Analysis of ship–ship collision damage accounting for bow and side deformation interaction

This paper presents a procedure to analyse ship collisions using a simplified analytical method by taking into account the interaction between the deformation on the striking and the struck ships. Numerical simulations using the finite element software LS-DYNA are conducted to produce virtual experimental data for several ship collision scenarios. The numerical results are used to validate the method. The contributions to the total resistance from all structural components of the collided ships are analysed in the numerical simulation and the simplified method. Three types of collisions were identified based on the relative resistance of one ship to the other. They are denoted Collision Types 1 and 2, in which a relatively rigid ship collides with a deformable ship, and Collision Type 3, in which two deformable ships are involved. For Collision Types 1 and 2, estimates of the energy absorbed by the damaged ships differ by less than 8% compared to the numerical results. For Collision Type 3, the results differ by approximately 13%. The simplified method is applicable for right angle ship collision scenario, and it can be used as an alternative tool because it quickly generates acceptable results.     

Extension of the super-elements method to the analysis of a jacket impacted by a ship

The aim of this paper is to present a simplified analytical method for estimating the crushing resistance of an oblique cylinder impacted by the stem of a striking ship. The collision angle of the vessel is arbitrary, i.e. oblique collisions are also considered in this article. The two extremities of the tube are assumed to be clamped. These developments are intended to be used for evaluating the crashworthiness of an offshore wind turbines jacket. To achieve this goal, closed-form expressions are first derived for the particular situations of a horizontal and a vertical cylinder by applying the upper-bound method. An interpolation formula is then proposed to get the resistance opposed by the tube for any inclination angle. In order to validate these theoretical developments, some comparisons are made with the results of numerical simulations. These latter are performed using the finite elements software LS-DYNA. In almost all cases, the analytical prediction of the resistance is found to be in quite good agreement with the numerical ones. Finally, another comparison is made by simulating an OSV collision with a full jacket. In this case, the theoretical model is found to be insufficient for large impact energies and points out the need of further research.     

Equivalent design pressure for ship plates subjected to moving slamming impact loads

When a ship navigates at sea, the slamming impact can generate significant load pulses which move up along the hull plating. The effect of the moving pressure has so far not been explicitly considered in the Rules and Regulations for the Classification of Ships. Based on a modal superposition method and the Lagrange equation, this paper derives analytical solutions to study the elastic dynamic responses of fully clamped rectangular plates under moving pressure impact loads. The spatial variation of the moving slamming impact pressure is simplified to three types of impact loads, i.e. a rectangular pulse, a linearly decaying pulse and an exponentially decaying pulse. The dynamic responses of fully clamped rectangular plates under the moving slamming impact pressure are calculated in order to investigate the influence of the load pulse shapes and moving speed on the plate structural behaviour. It is found that the structural response of the plate increases with the increase of the moving speed. The response of the plate subjected to a moving pressure impact load is smaller than the case when the plate is subjected to a spatially uniform distributed impact load with the same load amplitude and load duration. In order to quantify the effect of the moving speed on the dynamic load, a Dynamic Moving Load Coefficient (DMLC) is introduced as the ratio between the dynamic load factor for the moving impact load and that under the spatially uniform distributed impact load. An expression for DMLC is proposed based on analyses of various scenarios using the developed analytical model. Finally an empirical formula which transforms the moving impact loads to an equivalent static load is proposed.     

Behavior of a double hull in a variety of stranding or collision scenarios

A series of nine tests was conducted to investigate the behavior of a double hull in a variety of stranding or collision scenarios. Cones of five different nose radii were made to model accident scenarios ranging from grounding on a sharp rock to stranding on a relatively flat seabed or shoal, and collision with a sharp bulbous bow of a fast ship to collision with a large bow of a VLCC. Three sub-series were designed in which the cones pressed shell plating, main supporting members and intersections of main supporting members. The test results reveal that the nose radius and the location of penetration have a very strong influence on the behavior of a double hull. Therefore, careful definition of accident scenarios is of crucial importance to assess the strength of ship hulls in accidents, and it is necessary to base the assessment on probability of accidents. Characteristics of the response of structural members were identified and idealized as simple theoretical models. Analytical formulae were derived and discussed. Primary damage mechanisms include membrane stretching of shell panel, onset of rupture, crack propagation, folding of main supporting members, and crushing of intersections of main supporting members. The new plate punching model captures the phenomenon that the load-carrying capacity of a plate depends on the size of the striking object. The plate perforating model predicts the reduced strength of plates with cracks. It reflects the observed test phenomenon that loads do not drop to zero even after rupture occurs in shell plating. A simple analytical method was developed to calculate the global strength of a double hull. The method takes geometrical parameters of seabed rocks or bulbous bows into account, and can be used for a wide range of different accident scenarios. Calculations using this method compared satisfactorily with the test results. This method can be easily incorporated into a probability-based framework to properly assess structural performance for a variety of damage scenarios. Similar to the Wang et al. (J Ship Res 41 (1997) 241) paper on raking damage, which uses only four analytical models, this method also requires only a common calculator to carry out the calculations.     

Verification of a simplified analytical method for predictions of ship groundings over large contact surfaces by numerical simulations

In this paper, a verification is presented of a simplified analytical method for the predictions from numerical simulations of structural performance during ship groundings over seabed obstacles with large contact surfaces and trapezoidal cross-section. This simplified analytical method was developed by Lin Hong and Jørgen Amdahl and calculates grounding characteristics, such as resistance and distortion energy, for double-bottomed ships in shoal grounding accidents. Two finite-element models are presented. One was built for a hold, and the other was built for a hold and a ship hull girder and also considers sectional properties, ship mass, added mass and the hydrodynamic restoring force. The verification was completed by comparing horizontal and vertical resistances and the distortion energy between seven numerical-simulation cases and a set of corresponding cases computed by a simplified analytical method. The results show that the resistances obtained by the simplified analytical method are close to the mean values of the resistance curves obtained by numerical simulations. The comparisons prove that the energy dissipation-prediction capability of the simplified analytical method is valuable. Thus, the simplified analytical method is feasible for assessing ship groundings over seabed obstacles with large contact surfaces and trapezoidal cross-section. Furthermore, studies of the influence of ship motion during groundings ascertained that ship motion affects structural performance characteristics. Resistances are lessened at the end of the grounding due to the reduction of indentations caused by heave and pitch motions of the ship hull girder. Finally, a new method for predicting the structural performance of the time-consuming complete-ship model by applying a combination of normal numerical simulations and ship-motion calculations is proposed and proven.     

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.     

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.     

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.     

Strength of ship plates under combined loading

Strength of ship plates plays a significant role in the ultimate strength analysis of ship structures. In recent years several authors have proposed simplified analytical methods to calculate the ultimate strength of unstiffened plates. The majority of these investigations deal with plates subjected to longitudinal compression only. For real ship structural plating, the most general loading case is a combination of longitudinal stress, transverse stress, shear stress and lateral pressure. In this paper, the simplified analytical method is generalized to deal with such combined load cases. The obtained results indicate that the simplified analytical method is able to determine the ultimate strength of unstiffened plates with imperfections in the form of welding-induced residual stresses and geometric deflections subjected to combined loads. Comparisons with experimental results show that the procedure has sufficient accuracy for practical applications in design.     

Investigation on structural performance predictions of double-bottom tankers during shoal grounding accidents

An investigation is carried out in this paper for the predictions of structural performance of double-bottom tankers during ship grounding over the “shoal” type seabed obstacles. Hong and Amdahl developed a simplified analytical model for the unstiffened double bottom. This method is carefully studied, verified and then used as the first stage of our prediction. The second stage is concerned with stiffeners since stiffeners are indispensable components for double-bottom tankers. A prevailing way to handle is to smear stiffeners onto their attached plating known as the smeared thickness method. However, the effective ratio in this method is dubious in such shoal grounding accidents. Proper values of this parameter are determined in stage two, and then together with the method in stage one, constitute a reliable and efficient tool for structural performance predictions of double-bottom structures in shoal grounding accidents.A double-bottom tanker is chosen as object for the case study. Finite element models of the hold both stiffened and unstiffened are created for numerical simulations using the LS_DYNA software. Simulation cases cover a wide range of slope angles of the indenter and indentations. Numerical results show that Hong and Amdahl's model in stage one is capable of predicting energy dissipation with high precision but poor accuracy for grounding resistances, and a possible reason may be the neglect of vertical resistance. The updated smeared method proposed in stage two is also proved to be capable of grasping major characteristics of stiffeners. Results and conclusions drawn from this paper can be conveniently applied for assessments of the performance of ship double-bottom structures during shoal sliding grounding scenarios, and will benefit the application of accidental limit state design concept in the ship design stage.     

被撞船刚体运动响应的滞后特性

船舶碰撞过程中，被撞船的刚体运动较之碰撞区的局部损伤变形存在一定程度的滞后。本文以理论分析和数值仿真两种方法对该滞后现象进行了研究。提出了运动滞后分析的基本假定和计算公式。研究结果表明，被撞船的运动滞后与撞击速度有重要关系，在高速撞击时，船舶碰撞的内、外部机理计算可相对独立地进行而不会引起明显的分析误差。     

平板在组合载荷作用下的极限强度预报的一种简化解析法

船体平板强度在船舶结构极限强度分析中起到十分重要的作用。最近几年，一些作者提出了计算平板极限强度的一种简化解析方法。但绝大部分的研究只考虑了平板纵向受压这一种简单载荷的情况。在我们成功地解决了三向组合载荷(纵、横压缩和垂向均布压力)的基础上，在本文中，我们又进一步将此方法推广到包含面内剪力在内的所有组合载荷分量均存在的一般情况。通过与一些规范公式的比较表明，本文所推导的公式是可以比较精确地预报平板在一般组合载荷作用下的极限强度。这一工作一方面可以为规范中的一些经验公式提供理论依据，另一方面也许可以提供比经验公式更好的外插能力。为了简化使用本文的方法，本文也在大量参数系列计算的基础上给出了一个回归的经验公式。     

船舶碰撞运动的滞后特性

船舶碰撞过程中，被撞船的刚体运动较之碰撞区的局部损伤变形而言，存在一定程度的滞后效应。本文从理论分析和数值仿真两个方面对该滞后现象进行了研究。研究结果表明：被撞船的运动滞后与撞击速度有重要关系；在高速撞击时，船舶碰撞的内、外部机理计算可相对独立地进行，而不会引起明显的分析误差。     

大型浮式结构物结构碰撞性能分析

碰撞事故是基于事故极限状态设计重点考虑的对象,在设计中越来越受到重视。文章以某大型浮式结构物为研究对象,总结分析ISO、API、HSE、DNV、ABS、BV、LR等标准及规范对碰撞场景的相关规定,提出碰撞分析场景及设计衡准;基于简化分析技术建立碰撞力学模型,利用动态非线性结构分析软件ABAQUS进行仿真分析,通过分析塑性应变、塑性变形、吸能、碰撞力及运动等,校核评估舷侧结构的耐撞性能;分析不同碰撞位置、撞击船型式等对碰撞性能的影响。研究表明:目标大型浮式结构物舷侧结构碰撞事故极限强度满足规范要求,首柱撞击相对比较危险,可作为计算分析控制工况。     

Simplified buckling-and-contact-based expansion method for assessment of crashworthiness of double-hulled ship structure

Ship-to-ship collision events can have severe consequences such as loss of life and environmental degradation. For this reason, modern ship designs are required to incorporate a double-hulled structure to prevent inner-hull damage from such events. Using the experimental or numerical method to analyze the crashworthiness of double-hulled ship structures entails much effort, for which reason neither method is easy to adopt at the early design stage. In this paper, an existing simplified method called Ito's method is improved by a new buckling-and-contact-based expansion method. This method can be applied to double-hulled-structure or outer-hull-local-rupture failure mode. The perpendicular bow-to-side collision scenario is assumed for a conservative estimation of damage to a double-hulled structure. The method was verified in the present study by numerical ship collision simulations of several cases. The results for the buckling-and-contact-based expansion method and numerical simulation were similar for a blunt shape of striking body but different for a sharp shape.     

内河双壳油船舷侧结构耐撞性分析

提出了内河双壳油船舷侧结构耐撞性能的简化分析方法,详细讨论了球鼻艏撞击作用下内河双壳油船舷侧结构的总体破坏模式及其渐进破坏过程.在考虑舷侧外壳板发生断裂破坏后的剩余抗撞能力的基础上,给出了双壳舷侧结构的撞击力―撞深曲线和吸收能量-撞深曲线,并与有限元仿真分析结果进行了比较.简化分析方法得到的结果与有限元分析基本上是一致的,这表明该方法能对内河双壳油船结构的耐撞性能做出合理预报,可用于这类油船耐撞性能的评估.     

On the global ship hull bending energy in ship collisions

During ship collisions part of the kinetic energy of the involved vessels immediately prior to contact is absorbed as energy dissipated by crushing of the hull structures, by friction and by elastic energy. The purpose of this report is to present an estimate of the elastic energy that can be stored in elastic hull vibrations during a ship collision.When a ship side is strengthened in order to improve the crashworthiness it has been argued in the scientific literature that a non-trivial part of the energy released for structural deformation during the collision can be absorbed as elastic energy in global ship hull vibrations, such that with strong ship sides less energy has to be spent in crushing of the striking ship bow and/or the struck ship side.In normal ship–ship collision analyses both the striking and struck ship are usually considered as rigid bodies where structural crushing is confined to the impact location and where local and global bending vibration modes are neglected. That is, the structural deformation problem is considered quasi-static. In this paper a simple uniform free–free beam model is presented for estimating the energy transported into the global bending vibrations of the struck ship hull during ship–ship collisions. The striking ship is still considered as a rigid body. The local interaction between the two ships is modeled by a linear load–deflection relation.The analysis results for a simplified model of a struck coaster and of a large tanker show that the elastic energy absorbed by the struck ship normally is small and varies from 1 to 6% of the energy released for crushing. The energy stored as elastic global hull girder vibrations depends on the ship mass, the local stiffness of the side structure, and of the position of contact. The results also show that in case of highly strengthened ship sides the maximum global bending strains during collisions can lead to hull failure.     

A new formulation of the impact mechanics of ship collisions and its application to a ship–iceberg collision

A new formulation is proposed for the analysis of the impact mechanics of ship collisions that can be applied to both 2D and 3D cases. It is assumed that the impact force is large, and all other forces except the impact forces are neglected. The equations of motion are solved in a local coordinate system, and a transformation matrix between the global and the local coordinate system is proposed. The mass and inertia properties are formulated in the local coordinate system. The orientation of the local coordinate system is determined by the hull shape of the struck ship at the contact point. A closed form solution of the external mechanics of ship collisions is derived. Excellent agreement with an alternative 2D formulation for ship–ship collisions is achieved. The features of the proposed 3D method are demonstrated by numerical examples. An application of the method to estimate the required energy dissipation in ship–iceberg collisions is included. Results and discussions are presented and finally, conclusions are made.     

舰船RCS整形设计中的电磁分析

减小舰船雷达散射截面（RCS）需要对舰船进行整形设计。本文从分析舰船典型结构——金属板的RCS与雷达波的入射角、频率及几何尺寸的关系出发,采用物理光学法导出了金属平板RCS与倾斜角的理论公式,确定了在单频点或多频点对平板进行雷达隐身设计的最佳倾斜角,通过具体实例说明了在舰船整形设计时,采用本文给出的计算公式可以对舰船的RCS和舱室容积进行折衷设计。结论对舰船雷达隐身设计具有指导意义。     

Hydroelastic analysis of a rectangular plate subjected to slamming loads

A hydroelastic analysis of a rectangular plate subjected to slamming loads is presented. An analytical model based on Wagner theory is used for calculations of transient slamming load on the ship plate. A thin isotropic plate theory is considered for determining the vibration of a rectangular plate excited by an external slamming force. The forced vibration of the plate is calculated by the modal expansion method. Analytical results of the transient response of a rectangular plate induced by slamming loads are compared with numerical calculations from finite element method. The theoretical slamming pressure based on Wagner model is applied on the finite element model of a plate. Good agreement is obtained between the analytical and numerical results for the structural deflection of a rectangular plate due to slamming pressure. The effects of plate dimension and wave profile on the structural vibration are discussed as well. The results show that a low impact velocity and a small wetted radial length of wave yield negligible effects of hydroelasticity.