions through on-board stress measurements. [PERSON] [18] underscored the importance of whipping in fatigue assessment through experimental tests and numerical simulations on container ships ranging from 2800 to 8600 TEU. [PERSON] and [PERSON] [19] presented a methodology considering multiple sea states, devising a procedure to estimate the increase in vertical wave bending moment due to whipping through a hydroelastic fluid-structure interaction model in the time domain. The role of springing and whipping phenomena in fatigue determination is firmly established. [PERSON] et al. [20] delved into this phenomenon for two container ships of varying capacities and under different loading conditions, revealing that fatigue damage assessment, when influenced by both whipping and springing, is 18.75% higher compared with springing alone. Other researchers have explored the contribution of permanent and transient phenomena to fatigue damage. [PERSON] et al. [21] estimated that whipping contributes approximately 30% of fatigue damage, based on the experience of a 2800 TEU container ship operating in the Atlantic Ocean. [PERSON] and [PERSON] [22] observed that over 40% of fatigue cracks in ship structures occur in the side shell plating, particularly at the junction of primary and secondary elements. This structural detail has been the focal point of numerous studies in container ships. [PERSON] et al. [23] proposed a procedure for assessing fatigue in side-shell structures considering wave non-linearity and service speed. The maritime sector, driven by IMO targets, aims to reduce greenhouse gas emissions with environmentally friendly technology and fuels, such as methanol. A comparative study, such as the research by [PERSON] et al. [24], highlights the potential of renewable sources such as methanol to achieve significant reductions. [PERSON] et al. [25] conducted analyses in both linear and non-linear regimes to determine results, with assessments performed for two significant wave heights. [PERSON] et al. [26] investigated critical locations at the intersection of primary and secondary elements using diverse structural configurations, especially the arrangement between a bulb-type profile and an attached flat bar. Lastly, [PERSON] and [PERSON] [26] explored the influence of different loading conditions on this structural detail, incorporating various models. The distinctive aspects of this research lie in an exhaustive structural analysis designed to unveil the optimal structural configuration by varying critical vessel dimensions.