Ultimate strength analysis of a bulk carrier hull girder under alternate hold loading condition,Part 2: Stress distribution in the double bottom and simplified approaches

This is the second of two companion papers dealing with nonlinear finite element modelling and ultimate strength analysis of the hull girder of a bulk carrier under Alternate Hold Loading (AHL) condition. The methodology for nonlinear finite element modelling as well as the ultimate strength results from the nonlinear FE analyses was discussed in the companion paper (Part 1). The purpose of the present paper is to use the FE results to contribute towards developing simplified methods applicable to practical design of ship hulls under combined global and local loads. An important issue is the significant double bottom bending in the empty hold in AHL due to combined global hull girder bending moment and local loads. Therefore, the stress distributions in the double bottom area at different load levels i.e. rule load level and ultimate failure load level are presented in detail. The implication of different design pressures obtained by different rules (CSR-BC rules and DNV rules) on the stress distribution is investigated. Both (partially) heavy cargo AHL and fully loaded cargo AHL are considered. Factors of influence of double bottom bending such as initial imperfections, local loads, stress distribution and failure modes on the hull girder strength are discussed. Simplified procedures for determination of the hull girder strength for bulk carriers under AHL conditions are also discussed in light of the FE analyses.     

考虑晃荡耦合船舶运动的晃荡压力算法（英文）

The effect of coupling between sloshing and ship motions in the evaluation of slosh-induced interior pressures is studied. The coupling between sloshing loads and ship motions is modelled through a hybrid algorithm which combines a potential flow solution based on transient Green function for the external ship hydrodynamics with a viscous flow solution based on a multiphase interface capturing volume of fluid(VOF) technique for the interior sloshing motion. The coupled algorithm accounts for full nonlinear slosh forces while the external forces on the hull are determined through a blended scheme of linear radiationdiffraction with nonlinear Froude-Krylov and restoring forces. Consideration of this level of nonlinearities in ship motions is found to have non-negligible effects on the slosh-coupled responses and slosh-induced loads. A scheme is devised to evaluate the statistical measure of the pressures through long-duration simulation studies in extreme irregular waves. It is found that coupling significantly influences the tank interior pressures, and the differences in the pressures between coupled and uncoupled cases can be as much as 100% or more. To determine the RAO over the frequency range needed for the simulation studies in irregular waves, two alternative schemes are proposed, both of which require far less computational time compared to the conventional method of finding RAO at each frequency, and the merits of these are discussed.     

Review of the uncertainties associated to hull girder hydroelastic response and wave load predictions

This paper reviews the importance of uncertainties in hull girder loads influenced by flexible fluid structure interactions. The focus is on developments in the field of hydroelastic modelling, simulation and model tests of practical relevance to the prediction hull girder wave load predictions and their validation. It is concluded that whereas hydroelastic methods for use in design development and assessment become increasingly useful, challenges in realizing and modelling uncertainties can be attributed to: (1) the limitations of numerical methods to suitably model nonlinearities; (2) the ambiguity of model tests; and (3) the systematic use of data emerging from computational, model- or full-scale methods. An approach is recommended to assess the uncertainty in the hydroelastic responses to wave loading and an example is provided to demonstrate the application of the procedure.     

Experimental study on the nonlinear pressure acting on a high-speed vessel in regular waves

It is well known that the hydrodynamic responses of a high-speed vessel traveling in regular head waves of even moderate wave height can show significant nonlinear behavior, and so linear statistical techniques become insufficient for predicting the statistics of responses in irregular waves. On the other hand, it has been shown that an approximate third-order Volterra model is applicable to handling the statistics of some nonlinear seakeeping problems, such as motions and vertical hull girder loads. In the present study, the focus is on the nonlinear behavior of the pressure responses of the hull surface, especially on the pressures acting on alternately wet and dry areas near the waterline and on the bow zone with high deadrise angles that may be subject to slight impact and water pile-up effects. To clarify the validity of applying Volterra modeling to this problem, a series of experiments in regular and irregular head waves were carried out, and approximate third-order and fifth-order Volterra models with the proposed algorithm for finding frequency response functions (FRFs) were applied as a means of validation. In the present article, the first part of the validation was performed using experimental data in regular waves. It was confirmed that the third-order Volterra model has adequate accuracy to simulate deterministically the variation of pressure responses in regular waves of different wave steepness up to a wave amplitude to wavelength ratio of 0.01 even for the highly nonlinear pressures acting on the above-mentioned areas of the hull surface.     

Parametric dependencies of the post-ultimate strength behavior of a ship’s hull girder in waves

To rationally assess the consequence of a ship’s hull girder collapse, it is necessary to know the post-ultimate strength behavior of the hull girder including the global deformation and motions under extreme wave-induced loads. In the foregoing research, the authors proposed a numerical analysis system to predict the collapse behavior in waves including the post-ultimate strength behavior. The primary objective of the present paper is to clarify the parametric dependencies of the severity of the collapse in a rational manner. The parameters may include those related to load-carrying capacity and the extreme loads. To this end, an analytical solution to describe the post-ultimate strength behavior is derived. Assuming that a plastic hinge is formed at the midship during the collapse procedure, the whole ship is modeled as a two-rigid-bodies system connected to each other amidship via a nonlinear rotational spring, which represents the nonlinear relationship between the bending moment and the rotational angle. The relationship may be modeled as piece-wise linear curves. It is further assumed that large motions and elastic/plastic deformations of the hull girder may not affect the load evaluations, and that the hull girder is subjected to a large single wave. Some important parameters to predict the severity of the collapse are specified based on the analytical solution.     

A parametric study on water-entry of a twin wedge by boundary element method

High speed catamarans are used for pleasure, racing as well as passenger transportations. Optimal design of these crafts requires knowledge of sea loads exerted on their structures. The total load may be estimated by integration of loads exerted on a series of two-dimensional sections along the hull. In order to access the cross-sectional loads, the problem may be simplified to solve the water-entry problem of a twin hull. In this paper, water-entry problem of a twin wedge at constant vertical water-entry speed is studied. The problem is solved in the framework of potential theory using boundary element method where gravity effect on the flow is neglected. A simplified model based on Wagner theory is employed. Free surface elevation and pressure distribution on the body in different deadrise angles have been evaluated. A parametric study has been done to investigate effects of deadrise angle, distance between demi-hulls and free surface elevation on maximum pressure coefficient. Finally, a regression formula for maximum pressure coefficient has been proposed. Results of parametric study reveal that as time advances the interaction between two demi-hull gets more severe, besides the interaction effect on pressure coefficient is nonlinear.     

舰船波浪弯矩响应的频率特性

非直壁式舰船在高浪级和高航速下的弯矩响应中,除了含有低频遭遇频率成分外,还存在着一定数量的遭遇频率的倍频成分及船体各谐调的垂向总振动频率成份,它们都会对舰船波浪弯矩的非线性响应产生相应的影响。如果舰船的第一谐调垂向总振动频率正好是遭遇频率的整数倍,这时弯矩的非线性响应将达到极值。本文从模型试验及理论计算两方面分析了舰船波浪弯矩的频率特性,对船体载荷响应理论的发展及设计载荷的确定具有指导意义。     

Practical estimation methods of the design loads for primary structural members of tankers

Various design loads used in the strength evaluation of ship structures have been introduced currently by classification societies. As most of these design loads have been determined as the standard loads for the sake of convenience, the relationships between the design loads and the sea states actually encountered by ships seem to be weak. Accordingly, it may be difficult to refer and utilize them as the fundamental design concepts for ship designers or the operational guidelines for ship operators. To overcome these difficulties, the authors have developed practical estimation methods of the design loads having transparent and consistent backgrounds to the actual loads acting on primary structural members of tankers. In this paper, the design sea states that closely resemble the actual sea states which are considered as the most severe for hull structures are firstly proposed. Secondly, the practical estimation methods of the design sea states are proposed by parametric studies using the results of series calculation of representative tankers. Thirdly, the practical estimation methods of design regular waves resulting in the same level of stresses with that induced in irregular waves under the design sea states are proposed. Finally, the practical estimation methods of the design loads such as ship motions, accelerations, hull girder bending moments and hydrodynamic pressures that are induced under design regular waves are proposed.     

内倾船型的非线性横摇仿真分析

为解决内倾船型的非线性横摇工程分析问题,以内倾船型为对象,基于横摇、纵摇和升沉相互独立的假设,以线性耐波性计算软件预报的响应函数为基础,开发能计入船舶横倾过程中复原力臂的非线性因素对耐波性影响的预报软件,该软件可用于确定不同船型方案的非线性横摇时历曲线.采用该软件完成内倾船型与常规船型之间非线性横摇的差异对比,提出内倾船型在设计中需注意的地方：在设计过程中宜综合考虑内倾幅度与运动之间的影响后再确定内倾程度;采取措施减少内倾船型的纵摇幅值可在一定程度上减少内倾船型的横摇.     

耗散系数修正对波浪载荷预报的影响研究

在参考模型试验结果选取适当月池自由面耗散系数的基础上,对目标船进行波浪载荷预报。选取合理的月池自由面耗散系数,以准确模拟月池围壁压力;进而准确计算月池开孔对船体梁波浪载荷的影响,形成一套数值计算与模型试验相结合的带月池船体梁波浪载荷预报方法。研究成果为船舶波浪载荷预报提供参考。     

基于局部横向强度要求的船舶侧向承载板厚度设计研究

液体的压强作用一直是船体外板、液舱舱壁等位置板厚设计的主要考虑因素之一,且可归结为局部板格在侧向载荷作用下不屈服的安全衡准问题。结合理论分析及非线性有限元数值计算,对于受侧向载荷作用的局部板格极限强度的影响,探讨了包括边界条件、大挠度问题及相应的薄膜效应等各种影响因素,论证了一种优化的受侧向载荷作用的船体板厚约束设计公式,该公式经济适用且安全。整个探讨过程为船体结构规范的进一步完善提出了建议。     

Two- and three-dimensional hydroelastic modelling of a bulker in regular waves

The relatively high rates of bulk carrier casualties in recent years, as well as structural features such as large deck openings, make this vessel type a suitable example for investigating the influence of hydroelastic modelling on predicting wave-induced loads and responses. Two- and three-dimensional fluid–flexible structure interaction models, due to their different degree of complexity and associated data requirements, can be used at different stages of the design process when estimating wave-induced loads, namely preliminary and detailed design stages, respectively.

In this paper, therefore, two- and three-dimensional hydroelasticity theories are applied to predict and compare the dynamic behaviour of a bulk carrier hull, based on OBO MV Derbyshire, in waves. Both symmetric and antisymmetric motions and distortions are incorporated in these investigations. The three-dimensional structural model consists entirely of shell finite elements, representing all major external and internal structural components, whilst the two-dimensional model is generated using Timoshenko beam finite element and finite difference discretisations. Issues relevant to the structural modelling stage, for both idealisations, are discussed. The in vacuo dynamic characteristics are compared for all models, with particular emphasis on the influence of hatch openings, shear centre and warping on the antisymmetric dynamics of the structure. For the wet analysis the fluid–flexible structure interaction is carried out using two-dimensional (Timoshenko beam and strip theory) and three-dimensional (beam and shell finite element idealisations combined with potential flow analysis based on pulsating source distribution over the mean wetted surface) analyses. Comparisons are made between steady-state responses predicted by two- and three-dimensional models in bow quartering regular waves.

It is shown that whereas the predicted symmetric dynamic responses obtained from two- and three-dimensional models are in good agreement, differences are observed for the antisymmetric dynamic characteristics. It is thought that this may be due to inadequacies in the beam models employed when simulating the global dynamic behaviour of this highly non-prismatic hull girder whilst allowing for the effects of warping.     

A comparison of hydrodynamic impacts prediction methods with two dimensional drop test data

The effect of hydrodynamic impacts on a ship's bow structure is an important design consideration. In addition, to possible failure to local structure, such impacts can generate slam-induced whipping loads, the magnitude of which when combined with ordinary wave induced loads, could lead to first passage failure of a ship's hull girder. This paper presents the results of a recent study that compares select methods of predicting hydrodynamic impacts with available test data of 2-D wedge shaped section shapes. Results based on peak pressures at different impact velocities are presented. The results are compared with traditional prediction theories of Wagner and Chuang.     

分体式船体设计的水下测绘AUV回转运动的建模和分析（英文）

There is much need for autonomous underwater vehicles(AUVs) for inspection and mapping purposes.Most conventional AUVs use torpedo-shaped single-rigid hull,because of which their manoeuvrability is limited.Moreover,any increase in payload results in a larger hull size and the turning diameter,limiting its operation in constrained areas.As a solution to this problem,we develop M-Hull,a subsurface mapping AUV with a modular-split hull design that provides better manoeuvrability than a conventional torpedo-shaped vehicle.At the same time,it has more agility than an unconventional bio-inspired snake-like vehicle though their designs look similar.This approach makes it a hybrid solution between conventional torpedo-shaped AUVs and unconventional bio-inspired vehicles.We focus on improving the turning diameter during the mapping operation,and hence this paper concentrates on the dynamic aspects of the 2 D turning motion of the vehicle.It will provide the relationship between turning speed,thrust,and joint torque requirements for the multi-hull underwater vehicle.Different turning modes are compared to choose an optimum turning configuration,and the critical speed is calculated for the vehicle's safe operation.In the end,the modelling is verified using the experimental data.One can follow the method followed here for the 2 D motion analysis of similar underwater vehicles.     

Experimental and numerical study of containership responses in severe head seas

An accurate determination of the global load effects in a ship is vital for the design of the vessel. This paper addresses an experimental and numerical study of containership responses in severe head seas. Experimental results were obtained using a flexible model of a containership of newer design. The experiments showed that, taking hull flexibility into account, the fourth and sixth harmonic of the vertical bending moments had a maximum value of between 25% and 50% of the first harmonic. We also demonstrated that hull flexibility can increase the vertical bending moment by up to 35% in sea states relevant for design. Comparisons of moments found experimentally with results from a nonlinear hydroelastic strip theory method showed that the effect of nonlinearities on the rigid body moments was slightly over-predicted in the aft body. The method also tends to over-predict the increase of the bending moments due to hull flexibility. In general however, the numerical results compared reasonably well with the experimental ones.     

船体在波浪中的非线性水动压力

本文提出了一个预报船体在波浪中大幅运动时非线性水动压力场的二维时域理论。船体扰动势用时域自由面格林函数和在入射波下的瞬时湿表面上的分布源求解;与非线性水动压力场相匹配的船体运动用差分法求得。为提高计算效率和避免数值过程发散,采用了改进的数值模型和方案。通过线性理论计算与模型试验结果的比较,指出了线性切片理论在预报水动压力场时的不足,水动压力与波高的非线性关系及正负水动压力沿船体表面的分布在Wigley船的计算比较中得到了说明。初步计算表明,该理论的实用化发展前景是令有鼓舞的。相应的计算机程序可在PC机上运行。     

不同海况下艏部砰击及鞭状效应的试验与数值分析

为了更深入地研究船舶的鞭状效应,在拖曳水池中对某船进行了艏部砰击及鞭状效应分段模型试验研究。提出了一种可以考虑砰击力的非线性水弹性计算方法。并改进了传统的分段模型,采用变截面梁对船体刚度进行模拟以更好地接近实船。在规则波迎浪下观察到了严重的艏部砰击现象。试验数据表明,当波高从5.6m增大到21m时,由于鞭状效应原因,总弯矩相比低频波浪弯矩的增大值从24.64%增长到92.02%。最后,将不同海况下的测量结果与基于线性与非线性水弹性理论的计算结果进行了比较分析,初步验证了文中方法和程序在预报船体波浪载荷中的适用性。     

船舶砰击强度计算方法研究

船舶在航行时发生砰击是一种高度非线性的物理现象。本文基于势流理论Rankine源法,研究用时域非线性方法计算船舶运动响应,获得船波垂向相对运动速度;并选取合适的砰击压力系数,计算船舶砰击载荷。最后用该方法评估了一艘集装箱船艏部砰击强度,验证了该方法的合理性。     

不同航速下船体波浪诱导运动和载荷计算研究

应用三维时域水动力理论,以挪威船级社（DNV）的WASIM程序系统作为主要工具,分析研究了一条在国际航线上航行的某一集装箱船的水动力特性,包括船体运动与波浪诱导载荷的规律,给出了不同航速下的船体运动特性和剖面诱导载荷百年一遇长期预报结果,深入分析了船体的航速效应,为船体设计中船体波浪载荷设计提供了参考依据。     

Ultimate strength of container ships subjected to combined hogging moment and bottom local loads part 1: Nonlinear finite element analysis

This paper is the first of two companion papers concerning the ultimate hull girder strength of container ships subjected to combined hogging moment and bottom local loads. In the midship part of container ships, upward bottom local loads are usually larger than the downward ones. This leads to the increase of biaxial compression in the outer bottom plating and the reduction of the ultimate hull girder strength in the hogging condition. In this Part 1, the collapse behavior and ultimate strength of container ships under combined hogging moment and bottom local loads are analyzed using nonlinear finite element method. Buckling collapse behavior of bottom stiffened panels during the progressive collapse of a hull girder is closely investigated. It has been found that major factors of the reduction of ultimate hogging strength due to bottom local loads are (1) the increase of the longitudinal compression in the outer bottom and (2) the reduction of the effectiveness of the inner bottom, which is on the tension side of local bending of the double bottom. The obtained results will be utilized in the Part 2 paper to develop a simplified method of progressive collapse analysis of container ships under combined hogging moment and bottom local loads.