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.     

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.     

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.     

Deformation process of web girders in small-scale tanker double hull structures subjected to lateral impact

Experimental drop weight impact tests are performed to examine the dynamic response of web girders in a one-tenth scaled tanker double hull structure struck laterally by a knife edge indenter. The small stiffeners of the full-scale prototype are smeared in the small-scale specimen by increasing the thicknesses of the corresponding plates. The plastic response is evaluated at two impact velocities and the impact location is chosen between two web frames to assure damage to the outer shell plating and the stringers. The laboratory results are compared with numerical simulations performed by the LS-DYNA finite element solver. In the simulations, the strain hardening of the material is defined using experimental data of quasi-static tension tests and the strain rate sensitivity is evaluated using standard coefficients of the Cowper–Symonds constitutive model. The experimental permanent deflection and shape of the deformation show a good agreement with the collision simulations. It is found that the crushing resistance of the specimens is determined by the deformation mechanism of the stringers. Thus, the deformation process is described and compared with theoretical deformation modes for web girders subjected to large in-plane quasi-static loads. Additionally, the influence of the stiffeners on the shape of the deformation of the stringers is illustrated through simulations of stiffened structural elements.     

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.     

Estimation of the response of a deeply immersed cylinder to the shock wave generated by an underwater explosion

The work presented in this paper is focused on the development of a simplified method to study the structural response of a deeply immersed cylinder subjected to the primary shock wave generated by an underwater explosion. The proposed analytical model is based on the string-on-foundation method initially developed by Hoo Fatt and Wierzbicki, who converted the two dimensional boundary value problem of a cylindrical shell to an equivalent one-dimensional problem of a plastic string on a plastic foundation. This method has already been extended by the authors to study the shock wave response of an unstiffened cylinder immersed in shallow water. The present work focuses on deep-immersed cylinders subjected to both high hydrostatic pressure and explosion shock wave. The elastic deformation energy of the cylinder under hydrostatic pressure is first calculated and used to determine the initial conditions of the dynamic problem. Cylinder deflection and plastic deformation energy are then calculated for various immersion depths. When confronted to numerical results, the proposed model appears to underestimate the increase of deflection and absorbed energy with the immersion depth. A thorough analysis of the results post-processed from Ls-Dyna/USA finite element simulations highlights a new mechanism which is due to the action of hydrostatic pressure that continues to push inward the immersed cylinder. In order to improve the analytical model, a correction factor on the hydrostatic pressure is introduced but it is finally concluded that a new mechanism dedicated to the late action of the hydrostatic pressure still needs to be developed.     

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.     

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.     

Nonlinear numerical analysis and progressive damage assessment of a cable-stayed bridge pier subjected to ship collision

Despite many studies on barge collisions with girder bridges in the literature, this paper investigates the progressive damage behaviors and nonlinear failure modes of a cable-stayed bridge pier subjected to ship collisions using finite element (FE) simulations in LS-DYNA. The damages in the pier initiate with appearing of local shear failures in the slender columns during the ship collision stage and reach the severe cross-sectional fractures associated with the formation of plastic hinges which causes the combined shear-flexural failures during the free vibration phase of the pier response. In addition, an analytical simplified model with two-degree-of-freedom (2-DOF) is proposed to formulate the strain rate effects of the concrete materials as the dynamic increase factors in the global responses of the impacted pier. It is found that the analytical model is able to efficiently estimate the impact responses of the structure compared to those from the FE high-resolution simulations. Moreover, three different damage indices are proposed based on the pier deflection, the internal energy absorbed by the pier, and the axial load capacity of the pier columns to classify the damage levels of the pier. Finally, an efficient damage index method is determinant by comparing the calculated results with the damage behaviors of the pier observed from the FE simulations.     

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.     

水下非接触爆炸冲击下舱段模型的仿真分析

水下非接触爆炸冲击波容易引起舰船局部结构的大变形或破损。本文以舱段模型为基础,分别修改外底板板厚、增加强肋骨和龙骨数量得到了3种新的舱段结构模型。使用ABAQUS软件对各舱段水下非接触爆炸冲击下的动态响应进行仿真计算,对外板塑性变形、内底及各层甲板应力和加速度峰值进行分析和对比。结果表明：在本文的工况下,增加强肋骨数量能明显减小舷侧塑性变形;增加外底板厚度能提高舱段底部抗冲击性能;增加龙骨数量能减少船底板变形,但会增加舷侧变形及各甲板应力和加速度。     

水下爆炸气泡能载荷对单层板架塑性变形的影响研究

针对气泡能载荷对单层板架在水下非接触爆炸载荷作用下塑性变形的影响问题,运用能量法原理,计算了考虑气泡能载荷影响的单层板架的塑性变形,计算结果与试验结果一致。在此基础上,分析了径距比与由气泡能引起单层板架变形占总变形的比例之间的关系。结果表明：在计算工况下,气泡能载荷对单层板架塑性变形的影响不可忽略,其所引起的单层板架变形占总变形25%左右。     

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.     

On the fluid-structure response of elastic-plastic ship sides subjected to impact loads

This paper presents a simplified numerical model capable of analysing the interaction between the structural dynamic response of elastic-plastic struck plate wall of a fluid tank subjected to wedge impact and the resulting fluid motion. The Variational Finite Difference Method (VFDM) is applied to analyse the structural dynamics of the struck plate and 2-D linear potential flow theory is used to study the resulting fluid motion and its effects on the structural dynamics of the struck plate. Experiments of a wedge indenter impacting with both empty and 90% filled tanks are carried out to study the structural deformation of the struck plate. The accuracy of the developed numerical model is validated with published results and experimental results, and good agreement is achieved. Through the comparison of the impact behaviour of empty and partially filled water tank, it is found that the resulting water motion helps to reduce the structural deformation of the struck plate since part of the impact energy is dissipated by the resulting water motion. Parametric studies are performed to investigate the effect of impact velocity and water level on the structural dynamics of the struck plate of a partially filled water tank. A case study is also conducted to demonstrate the potential application of the proposed method in analysing ship-ice impact problems.     

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.     

Nonlinear dynamic response of blast-loaded stiffened plates considering the strain rate sensitivity

The aim of the present paper is to develop a simple theoretical method which can quickly calculate the nonlinear dynamic response of stiffened plates under a blast loading. The large deformation behavior of the stiffened plate is analyzed by using a singly symmetric beam model as representative of the stiffened plate. The material is assumed to be rigid-perfectly plastic, and the strain rate sensitivity is considered by using the Cowper–Symonds constitutive model (CS model). By Lee's extremum principle, the instantaneous modes of nonlinear structural response are determined. A series of calculations are performed to investigate the influence of pulse intensity, pulse duration, plate thickness, stiffener spacing and material property on the displacement response. The obtained results are in good agreement with those of numerical simulations performed by software package ABAQUS, and then a definition for the cases when the simplified method proposed here can be used is provided.     

考虑细长杆件不同坠落角度的海洋平台甲板损伤预报方法

[目的]在海洋平台吊装作业中,因吊机设备老化以及违规操作等而造成的坠物事故在海洋平台作业中时有发生,其中在杆件结构,如套管、钻铤等设备方面的问题最为常见,因杆件坠落时接触面积小,常会导致板架结构的损伤破坏。[方法]选取细长杆件坠物撞击甲板结构的场景开展结构损伤研究。在此基础上,考虑坠落角度对结构损伤的影响,确定结构损伤变形模型,并运用塑性力学理论,建立考虑杆件坠落角度影响的结构损伤解析预报方法。[结果]结果显示,小角度坠落场景下的结构损伤变形大,结构吸能高,根据结构响应可将坠落角度分为4个角度区间;解析计算结果与仿真计算得到的吸能曲线在数值以及变化趋势上相近。[结论]在杆状结构以一定角度撞击甲板结构时,甲板产生的塑性变形区域形状会随着撞深而产生变化,针对各阶段甲板变形特点的解析计算对海洋平台甲板板架结构抗撞设计评估具有一定的指导意义。     

A simplified analytical method to estimate the resistance of plane lock gates impacted by river barges

This paper presents a simplified analytical method to evaluate the resistance of a single plating lock gate impacted by a river barge. The approach is based on the assumption that the gate behavior may be divided into two successive phases. At the beginning of the collision, local crushing of some structural elements occurs concomitantly with small overall elastic motion of the entire gate. Then, when the penetration of the barge into the gate becomes important, a global plastic mechanism develops over the entire structure. In addition to the membrane and bending deformations occurring classically in such collisions, the particular flat shape of the striking barge bow leads to shear deformations near the gate edges. For all these deformation modes, closed-form expressions of the gate resistance are derived for both local and global deformation phases by applying the upper-bound method. These analytical developments are then validated through comparisons with numerical solutions obtained from non-linear finite-element simulations.     

裂纹尖端区的应变和三轴应力

鉴于全塑性解存在的问题,Tian and Gao(2004y1]导出能反映弹性应变的弹塑性裂纹尖端场.本文给出了其三轴应力和应变分布,并给出了相应的有限元数值解.分析表明,高三轴应力引起的高弹性体变形和弹性能是诱发裂纹扩展的主要因素.