A 3D BEM model for liquid sloshing in baffled tanks

The present work aims at developing a boundary element method to determine the natural frequencies and mode shapes of liquid sloshing in 3D baffled tanks with arbitrary geometries. Green's theorem is used with the governing equation of potential flow and the walls and free surface boundary conditions are applied. A zoning method is introduced to model arbitrary arrangements of baffles. By discretizing the flow boundaries to quadrilateral elements, the boundary integral equation is formulated into a general matrix eigenvalue problem. The governing equations are then reduced to a more efficient form that is merely represented in terms of the potential values of the free surface nodes, which reduces the size of the computational matrices considerably. The results obtained using the proposed model are verified in comparison with the literature and very good agreement is achieved. Finally, a number of example tanks having common configurations are used to investigate the effect of baffle on sloshing frequencies and some conclusions are outlined. Copyright © 2008 John Wiley & Sons, Ltd.     

A reduced order model for liquid sloshing in tanks with flexible baffles using boundary element method

In order to study the interaction of sloshing and structural vibrations of baffled tanks, a reduced order model based on modal analysis of structure model and boundary element method for fluids motion is developed. For this purpose, the governing equations of elastic structure and incompressible flow are used to derive simple models to simulate both fields. Using the modal analysis technique, the structural motions are applied to the fluid model and on the other hand by using boundary element method, the fluid loads are applied to the structural model. Based on this formulation, a code is developed which is applicable to an arbitrary elastic tank with arbitrary arrangement of baffles. The obtained results are validated with literature data and then the effects of baffle flexibility on the sloshing frequencies and structural vibration frequencies are investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

Boundary element analysis of liquid sloshing in baffled tanks

The paper concerns the natural frequencies and mode shapes of liquid sloshing in three dimensional baffled tanks with arbitrary geometries. The liquid is considered to be inviscid and incompressible and amplitudes of oscillations are assumed to be small. The tank bottom and the baffle are treated as rigid. The boundary element method is used to solve the considered problem. Triangular curvilinear 6-node boundary elements are applied. In the present formulation is not necessary to introduce the zoning method, because the baffles are treated as double layers immersed in liquid. After discretization the problem is formulated as the standard eigenvalue problem, which is limited to free surface degrees of freedom only. Several examples are given to verify the proposed method.     

贮箱内液体小幅晃动的频率和阻尼计算

根据小幅晃动条件下利用速度势函数推导的计算液体晃动频率和内部Rayleigh阻尼的特征值方程,利用简化处理转化为一般的广义特征值问题,并针对这种非对称大型稀疏矩阵采用了Arnoldi迭代方法,求解得到晃动频率和内部阻尼.将利用Stokes边界层理论计算得到边界上的阻尼与内阻尼之和作为晃动的等效阻尼,通过两个算例比较计算结果接近实验结果.这种方法可以计算任意形状贮箱内液体的小幅晃动频率和晃动阻尼.     

Free-surface oscillations of fluid in closed basins

The mild-slope equation, well-known in wave refraction theory, is used to calculate the natural frequencies of oscillation of fluid in a basin. The method may be applied to canals of variable cross-section and to axisymmetric basins provided that every point in the fluid lies directly beneath the free surface. Comparison is made with previously known solutions and some new results are presented for axisymmetric geometries.     

Sloshing effects on supersonic flutter characteristics of a circular cylindrical shell partially filled with liquid

This paper aims to revisit the effect of sloshing on the flutter characteristics of a partially liquid-filled cylinder. A computational fluid-structure interaction model within the framework of the finite element method is developed to capture fluid-structure interactions arising from the sloshing of the internal fluid and the flexibility of its containing structure exposed to an external supersonic airflow. The internal liquid sloshing is represented by a more sophisticated model, referred to as the liquid sloshing model, and the shell structure is modeled by Sanders' shell theory. The aerodynamic pressure loading is approximated by the first-order piston theory. The initial geometric stiffness due to prestresses in the initial configuration stemming from the fluid hydrostatic pressure, internal pressure, and axial compression load is also considered. The obtained results reveal that the sloshing of the internal fluid has little influence on the supersonic flutter boundary of a cylinder partially filled with liquid, at least for the case considered here. It is also shown that the critical freestream static pressure predicted by the sloshing model is negligibly larger than that calculated by the hydroelastic model of the internal fluid, which means that the sloshing of the internal fluid slightly overestimates the flutter boundary.     

Analysis of the small amplitude sloshing of a liquid in a rigid container of arbitrary shape using a low‐order boundary element method

A boundary element method for estimating the natural sloshing frequencies and forces developed due to an inviscid, incompressible liquid oscillating in a rigid‐walled tank is presented here. The amplitude of oscillation is assumed to be small enough to allow linearization of the boundary condition at the free surface. Both free and forced oscillation cases are studied. Comparison with results available in the literature shows good agreement. The present method offers significant economy of computing resources compared to the finite element method. Copyright © 2000 John Wiley & Sons, Ltd.     

Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell

In this paper, the axisymmetric vibration of a fluid-filled spherical membrane shell is studied based on nonlocal elasticity theory. The membrane shell is considered elastic, homogeneous and isotropic. The shell model is reformulated using the nonlocal differential constitutive relations of Eringen. The membrane shell is completely filled with an inviscid fluid. The motion of the fluid is governed by the wave equation. Nonlocal governing equations of motion for the fluid-filled spherical membrane shell are derived. Along the contact surface between the membrane and the fluid, the compatibility requirement is applied and Legendre polynomials, associated Legendre polynomials and spherical Bessel functions are used to obtain the natural frequencies of the fluid-filled spherical membrane shells. The frequencies for both empty and fluid-filled spherical membrane shell are evaluated, and their comparisons are performed to confirm the validity and accuracy of the proposed method. An excellent agreement is found between the present and previous ones available in the literature. The variations of the natural frequencies with the small-scale parameter, density ratio, wave speed ratio and Poisson’s ratio are also examined. It is observed that the frequencies are affected when the size effect is taken into consideration.     

Reduced order modeling of liquid sloshing in 3D tanks using boundary element method

This paper presents the application of reduced order modeling technique for investigation of liquid sloshing in three-dimensional tanks. The governing equations of sloshing are written using a boundary element formulation for incompressible potential flow. Then, the governing equations are reduced to a more efficient form that is represented only in terms of the velocity potential on the liquid free surface. This particular form is employed for eigen-analysis of fluid motion and the sloshing frequencies and mode shapes are determined. Then, the sloshing frequencies and the corresponding right- and left-eigenvectors are used along the modal analysis technique to find a reduced order model (ROM) for fluid motion. Using a rectangular and a cylindrical tank, the results of the ROM are verified in comparison with the analytical results. Then some example tanks are used to examine the ROM in comparison with the full boundary element model for determination of the free surface motion under the angular and lateral motion of the tank. The obtained results demonstrate the capability and accuracy of the reduced order modeling technique for analysis of sloshing using a few modes.     

R-ADAPTIVE BOUNDARY ELEMENT METHOD FOR UNSTEADY FREE-SURFACE FLOW ANALYSIS

An adaptive meshing based on the r-method is developed for two-dimensional unsteady non-linear flows with a free surface. Coupling of a boundary element equation and a weighted residual formulation of the pressure equation on the free surface is employed in solving the wave problems. A mesh optimization scheme is constructed for these two matrix equations. The final mesh distribution on the free surface is determined from the weighted average of these two adaptive meshes. Through numerical analyses of a non-linear sloshing problem and solitary waves in a tank, the influence of time interval of the remeshing and the weight factor for two adaptive meshes on the accuracy and efficiency of the proposed approach is investigated.     

地震作用下水-轴对称柱体相互作用的子结构分析方法

针对水-轴对称柱体动力相互作用问题,提出了一种地震作用下水-结构相互作用的时域子结构分析方法.基于三维不可压缩水体的波动方程和边界条件,利用分离变量法将其转换为环向解析、竖向和径向数值的二维模型;基于比例边界有限元推导了截断边界处无限域水体的动力刚度方程,并将水体内域有限元方程和人工边界处的动水压力进行耦合,从而得到结...     

A Fast Fourier-Boundary Element Method for axisymmetric potential and elasticity problems with arbitrary boundary conditions

This paper presents a new methodology, based on the Fast Fourier Transform (FFT), to solve axisymmetric potential and elasticity problems with arbitrary (non-axisymmetric) boundary conditions using the Boundary Element Method (BEM). The proposed technique is highly effective in cases where a large number of harmonics is required. The new feature concerns the efficient and reliable computation of the axisymmetric fundamental solutions. The methodology is applicable to any type of boundary elements, either continuous or discontinuous, for both direct and indirect BEM formulations. Numerical results are presented for constant boundary elements for typical potential and elasticity problems. Although the method is presented for static problems, it is general and can be applied to a wider class of boundary value axisymmetric problems, such as acoustics and elastodynamics in the frequency or the time domain.     

截面任意形状的柱形和环形容器内液体晃动特性的精确解法

本文研究截面任意形状的柱形和环形容器内液体的晃动特性，利用Ｆｏｕｒｉｅｒ级数匹配法将液体速度势沿容器壁面展开得频率方程，由行列式搜根法数值计算各阶固有振动频率，结果是精确的，方法具有通用性。     

轴向变速运动弯曲梁的固有频率分析

基于动力刚度矩阵法对轴向变速运动弯曲梁的固有频率进行分析,根据Hamilton原理,推导轴向变速运动弯曲梁的时域控制方程和边界条件,通过傅里叶变换得到频域控制方程和边界条件,求解频域控制方程,并结合位移边界条件和载荷边界条件,建立轴向变速运动弯曲梁的动力刚度矩阵模型;引入Hermite形式的形函数,建立了轴向变速运动弯曲梁的有限元模型。算例中,通过对比现有文献中的结果、有限元模型结果和动力刚度矩阵法模型结果,验证了该文所建立的力学模型,动力刚度矩阵法比有限元法具有更高的精度和效率,分析了轴向变速运动弯曲梁固有频率随着弯曲梁轴向运动速度、加速度、轴向受力、边界条件的变化规律。     

带隔板的矩形截面渡槽内液体的晃动特性

本文研究带有刚性隔板的矩形截面渡槽中液体的微幅线性晃动特性。将因隔板而导致的复杂液体域分割为若干个形状简单且边界条件均一的子域,分别研究各子域内液体运动的势函数。利用叠加原理和分离变量法,导出每个子域内液体速度势的一般解。根据液体子域界面处速度和压力的连续条件以及自由液面处的表面波条件,得到含有待定系数的级数方程。对方程作Fourier展开,即可求得液体的固有晃动频率和振型函数。     

A new boundary element approach for contact problems with friction

A new boundary element solution algorithm for two-dimensional and axisymmetric contact problems with friction, based on an independent discretization of the contacting surfaces and under static and proportional loading conditions, is presented. The solution procedure uses the element shape functions to distribute the geometry, tractions and displacements on each contact element. The contact constraints are then applied between each contacting node and the opposite contact segment. The overall boundary element matrix equations for the contacting bodies are coupled using the contact conditions at the interface without introducing any additional variables into the solution matrix. The algorithm is applied to several two-dimensional and axisymmetric frictional contact examples and the results obtained are in very good agreement with finite element and analytical solutions.     

Analysis of convergence and accuracy of the DRBEM for axisymmetric Helmholtz-type equation

This paper presents a study of the convergence properties of a new axisymmetric approximating function. This function, associated with a dual reciprocity boundary element model for axisymmetric Helmholtz-type equation, is independent of the wave number in order to avoid occasional singular matrix due to some particular wave numbers. Interpolation functions are derived from the approximating functions. Their properties are studied numerically and their local behaviour is illustrated. Numerical tests, carried out in the last section, show a reasonably good agreement with analytical solutions of two simple aeroacoustic problems. Some criteria concerning the number of nodes per wavelength needed to obtain satisfactory results are also presented.     

DRM-MD approach for modeling laser–material interaction with axial symmetry

A dual reciprocity method multi-domain (DRM-MD) approach for modeling laser–material interaction with axial symmetry was developed. The proposed approach is based on the fundamental solution for the Laplace equation in 2D and is much simpler for implementation than the dual reciprocity boundary element method (DRBEM) based on the fundamental solution for axisymmetric problems incorporating elliptic integrals. The thermal model of laser–material interaction was applied for the cases of mono as well as multi-layer structures. Different aspects of interaction up to the melting point of considered materials are presented. The effect of temperature dependence of the absorption coefficients on the process of laser heating was considered. Numerical results for spatial as well as temporal temperature distribution inside the material bulk are presented and compared to analytical solutions.     

hp Fast multipole boundary element method for 3D acoustics

A fast multipole boundary element method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three‐dimensional space is presented in this paper. The Collocation method is used, and the Burton–Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Because of the application of the combined integral equation, the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton–Miller formulation of the boundary integral equation, an integration technique for arbitrary element order is applied. The fast multipole method combined with an arbitrary order h‐p mesh refinement strategy enables accurate computation of large‐scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time. Copyright © 2016 John Wiley & Sons, Ltd.     

An integral equation analysis of inelastic shells

This paper presents an integral equation approach for the analysis of deformation and stresses in inelastic shells of arbitrary shape subjected to arbitrary loading. The proposed mathematical model is completely consistent and is derived by transforming the three-dimensional equations from the Cartesian to the appropriate curvilinear coordinates of the shell. Appropriate kinematic assumptions for the dependence of the displacements on the thickness coordinate of the shell and assumptions regarding the loads at the ends are introduced consistently in the model to take advantage of the thinness of the shell. Numerical implementation and numerical results are presented for elastic and inelastic deformation of axisymmetric shells subjected to axisymmetric loading. These results are compared against exact elasticity, Love-Kirchoff model analysis of inelastic cylindrical shells and finite element solutions.