Coupled BEM/FEM approach for nonlinear soil/structure interaction

A general coupled boundary element/finite element formulation is presented for the investigation of dynamic soil/structure interaction including nonlinearities. It is applied to investigate the transient inelastic response of structures coupled with a halfspace. The structure itself and the surrounding soil in the near field are modeled with finite elements. In this part of the model inhomogeneities and an elastoplastic material behavior with hardening effects can be taken into account. The remaining soil region, i.e. the elastic halfspace, is discretized with the boundary elements. Thus wave radiation to infinity is included in the model. In representative examples it is shown that the methodology is computationally powerful and can be used efficiently for the nonlinear analyses of complex soil/structure interaction problems.     

结构动应力分析的FEM-BEM耦合方法

本文提出了利用结构的有限元结点位移响应(或结点力)的计算值作为子域的边界条件,然后利用边界元方法计算子域内各瞬时的动应力的FEM-BEM耦合方法.文中给出了薄板在简谐激励下动应力响应的计算实例并与分析解进行了比较,结果表明,FEM-BEM耦合法比常规有限元法对结构动应力的计算精度有大幅度的提高.     

DOMAIN DECOMPOSITION WITH BEM AND FEM

The Finite Element Method and the Boundary Element Method are two different structure analysis methods with a totally different numerical character. Therefore, it makes no sense to couple these two methods pointwise at the interface. In contrast to a lot of coupling strategies in the past, in this paper a method is constructed where we have coupling of the two different methods in a weak form. As a result we can analyse the given structure with two different grids independent of each other. On this account, we see that the big advantage of the proposed method is in its ablity to couple BEM and FEM. The construction of a robust and reliable numerical algorithm depends on the adaptive control of symmetry and definiteness of the coupling matrix. Therefore, we use an iterative method for solving the boundary integral equation by expanding the Calderon projector in a Neumann series. Numerical results show the preciseness and efficiency of the method. © 1997 John Willey & Sons Ltd.     

Efficient non‐linear solid–fluid interaction analysis by an iterative BEM/FEM coupling

An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid–solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non‐linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non‐linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain. Copyright © 2005 John Wiley & Sons, Ltd.     

Symmetric collocation BEM/FEM coupling procedure for 2-D dynamic structural–acoustic interaction problems

 This paper presents a symmetric collocation BEM (SCBEM)/FEM coupling procedure applicable to 2-D time domain structural–acoustic interaction problems. The use of symmetry for BEM not only saves memory storage but also enables the employment of efficient symmetric equation solvers, especially for BEM/FEM coupling procedure. Compared with symmetric Galerkin BEM (SGBEM) where double boundary integration should be carried out, SCBEM can reduce significantly the computing cost. Two numerical examples are included to illustrate the effectiveness and accuracy of the proposed method. Received: 2 November 2001 / Accepted: 27 May 2002     

结构声辐射有限元/边界元法声学-结构灵敏度研究

声学-结构灵敏度用于预测结构辐射声压随结构设计变量的变化,该值对结构降噪设计有重要意义。提出了基于有限元法、边界元法的声学-结构灵敏度计算方法。基于有限元法计算结构动力学响应及响应速度灵敏度,基于边界元法计算结构辐射声压及声压对振动速度灵敏度。将两个灵敏度联合,得到声学-结构设计灵敏度。以中空六面体为研究实例,给出了激励频率为1~100 H z时,外场声压对壳厚度的灵敏度,并分析了灵敏度随激励频率、设计变量的变化规律。结果表明,基于有限元法、边界元法的声学-结构灵敏度是有效和正确的。     

基于有限元-边界元的声学构形灵敏度分析

通过灵敏度分析可以对由结构修改而引起的局部或全部结构状态特性的变化做出估计,为设计指明方向.对结构-声学优化设计中的构形灵敏度进行研究,利用有限元、边界元数值计算方法获得辐射声压关于组合结构各构件旋转角度的半解析声学构形灵敏度公式,扩大了声学灵敏度的范畴.该声学灵敏度公式可以用来预测结构组合方式的改变而导致的空间声学量的改变.对该灵敏度公式进行数值计算,与传统有限差分法对比,证明了本文方法的正确性.     

加劲板BEM—FEM耦联自由振动分析

本文将加劲板分为薄板和结合梁（格栅）两部分，薄板部分用无奇点边界元法（ＢＥＭ）处理，而格栅用有限元法（ＦＥＭ）处理，分别建立各自的方程，然后根据板与梁之间的平衡和协调条件加以耦合，导出加劲板的自振特征方程，从而求解各阶频率和振型。本方法适用于任意形状、任意边界条件的加劲板，且精度良好     

FEM/BEM for simulation of LSAW devices

This paper presents a modeling of the propagation of surface acoustic, leaky acoustic, and surface skimming bulk waves in piezoelectrics with a finite array of metallic electrodes over their surface. A combined method of matrix Green's function and the finite element method for computation of all acoustic wave fields is an effective tool for simulation of the propagation of acoustic waves in such structures. The proposed method is optimized in the speed of computation of all matrix Green's function components originally obtained. The Fourier transformations of Green's function from kappa-space domain to real space domain are performed by combined trapezoidal and Filon's integration methods for rapidly oscillating functions. The trapezoidal integration method is used on a distance from a point source from zero to a few wavelengths long, but the other has the advantage for a distance from some wavelength to infinity. That allows one, by selectively condensing computation grids around branch and singular points of the sharp behavior of Green's function, to maximize speed and accuracy of computation of integrals. FEM is used, modified originally to achieve acceleration without loss accuracy. Because of the simple geometry of the electrodes, unknown elastic fields are presented as a series of known eigenfunctions with unknown coefficients over the whole region of electrodes. All unknown coefficients are determined by applying the Galerkin method. There is good agreement between numerical and experimental conductances of acoustic wave transducers on materials such as lithium niobate and lithium tantalate.     

A general 3D BEM/FEM coupling applied to elastodynamic continua/frame structures interaction analysis

This paper presents a procedure for coupling general finite element models with three‐dimensional bodies modelled by the Boundary Element Method (BEM). Shells, plates and frames are modelled by the Finite Element Method (FEM) and coupled to the BEM domain directly or by means of rigid blocks. The coupling is used for the analysis of buildings connected to half‐space by means of rigid footings, piles or plates in bending and other problems where combinations of different types of sub‐domains are required, composite domains for instance. Several numerical examples are analysed to demonstrate the robustness and accuracy of the proposed scheme. Copyright © 1999 John Wiley & Sons, Ltd.     

Iterative coupling of BEM and FEM for nonlinear dynamic analyses

The present work deals with the iterative coupling of boundary element and finite element methods. First, the domain of the original problem is subdivided into two subdomains, which are separately modeled by the FEM and BEM. Thus the special features and advantages of the two methodologies can be taken into account. Then, prescribing arbitrary transient boundary conditions, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local nonlinearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the nonlinear system. The procedure turns out to be very efficient. Moreover, a special formulation allows taking into account different durations of the time steps in each subdomain.The financial support by CAPES (Fundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) through scholarship No. BEX0788/02-3 (first author) is gratefully acknowledged.     

Alternative time marching process for BEM and FEM viscoelastic analysis

Based on the weighted residual technique, both Finite Element and Boundary Element alternative procedures for viscoelastic analysis are proposed. After imposing the space approximations, applying the kinematical relations for material and strain velocities at the approximation level, the time integration is carried out using appropriate operators. The Kelvin‐Voigt viscoelastic model is implemented in order to validate the idea. The Newmark β time integral scheme is applied to the Finite Element procedure while the Houbolt scheme is applied to the Boundary Elements, allowing the consideration of dynamic analysis in future works. Copyright © 2001 John Wiley & Sons, Ltd.     

BEM and FEM analysis of Signorini contact problems with friction

In this paper, we present a comparative study of the boundary element method (BEM) and the finite element method (FEM) for analysis of Signorini contact problems in elastostatics with Coulomb's friction law. Particularities of each method and comparison with the penalty method are discussed. Numerical examples are included to demonstrate the present formulations and to highlight its performance.     

BEM and FEM based numerical simulations for biomagnetic fluid flow

We investigate numerically the biomagnetic fluid flow between parallel plates imposed to a magnetic source placed below the lower plate. The biomagnetic fluid is assumed to be Newtonian, viscous, incompressible, electrically nonconducting, and has magnetization varying linearly with temperature and magnetic field intensity. Both steady and unsteady, laminar, two-dimensional biomagnetic fluid flow equations taking into care the heat transfer between the plates are solved using both finite element and dual reciprocity boundary element methods. Treatment of nonlinear terms by using only the fundamental solution of the Laplace equation, and discretization of only the boundary of the region are the advantages of dual reciprocity boundary element method giving small algebraic systems to be solved at a small expense. Finite element method is capable of giving very accurate results by discretizing the region affected by the magnetic source very finely, but it results in large sized algebraic systems requiring high computational cost. The results indicate that the flow is appreciably affected with the presence of magnetic source in terms of vortices at the magnetic source area. The lengths of the vortices, and temperature increase with an increase in the intensity of the magnetic field.     

FEM and BEM coupling in elastostatics using localized Lagrange multipliers

The equations produced by the finite and boundary element methods in structural mechanics are expressed in different variables and cannot be linked without modifications. Conventional coupling methods of these numerical techniques have traditionally been based on the use of classical Lagrange multipliers making a direct connection of the two solids through their common interfaces using matching meshes and altering the formulation of one of the methods to make it compatible with the other. In this work, a discrete surface called frame is interposed between the connected subdomains to approximate their common interface displacements, it is treated using a finite element discretization and connected to each substructure using localized Lagrange multipliers collocated at the interface nodes. This methodology facilitates the connection of non‐matching finite and boundary element meshes avoiding modifications to the numerical methods used and providing a partitioned formulation, which preserves software modularity. Copyright © 2006 John Wiley & Sons, Ltd.     

Gradient weighted residuals for error indicators in FEM and BEM

A simple yet general approach is presented for checking the adequacy of approximate solutions obtained with FE and BE weighted residual methods. In this method, which is called the gradient weighted residual technique, the computed residuals in the elements are weighted by appropriate gradients and thereby an indicator of the quality of solution is calculated. Such computations are carried out a-posteriori and if need be a reanalysis is then carried out on a new mesh generated on the basis of the quality of the solution determined over the domain.     

结构——基础——地基共同作用的有限元、边界元联合解法

本文采用有限元和边界元的联合解法探讨了建筑物上部结构、基础和地基的共同工作效应。地基部分,采用边界积分方程;上部结构则采用有限单元,根据二部分交接面上位移协调和力的平衡条件联合求解,在微机IBM—PC上编制了通用程序,计算所得与C.J.W.King和W.J.Larnacn用有限元等方法的结果一致。由于边界元在半无限体应用的优势,本方法具有计算精度高、运算速度抉和内存需求量少等优点。     

FEM/BEM analysis of a generalized periodic array

Recent developments in wide bandwidth SAW filter design led to the use of complex electroacoustic cells, such as the Hanma-Hunsinger cell. For this kind of structure, it is not sufficient to use only a single electrode periodic FEM/BEM model to derive the P-matrix parameters. The present paper proposes a mixed FEM/BEM numerical model for the simulation of a periodic array of metallic electrodes, the elementary cell of which can be as complex as necessary: it can contain several electrodes, connected to active ports, or short-circuited, or floating.     

BEM and FEM combination parallel analysis using conjugate gradient and condensation

Boundary element and finite element combination analysis on parallel schemes are improved in this paper. The conjugate gradient method (CG method) is introduced for renewal of unknowns on the combination boundary in place of the Schwarz method previously used, which makes it possible to determine a parameter required in the renewal iteration automatically. Further, the condense method is employed for higher efficiency of solution by reducing the number of degree of freedoms in both equations for the finite element and boundary element domains. Comparison of the present algorithm with the previous one in some numerical examples shows marked improvement in computational efficiency.     

柱式负荷传感器的摆动支承振动分析

动态称重条件下,柱式负荷传感器的支承方式可分为弹性支承和摆动支承。动态称重时,摆动支承的称重系统表现出显著的振动特性,影响称重准确度和负荷传感器的疲劳寿命。针对摆动支承柱式负荷传感器,分析其运动特性得出摆动支承的稳定性条件,得到摆动支承下回复力与摆动角及施加的竖向力近似成正比的关系。利用达朗贝尔原理建立柱式负荷传感器摆动支承振动的动力学控制方程,分别对其自由状态和动态称重状态的动力学响应进行数值计算,得出支承振动振幅和回复时间的影响因素,为动态称重准确度的分析提供参考,同时也可作为称重系统减振的设计依据。