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.     

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.     

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.     

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.     

含损伤加筋板结构声辐射模态变异研究

本文采用声辐射模态的有关理论,用结构的声辐射模态参数来表征结构本身的固有声辐射特性.以加筋板结构为例,计算不同加筋情况和结构不同损伤情况下的声辐射模态.基于Mindlin理论,建立描述健康和损伤的四结点有限元板壳单元模型,采用有限元方法计算结构表面动力响应.各向同性损伤单元,采取刚度各向整体弱化的方法分析;对于各向异性损伤单元,采用K8chanov理论,引人了x和y两个方向的弹性损伤折减系数.考虑到不同损伤存在形式,计算分析了损伤对振动频率、模态以及声辐射模态的影响.文章建立了一种含损伤结构的分析方法,通过对一些典型算例分析,在评价损伤对船舶与海洋结构物常用的加筋结构声辐射特性影响方面做出了一定的探索.     

船体背液板架碰撞损伤机理研究

为研究舱内液货对船体结构损伤机理的影响,利用数值仿真软件MSC.Dytran,计算出背液板架流固耦合力、碰撞力、损伤变形以及能量吸收等,并与背空板架进行了对比分析.结果表明,背液板架的损伤机理明显区别于背空板架,流固耦合力使得结构的变形模式发生了改变、碰撞力增加、极限撞深减小.     

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.     

含损伤加筋板结构辐射声功率及指向性变异研究

本文采用结构声振特性中常用参数辐射声功率和辐射指向性来研究含损伤加筋结构的声辐射特性,计算不同加筋情况和结构不同损伤情况下的辐射声功率和远场指向性.基于Mindlin理论,建立描述健康和损伤的四结点有限元板壳单元模型,采用有限元方法计算结构表面动力响应.针对各向同性损伤单元,采取刚度各向整体弱化的方法分析;对于各向异性损伤单元,采用Kachanov理论,引入了x和y两个方向的弹性损伤折减系数.根据Rayleigh积分可以计算结构振动向外辐射的声压,进而可以得到辐射声功率和辐射指向性.考虑到不同损伤存在形式,计算分析了损伤对振动频率、模态以及辐射声功率和指向性的影响.文章建立了一种含损结构的分析方法,通过对一些典型算例分析,在评价损伤对船舶与海洋结构物常用的加筋结构声辐射特性影响方面做出了一定的探索.     

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.     

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.     

A simplified non-linear numerical method for the assessment of welding induced deformations

Welding numerical simulation has always been a formidable challenge because of the involved complex phenomena to be modelled. The task is increasingly challenging when multi-runs welding or welding of ships is needed to be modelled. In these cases, the computational effort is so high that solving the problem via computational welding mechanics is impossible so far. Alternatively, different simplified numerical strategies were developed to overcome this issue such as those based on the inherent strain. Unfortunately, such numerical models are rarely able to capture the effects induced by a variation of the welding sequence or clamping conditions since they are solved in the elastic filed; most of them are therefore not useful to the design optimization of a welded assembly. In this scenario, a new approach is proposed to quantify the welding induced deformations that uses virtual elements to model the weld bead in the elastic-plastic filed and auxiliary elements to apply equivalent loads determined by experiments on a single welded joint. A specific inverse analysis algorithm has been developed to use the method. The model was applied to a real welded assembly in which both the welding sequence and clamping condition were varied. In addition, for the numerical validation, a novel registration algorithm has been developed to move from solid geometries to middle plane representations. Numerical results were found in good agreement with those obtained by experiments even when the welding sequence and clamping conditions are changed.     

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.     

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.     

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.     

激光焊接夹层甲板板格强度计算的子模型方法

提出了基于有限元软件ANSYS的激光焊接钢质夹层甲板板格结构强度计算的子模型方法。分别对考虑激光焊接焊缝缺陷的I型夹层板格结构的壳单元计算模型和体单元子模型进行强度分析,并与全部体单元模型的芯层与上下面板连接处及面板中部处应力分布计算结果进行对比,验证壳单元计算模型和子模型方法用于计算夹层甲板板格强度的正确性。计算结果表明,对强度特征关注区域,可建立多个体单元子模型,确定子模型边界影响区域范围,从而可较为准确地评估夹层甲板板格结构强度特性,包括焊缝处应力分布。壳单元计算模型可获得较为精确的板格变形值,但无法考虑激光焊接焊缝缺陷,获得的焊缝处最大应力值明显偏小。