Simplified analytical method for evaluating web girder crushing during ship collision and grounding

The paper presents a simplified analytical method to examine the crushing resistance of web girders subjected to local static or dynamic in-plane loads. A new theoretical model, inspired by existing simplified approaches, is developed to describe the progressive plastic deformation behaviour of web girders. It is of considerable practical importance to estimate the extent of structural deformation within ship web girders during collision and grounding accidents. In this paper, new formulae to evaluate this crushing force are proposed on the basis of a new folding deformation mode. The folding deformation of web girders is divided into two parts, plastic deformation and elastic buckling zones, which are not taken into account for in the existing models. Thus, the proposed formulae can well express the crushing deformation behaviour of the first and subsequent folds. They are validated with experimental results of web girder found in literature and actual numerical simulations performed by the explicit LS-DYNA finite element solver. The elastic buckling zone, which absorbs almost zero energy, is captured and confirmed by the numerical results. In addition, the analytical method derives expressions to estimate the average strain rate of the web girders during the impact process and evaluates the material strain rate sensitivity with the Cowper-Symonds constitutive model. These adopted formulae, validated with an existing drop weight impact test, can well capture the dynamic effect of web girders.     

Experimental numerical and analytical analysis of the penetration of a scaled double-hull tanker side structure

The paper presents experimental, numerical and analytical analyses of a small-scale double-hull structure quasi-statically punched at the mid-span by a rigid flat edge indenter, to examine its energy-absorbing mechanism and fracture. The present study aims to further validate the numerical analysis procedure and the analytical method of individual stiffened panels and web girders against the experiment of the double-hull structure. The specimen, scaled from a tanker's double side structure, includes three spans between the web frames and two spans between the stringers. The paper provides practical information to estimate the extent of structural damage within ship sides during collision accidents. The experimentally obtained force-displacement response and deformation shape show a good agreement with the simulations performed by the explicit LS-DYNA finite element solver. The analysis of the double-hull structure demonstrates the accuracy of the procedure for identifying standard inputs used in numerical codes, in particular the definition of material plastic hardening and the calibration of the critical failure strain by tensile test simulation. The experimental and numerical results are used to validate the analytical method proposed in previous investigations at the plastic deformation stage and a revised semi-analytical method is proposed in the present study for the large penetration stage.     

碰撞/搁浅事故中船体强桁材结构损伤机理解析预报方法研究

随着航运业的快速发展,海上航行的船舶越来越多.尽管人们做了许多努力避免海上意外事故的发生,但海难事故依然不可避免.为了降低上述事故造成的损失,需要在设计阶段快速并准确地预报船舶的结构耐撞性.本文以强桁材结构为研究对象,通过开展准静态冲压试验及相应的数值仿真,分析强桁材结构在面内冲压载荷作用下的变形机理,并基于试验与仿真所得到的结构变形特点,提出强桁材面内受压时的变形模式.以此为基础,运用塑性力学理论,推导出结构变形能、瞬时结构变形抗力及平均结构变形抗力的解析预报公式,并将计算结果与试验结果进行比较验证.研究得到的结构面内受压变形能和抗力解析计算公式,可以快速评估事故载荷下结构的响应情况,包括结构变形阻力及能量耗散,具有使用方便,计算速度快,计算结果相对可靠的优点,对船体耐撞结构设计及抗撞性能评估具有一定的指导意义.     

Plastic mechanism analysis of structural performances for stiffeners on bottom longitudinal web girders during a shoal grounding accident

A theoretical model is introduced in this paper for structural performance of stiffeners on double-bottom longitudinal girders in a shoal grounding accident. Major emphasis is placed on establishing the characteristic deformation mechanism of stiffeners and identifying major energy dissipation patterns. Numerical simulations using the LS-DYNA nonlinear finite-element program were carried out to examine thoroughly the progressive deformation process during sliding deformation. Stiffener deformations were observed to fall into two categories: stiffeners fully contacted with the indenter, and stiffeners subjected to indirect deformation due to energy transfer from attached girders. Grounding performance of stiffeners is substantially influenced by that of the attached plating, and therefore a review of the existing deformation models of longitudinal girders (i.e. Simonsen 1997, Midtun 2006 and Hong 2008) was included. Hong's model of bottom girders was found not capable of representing the effects of stiffeners, and a new model of girders was thus developed. Based on observation of the numerical deformation process and the new analytical girder model, a kinematically admissible model of stiffeners on bottom longitudinal girders was built. Using the methods of plastic mechanism analysis, simplified analytical expressions for energy dissipation by girder-attached stiffeners, both fully contacted and noncontacted, were formulated, and equations for grounding resistance were subsequently obtained. The theoretical expressions agree favorably with results from nonlinear finite-element simulations and capture two significant characteristics of the problem: that energy varies little with indentation for stiffeners that fully contacting the indenter, and that energy is independent of slope angle for indirectly deformed stiffeners. The proposed theoretical model helps to predict analytically shoal grounding performance of stiffeners on longitudinal girders with reasonable accuracy.     

Use of localized necking and fracture as a failure criterion in ship collision analysis

This study explores the use of localized necking for failure modeling in maritime crash analysis, using large shell elements. The assumption that the failure of a large shell element occurs simultaneously with the onset of localized necking is revisited. This study particularly investigates the numerical implementation of the localized necking condition and its implications on the results of ship collision analysis involving not only plate rupture but also various failure mechanisms such as the crushing and tearing of web girders, stringers, and their intersections. Through a series of large-scale collision simulations, the effects of bending deformation on the initiation of necking, non-proportional loading paths, and ductile fractures not preceded by localized necking, are investigated. It is demonstrated that a localized necking-based fracture model provides a reasonable, relatively mesh-insensitive estimate of the onset of fracture in the outer hull panels; however, fracture propagation is very sensitive to the numerical implementation of the necking and fracture model, especially for the cases involving the crushing of web frames and stringers.     

Simplified method for quasi-static collision assessment of a damaged tanker side panel

The paper presents a simplified analytical method to examine the energy absorbing mechanisms of intact and damaged small-scale stiffened plate specimens, quasi-statically punched at the mid-span by a rigid wedge indenter. The specimens scaled from a tanker side panel are limited by one span between web frames and stringers. The influence of the initial damage on the impact response is based on the plastic behaviour of an intact specimen. The initial damage is provoked at one-quarter from the support by the same indenter that, afterwards, punches the specimen at the mid-span. In practice, initial imperfections of this type could be due to minor incidents during ship service operation, such as collision of ships with floating objects. To validate the proposed simplified method, experiments and numerical simulations are conducted. The experimentally obtained force-displacement responses and shapes of the deformation show good agreement with the simulations performed by the explicit LS-DYNA finite element solver. The analytical method derives expressions to estimate the energy dissipated by the intact and the damaged specimens based on the plastic deformation mechanisms, assuming that both the plate and stiffener structural components absorb the incident energy through the rotation of the plastic hinges at the point of contact and at the supports and the membrane tension over the plastically deforming region between the loading and the supports.     

Experimental and numerical analysis of a tanker side panel laterally punched by a knife edge indenter

The paper presents finite element simulations of a small-scale stiffened plate specimen quasi-statically punched at the mid-span by a rigid indenter, in order to examine its energy absorbing mechanisms and fracture. The specimen, scaled from a tanker side panel, is limited by one span between the web frames and the stringers. The paper provides practical information to estimate the extent of structural damage within ship side panels during collision accidents. Moreover, the results of this investigation should have relevance to evaluate grounding scenarios in which the bottom sustains local penetration. This is possible since the structural arrangement of the double hull and the double bottom of tanker vessels is very similar. The experimentally obtained force–displacement response and shape of the deformation show good agreement with the simulations performed by the explicit LS-DYNA finite element solver. The numerical analysis includes aspects of particular relevance to the behaviour of ship structures subjected to accidental loads which could give rise to difficulties in interpreting finite element calculations. In particular, the paper comments on the material nonlinearities, the importance of specifying the precise boundary conditions and the joining details of the structure. The considerable practical importance of these aspects has been the focus of attention in previous publications of the authors which evaluate the experimental-numerical impact response of simple ship structural components, such as beams and plates. Therefore, this paper uses the definitions proposed in those references to evaluate its applicability in the scaled tanker side panel, as an example of a more complex ship structure.     

Ice impact response and energy dissipation characteristics of PVC foam core sandwich plates: Experimental and numerical study

In this paper, the dynamic responses and energy dissipation characteristics of polyvinyl chloride (PVC) foam core sandwich plates under ice impact are investigated. The ice impact tests of PVC foam core sandwich plates were conducted by employing the horizontal impact experimental apparatus. The finite element simulations were conducted to analyze the dynamic response of PVC foam core sandwich plates based on soil and concrete material model for ice impactor. It was demonstrated that numerical results were in good agreement with experimental results. The deformation modes of the top facesheets were coupling of local indentation with global bending deformation, while the deformation modes of bottom facesheets were overall bending deformation. The permanent deformation of face sheets show that the impact resistance of sandwich plate is better than that of equivalent weight hull plate (EWHP). In addition, based on the actual navigation environment of ship, the effect of impact angle and ice floe shape on dynamic response and energy dissipation are analyzed.     

Influence of initial distortion of 3 mm thin superstructure decks on hull girder response for fatigue assessment

This paper investigates the influence of initial distortion of 3 mm thin superstructure decks on hull girder response and fatigue assessment. Part of the traditional superstructure of a prismatic passenger ship is replaced by thin decks with initial distortion amplitude of 0, 1 and 2 times the IACS limit value for thicker plates, i.e. 0, 6 and 12 mm. Both geometrically linear and nonlinear finite element (FE) analysis is used. For reference also traditional superstructure with 5 mm plate thickness is analyzed. Thin straight superstructure decks give 43% of weight reduction and carry approximately 30% less load than corresponding thick straight decks in traditional model. The load that is not carried by thin decks is divided between other traditional decks. The redistribution of forces also happens at the deck level between plates, stiffeners, girders and longitudinal bulkheads. The presence of initial distortion with the shape of one half wave between web frames and stiffeners causes an additional few percent-decrease in forces carried. The results and conclusions are similar for hogging and sagging loading conditions and differences between geometrically linear and nonlinear FE analysis are very small. This means time saving since the panel loading for fatigue assessment can be defined from geometrically linear hull girder response analysis without considering the initial distortions.     

An analytical method for predicting the ship side structure response in raked bow collisions

As an increasing number of ships continue to sail in heavy traffic lanes, the possibility of collision between ships has become progressively higher. Therefore, it is of great importance to rapidly and accurately analyse the response and consequences of a ship's side structure subjected to large impact loads, such as collisions from supply vessels or merchant vessels. As the raked bow is a common design that has a high possibility of impacting a ship side structure, this study proposes an analytical method based on plastic mechanism equations for the rapid prediction of the response of a ship's side structure subjected to raked bow collisions. The new method includes deformation mechanisms of the side shell plating and the stiffeners attached. The deformation mechanisms of deck plating, longitudinal girders and transverse frames are also analysed. The resistance and energy dissipation of the side structure are obtained from individual components and then integrated to assess the complete crashworthiness of the side structure of the struck ship. The analytical prediction method is verified by numerical simulation. Three typical collision scenarios are defined in the numerical simulation using the code LS_DYNA, and the results obtained by the proposed analytical method and those of the numerical simulation are compared. The results correspond well, suggesting that the proposed analytical method can improve ship crashworthiness during the design phase.     

轮压载荷下夹层板直升机平台结构响应特性

以直升机平台甲板为研究对象,基于数值仿真方法,考虑弹性工况和塑性工况,分别采用动态冲击、轮胎准静态压载、刚体准静态压载和均布压载4种处理方式模拟轮压载荷,分析夹层板上面板、夹芯层和下面板的响应特点,讨论载荷处理方式对轮压压力分布和结构响应的影响规律,并初步探讨4种载荷处理方式间的内在关系。研究结果表明:在轮压载荷作用下,板架产生高应力、高变形的局部结构响应,采用动态冲击、轮胎准静态压载和均布载荷3种处理方式均能较好地反映夹层板响应,这3种载荷处理方式之间存在联系,轮压载荷可通过等效处理达到一定程度的简化。     

Research on the dynamic buckling of a typical deck grillage structure subjected to in-plane impact Load

The dynamic buckling of the main deck grillage would result in the total collapse of the ship hull subjected to a far-filed underwater explosion. This dynamic buckling is mainly due to the dynamic moment of the ship hull when the ship hull experiences a sudden movement under impact load from the explosion. In order to investigate the ultimate strength of a typical deck grillage under quasi-static and dynamic in-plane compressive load, a structure model, in which the real constrained condition of the deck grillage was taken into consideration, was designed and manufactured. The quasi-static ultimate strength and damage mode of the deck grillage under in-plane compressive load was experimentally investigated. The Finite Element Method (FEM) was employed to predict the ultimate strength of the deck grillage subjected to quasi-static in-plane compressive load, and was validated by comparing the results from experimental tests and numerical simulations. In addition, the numerical simulations of dynamic buckling of the same model under in-plane impact load was performed, in which the influences of the load amplitude and the frequency of dynamic impact load, as well as the initial stress and deflection induced by wave load on the ultimate strength and failure mode were investigated. The results show that the dynamic buckling mode is quite different from the failure mode of the structure subjected to quasi-static in-plane compressive load. The displacements of deck edge in the vertical direction and the axial displacements are getting larger with the decrease of impact frequency. Besides, it is found that the dynamic buckling strength roughly linearly decreased with the increase of initial proportion of the static ultimate strength P₀. The conclusions drawn from the researches of this paper would help better designing of the ship structure under impact loads.     

Rapid prediction of structural responses of double-bottom structures in shoal grounding scenario

This study presents a simplified analytical model for predicting the structural responses of double-bottom ships in a shoal grounding scenario. This solution is based on a series of analytical models developed from elastic-plastic mechanism theories for different structural components, including bottom girders, floors, bottom plating, and attached stiffeners. We verify this simplified analytical model by numerical simulation, and establish finite element models for a typical tanker hold and a rigid indenter representing seabed obstacles. Employing the LS-DYNA finite element solver, we conduct numerical simulations for shoal-grounding cases with a wide range of slope angles and indentation depths. In comparison with numerical simulations, we verify the proposed simplified analytical model with respect to the total energy dissipation and the horizontal grounding resistance. We also investigate the interaction effect of deformation patterns between bottom structure components. Our results show that the total energy dissipation and resistances predicted by the analytical model agree well with those from numerical simulations.     

双层底船搁浅场景下结构响应的快速预报（英文）

This study presents a simplified analytical model for predicting the structural responses of double-bottom ships in a shoal grounding scenario. This solution is based on a series of analytical models developed from elastic-plastic mechanism theories for different structural components, including bottom girders, floors, bottom plating, and attached stiffeners. We verify this simplified analytical model by numerical simulation, and establish finite element models for a typical tanker hold and a rigid indenter representing seabed obstacles. Employing the LS-DYNA finite element solver, we conduct numerical simulations for shoal-grounding cases with a wide range of slope angles and indentation depths. In comparison with numerical simulations, we verify the proposed simplified analytical model with respect to the total energy dissipation and the horizontal grounding resistance. We also investigate the interaction effect of deformation patterns between bottom structure components. Our results show that the total energy dissipation and resistances predicted by the analytical model agree well with those from numerical simulations.     

散货船舱口盖剩余强度

通过对散货船舱口盖极限强度的理论分析，采用了正交各向异性板及刚塑性模型进行了理论上的推导，并对7万t散货船的1号舱的舱口盖(两块对称滚动式)，进行了ILL66及IACS URS21(1998年版与上述ILL66的88议定书中载荷的量级相当)的外载荷的比较及线性和非线性的有限元分析。本文所采用的有限元的线性及弹塑性计算对实际的舱口盖进行评估的结果证明，IACS URS21(ILL66的88议定书)的标准比ILL66的标准有所提高。采用非线性有限元法是在初始设计阶段使用的可行方法。这些结果可供规范研制工作参考。     

船舶典型管路冲击动力响应和变形特性数值模拟方法及试验研究

根据船舶典型管路段按1∶10比例设计管路试验模型,冲击试验台上分别进行了不同管夹及支吊架的布置方式下的冲击试验,并对试验结果进行分析,给出典型管路系统冲击响应及变形特点,在此基础上采用时域法结合接触有限元建模技术,对试验模型管路在试验工况下的冲击响应、动态变形进行了数值模拟并与试验结果进行对比分析,结果表明:数值模拟结果的仿真精度较高同时可以很好的模拟管路系统的破坏形式和变形特点.     

Experimental study on the collapse strength of wide stiffened panels

Five specimens are tested under axial compression until collapse to investigate the ultimate strength of wide stiffened panels with four stiffeners. To avoid the side bays collapse and reduce the influence of the clamped boundary condition on the collapse behaviour, the tests are made on panels with two half bays plus one full bay in the longitudinal direction with simply supported condition at the end edge of loading. Initial loading cycles are used to release the residual stresses of the stiffened panels and the gap between the stiffened panels and the supported steel block. Strain gauges are installed on the plates and the stiffeners to record the distribution of strain. This series of experiments is compared to a series of tests with narrow panels (two stiffeners), which allows analysing the effect of the width on the strength of stiffened panels.     

Towards a unified methodology for the simulation of rupture in collision and grounding of ships

The aim of the work is the definition of a procedure for the numerical simulation of the response of ship structures under accidental loading conditions, which suffer various different modes of failure, such as tension, bending, tearing and crushing and in particular to investigate the effect of material modeling, i.e. material curve and rupture criterion as well as mesh size and strain rate effect on the results. To this end, different material models and simulation techniques were used for the simulation of eighteen indentation tests conducted by different research groups. The simulations were performed using the explicit finite element code ABAQUS 6.10-2. The tests refer to the quasi-static and dynamic transverse and in-plane loading of various thin walled structures which represent parts of a ship structure. Three rupture criteria are incorporated into VUMAT subroutine, which interacts with the explicit finite element code and refers to an isotropic hardening material that follows the J₂ flow theory assuming plane stress conditions, in order to investigate the prediction and propagation of rupture. The focus is on investigating whether it is possible to define a unified methodology, which is appropriate for the simulation of all different tests. Consistency in the numerical results is observed with the use of an equivalent plastic strain criterion, in which formulation a cutoff value for triaxialities below −1/3 is included.     

Energy dissipation in high-energy ship-offshore jacket platform collisions

Ship collisions with offshore structures may be characterized by large amounts of kinetic energy that can be dissipated as strain energy in either the ship, or the installation, or shared by both. In this paper a series of FE numerical simulations are performed with the aim of providing a clearer understanding on the strain energy dissipation phenomenon, particularly upon the ship-structure interaction. Ships of different dimensions and layouts are modelled for impact simulations. Likewise, three platform jacket models of different sizes and configurations are considered. The collision cases involve joints, legs, and braces and are simulated for several kinetic energy amounts of the vessels and different impact orientations. An overview of the plastic deformation mechanisms that can occur in both ship and jacket structure is also given. The results from the various models with different collision scenarios are compared in terms of the strain energy dissipation with respect to the different ship/installation strength ratios. From the FEA simplified approaches are also derived in terms of the relative stiffness of the two structures for assessing the responses and energy absorptions of the two structures. The conclusions drawn from this study can be applied to a broader range of collision assessment of offshore steel jacket platforms subjected to high-energy ship impacts.     

用非线性有限元的方法研究准静态加筋方形管压溃破坏中加强筋的影响

在船舶碰撞和搁浅中,薄壁结构在轴向压力条件下的压溃破坏是一种重要的破坏模式.本文用非线性有限元方法研究了准静态条件下纵向和横向加强筋对加筋方形管压溃破坏的影响.基于实验结果和数值仿真的结果,给出了新的等效板厚和平均压溃载荷计算公式.计算结果表明新的平均压溃载荷计算公式能够更好地拟合实验结果.