论Hertz接触问题解的不唯一性

本文根据积分方程的理论,对Hertz接触问题的积分方程的特点进行了分析,指出该问题的解不是唯一的。     

Equivalence between the Local Boundary Integral Equation and the Mean Value Theorem in the Theory of Elasticity

The boundary element method based on a boundary integral equation has been very successful in computational mechanics. Atluri et al. [4] recently developed a new meshless method using the local boundary integral equations. It eliminates the tedious step of mesh generation and thus greatly simplifies the numerical computation process. This paper shows the equivalence between the local boundary integral equation and the mean value theorem in the theory of elasticity. In addition, it gives new proofs for the mean value theorem of elasticity and its converse based on the concept of a companion solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Hertz接触问题的解的唯一性条件

讨论了接触面为圆面的Ｈｅｒｔｚ接触问题。若压力分布是轴对称的，则该接触问题的解必是唯一的。且在上述条件下，该接触问题的积分方程可化为两个推广的Ａｂｅｌ积分方程组，此方程组的解便给出此接触问题的解。     

功能梯度材料涂层半空间的轴对称光滑接触问题

求解了功能梯度材料涂层半空间的轴对称光滑接触问题,其中梯度层剪切模量按照线性变化,利用Hankel积分变换方法求解微分方程,将问题化为具有Cauchy型奇异核的积分方程.数值方法求解表明:功能梯度材料涂层半空间在刚性柱形压头和球形压头作用下,接触表面分布应力,接触半径以及最大压痕受材料梯度效应的影响较大.     

Contact Problem for Porous Elastic Half-Plane

The paper is concerned with a static contact problem about a rigid punch on the free surface of a linear porous elastic half-plane. With the use of the Fourier transform the problem is reduced to a singular integral equation holding over the contact zone. This integral representation permits consideration of the Flamant problem (a line load on the half-plane) to be explicitly reduced to some quadratures. It is shown that in the classical linear elasticity limit the main integral equation has a Cauchy-type kernel, so distribution of the contact pressure is like in the Sadowsky punch-problem. For arbitrary porosity a numerical co-location technique is applied that allows one to analyze in detail the distribution of the contact pressure versus porosity. Both in the Flamant and Sadowsky problems we demonstrate a higher compliance of the porous foundation, with respect to the classical linear elastic results. This revised version was published online in July 2006 with corrections to the Cover Date.     

A necessary and sufficient set of boundary integral equations with indirect unknowns for plate bending problem

A boundary integral representation of plane biharmonic function is established rigorously by the method of unanalytical continuation in the present paper. In this representation there are two boundary functions and four constants which bear a one to one correspondence to biharmonic functions. Therefore the set of boundary integral equations with indirect unknowns based on this representation is equivalent to the original differential equation formulation.     

具周期裂纹的半平面周期接触问题的奇异积分方程数值解法

运用Hilbert核的奇异积分方程的数值解法研究具任意形状裂纹的各向同性弹性半平面在周期压头作用下的周期接触问题,将所考虑问题转化为第一型或第二型的奇异积分方程组.最后给出带垂直裂纹的半平面在光滑平底压头作用下的数值结果.令a→∞时,就得到非周期经典结果.     

Boundary integral equations in quasisteady problems of capillary fluid mechanics Part 2: Application of the stress-stream function

In this paper planar viscous flows with a free boundary are further studied using the quasisteady approximation [1]. The introduction of the bianalytical stress-stream function provides an opportunity to adopt the theory of analytical functions. The mode of construction of the Fredholm boundary integral equations is here proposed through the explicit solutions of two Hilbert problems for holomorphic functions with the application of the conformal mappings. The stabiligy of the equilibrium of the annulus liquid layer is investigated by way of example.

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Sommario Si prosegue lo studio di flussi piani viscosi con frontiera libera applicando l'approssimazione quasistazionaria [1]. L'introduzione della funzione stress-stream bianalitica consente l'uso della teoria delle funzioni olomorfe. La costruzione delle equazioni integrali di Fredholm al contorno proposta qui si basa sulla risoluzione esplicita di due problemi di Hilbert per funzioni analitiche mediante applicazione della tecnica delle trasformazioni conformi. Come esempio si studia la stabilità dell'equilibrio di uno strato liquido anulare.

     

GENERALIZED RAY APPROXIMATE METHOD TO INVERSE MEDIUM PARAMETERS

In this paper,the inverse problem of the medium parameters in an inhomogeneousmedium is studied and a generalized ray approximate form of the total wave field is described.First,the acoustic wave equation derived from the elastic wave equation is studied,the referential variablesand perturbational variables are introduced,and the integral equation of the medium perturbational pa-rameters is obtained.Then from the point of view of the local principles of the wave function in an in-homogeneous medium,a generalized ray approximate form of the total wave field in an inhomoge-neous medium is described,and attention is focused on the Fredholm integral equation of the firstkind.Finally,the medium parameters in half-plane are inversed.Numerical examples show when theperturbations of the medium parameters are about 0.5,this method can effectively inverse its varia-tion.Apparently,this method is better than the conventional Born weak scattering approximation.     

介质参数反演的广义射线近似方法

在对无粘性介质参数反演问题进行的研究中，引入一种全波场广义射线近似形式，提出一种新的反演参数的方法，文中，首先对由弹性波动方程演变成的声波方程进行分析，引入背景场量和扰动量，并结合Ｇｒｅｅｎ函数理论，得到了介质参数的积分方程；然后结合前人对非均匀介质中波函数局部理论的定性分析，引入一种全波场广度射线近似形式，把问题归结为一个第一类Ｆｒｅｄｈｏｌｍ积分方程；最后对半空间问题层状介质模型进行了反演，算     

Exact solutions of multi-term fractional difusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multiterm time-fractional difusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial diferential equations are converted into time-fractional ordinary diferential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-difusion problems are given to validate the proposed analytical method.     

饱和土埋置力源的三维动力Lamb问题解答

基于一组弹性土波动方程,应用Fourier级数展开和Hankel积分变换,得到了三维问题饱和土骨架与孔隙水的应力及位移分量在变换域内的积分形式通解考虑地基表面透水情形,由边界条件导出了半空间饱和土体在埋置力源作用下的三维动力Lamb问题的解答给出了埋置水平力作用下地基表面竖向位移、径向位移及周向位移的数值解该研究为运用边界元法求解饱和地基的动力响应课题奠定了理论基础.