用边界元法计算有反射面的结构体声辐射

本文在采用边界元方法计算无限域中任意形状结构声辐射的基础上,通过重新推导适用于半无限域问题的Ｇｒｅｅｎ函数,对存在反射面时结构的声辐射情况进行了研究并编制了相应的计算机程序;在此基础上,对放置在刚性反射面上的均匀脉动球的辐射声场进行了计算,与相应的解析解进行了比较并对计算误差作了分析。     

用边界元法计算声辐射时高次奇异积分的处理方法

边界元法应用于计算辐射声场时，由于奇积分的存在，会影响以计算结果的精度，本文描述了处理带有１／ｒ奇异积分和１／ｒ＾２二次奇异积分处理方法，包括数学证明和数值积分方法，计算结果表明这种方法能提高精度。     

室内声场重现中的时域去卷积方法

为了在带反射边界的普通房间内重现声场,需要对原始声场信号进行去卷积处理,以获得扬声器驱动信号。本文建立了房间内声场重现的时域模型,在模型中采用长时长的去卷积网络,以获得高精度同时抑制了时域混叠效应,再针对卷积滤波的海量计算问题使用了快速滤波算法,提高了计算效率。汽车车内加速噪声的重现实验结果表明：本文所提出的时域模型可以高效准确地完成声压信号的去卷积化,实现普通房间内声场的定量重现。     

A coupled interpolating meshfree method for computing sound radiation in infinite domain

In this paper, the coupling of the improved interpolating element‐free Galerkin (IIEFG) method and the variable‐order infinite acoustic wave envelope element (WEE) method is studied. A coupled IIEFG‐WEE method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages. The coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the IIEFG and WEE domains. In the IIEFG domain, the improved interpolating moving least‐squares (IIMLS) method is used to form the shape functions satisfying the Kronecker delta condition while nonsingular weight functions can be used. The impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated. The numerical results show that the coupled IIEFG‐WEE method can take full advantage of both the IIEFG and WEE methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the WEE. The experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain.     

舰船低频水下辐射噪声的声固耦合数值计算方法

针对舰船低频域水下辐射噪声计算问题,指出采用严格遵循声固耦合动力学方程的耦合声学有限元与远场自动匹配层(FEM/AML)方法以及耦合声学间接边界元(IBEM)方法是计算精度较高的策略。以某小水线面双体船(SWATH)为研究对象,使用声功率作为评价指标,探讨了声场区域特征尺度选取对计算精度的影响,比较了上述两种方法与常规基于流固耦合的两种方法在计算特性方面的差异。研究表明,声固耦合模式较流固耦合模式声学响应计算结果偏小,对于SWATH船的合成总声功率级两者偏差达到1dB~3dB,前者计算结果更为精确,基于声固耦合模式的耦合声学IBEM方法是舰船水下辐射噪声预报的首选算法。     

A time domain harmonic BEM implementation for non-homogeneous 3D solids

In the present work, a Boundary Element Method implementation is presented for a specific non-homogeneous elastic media. The media under consideration is a Poisson solid (ν=0.25), which requires additionally a quadratic variation for the material parameters along one cartesian axis (e.g. depth). The 3D problem for the time-harmonic case was implemented and numerically validated for specific problems. Moreover, the static version of the present problem was used to model a real functionally graded composite of alumina–nickel.     

Generic domain decomposition and iterative solvers for 3D BEM problems

In the past two decades, considerable improvements concerning integration algorithms and solvers involved in boundary‐element formulations have been obtained. First, a great deal of efficient techniques for evaluating singular and quasi‐singular boundary‐element integrals have been, definitely, established, and second, iterative Krylov solvers have proven to be advantageous when compared to direct ones also including non‐Hermitian matrices. The former fact has implied in CPU‐time reduction during the assembling of the system of equations and the latter fact in its faster solution. In this paper, a triangle‐polar‐co‐ordinate transformation and the Telles co‐ordinate transformation, applied in previous works independently for evaluating singular and quasi‐singular integrals, are combined to increase the efficiency of the integration algorithms, and so, to improve the performance of the matrix‐assembly routines. In addition, the Jacobi‐preconditioned biconjugate gradient (J‐BiCG) solver is used to develop a generic substructuring boundary‐element algorithm. In this way, it is not only the system solution accelerated but also the computer memory optimized. Discontinuous boundary elements are implemented to simplify the coupling algorithm for a generic number of subregions. Several numerical experiments are carried out to show the performance of the computer code with regard to matrix assembly and the system solving. In the discussion of results, expressed in terms of accuracy and CPU time, advantages and potential applications of the BE code developed are highlighted. Copyright © 2006 John Wiley & Sons, Ltd.     

3D Frequency domain BEM for solving dipolar gradient elastic problems

A three dimensional (3D) boundary element method (BEM) for treating time harmonic problems in linear elastic structures exhibiting microstructure effects is presented. These microstructural effects are taken into account with the aid of the dipolar gradient elastic theory, which is the simplest dynamic version of Mindlins generalized elastic theory. A variational statement is established to determine all possible classical and non-classical (due to gradient terms) boundary conditions of the general boundary value problem. The dipolar gradient frequency domain elastodynamic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well posed problem. Surface quadratic quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. The solution procedure is described in detail. A numerical example serves to illustrate the method and demonstrate its accuracy     

A parallel domain decomposition BEM for diffusion problems with surface reactions

A parallel domain decomposition boundary element method (BEM) is developed for the solution of three-dimensional multispecies diffusion problems. The chemical species are uncoupled in the interior of the domain but couple at the boundary through a nonlinear surface reaction equation. The method of lines is used whereby time is discretized using the finite difference method and space is discretized using the boundary element method. The original problem is transformed into a sequence of nonhomogeneous modified Helmholtz equations. A Schwarz Neumann–Neumann iteration scheme is used to satisfy interfacial boundary conditions between subdomains. A segregated solver based on a quasi-predictor–corrector time integrator is used to satisfy the nonlinear boundary conditions on the reactive surfaces. The accuracy and parallel efficiency of the method is demonstrated through a benchmark problem.     

Time discontinuous linear traction approximation in time‐domain BEM: 2‐D elastodynamics

This paper presents a further improvement of the standard time‐domain BEM formulation for 2‐D elastodynamics. Linear‐time interpolation is assumed for both boundary displacements and tractions.As this assumption implies time continuity for the variables, a procedure to consider tractions time discontinuities must be worked out. The initial step of this procedure consists of adding to the basic BEM integral equation the integral equation for velocities: after discretization is accomplished, this is done only for nodes with prescribed values of displacements. Additional equations are then incorporated to the final system of algebraic equations, providing the means for the determination of the extra unknowns (represented by the tractions at the begining of each time interval). The integral equations are presented by employing the concept of finite part of integrals, and the kernels are integrated analitically on time: complete time‐integrated expressions are included in an appendix. Three numerical examples are presented in order to assess the accuracy of the proposed formulation. Copyright © 2000 John Wiley & Sons, Ltd.     

Combined single domain and subdomain BEM for 3D laminar viscous flow

A subdomain boundary element method (BEM) using a continuous quadratic interpolation of function and discontinuous linear interpolation of flux is presented for the solution of the vorticity transport equation and the kinematics equation in 3D. By employing compatibility conditions between subdomains an over-determined system of linear equations is obtained, which is solved in a least squares manner. The method, combined with the single domain BEM, is used to solve laminar viscous flows using the velocity vorticity formulation of Navier–Stokes equations. The versatility and accuracy of the method are proven using the 3D lid driven cavity test case.     

利用声辐射模态进行声功率的灵敏度分析

采用声辐射模态进行结构辐射声功率计算,具有消除结构振动模态中复杂耦合项的优点,使得计算结构声辐射变得简单。结构声学灵敏度分析包括三类设计变量,以往绝大多数的研究只对其中一类或者两类设计变量进行了分析。而本文采用声辐射模态的方法,对全部三类设计变量进行声学灵敏度分析。对球源声辐射模型进行仿真,该方法计算结果接近理论解,由此证明了该方法的有效性。     

A BEM based domain decomposition method for nonlinear analysis of elastic space membranes

In this paper the Domain Decomposition Method (DDM) is developed for nonlinear analysis of both flat and space elastic membranes of complicated geometry which may have holes. The domain of the projection of the membrane on the xy plane is decomposed into non-overlapping subdomains and the membrane problem is solved sequentially in each subdomain starting from zero displacements on the virtual boundaries. The procedure is repeated until the traction continuity conditions are also satisfied on the virtual boundaries. The membrane problem in each subdomain is solved using the Analog Equation Method (AEM). According to this method the three coupled strongly nonlinear partial differential equations, governing the response of the membrane, are replaced by three uncoupled linear membrane equations (Poisson's equations) subjected to fictitious sources under the same boundary conditions. The fictitious sources are established using a meshless BEM procedure. Example problems are presented, for both flat and space membranes, which illustrate the method and demonstrate its efficiency and accuracy.     

A new boundary condition for energy radiation in covered reservoirs using BEM

In this paper, a new boundary condition accounting for energy radiation at the far end of covered reservoirs is proposed. Using boundary element modelling (BEM), the boundary condition is investigated through analysis of the hydrodynamic pressure within a two-dimensional ice-covered reservoir impounded by a gravity dam. The proposed boundary condition accounts for reservoir bottom absorption effects and the presence of an ice cover at infinity. Seismic excitation is introduced by subjecting the dam and the reservoir to a horizontal harmonic ground motion. The effectiveness of the proposed method and the accuracy of the boundary condition are examined through a parametric study. The boundary condition is shown to be accurate even when placed near the dam upstream face, and the results obtained are in excellent agreement when compared to those from a mathematical model developed by the authors in a previous work. Some fundamental aspects of hydrodynamic pressure within ice-covered reservoirs are also discussed.     

An advanced direct time domain BEM formulation for general 3-D elastodynamic problems

A new advanced time domain BEM formulation is presented for the study of general 3-D elastodynamic problems. The proposed method is based on the infinite space Stokes fundamental solutions, which, for the first time, are written in terms of body forces in the form of higher order B-spline time distributions. Higher order spatial and temporal discretization schemes are applied to the boundary integral equations of the elastodynamic system yielding a time marching solution for the characteristic response of the system due to an excitation with a B-spline distribution in time. This characteristic response due to a B-spline excitation forms the basis, within the framework of a general B-spline superposition scheme, for the calculation of the responses of the same elastodynamic system due to any transient forcing function.     

BEM treatment of two-dimensional anisotropic field problems by direct domain mapping

Using the method of characteristics, a steady-state anisotropic field problem can be reduced to one governed by Laplace's equation in a mapped plane. No rotation of axes is involved in the process, and the coordinate transformation equations are given in this paper. The advantage of this approach is that the anisotropic problem can be easily solved with any of the readily available boundary element method (BEM) programs for ‘isotropic’ potential theory, albeit on a distorted domain. Two numerical examples are presented to illustrate the scheme.     

A BEM formulation for inelastic transient dynamic analysis using domain decomposition and particular integrals

This study deals with the domain decomposition method and particular integrals for multi-region inelastic transient dynamic analysis. The particular integral formulation for single-region inelastic transient dynamic analysis is obtained by eliminating the acceleration volume integral and treating the initial stress term by volume cell. The Houbolt time integration scheme is used for the time- marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. In order to extend to multi-region problems, the domain decomposition method is examined. The domain of the original problem is subdivided into subregions. The interface boundary conditions are updated by using the iterative coupling employing Schwarz algorithm. Numerical results of two example problems are given to demonstrate the validity and accuracy of the present formulation.     

A time domain BEM for 3-D elastodynamic analysis using the B-spline fundamental solutions

A Boundary Element for 3-D elastodynamic analysis is introduced in detail. The method uses a new generation of the Stokes fundamental solutions that utilize the B-spline family of polynomials. The integration techniques of the boundary element kernels are also discussed for both the singular and non-singular cases. A number of numerical examples are presented for the validation of the proposed methodology.     

A general procedure transferring domain integrals onto boundary integrals in BEM

This paper is concerned with transferring to the boundary the domain type integrals occurring in the boundary integral approach applied to boundary value problems with nonzero body force terms. The framework used encloses many interesting engineering applications, e.g. elastostatics, heat conduction and magnetostatics. Beside this are pseudo plastic strains are incorporated due to interaction phenomena with relevant quantities. The proposed method is based upon the homogenization of the governing differential equation by using a particular solution of the inhomogeneous one. Various methods deriving such particular solutions are considered.