利用边界元法中的全特解场方法计算结构振动声辐射

本文通过利用边界元法中的全特解场方法，对结构振动声辐射的计算进行了研究，并以脉动球为算例，将计算结果与解析解进行比较，结果表明：该方法与一般边界元法相比，在边界剖分相同的情况下，能够在相当宽的振动范围内，给出满意的计算结果。     

用特解边界元法研究地基弹性和裂缝对重力坝动力特性的影响

本文研究动力问题的特解边界元法，给出了理论推导，并用该法分析了重力坝坝踵水平裂缝及其地基弹性和坝高对坝体自振特性的影响，并将特解边界元法推广应用到两个区域问题，同时得到了一些有益的结论。     

基于声辐射逆问题的故障诊断与噪声分析的研究

本文采用全特解场边界元求解声辐射逆问题的方法,通过对故障诊断和噪声源分析、相位分析、声环境设计的仿真计算与讨论,初步揭示了声源与其所发生声场的逆关系。计算结果可为噪声控制、故障诊断、声环境设计等工程实际应用提供有价值的参数。     

全特解场边界元方法在声辐射逆向问题中的应用研究

采用全特解场边界元方法求解声辐射逆问题，这种方法不需要变量插值、积分求解及奇性处理，因而计算量大幅度减少，且计算精度高。本文还从辐射声场的情况来探知声源的振动特性，这对噪声的主动控制及低噪声结构优化设计有着很大的意义，为噪声诊断提供直接的依据。     

重力坝坝踵区地震断裂分析

本论文根据实际的情况，把重力坝及地基作为粘弹性材料，利用特解边界元法计算了坝踵区非均质界面裂缝在地震作用下的动态应力强度因子，最后通过该结果的分析，得出了一些有益的结论。     

用边界元反分析构造平面残余应力场

基于固有应变概念,采用边界元方法,提出一种反方法构造连续的满足域内自平衡条件的平面残余应力场。考虑到反分析的稳定性,固有应变场用一系列光滑基函数(如多项式和三角函数)近似;为了识别由剪切固有应变引起的残余应力,求出对应于固有应变的位移特解与面力特解,将域内积分用双重互易边界元法转换为边界积分,保持了边界元法的优势;同时导出了灵敏度矩阵的显式表达,以提高反分析的效率。最后给出了两个算例验证方法的可行性。     

高层建筑—地基动力相互作用半解析法的研究

提出一种上部结构有限条法、地基（土）特解边界元法相结合的半解析方法，首次建立了这一力学模型在频域内的运动方程，并编制了求解结构－地基动力相互作用的程序。通过计算有关算例，并与ＳｕｐｅｒＳＡＰ程序计算结果进行比较，证明本文的基本理论和计算程序是正确、可行的。     

全特解场边界元方法在声辐射逆问题中的应用研究

采用全特解场边界元方法求解声辐射逆问题,这种方法不需要变量插值、积分求解及奇性处理,因而计算量大幅度减少,且计算精度高。本文还从辐射声场的情况来探知声源的振动特性,这对噪声的主动控制及低噪声结构优化设计有着很大的意义,为噪声诊断提供直接的依据。     

WB法分析声腔的中频响应

分析振动-声的数值方法主要是基于单元的方法，如有限元和边界元。由于计算效率低，基于单元的方法在实际中约束在低频段。近年来，基于间接Trefftz法的WB（Wave Based）法得到了发展。与基于单元的方法相比，结构和声域都不再需要划分成更小的单元以及在每个单元内采用简单、近似的形函数来求解动力学方程，而是整个域内的压力场由精确满足动力学方程齐次部分的波函数和满足动力学非齐次方程的特解函数组成。波函数的常数系数通过加权余量或者最小二乘法得到。基于二维的例子讨论了这种方法的收敛特性并与有限元结果进行了比较。结果表明WB法比有限元法计算效率更高以及更好的收敛特性。     

分裂四元数矩阵方程$AXB+CYD=E$的最小二乘$\eta$-埃尔米特解问题

分裂四元数矩阵方程求约束解问题在数学研究和物理应用中有重要的科学意义,针对分裂四元数矩阵的范数定义所造成的最小二乘解求解困难问题,研究了分裂四元数矩阵方程$AXB +CY D = E$的最小二乘$\eta$-埃尔米特解。首先定义分裂四元数反对合变换和$\eta$-埃尔米特矩阵,其次引入分裂四元数矩阵的Frobenius范数,通过基于分裂四元数矩阵的复表示,解决最小二乘解的求解困难问题。最后利用矩阵的Moore-Penrose广义逆以及Kronecker积,推导出分裂四元数矩阵方程的最小二乘$\eta$-埃尔米特解以及唯一极小范数解的表达式。数值实验验证了该方法的可行性。     

Radial integration boundary element method for acoustic eigenvalue problems

In this paper, the radial integration boundary element method is developed to solve acoustic eigenvalue problems for the sake of eliminating the frequency dependency of the coefficient matrices in traditional boundary element method. The radial integration method is presented to transform domain integrals to boundary integrals. In this case, the unknown acoustic variable contained in domain integrals is approximated with the use of compactly supported radial basis functions and the combination of radial basis functions and global functions. As a domain integrals transformation method, the radial integration method is based on pure mathematical treatments and eliminates the dependence on particular solutions of the dual reciprocity method and the particular integral method. Eventually, the acoustic eigenvalue analysis procedure based on the radial integration method resorts to a generalized eigenvalue problem rather than an enhanced determinant search method or a standard eigenvalue analysis with matrices of large size, just like the multiple reciprocity method. Several numerical examples are presented to demonstrate the validity and accuracy of the proposed approach.     

A boundary element method for analysis of thermoelastic deformations in materials with temperature dependent properties

In this paper, the boundary element method (BEM) for solving quasi‐static uncoupled thermoelasticity problems in materials with temperature dependent properties is presented. The domain integral term, in the integral representation of the governing equation, is transformed to an equivalent boundary integral by means of the dual reciprocity method (DRM). The required particular solutions are derived and outlined. The method ensures numerically efficient analysis of thermoelastic deformations in an arbitrary geometry and loading conditions. The validity and the high accuracy of the formulation is demonstrated considering a series of examples. In all numerical tests, calculation results are compared with analytical and/or finite element method (FEM) solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical stability in regular BEM schemes for elastostatic problems

The regular boundary element method is employed for the static analysis of boundary value problems of elasticity. This method allows one to reduce a given boundary value problem to a system of regular integral equations of the first kind with respect to source functions not located on the boundary. This paper is concerned with the numerical stability analysis of regular boundary element methods. In particular, the existence and stability of approximate solutions for integral equations of the first kind with continuous kernels are discussed. The special regularization technique for treating such a class of integral equations is developed. Numerical examples illustrate proposed algorithms and demonstrate their advantages.     

Dislocation and point-force-based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions

In this paper we give the theoretical foundation for a dislocation and point-force-based approach to the special Green's function boundary element method and formulate, as an example, the special Green's function boundary element method for elliptic hole and crack problems. The crack is treated as a particular case of the elliptic hole. We adopt a physical interpretation of Somigliana's identity and formulate the boundary element method in terms of distributions of point forces and dislocation dipoles in the infinite domain with an elliptic hole. There is no need to model the hole by the boundary elements since the traction free boundary condition there for the point force and the dislocation dipole is automatically satisfied. The Green's functions are derived following the Muskhelishvili complex variable formalism and the boundary element method is formulated using complex variables. All the boundary integrals, including the formula for the stress intensity factor for the crack, are evaluated analytically to give a simple yet accurate special Green's function boundary element method. The numerical results obtained for the stress concentration and intensity factors are extremely accurate. © 1997 John Wiley & Sons, Ltd.     

A hybrid finite difference and moving least square method for elasticity problems

In this paper, a novel hybrid finite difference and moving least square (MLS) technique is presented for the two-dimensional elasticity problems. A new approach for an indirect evaluation of second order and higher order derivatives of the MLS shape functions at field points is developed. As derivatives are obtained from a local approximation, the proposed method is computationally economical and efficient. The classical central finite difference formulas are used at domain collocation points with finite difference grids for regular boundaries and boundary conditions are represented using a moving least square approximation. For irregular shape problems, a point collocation method (PCM) is applied at points that are close to irregular boundaries. Neither the connectivity of mesh in the domain/boundary or integrations with fundamental/particular solutions is required in this approach. The application of the hybrid method to two-dimensional elastostatic and elastodynamic problems is presented and comparisons are made with the boundary element method and analytical solutions.     

Plane stress and plate bending coupling in BEM analysis of shallow shells

In this paper the shear deformable shallow shells are analysed by boundary element method. New boundary integral equations are derived utilizing the Betti's reciprocity principle and coupling boundary element formulation of shear deformable plate and two‐dimensional plane stress elasticity. Two techniques, direct integral method (DIM) and dual reciprocity method (DRM), are developed to transform domain integrals to boundary integrals. The force term is approximted by a set of radial basis functions. Several examples are presented to demonstrate the accuracy of the two methods. The accuracy of results obtained by using boundary element method are compared with exact solutions and the finite element method. Copyright © 2000 John Wiley & Sons, Ltd.     

The boundary element‐free method for elastoplastic implicit analysis

A meshless procedure, based on boundary integral equations, is proposed to analyze elastoplastic problems. To cope with non‐linear problems, the usual boundary element method introduces domain discretization cells, often considered a ‘drawback’ of the method. Here, to get rid of the standard element and cell, i.e. boundary and domain discretization, the orthogonal moving least squares (also known as improved moving least squares) method is used. The algorithm adopted to solve these particular inelastic non‐linear problems is a well‐established, criterion‐independent implicit procedure, previously developed by the authors. Comparative results are presented at the end to illustrate the effectiveness of the proposed techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

Efficient preconditioners for boundary element matrices based on grey‐box algebraic multigrid methods

This paper is concerned with the iterative solution of the boundary element equations arising from standard Galerkin boundary element discretizations of first‐kind boundary integral operators of positive and negative order. We construct efficient preconditioners on the basis of so‐called grey‐box algebraic multigrid methods that are well adapted to the treatment of boundary element matrices. In particular, the coarsening is based on an auxiliary matrix that represents the underlying topology in a certain sense. This auxiliary matrix is additionally used for the construction of the smoothers and the transfer operators. Finally, we present the results of some numerical studies that show the efficiency of the proposed algebraic multigrid preconditioners. Copyright © 2003 John Wiley & Sons, Ltd.     

A comparison of domain integral evaluation techniques for boundary element methods

In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible. Copyright © 2001 John Wiley & Sons, Ltd.     

基于有限元与边界元耦合法的波浪力分析

利用有限元与边界元耦合法对三维无界区域中直立圆柱所受的波浪力进行进行计算,把整个求解区域分成内域或外域两部分,在内域采用有限元法,对外域采用边界元法,数值计算的结果与理论解吻合良好,表明该方法有效。