边界元——有限元耦合方法分析

本文对边界元－有限元耦合方法分析二维弹性力学问题进行了探讨。采用非连续元离散边界积分方程，解决了耦合分析中的自由度约束问题。给出了利用非连续元实现边界元－有限元耦合的具体步骤。数值算例表明了本文方法的有效性。     

二维边界元分析强奇异积分确定的一种新方法

基于基本解的一种新的表达式，对二维边界元分析中强奇异积分的确定进行了讨论，从几何方面对基本解的奇异性进行了分析，给出了超参非连续元离散边界积分方程时，位势和弹性力学问题强奇异积分计算的精确表达式，为精确和有效地分析大规模问题提供了一条便利的途径。     

二维位势问题中边界点位势法向导数的一种精确积分解法

通过将内点位势梯度积分方程中的内点移至边界，并利用方向导数公式，推导出了一种求解边界点位势法向导数的积分方程，并以二维位势问题为例，给出了用非连续线性边界元离散这一积分方程时积分计算的精确表达式，用两个数值算例验证了这一精确积分表达式的正确性和精确性。     

无网格方法在二维弹性力学计算中的应用

通过选取合适的权函数和基函数，将无网格局部伽辽金法用于二维弹性力学计算．计算中，积分都在规则形状边界子域上完成，因而容易实现；通过罚因子添加本质边界条件，从而使得到的刚度矩阵是正定对称矩阵．将计算结果与ANSYS有限元法的计算结果进行比较，结果表明，无网格法用于二维弹性力学计算具有精度高、稳定性好和适应性强等优点．     

三维边界多域缩聚法分析

采用超参非连续边界元用积分方程及三角极坐标变换方法处理奇异积分。将超参非连元应用于多域边界元法分析，解决了自由度约束问题，提出了二次缩聚的概念，提高了我域缩聚边界元法的求解效率。     

用边界元法计算流固耦合问题时高次奇异积分的处理方法

边界元法应用于计算流固耦合问题时,由于奇异积分的存在,会影响到计算结果的精度.本文描述了处理带有(1)/(r)奇异积分和(1)/(r2)二次奇异积分的处理方法,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.     

边界元拟波阵解法的应用

为解决边界元法的非对称满阵的存贮和求解效率问题,本文应用了拟波阵算法求解线性方程组,并在二维边界元程序中应用了拟波阵解法,与高斯解在计算精度和时间上进行了比较,结果表明拟波阵解法是经济有效的。本文提出的程序设计思想可直接推广到三维或其他边界元方程的求解中去。     

流-固耦合问题边界元-有限元耦合方法分析

利用边界元－有限元耦合方法对流－固耦合振动问题进行了分析,假设流体控制方程为Ｌａｐｌａｃｅ方程,利用非连续边界元对流体域进行离散,从而有铲地解决了边界元分析中的“角点效应”问题。固体以平面梁为模型,采用有限元进行离散,对非连续边界元和有限元的耦合问题进行了分析,通过对悬臂梁在一侧受液体作用时的瞬态响应分析的数值解同解析解的比较,表明了本文所给方法的有效性,同时为利用边界元－有限元耦合方法对流－固耦     

自然单元法在弹性力学中的应用

介绍自然单元法（NEM）在处理二维弹性力学问题中的应用．该方法利用求解点的自然邻接点和Voronoi结构构造整体近似位移函数，且在求解区域的Delaunay三角形子域上采用Galerkin过程建立整体求解的系统平衡方程，其积分可在背景三角形网格上采用数值积分得到．     

斜射Rayleigh面波在粘弹性界面上的反射和透射

研究了由相同或不同材料所构成的两个四分之一空间的粘弹性界面上斜射Ｒａｙｌｅｉｇｈ面波的反射与透射。界面的力学性质用一薄粘弹性层表示，通过空间格林函数方法，将三维问题化为二维问题处理，导出了求解该问题的奇异积分方程，采用边界元法进行数值求解，得到了反射系数Ｒ与透射系数Ｔ，结果用弹性常数的可选值、界面参数Ｒａｙｌｅｉｇｈ面波的入射角表示。     

Influences on the spatial directivity of acoustic vector sensor by finite cylinder baffle and future prospects about eliminating the effects

The directivity of acoustic vector sensor can be distorted by the sound diffraction wave of baffle. According to Helmholtz integral equation, the directivity of acoustic vector sensor under the condition of finite cylinder baffle is calculated by using boundary element method (BEM). Considering the problem of nearly singular integrals of BEM, the exponent parts of fundamental solutions are expanded in trigonometric functions. The singular and the nonsingular parts are separated: the nonsingular parts are calculated by Gaussian integral method; the singular parts are regularized by subsection integral method. Then the surface integrals are reduced into line integrals along the elements?? contour which can be calculated by Gaussian integral method. The sound diffraction field of a plane wave under the condition of finite cylinder baffle at different frequencies and incident angles is calculated, and the characteristics of directivity of pressure and vibration velocity at different frequencies are analyzed. The experimental data are treated and the errors between the experimental and theoretical results are analyzed. Finally, according to the research results about the influences on the directivity of acoustic vector sensor by baffle at present, some future prospects about eliminating the effects of sound diffraction field by baffle are presented.     

Smolyak Type Sparse Grid Collocation Method for Uncertainty Quantification of Nonlinear Stochastic Dynamic Equations

This paper develops a Smolyak-type sparse-grid stochastic collocation method(SGSCM) for uncertainty quantification of nonlinear stochastic dynamic equations.The solution obtained by the method is a linear combination of tensor product formulas for multivariate polynomial interpolation.By choosing the collocation point sets to coincide with cubature point sets of quadrature rules,we derive quadrature formulas to estimate the expectations of the solution.The method does not suffer from the curse of dimensionality in the sense that the computational cost does not increase exponentially with the number of input random variables.Numerical analysis of a nonlinear elastic oscillator subjected to a discretized band-limited white noise process demonstrates the computational efficiency and accuracy of the developed method.     

有势流边界积分方程奇点的简洁处理法

本文结合笔者所做的多种流体在线混合的研究课题讨论了有势流直接数字积分的一般方法。为了使高斯积分法或其它的数字积分法能简单的直接用于求积分值 ,从而推导出了一个更简洁的计算公式 ,在该公式中格林函数中的奇点从理论上被消除。在本文中可以不用插值函数求解未知变量 ,因此 ,该方法比传统方法更为简单。     

Analysis of numerical integration error for Bessel integral identity in fast multipole method for 2D Helmholtz equation

In 2D fast multipole method for scattering problems, square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel, and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule, and the relationship between trapezoidal and square quadrature rule, sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.     

断裂力学中奇异积分方程的数值求解方法

对断裂力学中奇异积分方程的数值求解技术进行了综述。重点论述了第一类和第二类Cauchy型奇异积分方程以及超奇异积分方程的数值解法。这些方法的主要思想都是通过将奇异积分方程中的未知函数表示为多项式形式连续函数与特定形式权函数的乘积,然后借助Cauchy主值积分定义与超奇异积分的有限部积分定义,将奇异积分方程的求解归结为求解一组线性代数方程。本文拟结合一些具体的数值算例,对奇异积分方程中未知函数的不同表达方式、特点进行了评述,并比较了各种算法的优缺点。最后,指出了求解奇异积分方程的数值解法研究的未来发展方向。     

水下声散射问题的奇异积分研究

奇异积分和近奇异积分的数值计算是实施边界元法研究水下目标声散射特性的一个难点,全局法是一种可以将面积分转化为计算沿边界曲线的线积分,基于全局法的思想,推导得到了边界元法中奇异积分和近奇异积分的数值计算表达式．仿真结果表明通过奇异积分和近奇异积分的精确处理,提高了边界元法的数值计算精度;且由于得到的数值表达式是闭合的,提高了积分的计算速度;得到的数值表达式不仅可以用于水下声散射特性研究,在声辐射、电磁散射等研究中都可以得到满意的精度．     

大地测量混合边值问题的自然边界元解法

在物理大地测量边值问题的球近似下.将大地测量混合边值问题转化为Neumann外问题,用自然边界元法,对Neumann外问胚进行自然边界归化,得到自然边界积分方程,再求自然边界积分方程的数值解.在球界面下,利用自然边界元方法,将大地测量混合边值问题的求解,转化为线性方程组的求解,而线性方程组的解存在惟一稳定,因而大地测量混合边值问题的解存在惟一稳定.     

多边形孔奇异性应力干涉问题的研究

采用一种新型杂交元方法研究了多边形孔相互干涉条件下的奇异性应力场问题.首先运用多变量变分原理构造一种超级切口尖端单元,其中,假定的应力场和位移场变量是利用奇异性场数值特征解推导出来的.尔后将该超级切口尖端单元与传统4节点杂交应力元耦合在一起,即可建立起一种分析含任意多边形孔弹性结构分析的新型有限元模型.最后用该模型考察...     

Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems

The displacement discontinuity method (DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue, enlightened by the mapped finite element method (FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM (MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.     

Wave superposition based sound field reconstruction

In order to overcome the obstacle of singular integral in boundary element method (BEM), wepresented an efficient sound field reconstruction technique based on the wave superposition method (WSM). Itsprinciple includes three steps: first, the sound pressure field of an arbitrary shaped radiator is measured witha microphone array; then, the exterior sound field of the radiator is computed backward and forward using theWSM; at last, the final results are visualized in terms of sound pressure contours or animations. With thesevisualized contours or animations, noise sources can be easily located and quantified; also noise transmissionpath can be found out. By numerical simulation and experimental results, we proved that the technique aresuitable and accurate for sound field reconstruction. In addition, we presented a sound field reconstruction sys-tem prototype on the basis of this technique. It makes a foundation for the application of wave superpositionin the sound field reconstruction in industry situations.