层体边界元法在二维层体断裂分析中的应用

在刚度矩阵法的基础上建立了用于进行二维多层体结构断裂分析的边界单元法（ＢＥＭＬＭ）由于ＢＥＭＬＭ的基本方程中已经包含了层体表面和裂纹缝面的边界条件，因而不需要对这些边界进行单元离散，从而其断裂分析可望有较好的精度通过与柯西积分方程法进行结合，算例表明ＢＥ ＭＬＭ是可靠并有效的     

二维弹性结构入水冲击过程中的流固耦合效应

描述了一个研究弹性结构入水冲击过程中水弹性效应的数值方法,在弹性结构入水冲击过程中,流体域作用在结构上的水动力载荷由边界元法获得,而结构的弹性动力响应则由有限元方法求解,通过线性给离散Ｂｅｒｎｏｕｌｌｉ方程将有限元方程和边界元方程耦合到一起,从而获得了求解流场和结构动力响应的相互耦合的运动方程。在数值考虑了自由表面的非线性边界条件,通过引入射流单元以及最大射流厚度,较好地处理了冲击引起的射流问题。     

弹性力学平面问题的无奇异边界积分方程

将弹性力学平面问题归化成无奇异边界积分方程,避免了传统的边界元法中的柯西主值（CPV）积分和Hadamard-Finite-Parts(HFP)积分的计算,建立完整的数值求解体系。     

束破不稳定性的变换法解析理论

束破不稳定性（ＢＢＵＩ）是导致直线加速器中电子束横向运动的致命因素,因而必须进行研究,以便采取相应的扼制措施。我们利用傅立叶变换法求解了ＢＢＵＩ的基本方程,研究了在不同的此导磁场位形下的束破不稳定性（ＢＢＵＩ）增长情况和增长率的ｅ－指数值公式、考察并决定ＢＢＵＩ的增长率（即ｅ－指数值）的物理参数,提出了降低ＢＢＵＩ增长率的相应措施     

用格子Boltzmann方程模拟浅水波问题

提出了用格子Ｂｏｌｔｚｍａｎｎ方程（ＬＢＥ）模拟浅水波问题的方法．通过无粘气体运动方程与浅水波方程的比较，确定了ＬＢＥ方法中平衡态的形式，使宏观方程与浅水波方程一致．计算了二维浅水波的一个问题，数值结果与精确解做了比较．     

有限长压电层合简支板自由振动的三维精确解

基于三维弹性理论和压电理论，导出了有限长矩形压电层合简支板的动力学方程及相应的边界条件，给出了一种求解压电层合板自由振动三维精确解的方法；分析了正、逆向压电效应对层合板振动频率的影响．本文所述的方法和结果对于求解其他三维动态问题，验证、比较其他简化模型、有限元计算结果以及工程应用都有指导意义．     

应力边界元法解平面弹性问题

本文提出了求解平面弹性问题的应力边界元法。简述了边界积分方程的建立,给出了常单元离散化时求系数的解析式。这种方法适用于应力边界值问题。边界积分方程中的一个边界函数就是边界点法向应力和切向应力之和,因此计算孔边应力非常方便。作为数值算例,计算了有孔无限板的孔边应力。应力边界元法也可应用于平面热弹性问题和平板弯曲问题。     

弹性力学边界积分方程的一个发展

本文讨论二维弹性力学平面问题，独立于Ｒｉｚｚｏ型边界分方程，一类新型的边界积分方程，其边界场变量包含应力分量σｉｊｔｉｔｊ（其中ｔｉ是边界切向余弦）。该应力分量可直接用数值方法解边界积分方程求出，它比常规的边界元解提高一阶精度。文末的算例表明确定论的实用性和有效性。     

平面热弹性问题的边界元分析

本文利用位移法由平面热弹性问题的基本方程出发,简要地叙述了边界积分方程的建立及离散化手法,导出了由边界上的位移和表面力直接计算边界应力的公式。作为数值计算例,计算了圆形区域,同心圆区域和具有偏心圆孔的圆形区域的热应力。计算结果与解析解或实验结果进行了比较,两者相当吻合。计算表明,边界元法对求解平面热弹性问题十分有效.本文也适用于有体积力的平面弹性问题.     

考虑水弹性影响的水下航行体结构动响应研究

考虑水弹性的影响,计及惯性力、水动力和弹性力之间的相互耦合作用,将水动力学方程和结构动力学方程联合求解,采用三维势流理论和边界元法推导并计算了水下航行体结构的附加质量矩阵,对带空泡水下航行体出水过程中的结构动响应问题进行了分析.      

Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics

This article is mainly devoted to a review on fast BEMs for elastodynamics, with particular attention on time-harmonic fast multipole methods (FMMs). It also includes original results that complete a very recent study on the FMM for elastodynamic problems in semi-infinite media. The main concepts underlying fast elastodynamic BEMs and the kernel-dependent elastodynamic FM-BEM based on the diagonal-form kernel decomposition are reviewed. An elastodynamic FM-BEM based on the half-space Green’s tensor suitable for semi-infinite media, and in particular on the fast evaluation of the corresponding governing double-layer integral operator involved in the BIE formulation of wave scattering by underground cavities, is then presented. Results on numerical tests for the multipole evaluation of the half-space traction Green’s tensor and the FMM treatment of a sample 3D problem involving wave scattering by an underground cavity demonstrate the accuracy of the proposed approach. The article concludes with a discussion of several topics open to further investigation, with relevant published work surveyed in the process.     

Numerical comparison of two boundary element methods for plane harmonic functions

A direct boundary element method (BEM) has been studied in the paper based on a set of sufficient and necessary boundary integral equations (BIE) for the plane harmonic functions. The new sufficient and necessary BEM leads to accurate results while the conventional insufficient BEM will lead to inaccurate results when the conventional BIE has multiple solutions. Theoretical and numerical analyses show that it is beneficial to use the sufficient and necessary BEM, to avoid hidden dangers due to non-unique solution of the conventional BIE.     

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation(CVBIE) in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation(BIE) is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method.With this method, for the Neumann boundary value problem(BVP) of an interior region,a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.     

导数场边界积分方程分析近边界应力分布

研究二维弹性力学问题边界积分方程,通过分部积分变换消除了常规导数边界积分方程中的超奇异积分,获得仅含强奇异积分的应力自然边界积分方程.对于近边界应力的计算,进一步运用正则化算法解析计算其中的几乎强奇异积分.较常规边界元法相比,应力自然边界积分方程可以求解离边界更加接近的内点应力值.算例证明了文中方法的可应用性和有效性.     

弹性力学问题中一个新的边界积分方程——自然边界积分方程

位移导数边界积分方程一直存在着超奇异积分计算的障碍,该文提出以符号算子δye和εye作用于位移导数边界积分方程,施用一系列变换将边界位移、面力和位移导数转成为新的边界张量,从而得到一个新的边界积分方程－－自然边界积分方程,自然边界积分方奇异性为强奇性,文中给出了相应的Cauchy主值积分算式,自然边界积分方程与位移边界积分方程联合可直接获取边界应力,几个算例表明了自然边界积分方程的正确性。     

Crack propagation in an orthotropic medium with coupled elastodynamic properties

In this paper the Mode-I elastodynamic problem of a crack propagating in an orthotropic medium is studied under the condition that the matrix of elastodynamic coefficients has repeated eigenvalues. It is shown that the crack is constrained in an elastodynamic state which is defined through a compulsory condition coupling its velocity with the elastic parameters of the orthotropic medium. The dynamic stress and displacement components ahead of the crack tip as well as the energy release rate are explicitly obtained.     

A boundary element method for calculating the SH waves scattering from arbitrarily shaped holes in an anisotropic medium

The scattering problem of elastic wave by arbitrarily shaped cavities in an infinite anisotropic medium is investigated by the boundary integral equation (BIE) method. The formulations of BIE are derived with the help of generalized Green's formula. The discretization of BIE is based upon constant elements. After confirmation of the accuracy of the present method, some numerical examples are given for various cavities in a full space, in which an isotropic body with a circular cylinder hole is used for comparison and good agreement is observed. It has been proved that the method developed in this paper is effective.     

各向异性体内含任意孔洞对反平面波散射的边界元方法

本文借助于广义格林公式导出了用位移表示的各向异性介质中SH波入射时的边界积分方程.根据本文作者在文献[8]给出的基本解,求解了各向异性介质中孔洞对SH波的散射问题.边界积分方程的离散基于常数元模式.文中给出了一个圆柱、一个椭圆柱和两个椭圆柱形式的孔洞周围的位移场和应力场的数值结果.最后,对入射波频率较高时的情形作了说明.     

A NOVEL BOUNDARY INTEGRAL EQUATION METHOD FOR LINEAR ELASTICITY--NATURAL BOUNDARY INTEGRAL EQUATION

The boundary integral equation (BIE) of displacement derivatives is put at a disadvantage for the difficulty involved in the evaluation of the hypersingular integrals. In this paper, the operators δij and εij are used to act on the derivative BIE. The boundary displacements, tractions and displacement derivatives are transformed into a set of new boundary tensors as boundary variables. A new BIE formulation termed natural boundary integral equation (NBIE) is obtained. The NBIE is applied to solving two-dimensional elasticity problems. In the NBIE only the strongly singular integrals are contained. The Cauchy principal value integrals occurring in the NBIE are evaluated. A combination of the NBIE and displacement BIE can be used to directly calculate the boundary stresses. The numerical results of several examples demonstrate the accuracy of the NBIE.     

Application of the boundary integral equation (BIE) method to transient response analysis of inclusions in a half space

Transient scattering of elastic waves by inclusions in a half space is investigated by the boundary integral equation (BIE) method. The formulation of BIE presented here is based on the Fourier transform method, and involves the analysis of transformed problems and the reconstitution of transient solutions by Fourier inversion. After the BIE has been solved numerically in the transformed domain, the transient wave fields are obtained with the help of the fast Fourier transform (FFT) algorithm. After confirmation of the accuracy of the present method, some numerical examples are shown for various inclusions in a half space, such as a cavity, an elastic inclusion, and a fluid inclusion.