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。     

声学边界元拟奇异积分计算的自适应方法

提出一种自适应方法计算声学边界元中的拟奇异积分,通过单元分级细分将总积分转移到子单元上以消除拟奇异性。在此方法基础上深入研究拟奇异性,进一步提出接近度的概念,其中临界接近度可作为拟奇异积分计算的理论依据,并可用于预估拟奇异性是否存在。此方法的积分精度可调控,且不受场点位置限制,相比于已有方法更加灵活高效。数值分析表明拟奇异性强弱由场点与单元的相对位置决定,单元上远离场点的区域拟奇异性很弱,无需处理。研究结果为处理边界元法中的拟奇异性问题提供了新的选择和参考。     

论Helmholtz方程的一类边界积分方程的合理性

本文导出了Helmholtz 方程超定边值问题有解的一个充要条件,和用非解析开拓法证明了文[1]中的Helmholtz 方程在外域中的解的边界积分表示式的合理性,并将此类边界积分表示式推广用于带空洞的有限域。这样就比较严密而又浅近地证明了基于该表示式建立起来的间接变量和直接变量边界积分方程的合理性。     

二维边界元法中几乎奇异积分的解析法

边界元分析中的几乎奇异积分难题一直阻碍其在工程中应用.作者提出的半解析法有效计算了几乎奇异积分,在此基础上做进一步推演,得到线性单元和二次亚参元上几乎强奇异和超奇异积分的解析列式,摈弃了数值求积.该算式对高次单元也近似适用.这个算法使得边界元法能够分析弹性力学薄壁结构.     

结构振动辐射声场的预估——边界积分方程中奇异积分的间接处理

本文讨论了利用边界积分方程和边界元技术计算结构的稳态外辐射声场的方法,同时,对边界元方法所固有的奇异数值积分提出了一种简单方便的间接处理方法。计算实例证明所编计算程序和奇异积分处理方法是成功的。利用该程序在已知结构表面振速分布的条件下,可以求出该结构在自由声场中的声功率、表面辐射效率以及声场中任意点的声压值和相位。对一个实际钢质空心封闭圆筒作了计算与实测的比较,结果显示了该方法可应用于实际结构或机器的前景。     

求解夹杂问题的有限部积分──边界元法

利用Kelvin解及有限部积分的概念和方法,导出求解含夹杂二维有限弹性体的超奇异积分方程,继而使用有限部积分与边界元结合的方法,为其建立了数值求解方法,即有限部积分与边界元法.最后计算了若干典型数值例子夹杂端部的应力强度因子.      

三维粘性流体内流问题的边界元研究中求解奇异积分的一种新的数值解法

本文探讨了三维粘性流体内流问题的边界元法研究中奇异积分的一种有效的解法。对边界积分项,采用三角形极坐标来降低奇异积分的维数,从而将整体坐标系下的三角形单元转换成局部坐标系中的单位正方形单元;对域积分项,采用四面体极坐标,不但降低了奇异积分的维数,而且将整体坐标系下的四面体单元转换成局部坐标系中的单位立方体单元,从而使积分域简单化。最后利用高斯积分进行数值求解。     

一类二维奇异积分方程的解法

当|λ|≠1时,在空间L_P(GU Г),P>2,中按Hausdroff正规可解的充要条件。 本文在L_P(GUГ),P>2,中考虑奇异积分方程     

一类带平移的奇异积分方程的Noether可解性

本文讨论了一类具有变系数的带平移的奇异积分方程,获得了方程是Nocther可解(相应的算子为Nocther算子)的充分必要条件,并给出了指标计算公式。     

粘弹性分析的复变边界积分方程法

本文应用弹性－粘弹性对应原理提出了基于复位势基本解的二维粘弹性分析的复变边界积分方程方法，给出了所有基本关系式，编制了相应的计算程序并给出计算实例，与已有工作相比，本方法具有公式统一，程序简洁通用，边界单元数少和效率高等特点。     

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。     

Improved numerical method for the Traction Boundary Integral Equation by application of Stokes' theorem

This paper concerns the direct numerical evaluation of singular integrals arising in Boundary Integral Equations for displacement (BIE) and displacement gradients (BIDE), and the formulation of a Traction Boundary Integral Equation (TBIE) for solving general elastostatic crack problems. Subject to certain continuity conditions concerning displacements and tractions at the source point, singular integrals in the BIE and the BIDE corresponding to coefficients of displacement and displacement gradients at the source point are shown to be of a form that allows application of Stokes' theorem. All the singular integrals in 3-D BIE and BIDE are reduced to non-singular line integrals, and those in 2-D BIE and BIDE are evaluated in closed form. Remaining terms involve regular integrals, and no references to Cauchy or Hadamard principal values are required. Continuous isoparametric interpolations used on continuous elements local to the source point are modified to include unique displacement gradients at the source point which are compatible with all local tractions. The resulting numerical BIDE is valid for source points located arbitrarily on the boundary, including corners, and a procedure is given for constructing a TBIE from the BIDE. Some example solutions obtained using the present numerical method for the TBIE in 2-D and 3-D are presented. © British Crown Copyright 1997/DERA.     

带化学反应的边界层流动问题中一类弱奇异Volterra积分方程的近似解

研究带化学表面反应的边界层流动问题导出的一类弱奇异Volterra积分方程的近似解。以一些化学反应的阶数为例求出解在零点的分数阶级数展开式及其■有理逼近。通过将发散积分解释为Hadamard有限部分积分,并借助数值积分方法导出解在无穷远点的带高阶对数项的渐近展开式。实际计算表明,给出的解在零点和无穷远点展开式的联合使用可以在整个半无限区间上高效地求解这类带化学表面反应的边界层流动问题。     

具有边界摄动的反应扩散时滞方程奇摄动问题(英文)

本文研究了具有边界摄动的非线性时滞反应扩散方程奇摄动问题.首先得到了退化问题的解.其次构造了原问题的外部解.然后引入伸长变量构造了解的初始层校正项,得到了解的形式渐近展开式.最后在适当的假设下,利用微分不等式理论,证明了原初始边植问题解的渐近展开式的一致有效性.     

Singularity Analysis and Boundary Integral Equation Method for Frictional Crack Problems in Two-Dimensional Elasticity

This study investigates the stress singularities in the neighborhood of the tip of a sliding crack with Coulomb-type frictional contact surfaces, and applies the boundary integral equation method to solve some frictional crack problems in plane elasticity. A universal approach to the determination of the complex order of stress singularity is established analytically by using the series expansion of the complex stress functions. When the cracks are open, or when no friction exists between the upper and lower crack faces, our results agree with those given by Williams. When displacement and traction are prescribed on the upper and lower crack surfaces (or vice versa), our result agrees with those by Muskhelishvili. For the case of a closed crack with frictional contact, the only nonzero stress intensity factor is that for pure shear or sliding mode. By using the boundary integral equation method, we derive analytically that the stress intensity factor due to the interaction of two colinear frictional cracks under far field biaxial compression can be expressed in terms of E(k) and K(k) (the complete elliptic integrals of the first and second kinds), where k=[1-(a/b)2]1/2 with 2a the distance between the two inner crack tips and b- a the length of the cracks. For the case of an infinite periodic colinear crack array under remote biaxial compression, the mode II stress intensity factor is found to be proportional to [2b tan(π a/2b)]1/2 where 2a and 2b are the crack length and period of the crack array. This revised version was published online in July 2006 with corrections to the Cover Date.     

Domain-Decomposition Singular Boundary Method for Stress Analysis in Multi-Layered Elastic Materials

This paper applies an improved singular boundary method (SBM) in conjunction with domain decomposition technique to stress analysis of layered elastic materials. For problems under consideration, the interface continuity conditions are approximated in the same manner as the boundary conditions. The multi-layered coating system is decomposed into multiple subdomains in terms of each layer, in which the solution is approximated separately by the SBM representation. The singular boundary method is a recent meshless boundary collocation method, in which the origin intensity factor plays a key role for its accuracy and efficiency. This study also introduces new strong-form regularization formulas to accurately evaluate the origin intensity factors for elasticity problem. Consequently, we dramatically improve the accuracy and convergence of SBM solution of the elastostatics problems. The proposed domain-decomposition SBM is tested on two benchmark problems. Based on numerical results, we discuss merits of the present SBM scheme over the other boundary discretization methods, such as the method of fundamental solution (MFS) and the boundary element method (BEM).     

三阶奇异边值问题的多解性

利用锥上的不动点定理和Green函数的性质,本文在较弱条件下研究了三阶奇异非线性边值问题的多个正解的存在性。     

一类四阶奇异边值问题的正解

研究了一类四阶奇异边值问题，得到了C^3[0，1]正解存在的充分必要条件，以及C^2[0，1]正解存在的充分条件。     

上半平面上的第一类椭圆型方程组的自然积分方程

主要用Fourier变换法讨论第一类椭圆型方程组在上半平面的自然积分方程和Poisson积分公式。