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.     

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.     

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.     

船底座礁实验数值模拟中选择参数影响研究

非线性有限元方法是分析船舶碰撞和搁浅问题的一个强有力工具,但是数值模拟结果的可靠性很大程度上依赖于对工程问题的恰当处理和有限元软件中主要参数的准确控制.本文以某单壳船底结构准静态座礁实验结果为例,用非线性有限元软件LS-DYNA进行数值模拟,研究了下列选择参数对单壳船底结构抗撞性的影响:边界条件;船底结构的材料模型;壳单元类型;船底结构与礁石模型之间的摩擦系数;船底结构的残余应力.通过比较计算结果的碰撞力曲线,能量吸收曲线来评价这些参数对数值模拟的影响并给出了一些建议.     

Understanding ship-grounding events

The paper presents a simple procedure to estimate the damage to a ship bottom and the associated seabed topology that results from a dynamic grounding event. The seabed is modeled as a rigid body and parameterized by a quadratic surface, i.e., a paraboloid, which can in principle model a wide range of seabed topologies. A nonlinear finite element program (LS-DYNA) is used to simulate the contact force versus the lateral penetration, from which the horizontal force component of powered grounding is estimated. The simplified procedure for analyzing dynamic and static grounding events is outlined. Simulations are performed for different ship speeds and for different initial levels of obstruction over the keel. It is shown that a static approach may replace the dynamic grounding simulation, thereby considerably reducing the computational work. The static approach allows for the quick estimation of the energy absorption during powered grounding, which is imperative for decision making during critical situations. The ultimate goal of the study is to provide a near real-time prediction of the risk of rupture of the cargo tanks and hull girder failure. Moreover, the residual strength of damaged ships is an important issue that is related to operations involved in the salvage of wrecked vessels, such as re-floatation and towing.     

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.     

A simplified method to predict grounding damage of double bottom tankers

This paper presents a set of analytical expressions for the calculation of damage opening sizes in tanker groundings. The simplified formulas were given for the grounding force, longitudinal structural damage and the opening width in the inner and outer plating of a tanker's double bottom. The simplified formulas derived are based on a set of numerical simulations conducted with tankers of different dimensions- 120, 190 and 260 m in length. The simulations were performed for five penetration depths and for several rock/ground topologies.The formula for the horizontal grounding force was derived provided the grounding force is proportional to the contact area and the contact pressure. By use of regression analysis it was shown that the contact pressure for any combination of ship and rock size can be expressed with a single normalized polynomial. The actual contact pressure was found by scaling the normalized pressure with the structural resistance coefficient. Given the formulation for the normalized contact pressure, the actual contact force for a ship can be found as a product of average contact pressure and the contact area.The longitudinal length of the damage was evaluated based on the average contact force and the kinetic energy of the ship. The damage opening widths in the outer and inner bottom of the ship were derived separately for two ranges of relative rock sizes as they have strong influence on the deformation mode. The damage widths were given as a function of rock size, penetration depth and double bottom height. To improve the prediction of the onset of the inner bottom failure, a critical relative penetration depth as a function of the ratio of the rock size and the ship breadth was established.Comparison to the numerical simulations showed that the derived simplified approach describes the horizontal grounding force and the damage length well for the penetration depths above 0.5 m. For the range of specified relative rock sizes, the damage width in the inner and outer bottom deviates from numerical simulations approximately up to 25%, which was considered sufficient for the analyses where rapid damage assessment is needed. Comparison was also made to real accidental damage data and to the results of several simplified formulas.     

高能搁浅下双层底结构的损伤特性研究

船舶搁浅事故会引起船体破损、环境污染和人员伤亡等严重后果.研究船舶搁浅,不仅有利于海上生命安全、防止海洋污染,还可为船体结构的抗冲击设计及规范航运繁忙区域中船舶的航速、操作规程提供一定的依据.本文用数值仿真法研究了船舶高能搁浅中的内部力学问题,分析了典型双层底结构的损伤变形、受力和能量耗散等结果,提出了一种新式的抗搁浅YF双层底结构,并与原结构进行了比较.研究表明,损伤变形集中于结构与礁石相接触的区域,高能搁浅内部力学问题的研究可以主要考虑局部的船体结构;肋板的存在显著增加了船底结构的抗搁浅能力;高能搁浅过程中,由于垂直方向的接触力,礁石对双层底的垂向贯入量会略有减小;当纵桁远离搁浅区域时,它的吸能能力无法发挥,抗搁浅作用很弱;YF双层底结构比原结构具有更大的吸能能力和抗搁浅力.     

单壳船侧结构的碰撞能量吸收

文章提出一种近似的解析方法评估单壳船侧结构的耐撞性。首先研究了单轴对称工字梁在横向载荷作用下结构从形成塑性铰到弦响应的力学过程,导出能量和变形的近似解析关系,然后考虑球鼻首和船侧结构的碰撞性将主要受撞区域舷侧板梁组合结构离散成为多个单轴对称工字梁,得到单壳舷侧结构碰撞过程能量吸收的近似公式,同时研究了球鼻形状以及不同碰撞位置对结构变形与能量吸收的影响。对散货船单壳舷侧结构的耐撞性用本文近似理论公式     

无加筋平板极限强度的简化解析法与规范公式的比较

无加筋板是船舶结构的主要构件之一，船舶结构强度校核的一项重要内容就是校核各平板单元是否具备足够的强度储备。最近几年，作者们采用弹性大挠度理论和刚塑性分析相结合的简化解析方法，曾给出了板和加筋板格在联合载荷作用下的极限强度计算公式，并与部分实验值相比，吻合较好，但没有与目前船级社所采用的规范计算公式作过比较。现作这一比较工作，也包括与有限元分析的比较；同时对以前所开发的简化解析法又作了进一步的改进，文章报道这一改进结果。最后，采用上述三种方法，对影响平板极限强度的几个主要参数进行了研究，结果表明，简化解析法与规范计算公式吻合较好。     

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.     

船舶结构的搁浅数值仿真研究

文章用数值仿真法研究了船舶结构搁浅中的内部力学问题,分析了典型双层底结构的损伤变形、受力和能量耗散结果。研究表明,损伤变形集中于搁浅的区域,搁浅力学问题主要考虑局部的船体结构;肋板的存在显著地增加船底结构的抗搁浅能力,使礁石的垂向贯入量会略有减小;当纵桁远离搁浅区域时,它的吸能能力无法发挥,抗搁浅作用明显削弱。     

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.     

船艏横向加强框架对船艏耐撞性能的影响

在撞击过程中船艏结构的典型损伤是外壳板和内加筋的褶皱，撕裂和弯曲。在以前的船舶结构的碰撞分析的简化方法或数值模拟中往往略去横向肋骨框架对船艏碰撞性能的影响。本文利用有限元数值仿真方法研究了横向肋骨框架在碰撞损坏过程中的作用，发现其对船艏结构的损伤形态、碰撞力及能量耗散有重要影响。因而是碰撞计算中不可忽略的因素。     

Analysis of structural crashworthiness of double-hull ships in collision and grounding

A conceptual design framework for collision and grounding analysis is proposed to evaluate the crashworthiness of double-hull structures. This work attempts to simplify the input parameters needed for the analysis, which can be considered as a step towards a design-oriented procedure against collision and grounding. Four typical collision and grounding scenarios are considered: (1) side structure struck by a bulbous bow, (2) side structure struck by a straight bow, (3) bottom raking, (4) bottom stranding. The analyses of these scenarios are based on statistical data of striking ship dimensions, velocities, collision angles and locations, as well as seabed shapes and sizes, grounding depth and location. The evaluation of the damage extent considers the 50- and 90-percentile values from the statistics of collision and grounding accidents. The external dynamics and internal mechanics are combined to analyse systematically the ship structural damage and energy absorption under accidental loadings.     

Longitudinal strength of ships with accidental damages

This paper presents an investigation of the longitudinal strength of ships with damages due to grounding or collision accidents. Analytical equations are derived for the residual hull girder strength and verified with direct calculations of sample commercial ships for a broad spectrum of accidents. Hull girder ultimate strengths of these sample vessels under sagging and hogging conditions are also calculated, based on which correlation equations are proposed. To evaluate a grounded ship, using the section modulus to the deck would be optimistic, while using the section modulus to the bottom would be conservative. On the contrary, to evaluate a collided ship, using the section modulus to the deck would be conservative, while using the section modulus to the bottom would be optimistic. The derived analytical formulae are then applied to a fleet of 67 commercial ships, including 21 double hull tankers, 18 bulk carriers, 22 single hull tankers and six container carriers. The mean values, standard deviations and coefficients of variation for the coefficients in these new analytical formulae are obtained. The ship length exhibits little influence on these coefficients because they are close to the mean values although ship length spans from 150 to 400 m. The ship type shows some influence on the residual strength. Uniform equations are proposed for commercial ships which do not depend on a ship's principal dimensions. These formulae provide very handy tools for predicting the residual strength in seconds, without performing step-by-step detailed calculations, an obvious advantage in cases of emergency or salvage operation.     

船舶结构有限元分析中分布载荷的离散化

本文给出了船外水压力在船壳板及船体结构有限元网格节点上离散的一种方法。只要适当地选择本文所给出的计算公式，该方法可应用于任何受分布载荷作用的结构有限元分析或其它数值分析法中。     

船舶主动减振器安装位置选取和设备选型

开展伯努利梁受迫横向振动机理研究,采用模态叠加法推导了伯努利梁受迫振动的响应表达式,分析了振动响应与激振力和激振力矩作用位置间的关系。总结了减振器安装位置的选择规律和激振力幅值的计算方法,并采用有限元法进行验证,在某小型集装箱船的减振设计过程中进行了应用。