基于快速多极子边界元法的齿轮箱声场分析

齿轮箱是广泛应用的工程机械零部件,准确地模拟其辐射声场对后续的降噪优化设计有着重要作用。边界元方法非常适合分析此类无限域下的声辐射问题。但传统边界元方法有着计算效率低、内存占用高的缺点。该研究发展了宽频的快速多极子边界元方法,并运用该方法计算了齿轮箱在特定频率下的场点声压以及辐射声场。通过对比商用软件的分析结果,验证了所提快速边界元方法的准确性。此外,运用多核并行计算方法,对计算量较大的扫频分析进行加速计算,最终快速、准确地获取了齿轮箱辐射声场的扫频结果。     

快速多极子边界元法预测船舶舱室噪声

将快速多极子边界元法应用于船舶舱室噪声预测,考虑振动、刚性以及阻抗三类边界条件,计算得到舱室表面的辐射声压云图以及监测点处的声压级,通过和Virtual. Lab Acoustic软件计算结果比较验证方法的正确性;此外,通过和传统边界元法在总计算时间上的比较,表明快速多极子边界元法在计算大尺度声学问题中的高效性。     

弹性波三维散射快速多极子间接边界元法求解

边界元方法对于无限域中弹性波散射求解具有独特优势,但求解矩阵的非对称稠密特征极大限制了该方法在大规模实际工程中的应用。为此,基于单层位势理论,结合快速多极子展开技术,通过对球面压缩波和剪切波势函数的泰勒级数展开,建立一种新的快速多极间接边界元方法,以实现大规模弹性波三维散射的精确高效模拟。算例分析表明所提方法能够大幅度降低计算时间和存储量,可在目前普通计算机上快速实现上百万自由度弹性波三维散射问题的快速精确求解。最后以全空间椭球形孔洞群对平面P波、SV波的散射为例,揭示了三维孔洞群周围稳态位移场和应力场的若干分布规律。该文方法对低无量纲频率（ka<5.0）的大规模多体散射问题尤为适合。     

弹性波二维散射快速多极子间接边界元法求解

求解方程的稠密矩阵特征极大削弱了传统边界元法在求解大规模实际工程问题中的优势。为此,结合快速多极子展开技术,发展一种新的高精度快速间接边界元方法,用于求解大尺度或高频弹性波二维散射问题。以全空间孔洞周围SH波散射为例,给出了具体求解步骤。算例分析表明该方法具有很高的计算精度和求解效率,同时能够大幅度降低计算存储量,可在目前主流计算机上实现上百万自由度弹性波散射问题的快速求解。最后以半空间中凹陷场地对SH波的高频散射为例,讨论了凹陷周围高频波散射的基本特征,可为峡谷地形中大型工程抗震设计提供部分理论依据。     

快速多极与常规边界元法机群并行计算的比较

以三维弹性力学问题为例,对快速多极与常规边界元法机群并行计算进行了比较。其中常规边界元法求解方程采用高斯消去法,通过调用标准并行求解函数库ScaLAPACK实现;快速多极边界元法并行计算程序采用ANSIC++语言、调用MPI并行通信库自行编写。两种程序均运行于同一机群并行环境。数值算例表明,在同样的机群条件下,采用快速多极边界元法可使解题规模有数量级的提高,计算速度明显高于常规边界元法,并行效率也优于常规边界元法。     

基于有限元与宽频快速多极边界元的二维流固耦合声场分析

采用有限元/快速多极边界元法进行水下弹性结构的辐射和散射声场分析。Burton-Miller法用于解决传统单Helmholtz边界积分方程在求解外边界值问题时出现的非唯一解的问题。该文采用GMRES和快速多极算法加速求解系统方程。针对传统快速算法在高频处效率低和对角式快速算法在低频处不稳定这一问题,该文通过结合这两种快速算法形成宽频快速算法来克服。同时该文通过观察不同参数条件设置下,宽频快速多极法得到的数值结果在计算精度和计算时间上的变化,得到最优的参数组合值。最后通过数值算例验证该文算法的正确性和有效性。     

快速多极边界元法在大规模传热分析中的应用

该文将快速多极边界元法用于三维稳态传热问题的大规模数值计算。多极展开的引入使得该算法能够在单台个人电脑上完成30万自由度以上的传热边界元分析。统一展开的基本解能够处理混合边界。广义极小残差法作为快速多极边界元法的迭代求解器,数值算例分析了快速多极边界元法的计算效率。结果表明:快速多极边界元法的求解效率与常规算法相比有数量级的提高;在模拟复杂结构大规模传热问题上将具有良好的应用前景。     

边界元法在膜结构与风耦合研究中的应用

膜结构是一种风敏感性结构,结构与风的耦合作用不容忽视。本文将膜结构所处的风场简化为不可压缩势流,运用边界元法求解绕流后作用在膜结构上的风压,然后计算在风压作用下膜结构产生的变形,修正膜结构形状,再次求解变形后膜结构周围流场及作用在其上的风压,这样依次迭代,直至得到收敛的解。这种方法的有效性通过典型算例和其他方法计算结果的对比得到验证。变换膜结构的矢跨比、初始预张力及风场平均风速,研究参数变化对流固耦合的影响,为膜结构抗风研究与工程实践提供参考。     

子结构FMBEM在消声器声场计算中的迭代收敛

子结构快速多极子边界元法融合了快速多极子算法、边界元法与子结构技术,使复杂结构声学问题的高效准确计算成为可能。然而对于不同的求解模型,其迭代收敛速度不稳定甚至不能收敛,直接影响了其在工程实际问题中的广泛应用。鉴于此,文章对子结构快速多极子边界元法,按照不同的矩阵构建及预处理方案分析其迭代收敛特性及影响因素。研究发现,除了采取恰当的矩阵预条件处理技术之外,未知量列向量的构建次序及边界节点编号顺序对迭代收敛速度有着重要影响;单步迭代时间随着计算频率的增大而呈指数增长。此外,以内插管型消声器传递损失的计算为例,通过与实验值的比较证实了该方法的准确性与有效性。     

边界元法在环境声学中的应用

边界元法是边界积分方程的数值解法 ,是随着计算机技术的发展而出现的。建立声学边界积分方程分两种方法 :直接法与间接法。本文介绍了边界元法在环境声学中的应用 ,如声屏障和不同情况下道路周围的声场分布、复杂气象条件对声传播的影响的问题等。由于边界元法是半解析半数值解法。在解边界积分方程时会遇到解的存在与唯一性问题。     

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。     

A wideband fast multipole accelerated boundary integral equation method for time‐harmonic elastodynamics in two dimensions

This article presents a wideband fast multipole method (FMM) to accelerate the boundary integral equation method for two‐dimensional elastodynamics in frequency domain. The present wideband FMM is established by coupling the low‐frequency FMM and the high‐frequency FMM that are formulated on the ingenious decomposition of the elastodynamic fundamental solution developed by Nishimura's group. For each of the two FMMs, we estimated the approximation parameters, that is, the expansion order for the low‐frequency FMM and the quadrature order for the high‐frequency FMM according to the requested accuracy, considering the coexistence of the derivatives of the Helmholtz kernels for the longitudinal and transcendental waves in the Burton–Muller type boundary integral equation of interest. In the numerical tests, the error resulting from the fast multipole approximation was monotonically decreased as the requested accuracy level was raised. Also, the computational complexity of the present fast boundary integral equation method agreed with the theory, that is, Nlog N, where N is the number of boundary elements in a series of scattering problems. The present fast boundary integral equation method is promising for simulations of the elastic systems with subwavelength structures. As an example, the wave propagation along a waveguide fabricated in a finite‐size phononic crystal was demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

求解具有弱界面的复合材料有效性能的近似模型与边界元法

基于中间层模型, 建立了用于描述具有弱界面的多夹杂复合材料的三层嵌入式模型。首先, 给出了计算多夹杂复合材料有效性能的公式, 随后将三层嵌入式模型分成两种体系得到了相应的细观力学近似方法。此外, 针对中间层模型进一步给出了快速多极边界元的基本列式。最后, 通过算例验证所提出的两种方法的正确性及有效性, 并进一步考察了界面性能对复合材料整体宏观性能的影响。比较结果发现, 细观力学近似模型形式简单, 易于编程计算, 适用于快速预测具有弱界面的复合材料有效弹性性能。而数值算法能够快速有效直观的考察复合材料内部受弱界面影响后的应力分布。算例分析结果表明, 当中间层厚度较大而弹性模量较低时, 会使得夹杂不再具有增强效果。并且, 随着中间层厚度的增加, 基体内承担的最大应力也随之增加, 从而容易导致复合材料在界面处产生破坏。     

伴流声场计算的有限元方法及其应用

推导了势流中的声波方程,并运用伽辽金加权余量法建立了相应的有限元(Finite Element Method,FEM)弱形式.对于管道声学问题的计算,给出了所需边界条件的处理方法,通过离散和装配得到有限元矩阵方程.使用自行编写的有限元程序计算分析了 Herschel-Quincke(H-Q)管的消声特性.结果表明,在中...     

An extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials

We propose a formulation for linear elastic fracture mechanics in which the stress intensity factors are found directly from the solution vector of an extended boundary element method formulation. The enrichment is embedded in the boundary element method formulation, rather than adding new degrees of freedom for each enriched node. Therefore, a very limited number of new degrees of freedom is added to the problem, which contributes to preserving the conditioning of the linear system of equations. The Stroh formalism is used to provide boundary element method fundamental solutions for any degree of anisotropy, and these are used for both conventional and enriched degrees of freedom. Several numerical examples are shown with benchmark solutions to validate the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of particle simulation methods to composite materials: a review

Particle simulation methods represent deformation of an object by motion of particles, and their Lagrangian and discrete nature is suitable for explicit modeling of the microstructure of composite materials. They also facilitate handling of large deformation, separation, contact, and coalescence. Mesh-free particle methods will thus be appropriate for a part of issues throughout the lifecycle of composite materials despite their high calculation cost. This study focuses on three particle simulation methods, namely, smoothed particle hydrodynamics, moving particle semi-implicit method, and discrete element method, and reviews approaches for modeling composite materials through these methods. Applicability of each method as well as advantages and drawbacks will be discussed from the viewpoint of engineering of composite materials. This reviewing study suggests capability of particle simulation methods to handle multiphysics and to predict various complex phenomena that necessitate explicit modeling of the material’s microstructure consisting of reinforcements (inclusions), matrix, and voids.     

Application of the boundary element method to three-dimensional potential problems in heterogeneous media

The present work discusses a solution procedure for heterogeneous media three-dimensional potential problems, involving nonlinear boundary conditions. The problem is represented mathematically by the Laplace equation and the adopted numerical technique is the boundary element method (BEM), here using velocity correcting fields to simulate the conductivity variation of the domain. The integral equation is discretized using surface elements for the boundary integrals and cells, for the domain integrals. The adopted strategy subdivides the discretized equations in two systems: the principal one involves the calculation of the potential in all boundary nodes and the secondary which determines the correcting field of the directional derivatives of the potential in all points. Comparisons with other numerical and analytical solutions are presented for some examples.     

Numerical and experimental study of molten pool behaviour and defect formation in multi-material and functionally graded materials laser powder bed fusion

Laser powder bed fusion (LPBF) of multi-material and functionally graded materials (FGM) has attracted significant research interest due to its ability to fabricate components with superior performance compared with those manufactured with single powder material. However, the forming mechanisms of various defects remain unknown. In this paper, a DEM-CFD model was first established to obtain an in-depth understanding of this process. It was discovered that the defects including partially melted and un-melted Invar36 powder were embedded in the lower level of the powder layer; this was attributed to the low laser absorptivity, low melting point and high thermal conductivity of the Cu10Sn powder. Inter-layer defects were more likely to occur with an increased powder layer thickness. In addition, the scanned track width was found related to an equilibrium achieved among the thermal properties of the powder mixture. Process parameters were optimised to obtain FGM structures without defects in both horizontal and vertical directions. Invar36/Cu10Sn samples were fabricated with a multi-material LPBF system using different mixed powder contents and laser volumetric energy densities (VEDs). By increasing the VED, fewer defects were observed between the interface of two processed powder layers, which had a good agreement with the modelling results.     

Multiple pole residue approach for 3D BEM analysis of mathematical degenerate and non‐degenerate materials

In this paper we develop an alternative boundary element method (BEM) formulation for the analysis of anisotropic three‐dimensional (3D) elastic solids. Our implementation is based on the derivation of explicit expressions for the fundamental solution displacements and tractions, of general validity for any class of anisotropic materials, by means of Stroh formalism and Cauchy's residue theory. The resulting fundamental solution remains valid for mathematical degenerate cases when Stroh's eigenvalues are coincident, meanwhile it does not exhibit numerical instabilities for quasi‐degenerate cases when Stroh's eigenvalues are nearly equal. A multiple pole residue approach is followed, leading to general explicit expressions to evaluate the traction fundamental solution for poles of m‐multiplicity. Despite the existence of general displacement solutions in the literature, and for the sake of completeness, the same approach as for the traction solution is considered to derive the displacement fundamental solution as well. Based on these solutions, an explicit BEM approach for the numerical solution of 3D linear elastic problems for solids with general anisotropic behavior is presented. The analysis of cracked anisotropic solids is also considered. Details on the numerical implementation and its validation for degenerate cases are discussed. Copyright © 2010 John Wiley & Sons, Ltd.