非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

A new boundary integral equation for plane harmonic functions

In this paper, we propose a new boundary integral equation for plane harmonic functions. As a new approach, the equation is derived from the conservation integrals. Every variable in the integral equation has direct engineering interest. When this integral equation is applied to the Dirichlet problem, one will get an integral equation of the second kind, so that the algebraic equation system in the boundary element method has diagonal dominance. Finally, this equation is applied to elastic torsion problems of cylinders of different sections, and satisfactary numerical results are obtained.     

New integral equation for plane elasticity crack problems

In the usual formulation of singular equation approach for crack problems in plane elasticity [1,2], if one changes the right-hand term of the integral equation from tractions to resultant forces, a new integral equation can be obtained and is presented in this paper. The newly obtained integral equation has a log singular kernel. Interpolation equation for the dislocation functions (the undetermined functions in the integral equations) is proposed. Numerical examination is used to demonstrate the efficiency of the present technique, and a number of numerical examples are given.     

Integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frames

This paper establishes the integral theory for the dynamics of nonlinearnonholonomic system in noninertial reference frame.Firstly,based on the Routhequation of the relative motion of nonlinear nonholonomic system gives the firstintegral of the system.Secondly,by using cyclic integral or energy integral reduces theorder of the equation and obtains generalized Routh equation and Whittaker equationrespectively.Thirdly,derives canonical equation and variation equation and by usingthe first integral constructs integral invariant.And then,establishes the basic integralvariants and the integral invariant of Poincare-Cartan type.Finally,we give a series ofdeductions.     

各向异性柱体扭转的充分必要的边界积分方程

本文列出各向异性柱体扭转问题无量纲化后的有关方程的边界条件推导和验证了基本解，并指出一些书中基本解列式有误＾［９－１１］，列出了充分必要的边界积分方 程，进行了数据计算，并与习用的边界积分方程所得结果进行了比较，表明在退化值附近，习用的边界积分方程所得的边界剪应力会出现巨大的误差，扭转刚度的误差则要小得多，而充要的边界积分方程计算的结果则如终保持良好的精度，再次显示了它的优点。     

加权残数配点法解正交各向异性板的积分方程

本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积发方程,本文将部分配点取在边界上,另一部分配点取在域外,只用关于找度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序,由于正交各向异性板没有争析形式的、实用的基本解,本文提出了两种新的近似基本解;加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加,算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。     

A NECESSARY AND SUFFICIENT FORMULATION FOR TORSION PROBLEMS OF ANISOTROPIC BODIES

Non-dimensionalized equations and boundary conditions are presentedfor the torsion problem of an anisotropic body.The error of the fundamental solutioncited in some boundary element books is pointed out after an examination of thefundamental solution.Furthermore,a necessary and sufficient boundary integralequation is given for the problem and compared with the conventional boundaryintegral equation.Numerical results show that great errors of the boundary shearstresses obtained by the conventional boundary integral equation appear with a smallerror of torsion stiffness.Meanwhile,the necessary and sufficient boundary integralequation always gives accurate results.     

非均匀弹性材料中反平面的运动裂纹

用解析方法研究了非均匀弹性材料中反平面运动裂纹问题。首先采用余弦变换求解非均匀材料的基本方程，然后根据混合边值条件建立裂纹运动的对偶积分方程，再把对偶积分方程化为第二类Fredholm积分方程。给出了数值算例，计算结果表明材料的非均匀性对动应力强度因子有较大的影响。     

一种基于直接计算高阶奇异积分的断裂力学双边界积分方程分析法

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.      

各向异性势问题充要的随机边界积分方程

本文针对各向异性势问题提出了一类充分必要的随机边界积分方程。数值计算结果表明在退化尺度附近，充要的随机边界积分方程较习用的随机边界积分方程有较大的优越性。     

An integral equation approach to finite deflection of elastic plates

The present paper concerns an approximate integral equation approach to finite deflection of elastic plates with aribitrary plan form. With the combined help of the Berger equation governing non-linear bending and a weighted residual technique for boundary-value problem, a boundary integral equation is formulated for immovable edge conditions. We here clarify the formulation and show that the calculation can be performed, with a slight modification, through a procedure similar to that conventionally employed in the linear bending analysis. Availability of the derived integral equation and the solution scheme is shown by way of simple numerical examples.     

Singular integral equation for antiplane-wave scattering by a semi-infinite crack

The problem of antiplane-wave scattering by a semi-infinite crack is reduced to a singular integral equation of the Cauchy type. This equation is obtained by treating the problem as the limiting case of a sequence of problems for which the crack-opening displacements decay exponentially at infinity, and by using real-variable (as opposed to complex-variable) Fourier-transform methods. An integral identity is used to obtain the solution of the singular integral equation. The solution is shown to coincide with the classical Wiener-Hopf solution of the problem.     

Antiplane crack at the interface of two bonded dissimilar graded piezoelectric materials

The problem of an antiplane crack situated in the interface of two bonded dissimilar graded piezoelectric half-spaces is considered under the permeable crack assumption. The mechanical and electrical properties of the half-spaces are considered for a class of functional forms for which the equilibrium equation has analytic solutions. By using an integral transform technique, the problem is reduced to dual integral equations which are transformed into a Fredholm integral equation by introducing an auxiliary function. The stress intensity factors are obtained in explicit form in terms of auxiliary functions. By solving the Fredholm integral equation numerically, the numerical results for stress intensity factors are obtained which have been displayed graphically to show the influence of the graded piezoelectric materials.     

Multiple reciprocity method with two series of sequences of high-order fundamental solution for thin plate bending

IntroductionIt’swell_knownthatthecomplicatedfundamentalsolution[1,2 ]forHelmholtzequationΔu(x) +k2 u(x) =0　　(x∈Ω:boundedopenregioninR2 )isu (x,y) =-iH(2 )0 (k x-y ) 4,thusit’snotconvenientfornumericalcomputation .IfapplyingthesimplefundamentalsolutionofLaplaceequationu 0 (x ,y) =-ln｜x-y｜(2π) ,theexpressionforthesolutionofequationintheclosedregion Ωisc(y)u(y) + ∫Γu(x) u 0 (x,y) nx -u 0 (x ,y) u(x) n dsx =-k2∫Ωu(x)u 0 (x,y)dΩx.Astherightsideappearstheregionalintegrationinclu…     

多自由度非线性动力学方程的能量校准算法

针对非线性动力学方程,通过Taylor展开和Duhamel积分,得到一个具有待定参数的逐步积分求解公式;通过数学变换,将原动力学方程转换为一个能确定待定参数的能量校准方程;最后将该参数回代入逐步积分公式,得到数值解.数值算例的结果说明了该方法的有效性,可以消除算法阻尼和抑制数值解发散,同时,在大步长的条件下也得到了非常准确而且稳定的结果,可以对系统长期性态进行仿真.     

弹性力学中一种新的边界轮廓法

利用基本解的特性,将面力积分方程化成仅含有Ｃａｕｃｈｙ主值积分的形式,基于这种边界积分方程,提出了一种新的边界轮廓法,对于三维问题,该方法只须计算沿边界单元界线的线积分,对二维问题,则只需计算边界单元两点的热函数之差,无须进行数值积分计算,实例计算说明该方法是有效的。     

An analysis on the flow resistance in the entrance region of diffuse laminar flow between two parallel spherical surfaces

In this paper, V.V. Golubef method is first extended to the diffuse laminar flow between two parallel spherical surfaces. With the boundary layer motion equation in spherical coordinates, we derive the momentum integral equation together with the energy integral equation for the laminar boundary layer of the entrance region between two parallel spherical surfaces. And then by applying Picards gradually approaching method for the momentum integral equation, we get the approximate expression which the entrance region length varies with the thickness of boundary layer. In the end every coefficient of entrace region effect is analyzed and calculated. Projects Suported by the Science Fund of the Chinese Academy of Sciences.     

势问题的重构核粒子边界无单元法

将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性和正确性. }      

三维动态裂纹问题的超奇异积分方程法

基于弹性材料的动态基本方程,结合广义Betti-Rayleigh互易等式与时域下的边界积分方程,推导得到时域下的超奇异积分方程组。引入Laplace域下的动态基本解,将经过主部分析的积分核函数分解为静态和动态部分,其中动态积分核不具有奇异性。在裂纹前沿附近单元,采用与理论分析一致的平方根位移模型。结合Lubich时间卷积实现拉氏变换,采用配置点法计算超奇异积分,获得问题的数值解。并针对椭圆裂纹算例编写Fortran程序,得到冲击荷载作用下张开型裂纹的动态应力强度因子变化规律,数值结果稳定且收敛速度快。     

Singular loadings in elasticity problems and singular solutions of the corresponding integral equations

The method of singular integral equations is an efficient method for the formulation and numerical solution of plane and antiplane, static and dynamic, isotropic and anisotropic elasticity problems. Here we consider three cases of singular loadings of the elastic medium: by a force, by a moment and by a loading distribution with a simple pole. These loadings cause corresponding singularities in the right-hand side function and in the unknown function of the integral equation. A method for the numerical solution of the singular integral equation under the above singular loadings is proposed and the validity of this equation at the singular points is investigated.