Fast BEM–FEM mortar coupling for acoustic–structure interaction

A coupling algorithm based on Lagrange multipliers is proposed for the simulation of structure–acoustic field interaction. Finite plate elements are coupled to a Galerkin boundary element formulation of the acoustic domain. The interface pressure is interpolated as a Lagrange multiplier, thus, allowing the coupling of non‐matching grids. The resulting saddle‐point problem is solved by an approximate Uzawa‐type scheme in which the matrix–vector products of the boundary element operators are evaluated efficiently by the fast multipole boundary element method. The algorithm is demonstrated on the example of a cavity‐backed elastic panel. Copyright © 2005 John Wiley & Sons, Ltd.     

A comparison of FE–BE coupling schemes for large‐scale problems with fluid–structure interaction

To predict the sound radiation of structures, both a structural problem and an acoustic problem have to be solved. In case of thin structures and dense fluids, a strong coupling scheme between the two problems is essential, since the feedback of the acoustic pressure onto the structure is not negligible. In this paper, the structural part is modeled with the finite element (FE) method. An interface to a commercial FE package is set up to import the structural matrices. The exterior acoustic problem is efficiently modeled with the Galerkin boundary element (BE) method. To overcome the well‐known drawback of fully populated system matrices, the fast multipole method is applied. Different coupling formulations are investigated. They are either based on the Burton–Miller approach or use a mortar coupling scheme. For all cases, iterative solvers with different preconditioners are used. The efficiency with respect to their memory consumption and computation time is compared for a simple model problem. At the end of the paper, a more complex structure is simulated. Copyright © 2008 John Wiley & Sons, Ltd.     

Dispersion analysis of stabilized finite element methods for acoustic fluid interaction with Reissner–Mindlin plates

The application of stabilized finite element methods to model the vibration of elastic plates coupled with an acoustic fluid medium is considered. A complex‐wavenumber dispersion analysis of acoustic fluid interaction with Reissner–Mindlin plates is performed to quantify the accuracy of stabilized finite element methods for fluid‐loaded plates. Results demonstrate the improved accuracy of a recently developed hybrid least‐squares (HLS) plate element based on a modified Hellinger–Reissner functional, consistently combined with residual‐based methods for the acoustic fluid, compared to standard Galerkin and Galerkin gradient least‐squares plate elements. The technique of complex wavenumber dispersion analysis is used to examine the accuracy of the discretized system in the representation of free waves for fluid‐loaded plates. The influence of fluid and coupling matrices resulting from consistent implementation of pressure loading in the residual for the plate equation is examined and clarified for the different finite element approximations. Copyright © 2001 John Wiley & Sons, Ltd.     

Parametric design sensitivity analysis of high‐frequency structural–acoustic problems using energy finite element method

A design sensitivity analysis of high‐frequency structural–acoustic problems is formulated and presented. The energy finite element method (EFEM) is used to predict structural–acoustic responses in the high frequency range, where the coupling between structural junctions and the structural–acoustic interface are modelled using power transfer coefficients. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural–structural and structural–acoustic coupling matrices. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and numerical sensitivity results show excellent agreement as compared to analytical finite difference results. Copyright © 2004 John Wiley & Sons, Ltd.     

Coupled finite element – hierarchical boundary element methods for dynamic soil–structure interaction in the frequency domain

This paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil–structure interaction problems in the frequency domain. The application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods. Three coupling methodologies are presented and their computational performance is assessed through numerical examples. It is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient, as it requires the assembly of a dynamic soil stiffness matrix. Iterative solution procedures are presented as well, and it is shown that the application of such schemes to dynamic soil–structure interaction problems in the frequency domain is not trivial, as convergence can hardly be achieved if no relaxation procedure is incorporated. Aitken's Δ²‐method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter, while a novel relaxation technique is proposed for parallel iterative algorithms. It is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain; the fastest convergence is observed if Neumann boundary conditions are imposed on the stiffest subdomain. The use of a dedicated solver for each subdomain hence results in a reduced computational effort. A monolithic coupling strategy, often used for the solution of fluid–structure interaction problems, is also introduced. The governing equations are simultaneously solved in this approach, while the assembly of a dynamic soil stiffness matrix is avoided. Copyright © 2013 John Wiley & Sons, Ltd.     

Interface‐reduction for the Craig–Bampton and Rubin method applied to FE–BE coupling with a large fluid–structure interface

Component mode‐based model‐order reduction (MOR) methods like the Craig–Bampton method or the Rubin method are known to be limited to structures with small coupling interfaces. This paper investigates two interface‐reduction methods for application of MOR to systems with large coupling interfaces: for the Craig–Bampton method a direct reduction method based on strain energy considerations is investigated. Additionally, for the Rubin method an iterative reduction scheme is proposed, which incrementally constructs the reduction basis. Hereby, attachment modes are tested if they sufficiently enlarge the spanned subspace of the current reduction basis. If so, the m‐orthogonal part is used to augment the basis. The methods are applied to FE–BE coupled systems in order to predict the vibro‐acoustic behavior of structures, which are partly immersed in water. Hereby, a strong coupling scheme is employed, since for dense fluids the feedback of the acoustic pressure onto the structure is not negligible. For two example structures, the efficiency of the reduction methods with respect to numerical effort, memory consumption and computation time is compared with the exact full‐order solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of polyvinyl alcohol cryogel as an acoustic coupling medium for low‐intensity transcranial focused ultrasound

Transcranial focused ultrasound (FUS) has emerged as a noninvasive neuromodulatory modality with exquisite depth penetration and spatial selectivity. Liquids, such as degassed water or mineral oil, are used as acoustic coupling media between the ultrasound‐generating transducer and the brain; however, they require a separate container that limits the spatial orientation of the transducers with respect to the sonication target. Nonliquid, gel‐like materials that do not require a housing container have been sought after as coupling media to overcome such limitations. Polyvinyl alcohol (PVA), when dissolved in water and undergone freeze–thaw cycle(s), forms a flexible hydrogel having a high level of acoustic transmission. To examine the feasibility of the PVA cryogel as the coupling material for transcranial FUS, the mechanical properties (in terms of its Young's modulus) and acoustic attenuation of the PVA cryogel were examined using different concentrations and number of freeze–thaw cycles. The cryogel with 6 or 7% (w/v) concentrations and two freeze–thaw cycles showed minimum pressure attenuation (on the order of 1%) across the different ultrasound frequencies (250–650 kHz). The cryogel was molded to fit around a single‐element FUS transducer and was applied to a head phantom, showing the flexibility in orienting the sonication paths at different angles and depths. The use of the cryogel did not alter the location and shape of acoustic focal profile compared to the one measured in the degassed water. The present work suggests that PVA cryogel may be used as an alternative acoustic coupling medium for low‐intensity FUS applications.     

An adaptive domain decomposition coupled finite element–boundary element method for solving problems in elasto‐plasticity

The purpose of this paper is to present an adaptive finite element–boundary element method (FEM–BEM) coupling method that is valid for both two‐ and three‐dimensional elasto‐plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub‐domains in the standard FEM–BEM coupling approaches. The method estimates the FEM and BEM sub‐domains and automatically generates/adapts the FEM and BEM meshes/sub‐domains, according to the state of computation. The results for two‐ and three‐dimensional applications in elasto‐plasticity show the practicality and the efficiency of the adaptive FEM–BEM coupling method. Copyright © 2009 John Wiley & Sons, Ltd.     

FE/FMBE coupling to model fluid–structure interaction

In this paper, a finite element (FE)/fast multipole boundary element (FMBE)‐coupling method is presented for modeling fluid–structure interaction problems numerically. Vibrating structures are assumed to consist of elastic or sound absorbing materials. An FE method (FEM) is used for this part of the solution. This structural sub‐domain is embedded in a homogeneous fluid. The case where the boundary of the structural sub‐domain has a very complex geometry is of special interest. In this case, the BE method (BEM) is a more suitable numerical tool than FEM to account for the sound propagation in the homogeneous fluid. The efficiency of the BEM is increased by using FMBEM. The BE‐surface mesh required is directly generated by the FE‐mesh used to discretize the structural sub‐domain and the absorbing material. This FE/FMBE‐coupling method makes it possible to predict the effects of arbitrarily shaped absorbing materials and vibrating structures on the sound field in the surrounding fluid numerically. The coupling method proposed is used to study the acoustic behavior of the lining of an anechoic chamber and that of an entire anechoic chamber in the low‐frequency range. The numerical results obtained are compared with the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

The natural neighbour Petrov–Galerkin method for elasto‐statics

In this paper, an efficient and accurate meshless natural neighbour Petrov–Galerkin method (NNPG) is proposed to solve elasto‐static problems in two‐dimensional space. This method is derived from the generalized meshless local Petrov–Galerkin method (MLPG) as a special case. In the NNPG, the local supported trial functions are constructed based on the non‐Sibsonian interpolation and test functions are taken as the three‐node triangular FEM shape functions. The local weak forms of the equilibrium equation and the boundary conditions are satisfied in local polygonal sub‐domains. These sub‐domains are constructed with Delaunay tessellations and domain integrals are evaluated over included Delaunay triangles by using Gaussian quadrature scheme. As this method combines the advantages of natural neighbour interpolation with Petrov–Galerkin method together, no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. Several numerical examples are presented and the results show the presented method is easy to implement and very accurate for these problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

The paper presents a gradient‐based topology optimization formulation that allows to solve acoustic–structure (vibro‐acoustic) interaction problems without explicit boundary interface representation. In acoustic–structure interaction problems, the pressure and displacement fields are governed by Helmholtz equation and the elasticity equation, respectively. Normally, the two separate fields are coupled by surface‐coupling integrals, however, such a formulation does not allow for free material re‐distribution in connection with topology optimization schemes since the boundaries are not explicitly given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u /p‐formulation). The Helmholtz equation is obtained as a special case of the mixed formulation for the elastic shear modulus equating to zero. Hence, by spatial variation of the mass density, shear and bulk moduli we are able to solve the coupled problem by the mixed formulation. Using this modelling approach, the topology optimization procedure is simply implemented as a standard density approach. Several two‐dimensional acoustic–structure problems are optimized in order to verify the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

Energetic BEM–FEM coupling for wave propagation in 3D multidomains

Starting from a recently developed energetic space–time weak formulation of boundary integral equations for wave propagation problems, a coupling algorithm is presented, which allows a flexible use of FEMs and BEMs as local discretization techniques. Emphasis is given to theoretical and experimental analysis of the stability of the proposed method. Several numerical results on model problems are presented and discussed, showing that both bounded and unbounded three‐dimensional domains can be efficiently addressed. Copyright © 2013 John Wiley & Sons, Ltd.     

超声治疗中耦合液对声聚焦影响的研究

本文推导了凹球面聚焦换能器产生的声波经耦合液进入软组织后的声场计算公式，并对不同耦合液，耦合层厚度，温度对声聚焦的影响进行了研究，得到一一些对超声热疗具有指导意义的结果。     

A BEM sensitivity and shape identification analysis for acoustic scattering in fluid–solid problems

In this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented. Also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems. The formulation developed utilizes the boundary integral equation of the Helmholtz equation for the external problem and the Cauchy–Navier equation for the internal elastic problem. The sensitivities are obtained by the implicit differentiation technique. Examples are presented to demonstrate the accuracy of the proposed formulations. © 1998 John Wiley & Sons, Ltd.     

双腔结构消声器声学性能计算子域耦合方法

提出基于子域划分的耦合方法求解双腔结构消声器声学性能。据结构特点或材料属性将消声器分为不同子域,用数值模态匹配法或三维解析方法求解规则等截面子域结构传递矩阵,用三维数值方法求解非规则渐变截面子域结构传递矩阵,用子域连续条件求得消声器整体矩阵,进而获得消声器传递损失。分别用基于子域划分的耦合方法、三维有限元方法及数值模态匹配法计算典型双腔结构消声器的传递损失。结果表明,基于子域划分的耦合方法适用预测双腔结构消声器声学特性,与数值模态匹配法相比计算效率较高。     

Reissner–Mindlin shell implementation and energy conserving isogeometric multi‐patch coupling

A shear‐flexible isogeometric Reissner–Mindlin shell formulation using non‐uniform rational B‐splines basis functions is introduced, which is used for the demonstration of a coupling approach for multiple non‐conforming patches. The six degrees of freedom formulation uses the exact surface normal vectors and curvature. The shell formulation is implemented in an isogeometric analysis framework for computation of structures composed of multiple geometric entities. To enable local model refinement as well as non‐matching domains coupling, a conservative multi‐patch approach using Lagrange multipliers for structured non‐uniform rational B‐splines patches is presented. Here, an additional border frame mesh is used to couple geometries during structural analyses. This frame interface approach avoids the problem of excessive constraints when multiple patches are coupled at one point. First, the shell formulation is verified with several reference cases. Then the influence of the frame interface discretization and frame penalty stiffness on the smoothness of the results is investigated. The effects of the perturbed Lagrangian method in combination with the frame interface approach is shown. In addition, results of models with T‐joint interface connections and perpendicular stiffener patches are presented. Copyright © 2016 John Wiley & 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.     

E‐field Control of the RKKY Interaction in FeCoB/Ru/FeCoB/PMN‐PT (011) Multiferroic Heterostructures

E‐field control of antiferromagnetic (AFM) orders is promising for the realization of fast, compact, and energy‐efficient AFM applications. However, as the AFM spins are strongly pinned, the E‐field control process is mainly based on the exchange bias regulation that usually confines at a low temperature. Here, a new magnetoelectric (ME) coupling mechanism for the modulation of AFM orders at room temperature is explored. Based on the FeCoB/Ru/FeCoB/(011) Pb(Mg_1/3Nb_2/3)O₃‐PbTiO₃ (PMN‐PT) synthetic antiferromagnetic (SAF) heterostructures, the external E‐field generates relative magnetization switching in the two ferromagnetic (FM) layers, leading the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction tuning. This voltage‐induced switching behavior can be repeated in a stable and reversible manner for various SAFs, which is a key challenge in the E‐field control of AFM coupling and is not resolved yet. The voltage‐induced RKKY interaction changes by analyzing the dynamic optical and acoustic modes is quantified, and with first‐principles calculations, it is found that the distortion of the Fermi surface by the lattice reconstruction is the key of the relative magnetization switching and RKKY interaction modulation. This voltage control of the RKKY interaction in ME heterostructures provides an easy way to achieve the next generation of AFM/FM spintronic applications.     

Partitioned vibration analysis of internal fluid‐structure interaction problems

A partitioned, continuum‐based, internal fluid–structure interaction (FSI) formulation is developed for modeling combined sloshing, acoustic waves, and the presence of an initial pressurized state. The present formulation and its computer implementation use the method of localized Lagrange multipliers to treat both matching and non‐matching interfaces. It is shown that, with the context of continuum Lagrangian kinematics, the fluid sloshing and acoustic stiffness terms originate from an initial pressure term akin to that responsible for geometric stiffness effects in solid mechanics. The present formulation is applicable to both linearized vibration analysis and nonlinear FSI transient analysis provided that a convected kinematics is adopted for updating the mesh geometry in a finite element discretization. Numerical examples illustrate the capability of the present procedure for solving coupled vibration and nonlinear sloshing problems. Copyright © 2012 John Wiley & Sons, Ltd.