Equivalent design pressure for ship plates subjected to moving slamming impact loads

When a ship navigates at sea, the slamming impact can generate significant load pulses which move up along the hull plating. The effect of the moving pressure has so far not been explicitly considered in the Rules and Regulations for the Classification of Ships. Based on a modal superposition method and the Lagrange equation, this paper derives analytical solutions to study the elastic dynamic responses of fully clamped rectangular plates under moving pressure impact loads. The spatial variation of the moving slamming impact pressure is simplified to three types of impact loads, i.e. a rectangular pulse, a linearly decaying pulse and an exponentially decaying pulse. The dynamic responses of fully clamped rectangular plates under the moving slamming impact pressure are calculated in order to investigate the influence of the load pulse shapes and moving speed on the plate structural behaviour. It is found that the structural response of the plate increases with the increase of the moving speed. The response of the plate subjected to a moving pressure impact load is smaller than the case when the plate is subjected to a spatially uniform distributed impact load with the same load amplitude and load duration. In order to quantify the effect of the moving speed on the dynamic load, a Dynamic Moving Load Coefficient (DMLC) is introduced as the ratio between the dynamic load factor for the moving impact load and that under the spatially uniform distributed impact load. An expression for DMLC is proposed based on analyses of various scenarios using the developed analytical model. Finally an empirical formula which transforms the moving impact loads to an equivalent static load is proposed.     

Numerical study on the dynamic response of a truncated ship-hull structure under asymmetrical slamming

Dynamic response of ship-hull structure under slamming has tracked widespread attention in the marine structural design. However, our understanding on the dynamic characteristics largely relies on the symmetrical slamming cases. This paper presented a preliminary numerical investigation on the dynamic response of a truncated ship-hull structure under asymmetrical slamming based on the uncoupled CFD-FE method. Asymmetrical slamming loads were predicted through combining the seakeeping analysis and CFD method. In there, three kinds of motions (vertical, horizontal and roll motions) of 2D ship sections were obtained through the seakeeping analysis and then the slamming pressure was predicted through simulating the water entry with various motions based on CFD method. The dynamic response was analyzed through finite element method. Numerical predictions including ship motions, slamming loads and dynamic analysis were validated against published experimental data and numerical calculations. The characteristics of asymmetrical slamming loads were analyzed showing obvious asymmetry in space, and the dynamic characteristic of the ship bow structure was further clarified through discussing the deformation and stress distribution. These results are useful for readers for better understanding the dynamic characteristics of the bow structure under slamming.     

船首外飘砰击设计载荷直接计算

文章结合三维线性势流理论和砰击速度的长期分析方法,求解出船体外飘位置的设计砰击速度;以首垂线和静水面交点处的设计砰击速度为目标值,给出了用于确定船首外飘砰击设计载荷的等效设计波,进而得到了设计状态下船体外飘剖面与波面相对运动关系;将船体剖面与波面间的相对运动关系等效转化为船体剖面与静水面的相对运动,利用显式有限元方法实现了外飘剖面砰击设计载荷的预报。针对直接计算方法中涉及的设计砰击速度、砰击压力和砰击压力系数,对比分析了文中结果和相应的规范值或试验值,论证了文中船舶外飘砰击压力设计载荷直接计算方法的合理性。     

耦合板结构振动波传递及能量分布可视化研究

利用振动声强及能量可视化技术研究板结构中振动波传递及分布特性。首先介绍了结构振动声强分量的计算和流线可视化的相关理论以及振动能量流的计算公式;基于MATLAB与APDL语言编写了集成可视化计算程序,并介绍了程序实现流程。在数值计算中,先验证了可视化程序的有效性;以L形耦合板为例,实现振动波能量传递和分布的可视化,证明了计算程序的实用性和创新性;同时初步讨论了不同激励频率对能量传递及分布的影响,得到了一些有益的结论。振动波传递和分布可视化技术为进行合理优化的振动噪声控制提供了科学的依据。     

Prediction of slamming pressure considering fluid-structure interaction. Part II: Derivation of empirical formulations

This is Part II in a series of papers. Part I [1] investigated the slamming responses of flexible flat stiffened steel and aluminum plates using the nonlinear explicit finite element code LS-Dyna with the Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver. Subsequently, a simplified finite element FSI model of water hitting structures that is realistically close to the slamming phenomenon occurring on the bottom part of offshore structures was proposed. The proposed FSI methodology presented in Part I was verified by comparison with the relevant test data. It was evident that the use of the proposed numerical method presented in Part I was very effective for a benchmarking investigation of slamming load considering the hydroelastic effect. However, the method required much effort in terms of computation time and power analysis resources. The present study, Part II, aimed, as an alternative to the FSI analysis approach, to develop empirical formulae for prediction of slamming loads acting on deformable flat stiffened plates used in marine applications. This paper begins by describing the limitations of the existing approaches based on theoretical, experimental and even numerical studies conducted in the past for estimation of slamming loads. Next, it presents, based on the simulation methodology developed in Part I, rigorous parametric studies that had been performed on actual scantlings of marine-seagoing structures. The effects of structural geometry and water impact velocity on slamming pressure are then investigated in detail. Subsequently, the parametric results are analyzed and utilized to derive empirical formulations for the prediction of slamming loads acting on flat stiffened plates of marine structures. The accuracy and reliability of the proposed formulations are established by comparison with the results of the test and other existing formulations. The proposed formulations are expected to be used for the purposes of the design without any time-consuming FSI analysis of advanced and optimal structures that are robust to slamming.     

Benchmark study on slamming response of flat-stiffened plates considering fluid-structure interaction

This paper presents a benchmark study on the slamming responses of offshore structures’ flat-stiffened plates. The objective was to compare the fluid-structure interaction (FSI) simulation methodologies, modeling techniques, and established researchers' experiences in predicting slamming pressure. Three research groups employing the most common commercial software packages for numerical FSI simulations (i.e. LS-Dyna ALE, LS-Dyna ICFD, ANSYS CFX, and Star-CCM+/ABAQUS) participated in this study. Wet drop test data on flat-stiffened aluminum plates of light-ship-like bottom structures available in the open literature was utilized for validation of the FSI modeling. A summary of the experimental conditions including the geometry model and material properties, was distributed to the participants prior to their simulations. A parametric study on flat-stiffened steel plates having actual scantlings used in marine installations was performed to investigate the effect of impact velocity and plate rigidity on slamming response. The FE simulation results for the total vertical forces acting on the stiffened plates and their structural responses to those forces, as obtained from the participants, were analyzed and compared. The reliable and accurate predictions of slamming loads using the aforementioned commercial FSI software packages were evaluated. Additionally, equivalent static slamming pressures resulting in the same permanent deflections, as observed from the FSI simulations, were reported and compared with analytical models proposed by the Classification Standards DNV and existing experimental data for calculation of the slamming pressure. The study results showed that the equivalent load model depends on the water impact velocity and plate rigidity; that is, the equivalent static pressure coefficient decreases with an increase in impact velocity, and increases when impacting structures become stiffer.     

Numerical and experimental analysis of bow flare slamming on a Ro–Ro vessel in regular oblique waves

A method for the prediction of slamming loads on ship hulls is presented and validated for a 20-knot, 120-m car carrier. A nonlinear strip theory is used to calculate the relative motions of ship and wave. The relative vertical and roll velocities for a slamming event are given as input to the slamming calculation program, which is based on a generalized two-dimensional Wagner formulation and solved by the boundary element method. The method is fast and robust. Model tests of a car carrier have been carried out in regular head, bow, and bow quartering waves of various heights. Slamming on two panels in the upper part of the bow flare has been studied. It has been found that the water pile-up around the bow due to the forward speed of the vessel significantly increases the slamming pressures. A simplified way of including this effect is presented. When the calculated slamming pressures are corrected for 3D effects, they compare well with the measured data. Since the effect of the wave elevation due to the forward speed and the effect of three-dimensional flow act in opposite directions, excluding both of them produced results that also agreed quite well with the experiments, especially for the most severe slamming events.     

加载船模振动特性的数值与实验研究（英文）

In this paper, the vibration characteristics of the structure in the finite fluid domain are analyzed using a coupled finite element method. The added mass matrix is calculated with finite element method(FEM) by 8-node acoustic fluid elements. The vibration characteristics of the structure in the finite fluid domain are calculated combining structure FEM mass matrix. By writing relevant programs, the numerical analysis on vibration characteristics of a submerged cantilever rectangular plate in finite fluid domain and loaded ship model is performed. A modal identification experiment for the loaded ship model in air and in water is conducted and the experiment results verify the reliability of the numerical analysis. The numerical method can be used for further research on vibration characteristics and acoustic radiation problems of the structure in the finite fluid domain.     

拖航工况下半潜平台撑杆波浪砰击敏感性研究

半潜式平台在拖行过程撑杆等细长结构承受的波浪砰击对结构安全影响较大，相关船级社规范中明确要求结构分析过程中需要考虑波浪砰击载荷。基于传统势流理论的数值方法已经被广泛的应用于浮式海洋平台的水动力和砰击载荷的研究，但是对于复杂的粘性干涉效应、波浪爬升、波浪破碎和波浪砰击等实际工程问题不能够运用势流理论准确模拟。非定常的计算流体力学CFD (Computational Fluid Dynamics)方法能够较为准确解决上述问题。因此，本文以982半潜式海洋平台为研究对象，采用计算流体力学中的动态重叠网格方法和流域体积域方法VOF(volume of fluid)，结合水池物理模型试验结果，对平台在拖行工况下撑杆的波浪砰击进行研究。主要对半潜平台撑杆在三种不同流速和风速的拖航工况下撑杆受到的砰击压力的敏感性进行了分析研究，分析波浪砰击下撑杆的瞬态砰击压强分布情况，得到波浪砰击压力危险区域，同时给出拖航工况下撑杆砰击压力系数的变化规律，为分析预报半潜式平台撑杆在复杂的拖航海况下受到的砰击压力提供了参考。     

Experimental and numerical investigations on vibration characteristics of a loaded ship model

In this paper, vibration characteristics of the structure in the finite fluid domain are analyzed using a coupled finite element method. The added mass matrix is calculated with finite element method (FEM) by 8-node acoustic fluid elements. Vibration characteristics of the structure in finite fluid domain are calculated combining structure FEM mass matrix. By writing the relevant programs, numerical analysis on vibration characteristics of a submerged cantilever rectangular plate in finite fluid domain and loaded ship model is performed. A modal identification experiment for the loaded ship model in air and in water is conducted and the experiment results verify the reliability of the numerical analysis. The numerical method can be used for further research on vibration characteristics and acoustic radiation problems of the structure in the finite fluid domain.     

参数横摇下大型集装箱船外飘砰击的近似计算方法（英文）

Since the research of flare slamming prediction is seldom when parametric rolling happens, we present an efficient approximation method for flare slamming analysis of large container ships in parametric rolling conditions. We adopt a 6-DOF weakly nonlinear time domain model to predict the ship motions of parametric rolling conditions. Unlike previous flare slamming analysis, our proposed method takes roll motion into account to calculate the impact angle and relative vertical velocity between ship sections on the bow flare and wave surface. We use the Wagner model to analyze the slamming impact forces and the slamming occurrence probability. Through numerical simulations, we investigate the maximum flare slamming pressures of a container ship for different speeds and wave conditions. To further clarify the mechanism of flare slamming phenomena in parametric rolling conditions, we also conduct real-time simulations to determine the relationship between slamming pressure and 3-DOF motions, namely roll, pitch, and heave.     

基于CFD技术的砰击载荷强度直接计算

研究基于CFD技术的船舶砰击载荷预报及强度的直接计算,以通过对船波相对运动的短期预报得到入水速度极值,由积分变换得到入水速度的时历曲线,以CFD软件实现船体典型剖面入水砰击载荷的计算,得到船体剖面压力的空间分布,结果表明,船体剖面的压力随着位置高度的增加呈减小趋势,最后通过对某集装箱船进行有限元强度评估,验证了本文砰击强度直接计算方法的合理性和实用性。     

Efficient calculation of slamming pressures on ships in irregular seas

An efficient method for calculation of the slamming pressures on ship hulls in irregular waves is presented and validated for a 290-m cruise ship. Nonlinear strip theory was used to calculate the ship–wave relative motions. The relative vertical and roll velocities for a slamming event were input to the slamming calculation program, which used a two-dimensional boundary element method (BEM) based on the generalized 2D Wagner formulation presented by Zhao et al. To improve the calculation efficiency, the method was divided into two separate steps. In the first step, the velocity potentials were calculated for unit relative velocities between the section and the water. In the next step, these precalculated velocity potentials were used together with the real relative velocities experienced in a seaway to calculate the slamming pressure and total slamming force on the section. This saved considerable computer time for slamming calculations in irregular waves, without significant loss of accuracy. The calculated slamming pressures on the bow flare of the cruise ship agreed quite well with the measured values, at least for time windows in which the calculated and experimental ship motions agreed well. A simplified method for calculation of the instantaneous peak pressure on each ship section in irregular waves is also presented. The method was used to identify slamming events to be analyzed with the more refined 2D BEM method, but comparisons with measured values indicate that the method may also be used for a quick quantitative assessment of the maximum slamming pressures.     

Bow door slamming of Ro/Ro ferries

This paper addresses the structural response of clam-type bow doors of Ro/Ro vessels under slamming loading conditions. The structural analysis is performed with the finite element code MSC/NASTRAN. The loading conditions were determined on the basis of towing tank tests, numerical calculation and regulations of classification societies. Slamming loads are applied statically and the FE code accounts for both material and geometrical nonlinearities. Apart from stress distributions, which are determined for different loading patterns, the results are used to calculate the forces and moments induced on the locking and securing elements, which secure the doors among themselves and the doors to the bow structure. The modelling methods reported may be used for the finite element analysis of similar structures. Such analyses of bow doors response under slamming loading could be submitted to classification societies for approval.     

矩形结构以一定倾角砰击水面所引起的流体动力特性分析

本文采用VOF和动网格方法、考虑限制水域边界条件的约束因素，利用CFD商业软件FLUENT通过求解脉冲砰击压力作用下具有自由表面限制水域上的Navier-Stokes方程来分析与观察一定倾角的矩形结构从一定高度自由落下砰击限制水域的水面所引起的三维流体动力现象，并与无倾角的矩形结构撞击有限水深水域的水面所引起的三维水面波动和水下压力场变化问题做对比分析。数值模拟结果表明采用本文所提出的数值方法可以对大型结构作用于封闭或开放水域的水面所激发起的水面波动和水下压力场变化进行有效的数值模拟。这一数值方法为工程上分析大型结构砰击限制水域水面所产生的水动力现象提供了一种实用的手段。     

铝合金穿浪双体船波激振动响应计算研究

对穿浪型双体船在波浪中航行时的受载状况进行研究,采用规则波理论计算其所受波浪外载荷。利用有限元法建立了铝合金穿浪双体船波激振动响应数值计算模型。基于水弹性理论,采用所建立的数值模型对某全铝合金穿浪双体船高海情试验进行了数值模拟,将数值模拟结果与实船试验数据进行了比较,证明本文方法可靠。进行了该船受6级海况波浪激励的振动响应计算,发现全铝合金穿浪双体船波激振动位移响应较大,远大于常规单体船。还发现高海情中航行时的波激振动应力响应值亦较大。     

基于改进Wagner方法的轴对称体入水“后时段”砰击载荷数值计算

文章基于三维边界元方法研究了三维轴对称体入水砰击载荷的数值算法。算法从三维力学模型出发,继承Wagner自由液面抬升理论,引入浸深因子Cw以确定自由液面抬升高度,将自由液面线性化处理,同时考虑网格运动,在自由液面附近对网格进行截断重构,以确保水下湿面积的精准。算法中使用考虑加权运动项的非线性伯努利方程计算得到入水结构的表面压力,进一步积分可得入水结构的总体受力;另外,算法中引入虚拟面元的概念,将砰击载荷计算时历延长至液面高于坠物制高点之后,扩大了传统入水载荷计算的时历范围,并且文中引用Alaoui半球入水试验,对算法的正确性及适用性进行了验证。     

Experimental study of slam-induced stresses in a containership

Experiments for the ship motions and sea loads were carried out on a segmented model of a container ship in ballast condition. Comparisons between the measurements and the theoretical results were carried out for the vertical motions and bending moments. For the evaluation of the primary stresses it is assumed that the total vertical bending moment induced by waves is divided into one component obtained by the linear theory and another one is due to the slamming loads. Several formulations for the determination of the slamming loads are compared with experimental results. The vibratory response of the model is calculated by modelling the hull with rotational springs and rigid links. Linear finite elements with a consistent mass formulation are adopted for the structural model and the response is obtained by modal superimposing and direct integration methods.     

基于混合两步法的船舶砰击载荷预报研究

文章针对船舶结构设计时重点关注的艏部砰击载荷问题,综合考虑计算效率及精度,提出了基于势流理论和计算流体力学方法的混合两步法。第一步,采用三维势流理论预报波浪中有航速船舶的运动响应,分析船波相对运动;第二步,根据预报砰击载荷所在位置的船体横剖面,建立等截面的三维立体模型,采用基于有限体积法与动网格技术的计算流体力学方法,基于第一步得到的相对运动结果模拟落体入水过程,计算砰击压力。使用该两步法预报了某超大型油轮在压载工况顶浪航行时候的艏部砰击压力,并讨论了相对运动和砰击压力的时域历程规律。文中数值预报结果得到了水池模型实验的验证,表明该方法的可行性和预报结果的合理性。     

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。