1. Introduction

The maritime industry is leading the effort to tackle the twin challenges of sustainability and energy efficiency. With global imperatives like the International Maritime Organization's (IMO) 2050 decarbonization strategy, the shift towards eco-friendly practices has never been more critical. This ambitious agenda seeks to significantly reduce greenhouse gas emissions through the adoption of innovative technologies and alternative energy sources. Among the myriad of solutions, wind energy conversion systems and aerodynamic optimizations stand out as pivotal measures for reducing fuel consumption and enhancing environmental stewardship in the shipping sector. As wind energy becomes increasingly viable, the focus has shifted toward its seamless integration into modern vessel designs. These systems, inspired by traditional sailing techniques but enhanced with advanced materials and engineering, offer a renewable and cost-effective energy source. For instance, wind shields and sails are being repurposed as dynamic elements that not only reduce aerodynamic drag but also harness wind power to drive vessels more efficiently. Such innovations underscore the convergence of age-old maritime wisdom with contemporary technological advancements. This study delves into a specific aspect of this transition: the structural challenges posed by green water pressure on wind shield structures. Green water, a phenomenon where large waves crash onto the deck, exerts substantial loads on exposed structures, testing their resilience and safety. The analysis and subsequent reinforcement of these structures are critical for ensuring that energy-saving devices like wind shields can operate reliably in harsh marine environments.

This study evaluates the structural integrity of wind shields and proposes reinforcement strategies, including carling stiffeners and thickness optimization, this research contributes to the broader narrative of sustainable and efficient shipping. The findings aim to provide practical insights into balancing environmental aspirations with engineering feasibility, advancing the maritime industry's journey toward a greener future. Previous studies related to this study are summarized below.

A.D Wnek and C.Guedes Soares(2015) conducted a study comparing the wind loads acting on LNG carriers and floating LNG platforms between numerical analysis (CFD) and wind tunnel experiments. The wind coefficients in the X and Y directions and the yaw moment coefficients were calculated through numerical analysis, and various mesh settings and analysis models were applied to increase the reliability of the results. The numerical analysis results were generally in reasonable agreement with the wind tunnel experiment results. In this study, the measured loads were minimal due to the low wind speed (10 m/s), and sensor sensitivity limitations impacted the accuracy of the results. Additional experimental studies under high wind speed conditions are necessary. In addition, the effects of environmental conditions such as temperature and humidity should be quantitatively evaluated to minimize the differences between the experiments and numerical analysis.

W.D. Janssen et al.(2017) quantitatively analyzed the effects of increasing wind resistance as container ships become larger on ship operation and port operations using numerical analysis and wind tunnel test data. The numerical analysis modeling used Reynolds-Averaged Navier-Stokes (RANS) to calculate the wind load coefficient. The effects of considering the space between containers and the level of detail in the hull shape on the wind load results were analyzed. The difference between the numerical analysis and wind tunnel test results decreased as the ship shape was refined, and the wind load was reduced by an average of 10% when the space between containers was reflected in the modeling. It is necessary to develop generalized design guidelines by improving the verification accuracy of the numerical analysis model by securing wind tunnel test data under various wind speeds and conditions.

A. Ricci et al. (2020) derived the results of numerical analysis (CFD) of wind loads acting on a large passenger ship moored at the Rotterdam passenger terminal according to various wind directions. High-resolution mesh was used to reflect the structure of the ship and the wind load distribution with respect to the surrounding high-rise buildings. Tall buildings amplified the local pressure on the surface of the ship, but the overall horizontal force tended to decrease. There are some deviations between the numerical analysis results derived from the study and the wind tunnel experiment, and it is necessary to always use the LES (Large Eddy Simulation) model to improve the accuracy. It is also necessary to collect data from additional wind speed measurement points and various wind speed conditions to strengthen the verification of the analysis model and develop generalized design guidelines that include various ship types and port structures.

Jose Maria Portell (2021) obtained results using numerical simulation (CFD) of the aerodynamic performance of a wind sail of a car carrier under extreme conditions. The lift and drag coefficients generated by the sail were calculated using the NACA 0015 cross section. The lift and drag coefficients including the dynamic stall phenomenon were calculated through 2D analysis, and the IDDES (Improved Delayed Eddy Simulation) model was used to evaluate the interaction between the blades and the vibration frequency. The simulation results were all similar to the experimental data, but there were differences at some angles. In order to verify the numerical analysis results more reliably, additional wind tunnel experimental data should be secured, and the effects of vibration and fatigue caused by dynamic stall and vortex on structural safety need to be analyzed more in depth.

Jung-Hee Yoo et al. (2022) quantified the wind load generated when an FPSO and a shuttle tanker are located side by side and performing unloading operations through numerical analysis simulation. The wind load change and shielding effect according to the distance between the two vessels were analyzed and compared with the wind tunnel experiment. When the FPSO and the shuttle tanker are located side by side, the FPSO is shielded from the wind load by the shuttle tanker, but the effect decreases as the distance increases. The shuttle tanker sees a greater shielding effect from the FPSO, which is shown as a decrease in the wind load coefficient. Due to the limited accuracy of the experimental data and differences in the experimental environment, there was a difference in the agreement with the numerical analysis results at some angles. To resolve this, research is needed to verify the results by securing various conditions and an expanded data set.

Nan Gu et al. (2023) analyzed the dynamic response of a structure by applying a numerical analysis technique considering the combined effects of nonlinear wave loads and structural deformation. The validity of the CFD-FEA method was verified by comparing it with the existing latent flow-based model and the nonlinear numerical model. The CFD-FEA method represented nonlinear wave interaction well and simulated it more realistically than the existing latent flow-based model. Through this, it was confirmed that it has the advantage of predicting complex nonlinear behavior by well representing wave reflection and interference phenomena between multiple floating bodies. In order to reduce the high computational cost of the CFD-FEA method, efficient mesh configuration and improvement of the calculation algorithm are required, and additional tank experimental data should be secured to further secure the reliability of the numerical analysis results.

Prior research has extensively examined the aerodynamic and hydrodynamic loads on marine structures, employing Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) to improve predictive accuracy and structural reliability. Wnek and Soares (2015) conducted comparative studies on wind loads acting on LNG carriers and floating platforms, revealing discrepancies between CFD and wind tunnel experiments due to limitations in sensor sensitivity and wind speed constraints. They emphasized the necessity of high-wind-speed experimental validation to enhance computational accuracy. Janssen et al. (2017) focused on container ships, illustrating the impact of increased vessel size on wind resistance and proposing numerical modeling improvements using Reynolds-Averaged Navier-Stokes (RANS) simulations. Their findings highlighted the importance of refining ship geometries to achieve more accurate wind load predictions. Similarly, Ricci et al. (2020) analyzed wind loads on passenger ships moored in urban environments, demonstrating the influence of high-rise structures on localized wind pressure variations and stressing the need for advanced turbulence models, such as Large Eddy Simulation (LES), to improve predictive reliability. Other studies have explored the structural behavior of wind-powered vessels. Portell (2021) investigated the aerodynamic performance of wind sails on car carriers under extreme conditions, utilizing the NACA 0015 cross-section to assess lift and drag coefficients. The study recommended further analysis of dynamic stall effects and structural fatigue due to vortex shedding. Yoo et al. (2022) examined the shielding effects of shuttle tankers on FPSOs during side-by-side operations, showing the necessity of additional validation through expanded datasets and varying wind speed conditions. Gu et al. (2023) introduced a CFD-FEA hybrid method for analyzing floating structures, demonstrating its effectiveness in capturing nonlinear wave interactions and structural deformations. However, they noted that the high computational cost remains a significant challenge, necessitating mesh optimization and algorithmic improvements. These prior studies collectively underscore the importance of CFD-based evaluations in maritime engineering but also reveal key limitations, such as computational expense, sensitivity to experimental conditions, and the need for refined modeling techniques. This study builds upon these findings by addressing the structural challenges associated with wind shields under green water pressure, integrating reinforcement techniques to enhance buckling resistance, and optimizing material distribution to improve structural integrity.

This research advances the field by providing a comprehensive structural assessment of wind shields installed on MPVs, focusing on their resilience under green water pressure. Using Finite Element Analysis (FEA), the study identifies potential weaknesses in the initial design and proposes reinforcement solutions. This research contributes to the ongoing development of aerodynamic drag reduction structures by offering a validated methodology for enhancing wind shield safety in harsh marine environments. Future studies should focus on developing simplified computational models to expedite structural evaluations, enabling broader implementation across various ship types. Through these advancements, the maritime industry can achieve more sustainable, resilient, and energy-efficient vessel designs.

2. Air resistance reduction structure

2.1 Main components and specifications

This Fig. 1 illustrates a typical aerodynamic drag reduction structure installed on the bow of a container vessel. The design aims to minimize air resistance during operation by streamlining the upper structure, contributing to improved fuel efficiency and reduced greenhouse gas emissions.

This figure sets the context for understanding how aerodynamic modifications integrate with vessel design, highlighting the relevance of drag-reducing devices in modern shipping. Figure 2 shows the multi-purpose vessel. A MPV with a total length of 91.4 meters is a medium-sized, specialized ship designed primarily to transport supplies, equipment, and personnel to offshore facilities like oil rigs, platforms, or ships. The illustration underpins the study by showing where the wind shield structure is installed, facilitating a clear understanding of its placement and interaction with other ship components. Table 1 lists the key specifications of the multi-purpose vessel, including dimensions such as length overall (91.4m), length between perpendiculars (88.0m), breadth (19.0m), and draft (5.0m). These parameters provide a foundation for the structural analysis by defining the operational and dimensional scope of the vessel.

2.2 Green water pressure calculation

The calculation of green water pressure on exposed decks is an essential aspect of structural safety evaluation for marine vessels. The formula presented in the Korean Register (KR, 2022) rules provides a structured methodology to determine the minimum pressure acting on exposed decks, accounting for vessel length and the position along the ship as indicated equation (1) and (2). This section explains the formula and its application to ensure clarity and alignment with engineering principles. The pressure acting on a specific location, such as the superstructure deck including the forecastle, is adjusted using a location factor (x).

where, x is 0.75 and P_W is 37.51kN/m², the pressure on the superstructure deck becomes;

This formula provides a detailed and flexible framework for determining green water pressure, crucial for the structural design of exposed decks. The pressure variations captured by the equations ensure that different sections of the vessel's deck are evaluated with KR’s allowable criteria as indicated Table 3. The calculation also highlights the importance of considering location-specific coefficients, such as x , to tailor the results to particular structural elements.

2.3 Methodology

The process follows a structured sequence of reinforcement, modeling, analysis, and iterative validation of structural performance, ensuring compliance with established standards as indicated Figure 3. The process begins with the reinforcement phase, where structural enhancements such as stiffeners and material thickness optimization are applied to improve strength and stability. Following reinforcement, a Finite Element Model (FE-model) is built, incorporating accurate boundary conditions, material properties, and loading scenarios relevant to the operational environment.

Once the model is established, a structural FE-analysis is conducted, evaluating the stress distribution, deformation, and stability of the structure under applied loads. The first critical assessment in this analysis is yielding verification, where the structure’s resistance to plastic deformation is assessed against the criteria outlined in Korean Register (KR, 2024). If yielding occurs beyond permissible limits, further reinforcement is required, and the process loops back to the reinforcement phase. If the yielding assessment is passed, the next evaluation step is buckling verification, ensuring the structure's ability to withstand compressive and shear loads without structural collapse. This verification follows the standards defined by the American Bureau of Shipping (ABS, 2020). Should the structure fail this assessment, modifications and reinforcements are necessary, returning to the reinforcement stage. The final stage of evaluation is displacement verification, which measures deflections under operational loads to confirm compliance with NORSOK (2013) standards. If displacement exceeds acceptable limits, reinforcement adjustments are implemented, ensuring the final design remains within allowable tolerances. Once all three critical assessments—yielding, buckling, and displacement—are successfully passed, the design process concludes, ensuring the structural model meets all necessary performance and safety standards.

3. FE-Analysis and results

3.1 Model and allowable criteria

In this study, a commercial program (NASTRAN) capable of engineering analysis based on the finite element method (Hexagon, 2022), was used. The elements used have 4 nodes, and each node has 6 degrees of freedom. The MPV hull model consists of 205,445 shell elements, 29,720 beam elements, and 201,675 nodes. The wind shield structure consists of 30,421 shell elements and 29,598 nodes, and the size of one element is set to a maximum of 100 mm, as shown in Fig. 4.

In general linear analysis, the maximum stress that occurs depending on the element size shows a large difference. In this study, the element size was selected as 100 mm to express the geometric shape of the stiffeners. If the element size is changed, the element size coefficient value will change when calculating the allowable stress by KR criteria (2024).The material used in the analysis is carbon and low alloy steel (SS400) registered with the Korean Register of Shipping (2024), and the main material properties used in the analysis are as shown in Table 2. Table 2 outlines the material properties of the wind shield structure, Elastic modulus define 210,000 MPa, Yield strength is 235 MPa and tensile strength applied 480 MPa. These properties set up the structural material’s behavior under stress and are integral to the finite element analysis.

The boundary conditions of the analysis were applied as a fixed support (x, y and z: fix) condition to the buoyant part of the lower hull, as shown in Fig. 5. The ballistic resistance reduction structure is fixed to the bow of the ship by welding, and is subject to dead weight, wind load, and green water pressure. The justification for these boundary conditions can be linked to established classification society guidelines and international standards. The paper references the Korean Register (KR, 2024). For further validation of the applied boundary conditions, reference could also be made to ISO 19902 (fixed steel offshore structures) or DNV-RP-C208 (structural analysis of ship and offshore structures), which provide methodologies for defining constraints and load applications in FEA. Here, the wind load is insignificant, so the actual analysis was performed with a combination of dead weight and green water pressure, as shown in Fig. 6. If the maximum von-Mises stress after the load is applied is less than the allowable stress suggested by the classification society, the buckling safety is examined in the next step. The classification society's guidelines are used to calculate the buckling stress of the effective plate between stiffeners, which is then compared against the allowable criteria. In this study, the buckling evaluation results of the classification society are additionally subjected to eigenvalue buckling analysis to verify the results once more. In addition, a step-by-step evaluation method was proposed to determine the safety of the structure by applying the maximum allowable displacement criterion.

The allowable stress criteria established by the KR (2024) rules provide a comprehensive methodology for evaluating material safety under operational conditions. According to Table 3, the allowable stress is determined using the formula as namely Criteria. This criterion ensures that the structural design remains within safe stress limits, accounting for mesh precision and material properties, thus providing a reliable framework for assessing structural integrity under various loading conditions.

where, Criteria is a formula about allowable stress calculation, β is coefficient of mesh density(100mm, 1.25), k is material coefficient(MILD, 1.0), σ_y is yield strength of material and σ_a indicate allowable stress.

3.2 Ultimate Limit State (ULS)

ULS evaluations are essential to prevent structural failures that could lead to loss of life, environmental damage, or significant financial losses.

Offshore and shipbuilding structures operate in harsh environments where high winds, waves, and other dynamic forces can occur unexpectedly. Figure 6 illustrates the von-Mises stress distribution across the wind shield under green water pressure. By assessing ULS, designers ensure that structures perform reliably under extreme conditions, enabling uninterrupted operations in shipbuilding and offshore industries. For instance, oil and gas platforms and wind turbine foundations must remain stable even under hurricane-level forces. The results show that the maximum stress remains below the allowable stress, confirming structural safety against anticipated loads. Figure 7 illustrates the von-Mises stress distribution across the wind shield under green water pressure. The results show that the maximum stress remains below the allowable stress, confirming structural safety against anticipated loads.

3.3 Buckling Limite State (BLS)

Buckling is a failure mode that can occur suddenly and without warning, potentially leading to catastrophic collapse.

Ensuring buckling safety is essential for maintaining the structural integrity of ships and offshore platforms. Thin plates used in decks and wind shield structures are prone to buckling under localized or distributed loads. Evaluating their stability ensures safe operations and structural integrity. The results of the evaluation based on the buckling evaluation criteria presented by ABS Classification for safety evaluation of the wind shield's buckling limit state are shown in Fig. 8. Figure 8 evaluates the buckling stability of the initial design using the American Bureau of Shipping (ABS) criteria. To satisfy buckling, the buckling coefficient must be less than 1.0, with a maximum value of 1.99, requiring appropriate buckling reinforcement. The results reveal potential buckling risks, necessitating design modifications. It can be seen that the risk of buckling was increased by additional green water pressure under conditions where vertical compressive force was applied due to self-weight on the lower part of the ship.

Figure 9 presents the eigenvalue-based buckling analysis for the initial design. It identifies the structural weaknesses that could lead to instability under operational conditions. In the eigenvalue analysis, the risk of buckling occurrence was high in the same panel, and the trend was the same as the ABS classification calculation results. The final buckling safety factor value was different, which seems to be due to the influence of the safety factor used in the classification calculation results.

Figure 10 shows a case where a carling stiffener(flat-bar, web height 100mm, thickness 10mm) was added to the upper center of the wind shield to increase the insufficient buckling stiffness. This reinforcement is a method of inducing a transition to a local buckling mode by adjusting the size of the buckling panel. The thickness of the lower panel was changed from the existing 6 mm to 8 mm, and additional carling stiffeners were added to six locations. The reinforcement thickness and the location and number of reinforcements were determined to meet the purpose of minimum weight. The reinforced design is analyzed using ABS buckling criteria, demonstrating significant stability improvements, as shown in Figure 11. This demonstrates the effectiveness of the proposed reinforcements.The implementation of carling stiffeners and increased plate thickness resulted in substantial improvements. The eigen buckling factors for the reinforced model exceeded the safety threshold, achieving compliance with ABS criteria. Fig. 9 illustrates the maximum buckling factor in the initial design, while Fig. 12 demonstrates the improvements post-reinforcement. Reinforcing wind shields using carling stiffeners and increasing thickness is a practical approach to enhancing structural integrity under green water pressure. These measures effectively redistribute stresses, minimizing localized buckling risks. The study highlights the importance of targeted reinforcements in achieving cost-effective and safe designs. This analysis underscores the necessity of addressing buckling safety in marine wind shields exposed to extreme environmental loads. The reinforcement strategies employed in this study successfully improved buckling performance, ensuring compliance with safety standards.

3.4 Serviceability Limite State (SLS)

Serviceability limit states are those in which the behaviour of the structure is unsatisfactory, and include excessive deflection, excessive vibration and excessive permanent deformation.

Serviceability Limit States (SLS) refer to the performance criteria that ensure a structure remains functional and fit for purpose under normal operating conditions. Unlike Ultimate Limit States (ULS), which focus on preventing catastrophic failure, SLS assessments evaluate a structure's ability to maintain usability, comfort, and serviceability over its operational life. For shipbuilding and offshore structures, SLS is critical to addressing issues such as deformation, vibration, and durability. The NORSOK N-004(2013) specify the maximum allowable displacement of the free end structure as L/100. The cantilever beam deflection of the wind shield with reinforced buckling stiffness is a maximum of 1.55 mm, well within the allowable standard of 3.42 mm, as shown in Figure 13. This confirms that the yield strength, buckling strength, and deflection criteria are all satisfied.

4. Conclusions and future works

This paper addresses the structural safety and aerodynamic performance of a wind shield designed to reduce drag on Multi-Purpose Vessels (MPVs) under the influence of green water pressure. The study aligns with the International Maritime Organization's (IMO) 2050 decarbonization agenda, emphasizing innovative technologies for fuel efficiency and sustainability in maritime operations. Using Finite Element Analysis (FEA), the research investigates the initial wind shield design's ability to withstand operational conditions, focusing on yield strength, buckling safety, and maximum displacement criteria. The results revealed areas of potential structural vulnerability due to green water pressure. To mitigate these risks, the design was reinforced with carling stiffeners and increased plate thickness, redistributing stress and improving stability. Post-reinforcement analysis confirmed significant improvements in buckling factors, ensuring compliance with American Bureau of Shipping (ABS, 2020) safety standards. The findings emphasize the dual advantages of drag reduction and enhanced structural integrity, which contribute to increased fuel efficiency and reduced greenhouse gas emissions.

As a future research task, it is necessary to develop an algorithm that can quickly evaluate structural safety by beam structure modeling without complex shell modeling. The structural stiffness of the end of the beam that constitutes the shell is extracted, and the dummy shell stress evaluation that can be evaluated equivalently is evaluated and combined with a theoretical formula. If this method is formalized, it is expected that it will be possible to simplify modeling and make quick decisions when evaluating the structural safety of similar local structures.