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Equivalent method of different grades of steel target plates under blast loads in the cabin based on plate thickness compensation
Explosion and Shock Waves 2025, 45(12)
Published: 05 December 2025
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Experimental investigation of internal explosion effects on ship structures still faces fundamental challenges. The prohibitively high costs of specialized naval steel plates impose disproportionate financial burdens on experimental budgets. Additionally, the restricted availability of standardized thickness variants has dimensional scaling conflicts during reduced-scale internal explosion experiments. This research proposes an equivalent substitution method for scaled model testing. The methodology enables a strategic replacement of naval steel with conventional steel while maintaining response similitude during the internal explosion of ship structures. The primary research objective focuses on validating the equivalent substitution method for conventional steel as a replacement for specialized naval steel without degrading the accuracy of the recorded data. According to the principle of central deformation similarity, the equivalence relationship among target plates of different grades was established under the assumption of structural integrity during the explosion. Based on the theory of large deflection of thin plates, the relationship between plate thickness and deformation was clarified thoroughly. An equivalence substitution method for different plate grades was explained, and an equivalence substitution method for different plates was proposed. It provides a theoretical foundation for substituting specialized naval steel with conventional steel. Comprehensive numerical simulations were conducted using the finite element analysis software AUTODYN to validate the proposed method. The simulations modeled the dynamic response of four different grades of steel target plates (921A steel, 907A steel, Q235 steel, and Q355 steel) under internal blast loading. The maximum deviation between the simulation results and experimental data is only 5.6%, thereby fully confirming the accuracy and reliability of the numerical model. The equivalence relationships among grades under internal blast loading with different charge volume ratios (0.1, 0.2, 0.4, 0.8, and 1.0) were further explored through extensive numerical simulations involving four plates grades (Q235, Q355, 907A, and 921A) with various thicknesses. A fitting analysis of equivalent plate thickness was conducted. By integrating empirical formulas correlating equivalent plate thickness with dynamic yield strength, the substituted target plate showed less than 10% deviation in central deformation compared to the original plate. The proposed equivalence method for steel target plates of different grades under internal explosion loads has been demonstrated to be both rational and practically applicable. This provides a theoretical foundation and empirical reference for substituting specialized naval steel with ordinary steel in internal explosion experiments.

Issue
Experimental and numerical analysis of ultimate strengths of long-span double-deck plate frame structures in ships under compressive load
Chinese Journal of Ship Research 2025, 20(3): 184-193
Published: 28 March 2025
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Objectives

This study investigates long-span, double-deck plate frame structures commonly used in ship construction. The main objectives are: to comprehensively analyze the stability of these structures under axial compression and to develop a method for accurately evaluating their ultimate load-carrying capacity. This research is of great significance as it provides essential technical support for the design and safety assessment of ship structures, ensuring the reliability and safety of ships with long-span double-deck plate frame structures.

Method

A comprehensive approach is adopted to achieve these objectives. Firstly, an ultimate strength test is conducted on a specially designed long-span double-deck structure model. The test model is fabricated from Q550 structural steel with detailed dimensions. A closed-frame loading system is utilized during the experiment, along with various measurement devices, including hydraulic jacks, force sensors, and displacement gauges, to accurately record load and displacement data. Additionally, a three-directional resistance strain gauge is used to monitor stress variations at multiple locations on the model. Moreover, the initial defects of the model are measured and incorporated into the analysis, and the mechanical properties of the material are determined through tensile testing. Secondly, numerical simulations are performed using ABAQUS. A finite element model is constructed with proper boundary conditions, and initial defect data are incorporated to improve the simulation accuracy.

Results

The test results reveal that global buckling involving both the upper and lower decks is the main cause of the failure of the long-span double-deck structure. Pronounced buckling is observed on the upper deck near the loading end, with the deformation gradually propagating toward the side plates. The stress analysis indicates that the axial load is unevenly distributed between the upper and lower decks, with the lower deck carrying a smaller proportion of the load. The load-displacement curve shows that the structure begins to undergo inelastic deformation when the load reaches approximately 500 t, with the ultimate load of 583.4 t. The simulation results show that the simulated load-displacement curve generally agrees well with the experimental curve, although it slightly overestimates the ultimate strength, with an error of 8.5%. Moreover, the simulation shows that both buckling in both the upper and lower decks, which differs from the experimental result of the lower deck. Further analysis reveals that eccentric compression has a significant impact on the failure mode and the ultimate load-carrying capacity of the structure.

Conclusion

In conclusion, it is crucial to account for the effect of eccentric compression in practical simulations of long-span double-deck plate frame structures. Including this factor in the analysis improves the accuracy of the evaluation, thereby benefiting the design and safety assessment of ship structures. This research provides a valuable reference for future studies on similar structures and offers practical guidance for shipbuilding engineering.

Issue
Analysis of the influence of different damage forms on the residual ultimate strength of ship structure
Chinese Journal of Ship Research 2025, 20(4): 152-163
Published: 18 March 2025
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Objectives

Ships are essential for waterborne transportation, and the safety of their structures is of utmost importance. However, during operation, ships may encounter various accidents such as collisions and groundings, which may damage the hull integrity. Such accidents not only pose risks to the safety of the crew and cargo but can also cause significant environmental damage. To ensure ships maintain sufficient safety reserves after damage and avoid catastrophic consequences, accurately evaluating the residual strength of ships in extreme collision scenarios is essential. This study aims to deeply analyze factors such as the shape, area, and location of hull breaches to comprehensively understand their impact on the residual ultimate strength of the hull, providing a basis for assessing residual strength and responding to emergencies after collisions.

Methods

First, a simplified numerical calculation method was employed to conduct a series of collision structure response calculations. By considering different speeds, angles, and impact locations, the damage conditions of the hull structure were obtained. Specifically, based on a reference experiment, finite element models of the struck and impact ships were established. The fluid's influence on the ships was simulated using the added mass coefficient to improve calculation efficiency. After verifying the accuracy of the simplified numerical calculation method by comparing with experimental results, it was applied to the collision response calculation of the Coast Guard 2501 ship. Then, using the nonlinear finite-element software Abaqus-Explicit, the residual ultimate strength of the ship was studied. The quasi-static method calculated the residual ultimate strength of the damaged cabin section under collision loads, and explored the influence of different breach forms on the residual ultimate strength of the ship structure.

Results

The research results show that two key factors significantly affecting the residual ultimate strength of the ship are the breach area and location. The breach shape has a smaller effect on the residual ultimate strength magnitude but a greater impact on the structural fracture pattern. As the breach area increases with the same shape, the residual ultimate strength of the structure continuously decreases. For example, in the case of a 30-degree impact angle and a speed of 15 kn, the residual ultimate strength decreased by 10% in the hogging state and 18% in the sagging state. When the breach areas are similar in size, as the breach edge becomes sharper, the angle between the fracture path and the middle cross-section of the cabin section gradually decreases, and the fracture location moves towards the center of the structure. In addition, the impact speed has the most significant effect on the breach area, showing a positive correlation. As the impact angle changes, the breach shape also changes. When the impact angle is small, damage along the ship's length is larger, and as the angle increases, damage along the ship's width gradually increases. When the impact angle is 90 degrees, the side breach forms an isosceles triangle, causing greater damage to the internal structure.

Conclusions

These findings provide a foundation for evaluating the residual ultimate strength of ships. By varying the impact speed, angle, and location, the effects of the breach area, shape, and location on the residual ultimate strength of the structure can be equivalently simulated. This provides important reference for emergency handling after ships encounter collisions during navigation, helping formulate more scientific and reasonable emergency response strategies and improving ship safety after accidents.

Issue
Optimal design of the ballistic resistance for new titanium alloy composite armor based on SVR surrogate model and NSGA-II algorithm
Chinese Journal of Ship Research 2026, 21(1): 203-216
Published: 22 January 2025
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Objective

To reduce the damage range of traditional spliced composite armor, a novel composite armor structure composed of titanium alloy faceplate, silicon carbide (SiC) ceramic, ultra-high-molecular-weight polyethylene(UHMWPE) laminate, and integrated titanium alloy lattice and back plate is proposed. And we employ optimal design of the structure to achieve the enhancement of the ballistic resistance and weight reduction.

Method

Comparative studies on the ballistic resistance of the novel composite armor is conducted by numerical methods. A high-accuracy surrogate model is established to rapidly predict the ballistic performance of the composite armor, and correlation analysis is performed between structural parameters and residual velocity and areal density. The structural parameters of the composite armor are optimized based on the NSGA-II multi-objective genetic optimization algorithm.

Results

The results indicate that, compared with traditional spliced composite armor, the new composite armor reduces the residual velocity of the projectile by 11.7% and the damage range by 60.9% due to the presence of the integrated titanium alloy lattice and back plate. The damage range is confined to the inside of the grill, while the rest of the structure maintains better integrity. The anti-penetration performance of the areas with weak protection located at the splices is improved. After optimization, the residual velocity of the projectile is reduced by 21.0%, while the areal density decreases by 5.3%. The residual velocity of the projectile shows the strongest correlation with the thickness of the UHMWPE laminate and the weakest correlation with the thickness of the titanium alloy back plate. The optimized structural design scheme is as follows: the thickness of SiC ceramic is 4.25 mm, the thickness of UHMWPE laminate thickness is 10.65 mm, and the thickness of titanium alloy backplate thickness is 0.52 mm. After optimization, the residual velocity of the projectile is reduced by 21.0%, while the areal density reduced by 5.3%.

Conclusion

Compared with the traditional spliced composite armor, the novel composite armor structure demonstrates superior anti-penetration performance. The method for structural optimization design of composite armor based on the SVR surrogate model and NSGA-II algorithm is effective and feasible.

Issue
High hydrostatic pressure test and ultimate load capacity of composite shell in water
Chinese Journal of Ship Research 2024, 19(5): 122-130
Published: 08 August 2024
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Objectives

This study proposes a structural strain test method for investigating the buckling pressure of a composite shell in a high hydrostatic pressure water environment and the effects of different initial defects.

Methods

A high hydrostatic pressure test is conducted on a composite shell, and the strain of the structure is measured under 15 MPa hydrostatic pressure using the deep-water 3D-DIC (digital image correlation) method based on a high pressure shield. The results are compared to numerical simulations to confirm the feasibility of the 3D-DIC test system in a high hydrostatic pressure environment and verify the accuracy of the numerical method. Based on the numerical simulation method, research is then conducted on the buckling behavior of the composite shell.

Results

The average error between the experimental results and numerical simulation results is found to be 7.2%. In addition, the ultimate load capacity of the composite shell is found to be in an almost quadratic function relationship to the size of the added geometric defects in different modes, and the average gradient of change in the ultimate load capacity is 1.48−2.12 MPa/mm in the first order mode and 1−4.32 MPa/mm in the third order mode.

Conclusions

3D-DIC test technology allows for the accurate strain measurement of composite shells in high hydrostatic pressure environments. Moreover, in such an environment, geometric defects largely affect the ultimate load capacity of the composite shell, while third-order modes are affected to a greater extent than first-order modes.

Issue
TNT equivalency method in confined cabin based on structural response
Chinese Journal of Ship Research 2024, 19(3): 86-95
Published: 06 May 2024
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Objective

This paper aims to reveal the influence of the afterburning effect of explosive materials in confined space explosion.

Methods

A series of TNT blast tests are performed in a confined cabin filled with two different atmospheres, air and nitrogen. The temperature, pressure-time histories and deflection of the blast-loaded steel plate are recorded. The relationship between the deformation of the target plate and the energy released by the explosive is established. On this basis, a TNT equivalent method is proposed which takes into account the afterburning effect in a confined cabin.

Results

The pressure, temperature and dynamic response of the target plate are significantly lower in the nitrogen environment than in the air environment due to the difference in the amount of energy released by the combustion of the explosive material. Thus, the energy released by the burning of TNT explosive materials and their enhancement effects should be considered in blast load analysis.

Conclusion

The validity and applicability of the method are illustrated through a comparison with the existing TNT equivalent method based on quasi-static pressure.

Issue
Experimental and simulation study of afterburning effect for blast load in confined cabin
Chinese Journal of Ship Research 2023, 18(4): 223-232
Published: 17 August 2023
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Objectives

The afterburning effect need to be considered when TNT explodes inside a confined space. In order to accurately analyze the internal blast load, it is necessary to explore the relationship between the afterburning energy value and the charge volume ratio.

Methods

The explosion experiments of 5 different masses of TNT were performed in the confined spaces filled with air and helium. Based on three different methods of chemical reaction analysis, energy conservation law and hypothetical isentropic process, the corresponding afterburning energy of five different charge volume ratios is calculated. The numerical simulation of explosion in confined space considering afterburning effect was realized by ANSYS/AUTODYN program.

Results

The comparison between quasi-static pressure simulation results and experimental results shows that the theoretical value of afterburning energy calculated by chemical reaction analysis method can only be used as the upper limit value, the accuracy of energy conservation method depends on the adiabatic index of mixed gas, and the error of assumed isentropic process method is stable between 4% ~ 7%. Different afterburning energy release processes do not change the final quasi-static pressure, but only the reflected shock wave pressure.

Conclusions

The research results can provide more accurate input load for the design and damage assessment of anti-explosion structures.

Issue
Study of similarity characteristic for the buckling process of box girders subjected to bending load
Chinese Journal of Ship Research 2023, 18(3): 173-185
Published: 27 June 2023
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Downloads:5
Objectives

This study aims to explore nonlinear similarity criteria for box girders under pure bending load, improve the prediction accuracy of the model on the response of prototype structures and provide a theoretical basis for establishing a distortional similarity model design method for actual ship structures.

Methods

First, based on the stability and nonlinear criteria of axially compressed reinforced slabs, a nonlinear similarity criterion for box girders under pure bending load is established using the theoretical analysis method. Second, the ultimate load-carrying capacity and buckling response of scaled-down prototype box girder models are then analyzed using the numerical calculation method to verify the validity of the similarity criterion.

Results

The numerical calculation results show that different scale designs based on the proposed method have high similarities in their flexural failure modes, and the ultimate strength of the scaled-down prototype models can be accurately predicted. Under a specific flexural mode, an increase in the initial deformation reduces the ultimate load-carrying capacity of the box girder. In contrast, the initial deformation factor has less influence on the prediction accuracy of the scaled-down model.

Conclusions

This paper provides an effective nonlinear similarity model design method for the ultimate strength testing of hull beams under pure bending load, which has value for the study of the structural safety of ships.

Issue
The influence of structural characteristics of stiffened plate on the resistance ability to underwater explosion
Chinese Journal of Ship Research 2023, 18(5): 180-193
Published: 25 April 2023
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Downloads:10
Objectives

The structural parameters of the stiffened plate have an essential influence on its resistance to underwater explosion. It is necessary to analyze the specific influence degree of different parameters such as the stiffeners' height, number, and thickness.

Methods

A series of numerical simulations were performed using the CEL method. Then, the influence of stiffened plates' structural parameters on their resistance to underwater explosion was analyzed. Based on the energy absorption law of stiffened plates underwater explosion load, a coefficient was introduced to characterize the influence degree of stiffeners. A calculation method of equivalent thickness was proposed considering stiffener coefficients.

Results

The height of the stiffener, the panel thickness, and the stiffener's thickness have remarkable effects on the resistance to underwater explosion. In contrast, the thickness of the wing plate has an insignificant impact. Under the condition of the same amount of structural mass change, the influence of the height of the transverse/longitudinal stiffener on the damaged area of the stiffened plate is 2.5 times that of the wing panel thickness. The impact of the panel thickness and the thickness of the transverse/longitudinal stiffener on the damaged area is twice that of the wing panel thickness. With the increase of the stiffeners' height, number, and thickness, the structural strength and resistance to underwater explosion of the stiffened plate are enhanced, and the damage degree of the stiffened plate is reduced. The correlation coefficient of the proposed equivalent thickness calculation method considering the stiffener coefficient is −0.94. The method can adequately reflect the stiffened plate's resistance to underwater explosion.

Conclusions

The research results can be used as the basis for evaluating the ship structure against underwater explosion load and provide a reference for the design of the ship's anti-explosion structure.

Issue
Direct calculation design method for atrium in superstructure of large cruise ship
Chinese Journal of Ship Research 2023, 18(5): 141-149
Published: 17 April 2023
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Objectives

The atrium structure is an important functional cabin in the superstructure of a large cruise ship. Atriums have a large spatial span and are always subjected to complex loads. A fast and reliable safety assessment simulation method for atrium structures is required to assist in their structural design.

Methods

Based on the Guidance for Direct Calculation of Local Structures of Cruise Ships 2021 by the China Classification Society (CCS) and the loading characteristics of atriums, a direct calculation design method is proposed in which loads on structures are equivalent to combined simplified loads in three groups, namely longitudinal bending, vertical shear and local cargo pressure.

Results

The results of the proposed direct calculation design method of a specific atrium structure are in good agreement with the whole-ship finite element analytical results, verifying its effectiveness.

Conclusions

This study can provide guidance for the design process of atrium structures in large cruise ships.

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