基于有限元法的管形振子声场特性研究

利用有限元分析软件ANSYS,对管形振子的振动模态及在清洗槽中的辐射声场进行数值计算分析,并用铝箔腐蚀的方法记录了管形振子的声场分布情况。结果表明基于线性理论的ANSYS软件能够较好地预测低强度的超声场;管形振子在清洗槽中的辐射声场在径向方向出现驻波,驻波沿管形振子的轴向间断出现,驻波数等于振子的半波长数,此外作耦合振动的管形振子和非耦合振动的振子相比其辐射的声场更均匀,表明这种新型辐射器有很好的应用前景。     

非均质岩石力学问题的间接边界元法

本文从非均质体边界元法的基本原理出发，以四周受有均匀液压的非均质弹性体为全钮出了该类问题的间接边界元法的基本方程，并针对衬砌隧洞围岩的应力分析，探讨了该方法的具体实施及程序编制。     

用边界元法进行形状优化

本文用边界元法与序列无约束优化方法相结合,对平面应力下的弹性体进行了形状优化,在优化过程中,用虚拟目标法处理多目标问题。为避免烦锁的灵敏度分析,采用了“新单纯形方法”。文中作的例题,获得满意结果。     

基于间接边界元法开孔板声辐射研究

针对开孔板结构进行声学数值模拟。首先利用有限元软件Patran进行开孔板建模、网格生成以及模态分析,并将模型和模态结果导入声学仿真软件Virtual. Lab Acoustics进行声辐射分析,得到开孔板结构的辐射声功率以及指向性声功率。并在此基础上研究开孔形状、开孔尺寸以及加强筋对板结构声辐射的影响,发现板结构固有频率是影响声辐射的重要因素。     

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。     

边界元法分析中的边界切向应力差分算法

在用边界元法作弹性应力分析中,不能直接计算出弹性体边界切向应力。本文在边界元法分析的基础上,用差分法计算边界切向应力。推导出常边界单元情况下边界切向应力的差分公式。计算表明文中所述方法是可行的,并且简单实用。所研究的方法和公式也适用于高次边界单元的边界切向应力的计算。     

集中荷载下的边界元法

本文应用Betti互等定理,推导出弹性体边界和体内受有限个集中荷载作用时的边界元法,弥补了常规边界元法在处理集中荷载方面的不足。算例结果表明本文方法是有效的。     

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。     

高层建筑结构分析的边界元法

首先简述弹性力学平面问题分域样条虚边界元法的计算原理，该法可用于高层建筑平面结构（如框支剪力墙，联肢墙，框架－剪力墙等）的静力分析，为了能对高层建筑进行整体分析，进一步采用分域样条虚边界元法导出高层建筑侧向刚度矩阵，据此即可对高层建筑进行整体的静力和动力分析，文中给出若干工程算例，说明了方法的可行性和实用性。     

无奇点边界元法分析板的稳定

根据板的稳定问题控制微分方程，利用无奇点边界元法（域外奇点法）离散比，导出稳定特征方程，从而求出临界荷载因子。经编程计算例题，效果良好。     

管式间接蒸发冷却器性能分析及数值方法

现有的管式间接蒸发冷却技术分析,其机理研究有待深入。虽然数值技术省时省力,但针对管式间接蒸发冷却空调的数值方法并不完善。通过对兰州地区管式间接蒸发冷却空调试验测试数据的反复比对验证,本文得到了较为合理的三维全尺寸数值模型和方法,得出结构参数、介质参数等众因素对空调器的性能均有较大影响。     

An indirect elastodynamic boundary element method with analytic bases

An indirect time‐domain boundary element method (BEM) is presented here for the treatment of 2D elastodynamic problems. The approximated solution in this method is formulated as a linear combination of a set of particular solutions, which are called bases. The displacement and stress fields of a basis are analytically derived by means of solving Lame's displacement potentials. A semi‐collocation method is proposed to be the time‐stepping algorithm. This method is equivalent to a displacement discontinuity method with piecewise linear discontinuities in both space and time. The resulting time‐stepping scheme is explicit. The BEM is implemented to solve three numerical examples, Lamb's problem, half‐plane with a buried crack and Selberg's problem. Though Lamb's problem is considered a difficult problem for numerical methods, the current numerical results for the surface displacements show accurately the characteristics of the Rayleigh wave. This method is efficient and accurate. Copyright © 2003 John Wiley & Sons, Ltd.     

An indirect boundary element method for three-dimensional dynamic fracture mechanics

Indirect boundary element methods (fictitious load and displacement discontinuity) have been developed for the analysis of three-dimensional elastostatic and elastodynamic fracture mechanics problems. A set of boundary integral equations for fictitious loads and displacement discontinuities have been derived. The stress intensity factors were obtained by the stress equivalent method for static loading. For dynamic loading the problem was studied in Laplace transform space where the numerical calculation procedure, for the stress intensity factor K_I(p), is the same: as that for the static problem. The Durbin inversion method for Laplace transforms was used to obtain the stress intensity factors in the time domain K_I(t). Results of this analysis are presented for a square bar, with either a rectangular or a circular crack, under static and dynamic loads.     

A fast convergent iterative boundary element method on PVM cluster

This paper reports a fast convergent boundary element method on a Parallel Virtual Machine (PVM) (Geist et al., PVM: Parallel Virtual Machine, A Users' Guide and Tutorial for Networked Parallel Computing. MIT Press, Cambridge, 1994) cluster using the SIMD computing model (Single Instructions Multiple Data). The method uses the strategy of subdividing the domain into a number of smaller subdomains in order to reduce the size of the system matrix and to achieve overall speedup. Unlike traditional subregioning methods, where equations from all subregions are assembled into a single linear algebraic system, the present scheme is iterative and each subdomain is handled by a separate PVM node in parallel. The iterative nature of the overall solution procedure arises due to the introduction of the artificial boundaries. However, the system equations for each subdomain is now smaller and solved by direct Gaussian elimination within each iteration. Furthermore, the boundary conditions at the artificial interfaces are estimated from the result of the previous iteration by a reapplication of the boundary integral equation for internal points. This method provides a consistent mechanism for the specification of boundary conditions on artificial interfaces, both initially and during the iterative process. The method is fast convergent in comparison with other methods in the literature. The achievements of this method are therefore: (a) simplicity and consistency of methodology and implementation; (b) more flexible choice of type of boundary conditions at the artificial interfaces; (c) fast convergence; and (d) the potential to solve large problems on very affordable PVM clusters. The present parallel method is suitable where (a) one has a distributed computing environment; (b) the problem is big enough to benefit from the speedup achieved by coarse-grained parallelisation; and (c) the subregioning is such that communication overhead is only a small percentage of total computation time.     

Multinode finite element based on boundary integral equations

A finite element constructed on the basis of boundary integral equations is proposed. This element has a flexible shape and arbitrary number of nodes. It also has good approximation properties. A procedure of constructing an element stiffness matrix is demonstrated first for one-dimensional case and then for two-dimensional steady-state heat conduction problem. Numerical examples demonstrate applicability and advantages of the method. © 1998 John Wiley & Sons, Ltd.     

Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method

In this paper, the fast Fourier transform on multipole (FFTM) algorithm is used to accelerate the matrix-vector product in the boundary element method (BEM) for solving Laplace equation. This is implemented in both the direct and indirect formulations of the BEM. A new formulation for handling the double layer kernel using the direct formulation is presented, and this is shown to be related to the method given by Yoshida (Application of fast multipole method to boundary integral equation method, Kyoto University, Japan, 2001). The FFTM algorithm shows different computational performances in direct and indirect formulations. The direct formulation tends to take more computational time due to the evaluation of an extra integral. The error of FFTM in the direct formulation is smaller than that in the indirect formulation because the direct formulation has the advantage of avoiding the calculations of the free term and the strongly singular integral explicitly. The multipole and local translations introduce approximation errors, but these are not significant compared with the discretization error in the direct or indirect BEM formulation. Several numerical examples are presented to compare the computational efficiency of the FFTM algorithm used with the direct and indirect BEM formulations.     

Flaw identification using the boundary element method

In this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two-dimensional structures. An introduction to inverse analysis is given, with special reference to methods of flaw identification, along with a brief review of the optimization methods employed. Both the standard boundary element and the dual boundary element method are presented, with the dual boundary element method proposed as the basis for the new formulation. The flaw identification method is presented, along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries. Examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location.     

Local discretization error bounds using interval boundary element method

In this paper, a method to account for the point‐wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd.     

大尺寸超声振动体的研究

文章中介绍了大尺寸超声振动体的研究进展。包括分析耦合振动的表观弹性法；用表观弹性法对短圆柱体、空心圆柱体和矩形六面体的振动进行分析；用开槽、开狭缝、附加弹性体和二次设计等方法对超声振动体的振动进行控制。对有关结果与用有限元方法进行计算的结果进行了比较，并作出了评价。