Ship longitudinal strength analysis is critical for ensuring structural integrity and safety throughout the vessel's

operational life. This study presents a comprehensive finite element analysis (FEA) of the MST-3 vessel's

longitudinal strength using ANSYS software, focusing on hull girder behaviour under extreme loading

conditions. The research employed advanced computational methods to evaluate structural response under

sagging and hogging conditions, incorporating material nonlinearity, initial imperfections, and residual stresses

from welding processes. The MST-3 vessel, with principal dimensions of 185.0m LOA, 28.5m beam, and

15.2m depth, was modelled using 68,530 finite elements (SHELL181 and BEAM188) with 72,840 nodes. The

analysis incorporated AH36 steel material properties with yield strength of 355 MPa and considered initial

(267.3 MPa), engine room bulkheads (245.8 MPa), and cargo hold corners (231.5 MPa). The progressive collapse

analysis revealed ductile failure behaviour with adequate post-ultimate strength reserves. Buckling analysis

showed minimum safety factors of 1.85 for all structural components, with longitudinal girders exhibiting the

lowest buckling margins. The finite element methodology demonstrated excellent correlation with analytical

beam theory solutions, validating the computational approach with maximum differences below 1%. Key findings

indicate that while the vessel structure is adequate, hatch corner reinforcement is recommended to address stress

concentrations. The study concludes that modern finite element techniques provide reliable tools for ship

structural assessment when properly validated. The developed methodology offers practical engineering

solutions for longitudinal strength evaluation and optimization of marine structures.

Keywords: Ship longitudinal strength, finite element analysis, hull girder, structural assessment, ANSYS

Recent literature highlights a clear shift toward advanced finite element analysis (FEA), which allows for higher-

fidelity representation of material nonlinearity, geometric imperfections, and progressive failure mechanisms

(Caridis, 2025). FEA has therefore emerged as a superior tool for accurate hull-girder strength assessment.

Caridis (2025) provides a comprehensive evaluation of the method, illustrating how both linear and nonlinear

finite element models can be used to predict global bending behavior, elastic-plastic deformations, and ultimate

strength. His work also reflects evolving regulatory trends, showing that classification societies increasingly

expect FE-based evaluations to complement or replace empirical and rule-based design approaches.

A major development in recent research is the transition from simplified global-beam modeling to fully

discretized finite element hull representations. Yu et al., (2024) propose a novel hull-girder design methodology

that models the girder as a complete, fully meshed FE system rather than as a conventional beam. This enables

but is frequently overlooked in traditional assessment methods. Their findings reinforce the importance of

nonlinear dynamic FEA in realistic accident simulations. Chuku et al,.(2024), informed that when running at

low speed inside or below 12 knots, it is evident that the EDDI for all of the vessels was improved due to their

short length, breadth, draft, and prismatic coefficient. This is due to the observation that lowering these settings

causes the EEDI achieved value to fall. This can be problematic for the ship’s intact stability.

Structural imperfections are increasingly recognized as critical parameters in hull-girder strength predictions.

Cui et al. (2024) investigate the influence of welding-induced initial imperfections on ultimate strength using

nonlinear FEA. Their results demonstrate that even minor deviations from ideal geometry can lead to substantial

reductions in load-carrying capacity. This aligns with industry observations that modern thin-walled stiffened

panels are particularly sensitive to fabrication quality and geometric tolerances. Corrosion, fatigue, and service-

strength of inland dry-cargo vessels using nonlinear FEA. The results show that the unique operational

environment and structural configurations of inland vessels require tailored assessment methods rather than

applying assumptions derived from larger seagoing ships.

Another significant development is the application of multi-scale FEA, where global hull-girder responses are

linked to local structural behaviors. This approach provides deeper insight into panel buckling, stiffener failure,

crack propagation, and progressive collapse. Studies show that multi-scale models outperform traditional single-

scale analyses, especially in predicting ultimate limit states and failure interactions under combined loads.

Beyond deterministic FE modeling, researchers are increasingly integrating probabilistic frameworks to capture

uncertainties in loads, material properties, manufacturing tolerances, and degradation rates. Probabilistic FEA,

supported by machine learning, improves reliability-based design and optimization. These approaches offer

of the structure and deck holes. Ostapenko, (1986) showed that when a ship travels in oblique seas with heavy

waves, torsion may reduce the longitudinal strength of the hull. Their study is vital for ship hull design and safety,

(2021) assessed the strength of two general cargo ships and found sufficient stress levels and safety parameters in

all loading conditions. The stress distributions for specified load circumstances met the Croatian Registry of

Shipping rules, suggesting an acceptable and redundant ship structure. Results indicated that ships can be used

under intended loading circumstances. Vemon & Nadeau (1987) compared the St. Venant and warping-based

thin-walled beam theories. They concluded that warping-based theory provides a better model of the behavior of

prismatic thin-walled sections because longitudinal deformation is considered. (Tang, et al., 2019) used three

real-time structural strength assessment methods to identify hull longitudinal strength, yield local strength, and

fatigue strength. The system evaluates short- and long-term structural strength. Comparing and analyzing

assessment data in different wave azimuths revealed certain problematic areas and causes of structural damage.

bending and torsion loads, noting their correlation. According to this investigation, hull stresses occurred during

simultaneous bending and torque moments, and wider main deck openings increased hull torsion stresses.

(Rorupet al., 2016) used more complex loads and improved methods for various FE analysis types, such as

global models, partial ship modeling, and fine mesh models, to improve the design process and class approval

while emphasizing the need for effective design tools. In addition, the regulations effectively support the use of

finite element analysis. The most typical FE application for class approval is cargo hold analysis. Vladimir &

Senjanovic, (2016) assessed the structural design of a ship, specifically its ability to withstand fatigue and

extreme loads, using a conventional container ship as a reference. Their research focused on applying direct

calculations to the design of ultra- large ships, emphasizing evaluating structural reliability.

The strength of a ship is usually considered when building. Improper analysis can cause problems such as ship

The aim of this project is to create a computer base program that can calculate the ship’s longitudinal

strength using finite element method. Based on the above stated aim, the following objectives were utilized to

achieve needed results. The finite element formulations were developed and validated, the assessment of the hull

girder strength of the MST-3 vessel and evaluation of its structural performance under various loading

conditions were conducted, t he stress distribution patterns throughout the hull structure were investigated and

critical areas of stress concentration were identified and finally, the numerical analysis using ANSYS software

for calculating longitudinal strength parameters was carried out. The scope of this study was limited in analyzing

the various parameters needed to suitably carry out calculation on a ship longitudinal strength using MATLAB

software. This project covers the use of scale finite element methods to calculate the vessels longitudinal

strength, and how it plays a crucial role in designing and analyzing the safety of a ship. The approach to this

project proposal by learning about the underlying assumptions of ship longitudinal strength, we will be able to

derive some calculations and programs used to analyze the ships longitudinal strength.

The approach to this study included calculating the longitudinal strength of a ship involves complex calculations

This study is significant because it enables you understand and be able to evaluate a ship longitudinal strength

with the application of scale finite element method with the help of MATLAB. In other words, studying the

longitudinal strength of a ship is significant for various reasons which include safety, structural integrity and

regulatory compliance, while also driving innovation and advancement in the maritime industry. Assessing the

longitudinal strength of a ship also helps in the maintenance and lifecycle management of ship, ensuring their

continued safe operation throughout their service life at sea. The study of longitudinal strength of a ship involves

lots of challenges and limitations. One of the challenges is the complexity of ship structure, making it challenging

to accurately model their behavior under different loading conditions. The behavior of ship materials such as

steel can vary under different loading rates, temperature and environmental conditions, affecting the accuracy of

the longitudinal strength calculation.

consideration of the underlying assumptions, limitations, and uncertainties associated with each numerical

method. Extrapolating results beyond the scope of the analysis or making direct comparisons between inherently

different methods can lead to misinterpretation or overgeneralization of findings.

The materials for this research work involve the use of ABAQUS/SOLIDWORKS software to conduct a finite

element analysis on the MST-3 vessel. The MST-3 vessel is used as a case study for this research work.

In an intact condition, a ship hull will sustain applied loads smaller than the design load, and in normal seagoing

and approved cargo loading conditions will not cause any structural damage. However, the loads acting on the

ship hull are uncertain due to the nature of rough seas and the possible unusual loading/unloading of cargo. In

Where:

∆Q = 78.8l2, l = 0.7tw when 0.7tw< 7.0 mm, l = 0.7 when 0.7tw≥ 7.0 mm.

Where:

The shear force at a section can be calculated as (5):

(6)

Where:

M is the bending moment (Nm)

C is the distance from the neutral axis to the outer fibre (m)

I is the moment of inertia (m^4)