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.     

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.     

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.     

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.     

FEM approach to the simulation of collision and grounding damage

Recently, finite element detailed simulations of collision and grounding damage to the hull structures have been practicable. For example, rigid body motions and non-linear structural responses can be calculated by a desk-top engineering workstation within a CPU time of one week, employing finite element models assembled by more than 700,000 elements. Although considerable preparatory man-power is required and the accuracy of the results is still open for further improvement, finite element method approach is the most powerful way at present. On the other hand, simplified analytical approach is suited for a series of qualitative survey, however, it tends to be erroneous when the subject is varying from the fundamental assumptions laid originally for the specific case. The present paper points out several uncertain factors involved in the typical simplified analytical approach such as hull girder bending, forward velocity of a collided ship, etc., that may affect the crashworthiness significantly.     

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.     

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.     

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.     

A simplified method to efficiently design steel fenders subjected to vessel head-on collisions

Steel fenders have been widely used to protect bridges from vessel collisions because of their relatively large plastic deformability and energy dissipation capacity. In the design of a steel fender, detailed finite element (FE) models are usually employed. However, detailed FE analysis involves complicated modeling and substantial computation time. This method is often not applicable, particularly during preliminary design iterations. For this reason, a simplified analytical method was developed in this paper with the aim to efficiently design steel fenders under vessel collisions. For primary individual members of steel fenders, the deformation mechanisms and models as well as participations during various collision scenarios were discussed in detail. By combining the contributions of primary members, a general analytical procedure was presented to rapidly estimate the force-deformation relationship of steel fenders under various bow impacts. For the fixed and floating steel fenders, several collision scenarios were simulated by FE models to verify the accuracy of the developed analytical method. The crushing resistances and energy dissipation capacities estimated by the developed analytical method were in good agreement with those obtained from the FE simulations. Based on the analytical method, an energy-based design approach was proposed for the efficient design of steel fenders. The developed design approach was demonstrated to be capable of predicting the crush depth and peak impact force of a steel fender with good accuracy.     

Analytical modelling of ship bottom grounding considering combined surge and heave motions

This paper provides a new contribution to the analytical treatment of ship grounding accidents. New formulations are proposed to assess the resisting force of outer/inner bottom plating and transverse floors when the vessel undergoes combined surge and heave motions during the grounding event. Considering shallow and sharp rocks described by parabolic functions, analytical solutions are derived from plastic limit analysis and validated by comparison to non-linear finite element simulations. A failure criterion is also proposed to trigger the rupture of the bottom plating and all the derived closed-form expressions are implemented into an in-house solver. The solver is then coupled to a 6-DOFs external dynamics program, which allows to account for the action of the surrounding water. Resulting tool is first validated on a full scale cruise ship by comparison to finite element results. It appears than although some discrepancies arise, especially in the response of transverse floors after rupture, the bottom damage distribution seems to be well predicted. Finally, the developed tool is used to quickly predict the grounding response of different types of ships and the influence of their mass and hydrodynamic properties on the damage extent is investigated.     

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.     

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.     

Three-dimensional fluid-structure interaction case study on cubical fluid cavity with flexible bottom

In this paper, we report our study on a numerical fluid-structure interaction problem originally presented by Mok et al.(2001) in two dimensions and later studied in three dimensions by Valdés Vazquez(2007), Lombardi(2012), and Trimarchi(2012). We focus on a 3D test case in which we evaluated the sensitivity of several input parameters on the fluid and structural results. In particular, this analysis provides a starting point from which we can look deeper into specific aspects of these simulations and analyze more realistic cases, e.g., in sails design. In this study, using the commercial software ADINATM, we addressed a well-known unsteadiness problem comprising a square box representing the fluid domain with a flexible bottom modeled with structural shell elements. We compared data from previously published work whose authors used the same numerical approach, i.e., a partitioned approach coupling a finite volume solver(for the fluid domain) and a finite element solver(for the solid domain). Specifically, we established several benchmarks and made comparisons with respect to fluid and solid meshes, structural element types, and structural damping, as well as solution algorithms. Moreover, we compared our method with a monolithic finite element solution method. Our comparisons of new and old results provide an outline of best practices for such simulations.     

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.     

The influence of fluid structure interaction modelling on the dynamic response of ships subject to collision and grounding

Analysis of the dynamic response of ships in accident scenarios requires a realistic idealisation of environmental and operational conditions by multi-physics models. This paper presents a procedure that simulates the influence of strongly coupled FSI effects on the dynamic response of ships involved in typical collision and grounding events. Our method couples an explicit 6-DoF structural dynamic finite element scheme with a hydrodynamic method accounting for (a) 6-DoF potential flow hydrodynamic actions; (b) the influence of evasive ship speed in the way of contact and (c) the effects of hydrodynamic resistance based on a RANS CFD model. Multi-physics simulations for typical accident scenarios involving passenger ships confirm that suitable FSI modelling may be critical for either collision or grounding events primarily because of the influence of hydrodynamic restoring forces.     

双壳型船体结构稳态温度场和温度应力

用简化解析方法和有限元数值方法,分析了双壳型船体货舱区域在运载高温液货时的稳态温度场;根据船体结构的温度分布,用有限元法计算了其温度应力,同时与货物压力、海水静动压力、总纵弯矩等载荷作用下的结构应力做了比较。研究结果表明：在货舱结构温度场分析中用简化分析方法和有限元数值方法所得的计算结果相当一致;高温液货大幅度增加船体结构的纵向应力和横向应力,同时加剧结构不连续处的应力集中;槽型舱壁可以有效地释放     

A simplified analytical method for estimating the crushing resistance of an inclined ship side

This paper provides a new contribution to the simplified analytical treatment of collisions between two ships. It is directly connected to the well-known super-elements method, which is a simplified procedure allowing for a quick estimation of the damages caused to both the striking and struck vessels during such events. In this article, a new analytical formulation is presented for estimating the impact resistance provided by inclined ship side panels. Two different scenarios are treated. We first deal with the case of an impact between the oblique plate and the stem of the striking ship, and then we consider the situation where the inclined panel is impacted by the bulb. For these two scenarios, an analytical formulation relating the force and the penetration is provided and these developments are validated by comparing them to the results of finite elements simulations. Finally, the new inclined plate super-element is integrated in a simplified model of a frigate collided by another ship, and the resistance given by the super-elements method is then compared to the one obtained by a numerical simulation of this collision.