BOUNDARY INTEGRAL EQUATIONS FOR BENDING PROBLEM OF REISSNER'S PLATES ONTWO-PARAMETER FOUNDATION

I.IntroductionThickplatesonelastict'oundationarewidelyusedinengineering,suchasthebottomplatesofoffShorestructures,surfaceplatesonrunwayofairportsandfoundationsofhigh-risebuildingsandthelike.Itisextremelydifficulttoobtainanalyticalsolutiontarathickplatewithcomplicatedshapeorcomplicatedboundaryconditiononelasticfoundation.Inrecentyears,theboundaryelementmethod(BEM)hasbeensuccessl'ullyusedtoanalyzethebendingproblemofplatesoneverykindofelasticfoundation(Ref.[l,2.3]).Butthereareonlyfewreferences…     

域内具有支承及集中质量的薄板自由振动的边界元分析

本文基于薄板小挠度弯曲问题的基本解,建立了任意边界条件、域内具有支承及附有征意个集中质量的薄板自山振动的边界积分方程,文中计算了若干算例,其精度是实际工程中所允许的。     

Boundary integral equations for bending problem of Reissener's plates on two-parameter foundation

Two fundamental solutions for bending problem of Reissner's plates on two-parameter foundation are derived by means of Fourier integral transformation of generalized function in this paper. On the basis of virtual work principles, three boundar integral equations which fit for arbitrary shapes, lods and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods. Project supported by the P.H.D. Foundation of National Education Committee of China     

Boundary element method for arbitrary elastic thin shell

In this paper, a boundary element scheme for arbitrary elastic thin shells is elaborated, Based on BEM of 3D linear elasticity and Kirchhoff's hypothesis, boundary integral equations for shells are deduced. As a result, only Kelvin's solution is used, the difficulty in finding a fundamental solution of arbitrary shells is successfully avoided. The project supported by National Natural Science Foundation of China     

On the mathematical problems of composite materials with a doubly periodic set of cracks

In this paper,the mathematical problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated,and the interface are arbitrary smooth closed contours.At first,we establish mathematical models by using Muskhelisvili complex variable methods,change the primitive problems into searching complex stress functions which satisfy four boundary value problems and construct forms of the solution,then,under some general restrictions it is reduced to normal type singular integral equation,the unique solvability is proved mathematically     

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。     

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.     

横观各向同性材料三维裂纹问题的数值分析

严格从三维横观各向同性材料弹性空间问题的Green函数出发,采用Hadamard有限部积分概念,导出了三维状态下单位位移间断(位错)集度的基本解.在此基础上,将三维任意形状的片状裂纹问题归结为求解-组以未知位移间断表示的超奇异积分方程;并给出了边界元离散形式.对方程中出现的超奇异积分,采用了Had-alnard定义的有限部积分来处理.论文最后给出了若干典型片状裂纹问题的数值算例,数值结果表明了本文方法是非常有效的.     

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…     

双材料中平片裂纹问题的超奇异积分方程解法

利用三维断裂力学的超奇异积分方程方法,对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位罗间断为未知函数的超奇异积分方程,并为其建立了数值法。在此基础上,讨论了用裂纹面位移问题计算应力强度因子的方法。最后用此计算了几个典型的Ⅰ型下片裂纹问题的应力强度因子,其数值结果令人满意。     

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。     

正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

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.     

Degenerate scale problem for plane elasticity in a multiply connected region with outer elliptic boundary

This paper investigates the degenerate scale problem for plane elasticity in a multiply connected region with an outer elliptic boundary. Inside the elliptic boundary, there are many voids with arbitrary configurations. The problem is studied on the relevant homogenous boundary integral equation. The suggested solution is derived from a solution of a relevant problem. It is found that the degenerate scale and the non-trivial solution along the elliptic boundary in the problem are same as in the case of a single elliptic contour without voids. The present study mainly depends on integrations of several integrals, which can be integrated in a closed form.     

一种处理弹性动力边界元法中奇异积分的方法

利用边界元法求解瞬态弹性动力学问题时，时域基本解函数的分段连续性和奇异性为该问题的求解带来很大的困难。为了解决时域基本解中的奇异性问题，本文依据柯西主值的定义，对经过时间解析积分之后的时域基本解进行奇异值分解，将其分成奇异和正则积分两部分；其中正则部分可通过采用常规高斯积分方法来计算，而奇异部分具有简单的形式，可以利用解析积分计算。经过上述操作之后，就可以达到直接消除时域基本解中奇异积分的目的。和传统方法相比，本文方法并不依赖静力学基本解来消除奇异性，是一种直接求解方法。最后给定两个数值算例来验证本文提出方法的正确性和可行性，结果表明使用本文算法可以解决弹性动力学边界积分方程中的奇异性问题。     

薄板稳定问题的边界元法

本文基于小挠度薄板弯曲问题的基本解,建立了求解薄板稳定问题的边界积分方程,并计算了若干算例,结果表明用边界元法求解薄板的稳定问题是行之有效的.     

The Solution to the Form of Poisson Equation by the Boundary Element Methods

ＳＯＬＵＴＩＯＮＴＯＴＨＥＦＯＲＭＯＦＰＯｌＳＳＯＮＥＱＵＡＴＩＯＮＢＹＴＨＥＢＯＵＮＤＡＲＹＥＬＥＭＥＮＴＭＥＴＨＯＤＳＬｉｕＸｉ－ｙｕｎ（刘希云）（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆｓｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ）Ｎａｎｊｉｎｇ（Ｒ...     

Boundary element method for orthotropic thick plates

The fundamental solutions of the orthotropic thick plates taking into account the transverse shear deformation are derived by means of Hörmander's operator method and a plane-wave decomposition of the Dirac δ-function in this papey. The boundary integral equations of the thick plates have been formulated which are adapted to arbitrary boundary conditions and plane forms. The numerical calculation of the fundamental solutions is discussed in detail. Some numerical examples are analyzed with BEM.     

Diffraction of an arbitrary acoustic wave by a strip of finite width

The problem of the diffraction of an arbitrary acoustic wave by a strip of finite width is solved. The solution is constructed by means of a generalization of the previously obtained integral for the problem of the diffraction of acoustic waves by a half-plane [5]. The problem of the diffraction of an arbitrary acoustic wave by the Riemannian manifold corresponding to the strip of finite width is first found. After this, by substitution of the values of the polar angle a solution is obtained for the reflected wave associated with diffraction on the Riemannian manifold, and then the boundary conditions on the surface of the strip are satisfied by means of a linear combination of these solutions. The problem of the diffraction of an arbitrary acoustic wave by a slit of finite width could be constructed in exactly the same way.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1991.     

Anti-plane dynamic hole–crack interaction in a functionally graded piezoelectric media

The anti-plane dynamic problem of a functionally graded piezoelectric plane containing a hole–crack system is treated by a non-hypersingular traction-based boundary integral equation method. The material parameters vary exponentially in the same manner in an arbitrary direction. The system is loaded by an incident SH-type wave, and impermeable boundary conditions are assumed. Using a frequency-dependent fundamental solution of the wave equation, the boundary value problem is transformed into a system of integro-differential equations along the boundary of the hole and on the crack line. Its numerical solution yields the dynamic stress intensity factors and stress concentration factors. A parametric study reveals their dependence on the hole–crack scenario and its geometry, characteristics of the dynamic load and magnitude and direction of material inhomogeneity.