A coupled FDM–FEM method for free surface flow interaction with thin elastic plate

A partitioned approach by the coupling finite difference method (FDM) and the finite element method (FEM) is developed for simulating the interaction between free surface flow and a thin elastic plate. The FDM, in which the constraint interpolation profile method is applied, is used for solving the flow field in a regular fixed Cartesian grid, and the tangent of the hyperbola for interface capturing with the slope weighting scheme is used for capturing free surface. The FEM is used for solving structural deformation of the thin plate. A conservative momentum-exchange method, based on the immersed boundary method, is adopted to couple the FDM and the FEM. Background grid resolution of the thin plate in a regular fixed Cartesian grid is important to the computational accuracy by using this method. A virtual structure method is proposed to improve the background grid resolution of the thin plate. Both of the flow solver and the structural solver are carefully tested and extensive validations of the coupled FDM–FEM method are carried out on a benchmark experiment, a rolling tank sloshing with a thin elastic plate.     

基于显式有限元方法的二维楔形体砰击压力系数预报

利用LS-DYNA软件对二维楔形体入水问题进行研究。基于显式有限元方法,选用任意拉格朗日-欧拉算法,建立了包含空气、水和楔形体的完全耦合的二维有限元模型,研究流场的射流现象与压力变化情况,预报了二维楔形体砰击压力系数,并与已公开发表的模型试验结果吻合较好,从而为后续砰击载荷计算提供可靠的方法。     

粘性流体晃荡与弹性结构的相互耦合作用

提出了处理粘性流体晃荡与弹性结构相互耦合作用的理论及相应数值计算方法.流体运动采用N-S方程描述,控制方程采用有限差分法离散,并由超松弛迭代法求解.液体自由表面通过流体体积法进行重构.为了考虑液舱结构变形对液体晃荡的影响,应用了FAVOR技术.由此建立了描述液体晃荡与结构相互耦合作用的水弹性理论,并由相应的计算方法进行了系列运算,以考察二维液舱不同结构刚度对液体晃荡的影响.计算结果有助于进一步理解此类问题的物理现象.     

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.     

Numerical simulation of the solitary wave interacting with an elastic structure using MPS-FEM coupled method

Fluid-Structure Interaction (FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method (MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit (MPS) method is used to calculate the fluid domain, while the Finite Element Method (FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.     

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.     

采用面向对象有限元法程序分析逆作法施工

将现代软件工程方法（面向对象方法）与有限元方法结合起来,开发了对逆作法施工进行数值模拟分析的面向对象三维有限元分析软件。其中土体力学本构模型采用修正剑桥模型,并且用试验数据进行了程序验证。然后用该程序对某市人防工程逆作法施工进行了数值模拟计算分析,通过两方案比较,最后提出有关施工建议。     

桁架式Spar平台与系泊/立管系统的全时域非线性耦合动态分析

开发了对浮式平台系统进行耦合动态分析的全时域程序。采用二阶时域方法计算水动力荷载,在此方法中,对物面边界条件和自由水面边界条件进行泰勒级数展开,利用Stokes摄动展开分别建立相应的一阶、二阶边值问题,而且此边值问题的计算域不随时间变化。采用高阶边界元方法计算每一时刻流场中的速度势,利用四阶预报校正法对二阶自由水面边界条件进行数值积分。在自由表面加入一个人工阻尼层来避免波浪的反射。对于系泊缆索/立管/张力腿的动力分析,在一个总体坐标系中对控制方程进行描述,采用基于细长杆理论的有限元方法进行求解。在耦合动态分析中,采用Newmark方法对平台和系泊缆索/立管/张力腿的运动方程同时进行求解。利用开发的耦合分析程序对一个桁架式Spar平台的运动响应进行了数值模拟,给出了平台的位移和系泊缆索/立管上端点的张力,并得到了一些重要结论。     

淹没高压射流垂直切削硬质黏土数值与试验研究

针对淹没高压水射流对硬质黏土进行切削的问题,基于耦合的欧拉-拉格朗日方法,引入射流经过淹没水域发生速度衰减规律,建立有限元模型对切削效果进行分析研究,最后通过室内试验加以验证。该方法集合了欧拉算法和拉格朗日算法的优点,适用于射流和土体之间流固耦合的分析计算,其中,水体采用欧拉算法,土体采用拉格朗日算法,水土的接触面可被精确捕捉。数值结果显示,高压射流作用下,硬质黏土切削深度随切削速度的增大而减小,随射流压力的增大而增大。并与试验结果进行定量对比,两者较为吻合。该模型较好地模拟了淹没条件下高压射流对硬质黏土的切削过程,为解决这一问题提供了新的思路。     

Numerical analysis of the hydroelastic behavior of a vertical plate due to solitary waves

Interactions of a vertical elastic plate with fully nonlinear water waves were simulated. Utilizing the mixed Eulerian Lagrangian method for the free-surface flow and the finite element method for the deflection of an elastic plate, a fully coupled scheme for accurately determining fluid–plate motions was developed. Using this scheme, some modifications to the solvers for both fluid and plate were made. A hybrid wave-absorbing beach was installed to prevent wave reflection from the end of the wave tank. A fourth-order Runge–Kutta time-marching scheme with a uniform time step was applied to achieve numerical stability. The method was validated by simulating the wave generated by the initial deformation of a vertical plate and comparing the result with the corresponding analytical solution. For further validation, the hydroelastic behavior of a vertical plate induced by a pulse-type wave (where the initial pulse-type elevation of the free surface is specified) was computed, and the result was compared with another numerical result from a mode-expansion method. The interaction of a surface-piercing plate with nonzero initial free surface was then simulated, and the result was compared with the corresponding linear analytical solution. Finally, the hydroelastic response of a surface-piercing vertical plate due to a solitary wave (generated by actuating the vertical plate at the right end of the tank only at the beginning) was computed and investigated systematically.     

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.     

深海系泊浮体物面非线性时域耦合动力分析

文章基于三维时域势流理论和弹性细长杆理论,研究并提出了深海系泊浮体物面非线性时域耦合动力分析方法。该方法采用时域物面非线性理论方法在瞬态位置直接时域模拟系泊浮体所需水动力,结合有限元方法计算系泊缆索的动力响应,利用异步耦合方法实现浮体和系泊缆索的时域耦合动力求解。既满足系泊浮体时域水动力耦合,又满足系泊浮体和系泊缆索动力耦合。通过对二阶非线性不规则波作用下深海系泊半潜式平台的时域耦合响应特性进行研究,将不同海况下物面非线性时域耦合静力响应和动力响应与间接时域耦合动力响应的三种方法计算结果进行比较。研究结果表明,系泊缆索动力响应明显,平台瞬态空间位置对垂荡低频运动影响较大,有必要在平台瞬时湿表面采用动力响应方法进行深海系泊浮体时域耦合响应分析。     

采用高阶边界元法的楔形体变速度入水数值模拟(英文)

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.     

采用有限元和边界元方法分析弹性加肋圆柱壳的声学相似性

本文采用有限元和边界元方法,分析水下运动体的典型结构──有限长弹性加肋圆柱壳的振动、耦合振动和声辐射的相似性,给出这种结构的声学相似条件和相似关系。     

船体加筋板结构焊接变形和残余应力热弹塑性有限元分析

为提高焊接热弹塑性数值模拟的效率,采用静态子结构方法实现焊接热传导分析计算。根据船体加筋板结构的重复性和对称性特点,将整个结构根据加强筋划分为若干相同的静态子结构,计算得到1条焊缝的温度分布后,通过温度场的镜像和平移获得整个结构的温度场。以船体加筋板为例,采用静态子结构方法并结合温度场的镜像和平移技术,计算分析船体加筋板的焊接温度场和应力场结果。计算表明,该方法在保证计算精度的前提下,极大地提高了计算效率。     

基于声振耦合理论的压电智能板结构水下声辐射控制研究(英文)

对水下结构声辐射压电控制的压电片布置问题进行了深入的理论和数值分析.首先基于声振耦合理论,对低频段声辐射板的压电传感器和作动器的布置做了定性的分析,给出了声辐射功率与结构模态比和模态积之间的关系式.其次基于有限元/边界元数值计算方法,对所提出的压电片布置方案进行了辐射声场控制的定量计算.通过计算比较可以看出,基于声振耦合理论的压电片布置方案在低频段所得到的多阶模态控制效果,优于基于振动模态应变贴片理论控制方法所得到的控制效果,可以用来进行流体加载板结构声辐射控制的设计和预测.     

基于改进的Logvinovich法对带横摇运动非对称楔形体入水砰击力的计算(英文)

The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.     

Water wave scattering by a sphere submerged in uniform finite depth water with an ice-cover

Using the multipole method, we formulate the problem of water wave scattering by a submerged sphere in uniform finite water depth with an ice-cover, the ice-cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The vertical and horizontal forces on the sphere are obtained and depicted graphically against the wave number for various values of the depth of water and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover and also the effect of varying depth of water on these quantities. When the flexural rigidity is taken to be zero, the numerical results exactly coincide with the curves of the vertical and horizontal forces on the sphere for the cases of uniform finite depth water with a free surface.     

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.     

Structural-acoustic optimization of stiffened panels based on a genetic algorithm

For the structural-acoustic radiation optimization problem under external loading,acoustic radiation power was considered to be an objective function in the optimization method. The finite element method(FEM) and boundary element method(BEM) were adopted in numerical calculations,and structural response and the acoustic response were assumed to be de-coupled in the analysis. A genetic algorithm was used as the strategy in optimization. In order to build the relational expression of the pressure objective function and the power objective function,the enveloping surface model was used to evaluate pressure in the acoustic domain. By taking the stiffened panel structural-acoustic optimization problem as an example,the acoustic power and field pressure after optimized was compared. Optimization results prove that this method is reasonable and effective.