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.     

Development of simplified method for prediction of structural response of stiffened plates under explosion loads

During their lifetime, marine structures may be exposed to accidental loadings such as from collisions or explosions, as well as environmental loadings such as from slamming, sloshing and green water. Such loadings can cause damage to structures. Therefore, to minimize such damage, advanced and robust design guidelines should be formulated. Among those loads, in this study, explosions imparting an impulsive pressure loading containing a rapid increase in pressure and a short duration that can cause serious casualties, property losses, and marine pollution were considered. In this paper, a practical and robust method for damage assessment of marine structures exposed to explosion loads based on a single degree of freedom (SDOF) system and numerical simulations is proposed. The SDOF method was improved by introduction of new and better idealization resistance for the system and consideration of the effect of strain-rate, and subsequently was verified by a numerical method developed using the commercial ABAQUS software package. The numerical method was itself validated by comparison with relevant pulse pressure test data available in the open literature (good correlation was shown). Based on the validated numerical models, a rigorous parametric study of the structural response of stiffened plates having actual scantlings of offshore structures was performed. The numerically obtained maximum deformations were compared with the results from the improved SDOF method in a parametric study, and the variation of both methods was verified. Finally, simple yet accurate and reliable formulations for prediction of structural response were empirically derived. These formulations are expected to be usefully employed as a first-hand tool for prediction of damage extent of marine structures (including offshore structures) due to explosion loads.     

A study on slamming pressure on a flat stiffened plate considering fluid–structure interaction

Normally, the design slamming pressure on the bottomof a semi-submersible-type floating rig is determined in a simple way using the relative speed obtained from an air-gap analysis. However, few studies have taken a thorough, robust, and deep-background approach to the estimation of design pressure. To investigate the slamming pressure on the bottom of a semi-submersible rig, a simplified deformable stiffened plate of a zero-degree deadrise angle is simulated using the nonlinear FEM software LS-DYNA, which can take the influence of fluid–structure interaction (FSI) into account. Various parametric studies are carried out to examine the effects of structural flexibility, coupling stiffness, mesh size, velocity, stiffener size, and air cushion. The pressure response on the plate by the coupling of fluid and structure is studied and the FSI effect of each parameter is discussed. Then, equivalent transient and static loads that result in the same maximum or permanent deformation as FSI are evaluated for design purposes through a series of parametric studies.     

典型舱内爆炸载荷对加筋板的毁伤特性

[目的]为研究典型舱内爆炸载荷对加筋板的毁伤特性,将舱内爆炸载荷分为初始爆炸冲击波载荷和准静态气压载荷,利用有限元分析软件LS-DYNA开展爆炸载荷下固支单向加筋板毁伤特性的数值模拟。[方法]主要模拟载荷冲量相等和载荷峰值相等时固支单向加筋板的变形特性,以及加筋板分别在初始爆炸冲击波载荷、准静态气压载荷及2种载荷联合作用下的毁伤特性,并分析上述载荷作用下加筋板的变形特点。[结果]结果表明:当作用在加筋板上的冲量相等、载荷作用时间小于0.05倍垂向一阶自振周期时,加筋板的最终挠度值处于最大值附近;当载荷峰值相同时,存在饱和冲量值,达到饱和冲量值以后,载荷作用时间不再影响加筋板的最终变形。[结论]在舱内爆炸载荷作用下,加筋板的最终变形不是2种载荷作用下的简单叠加,2种载荷的联合作用会增强毁伤效果。     

Design method for steel deck plates under quasi-static patch loads with allowable plastic deformations

Plastic deformation of plates in steel deck structures under heavy vehicle or helicopter wheel loads is common in ships and offshore structures, and is therefore of significant interest to designers of ro-ro/cargo ships, helicopter-carrying ships and offshore platforms. To provide insight into the plastic deformation of plates, the nonlinear elasto-plastic response of stiffened steel plates loaded quasi-statically by a central rigid rectangular indenter is investigated both experimentally and numerically. The numerically-determined stiffened plate permanent deflections compare well with those obtained experimentally. The concept of applying the elasto-plastic method to the design of deck plates under wheel patch loads is introduced, and the design principle of wheel patch loaded plating is studied together with the design criteria. A simple design formula to determine plating thickness is proposed based on an acceptable level of permanent set. Ship-mounted helideck plating design cases are given to illustrate the elasto-plastic method, and comparisons are made between the thicknesses derived using the proposed design formula and those found from Lloyd's Register (LR), Bureau Veritas (BV) and DNV-GL rule requirements.     

Review of ship slamming loads and responses

The paper presents an overview of studies of slamming on ship structures. This work focuses on the hull slamming, which is one of the most important types of slamming problems to be considered in the ship design process and the assessment of the ship safety. There are three main research aspects related to the hull slamming phenomenon, a) where and how often a slamming event occurs, b) slamming load prediction and c) structural response due to slamming loads. The approaches used in each aspect are reviewed and commented, together with the presentation of some typical results. The methodology, which combines the seakeeping analysis and slamming load prediction, is discussed for the global analysis of the hull slamming of a ship in waves. Some physical phenomena during the slamming event are discussed also. Recommendations for the future research and developments are made.     

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.     

New simplified approach to collapse analysis of stiffened plates

A new simplified model for collapse analysis of stiffened plates is developed in the framework of the idealized structural unit method (ISUM). By idealizing material and geometrical nonlinearities, larger structural units are defined as an element in ISUM than in conventional finite element analysis (FEA). The proposed stiffened plate model consists of ISUM plate elements and beam-column elements. The formulation of the plate element is performed by introducing accurate shape functions to simulate the buckling/plastic collapse behaviour of plate panels. Combining plate and beam-column elements allows for both local buckling of the plate panel and overall buckling of the stiffener.Fundamental collapse modes of plate panels and stiffened plates are investigated by conventional FEA. According to the observed characteristics, the new simplified model is formulated. Comparisons with FEA demonstrate the accuracy of the simplified model and its high applicability to typical stiffened plates in marine structures.     

Experimental and numerical investigation on welding simulation of long stiffened steel plate specimen

The paper presents the results of metal inert gas T-joint fillet welding tests of small scale rectangular stiffened steel plates longer than the standard test specimen. In the literature the focus is typically on plates with a small aspect ratio and the present work deals with plates of higher aspect ratio, which are the typical ones in marine structures, aiming to determine if there is any significant effect of welding along the longitudinal direction. Nonlinear thermo-elasto-plastic finite element models are adopted to evaluate the temperature distribution, welding induced distortions and residual stress in the stiffened plates of shipbuilding steel. Given the difficulty in data acquisition of temperature-dependent properties of the material, a simplified model of the properties is proposed, based on the values at room temperature. Good agreement is observed between the measured and simulated temperatures, indicating that the current finite element approach is appropriate to simulate the welding process. The proposed simplified material model can be efficiently used in the finite element analysis of welded steel structures. It is concluded that the welding parameters have more significant influence on the structural responses than the dimension of the plate.     

Experimental and analytical investigations on the response of stiffened plates subjected to lateral collisions

Rational structural design of ships or offshore platforms against collisions requires prediction of the extent of damage to stiffened plates generated by lateral impact. In predicting the extent of collision damage, most researchers employ numerical analysis methods using commercial software packages. Like other structural problems, any nonlinear dynamic analysis methods should be substantiated with relevant test data prior to being employed for design. Unfortunately, full-scale collision tests on marine structures are very rare. Still, results from collision tests on marine structural elements can help to substantiate theoretical methods for collision analyses. Lateral collision test data for unstiffened plates are available, but it is difficult to find results from tests on stiffened plates in the open literature. In this paper, the results of lateral collision tests on 33 stiffened plates are reported. A simplified analytical method is developed for the prediction of the extent of damage to stiffened plates due to lateral collisions and this method is substantiated with the test results. Also proposed is a simple criterion with which the occurrence of crack damage can be judged.     

砰击载荷下轻质波纹夹芯夹层板动力响应特性分析

文章对轻质波纹夹芯夹层板(Light Weight Corrugated-Core Sandwich Plates,LWCCSP)在不同入水速度下(1-6 m/s)的流-固耦合非线性动力学行为进行了分析。建立了气—液—固三相数值模型,通过显式动力求解获得了轻质波纹夹芯夹层板砰击压力的分布特点及结构变形规律,并与同等质量的加筋板在流固砰击下的非线性力学行为进行了对比,并研究了轻质波纹夹芯夹层板主要设计参数对其砰击响应的影响。研究结果表明,轻质波纹夹芯夹层板较同等质量的加筋板表现出更好的抗砰击性能;下面板厚度、芯层厚度的增加在一定范围内可以有效提高轻质波纹夹芯夹层板的抗砰击性能。     

基于MPS-FEM耦合方法研究波浪与结构的相互作用（英文）

Nowadays, an increasing number of ships and marine structures are manufactured and inevitably operated in rough sea. As a result, some phenomena related to the violent fluid-elastic structure interactions(e.g., hydrodynamic slamming on marine vessels, tsunami impact on onshore structures, and sloshing in liquid containers) have aroused huge challenges to ocean engineering fields. In this paper, the moving particle semi-implicit(MPS) method and finite element method(FEM) coupled method is proposed for use in numerical investigations of the interaction between a regular wave and a horizontal suspended structure. The fluid domain calculated by the MPS method is dispersed into fluid particles, and the structure domain solved by the FEM method is dispersed into beam elements. The generation of the 2D regular wave is firstly conducted, and convergence verification is performed to determine appropriate particle spacing for the simulation. Next, the regular wave interacting with a rigid structure is initially performed and verified through the comparison with the laboratory experiments. By verification, the MPS-FEM coupled method can be applied to fluid-structure interaction(FSI) problems with waves. On this basis, taking the flexibility of structure into consideration, the elastic dynamic response of the structure subjected to the wave slamming is investigated, including the evolutions of the free surface, the variation of the wave impact pressures, the velocity distribution,and the structural deformation response. By comparison with the rigid case, the effects of the structural flexibility on wave-elastic structure interaction can be obtained.     

均匀受压含裂纹损伤加筋板的极限承载能力分析

在均匀受压下,针对含损伤裂纹缺陷的加筋板的承载力学特性进行研究,探讨了裂纹参数对其承载能力的影响。通过改变加筋板上裂纹的位置和裂纹尺寸,利用非线性有限元分析软件Abaqus对其进行系列非线性仿真分析,得到含损伤裂纹加筋板的破坏力学特性以及破坏模式。结果表明,损伤裂纹会削弱加筋板架的承载能力,并且当裂纹尺寸超过某临界值时,板架的极限承载力会急剧减小。     

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.     

计及水-空气-结构耦合的结构砰击载荷预报方法研究

船舶在恶劣海况下航行时,船体与波浪之间会发生剧烈的砰击现象,严重时会造成船体局部结构损坏或降低船舶总纵强度。随着工业技术的革新和海洋资源开发的需要,当代船舶不断向高速化和大型化发展,船舶发生砰击现象的概率也越来越高。开展结构砰击特性研究,准确地预报结构物的砰击载荷,对船舶航行和人员安全有重要的意义。本文基于水动力学软件 Fine/Marine,建立水域-空气域-结构耦合的分析模型,对楔形结构的砰击特性进行数值仿真分析,并研究不同斜升角及不同入水速度对砰击载荷的影响。     

客滚船首尾部砰击计算研究

客滚船的特殊线型——艏部外飘幅度较大和艉部的扁平肥大型结构,在营运过程中易受到砰击载荷的作用。由于该类船舶砰击问题显著,故一直是业内研究的热点。以某客滚船为例,针对其艏艉结构进行砰击计算,采用计算量适中,且可实现砰击载荷预报的频域法,将砰击载荷映射到相应各部分的有限元计算模型上,经计算分析,得到艏艉结构在砰击压力下的应力结果,最终实现对客滚船砰击强度的安全评估。整个计算探讨过程,可供同类船舶的设计研究人员借鉴。     

Uncertainty due to discretization on the ALE algorithm for predicting water slamming loads

Numerical uncertainty due to discretization on the Arbitrary Lagrangian-Eulerian (ALE) Finite Element method is investigated in the study. The paper quantifies uncertainty using two ITTC recommended methods, and also applies a constant Courant-Friedrichs-Lewy (CFL) number based discretization approach, instead of performing the independent grid and time-based discretization recommended by ITTC. As a case study, water entry of a flat bottom rigid and flexible plate is simulated considering various entry velocities. The total slamming loads and structural responses on both the rigid and elastic bottom plates are predicted and validated against available experimental data. Results indicate that numerical errors due to discretization differ in the various parameters and from case to case. They do affect the analysis of slamming loads and associated structural responses, and the hydroelasticity analysis as well. The hydroelasticity effects on the slamming force generally increase as the entry velocity increases, however, the quantitative results differ much for models with different grids. For example, when the hydroelasticity effect is estimated using the finer model, the deviation of the total slamming force on the elastic plate relative to the one on the rigid body are 56%, 57%, and 63% respectively for the three constant entry velocities, whereas the estimations are −27%, −4% and 3% with the coarser model. The study concludes that the uncertainty due to discretization in ALE is not just case-specific, but also parameter specific. The uncertainty quantification procedures with a constant CFL number based refinement are recommended to investigate the uncertainty comparing to the individual grid and time step study, in particular for the ALE solution where the time step is adjusted automatically as the grid changes. Thus, consideration should be given to updating the ITTC guidelines to incorporate the constant CFL based discretization approach.     

基于ALE算法的无转角和有转角铝制加筋板楔形体水弹性砰击的数值模拟研究

文章采用基于任意拉格朗日—欧拉(ALE)算法的显式有限元技术研究水弹性砰击现象,针对已开展的铝制加筋板楔形体结构入水砰击模型实验,开展了数值模拟比较工作。该楔形体底部斜升角为20度,底部两侧是包含三根纵骨和两根横梁的加筋板结构,两侧结构刚度不同。预报了模型无转角和有转角典型工况的砰击入水过程,得到的入水加速度、底部加筋板结构纵骨应力和横梁响应与模型实验结果吻合较好。研究表明该ALE算法具备模拟船舶局部结构的水弹性砰击流固耦合问题的能力。     

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.