Plane Problem of Surface Wave Diffraction on a Floating Elastic Plate

The problem of the behavior of a floating elastic strip-shaped plate in waves is considered. A new numerical method for solving this problem based on the Wiener-Hopf technique is proposed. The solution of the boundary value problem is reduced to an infinite system of linear algebraic equations which satisfies the reduction conditions. The calculation results are compared both with experiment and with the calculations of other authors. In the case of short incident waves the system of equations obtained can be essentially simplified. Three short-wave approximations are proposed, namely, the single-mode, four-mode and uniform approximations, which ensure good agreement with calculations based on the complete model. Simple explicit formulas are obtained for the single-mode and uniform approximations.     

Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

Plane Collision Problem for Two Identical Elastic Parabolic Bodies—Direct Central Impact

A direct central collision of two identical infinite cylindrical bodies is studied. A nonstationary plane elastic problem is solved. The variable boundary of the contact area is determined. A mixed boundary problem is formulated. Its solution is represented by Fourier series. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying boundary conditions. The basic characteristics of the collision process are determined numerically depending on the curvature of the frontal surface of the bodies     

Solving the Contact Problem for a Rectangular Die on an Elastic Foundation

A method of orthogonal polynomials is proposed to solve the contact problem for a rectangular die on an elastic foundation. For the case of an elastic half-space, an exact formula is derived for the translation of the die under symmetric loading     

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.     

弹性力学平面问题中一类无奇异边界积分方程

从理论上提出一种新的方法，归化出间接变量无奇异边界积分方 程. 采用Lagrange二次单元，建立一个数值求解框架系统. 此外，基于问题的计算区域的 特殊性，给出一种边界近似方法. 数值算例表明该方法所取得的数值结果与精确解相当接 近，特别是边界量的数值结果. 此外，该方法容易被推广到三维问题. 和已有的直接变量的情形相比较，具有优点：1)无需处理HFP积分. 大大降低处理问 题的复杂性，并提高了计算效率和解的精度；2)摆脱了问题的具体形式，进入纯代数操作. 这样做的好处是从理论上建立一种普遍适用的方法，不仅适用于弹性力学问题，同样可应用 于其它问题，如位势问题, Stokes问题等. 3)提供了一种计算CPV积分的方法.     

Contact Problem for an Elastic Orthotropic Half-Strip

The paper discusses the problem on a rigid flat-based die forced into a half-strip. The material of the half-strip, whose semiinfinite sides are fixed, is orthotropic; the principal axes of anisotropy coincide with the Cartesian coordinate axes. Friction between the die and the half-strip is taken into account. The problem is solved by an asymptotic method developed by the authors. Some numerical results are presented     

Contact Problems for Prestressed Elastic Bodies and Rigid and Elastic Punches

Contact problems for prestressed bodies and rigid and elastic punches are discussed. The influence of the prestresses on the contact characteristics is analyzed numerically     

线接触弹性接触变形的解析算法

以一般光滑性体接触理论为基础,结合有限长弹性体接触的特点,求出线接触弹性接蟹变形的解析公式,并发现其解析解与数值解具有很好的一致性,所得公式可以对赫兹线接触理论加以补充,与经验公式相比,它能够确切反映材料、载荷以及曲率半径等对接触变形的影响,为工程中的精确计算提供了方便。     

Evolution Equations for Plane Cubically Nonlinear Elastic Waves

Consideration is given to the nonlinear theory of elastic waves with cubic nonlinearity. This nonlinearity is separated out, and the interaction of four harmonic waves is studied. The method of slowly varying amplitudes is used. The shortened and evolution equations, the first integrals of these equations (Manley–Rowe relations), and energy balance law for a set of four interacting waves (quadruplet) are derived. The interaction of waves is described using the wavefront reversal scheme     

结合部切向接触刚度分形模型研究

根据球体与平面接触的切向接触刚度和粗糙表面的接触分形理论，从理论上首次建立了结合部切向接触刚度分形模型，该模型具有尺度独立性。通过对所建模型的数字仿真，直观地给出了结合部切向接触刚度与其影响因素之间的非线性关系，并与实验研究结果具有较好的一致性，从而说明了该模型是合理的。     

粗糙表面法向接触刚度的分形模型

提出了以往有关粗糙表面法向接触刚度理论研究工作的缺陷与不足,并在一定的前提假设下,基于球体与平面的接触理论和粗糙表面的分形接触理论,从理论上给出了具有尺度独立性的粗糙表面法向接触刚度分形模型,并进行了数字仿真研究。     

Dynamic Contact Problem for a Plane with a Finite Crack

We study the contact interaction of the faces of a finite rectilinear crack under harmonic compression–expansion and shear waves incident at an arbitrary angle. An iterative algorithm based on the variational principles of elastic theory is used. The contact interaction and displacement discontinuity of the crack faces are analyzed. The crack-tip stress intensity factors are calculated. The results are compared with those obtained regardless of the contact interaction     

一维正方准晶非周期平面弹性有限摩擦接触问题

利用平面弹性复变方法和解析函数边值理论,讨论了一维正方准晶材料非周期平面上的有限摩擦接触问题.基于一维正方准晶非周期平面内应力和位移分量的广义复变函数表示,有限摩擦接触问题被转换为Riemann-Hilbert边值问题.对于平底压头,得到了压头下方接触应力的显式表达式,并用数值算例分析了摩擦系数和声子场-相位子场耦合系数对压头下方接触应力分布的影响.结果表明:(1)摩擦系数对接触应力大小和分布规律的影响几乎可以忽略;(2)耦合系数对接触应力的分布规律无影响,对声子场接触应力值的影响微乎其微,对相位子场接触应力大小的影响比较明显.特殊条件下,本文所得结论可退化为一维四方准晶和一维六方准晶非周期平面内有限摩擦接触问题的解.当摩擦系数等于0时,还可以得到对应无摩擦接触问题的解.     

弹性半平面中的斜边界裂纹问题

讨论了一群性半平面无限体中含有一斜烈纹的静力学问题,研究中以断裂力学原理为基础,采用了复变函数的方法,将原问题化为一组解析函数边值问题的求解。文中通过分析函数法以及应用Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ（Ｒ－Ｈ）边值问题的一般理论,给出了所研究问题的解析解,并且给出了此问题的应力强度因子Ｋ１,Ｋ１的显式形式,此外,裂纹上的位移发生的错动可以得以进一步的讨论,文中的结论对地学的研究有一定的应用价值。     

平面杆系结构弹性波传播的实验研究

利用ＳＨＰＢ装置，用空气枪加载就３５ＣｒＭｎＳｉ钢组成的平面杆系结构受冲击载荷作用的弹性波传播进行了实验研究，给出了一些力学现象，并利用广义特征线法给出了理论与实验的比较曲线，得到了一些有益的结论．     

Plane Problem of Vibrations of an Elastic Floating Plate under Periodic External Loading

The Wiener–Hopf technique is used to construct an analytical solution of the problem of vibrations of a semiinfinite elastic floating plate under periodic external loading. The solution is obtained in explicit form ignoring draft. The dependences of the amplitudes of surface waves and iceplate deflection on the loading distribution and frequency, ice thickness, and liquid depth are studied numerically. It is established that for some types of acting load, no waves propagate in the plate and liquid and the plate vibrations are standing waves localized near the loading region. An example of such vibrations is given and a condition for the occurrence of localized vibrations is found.     

Contact Problem for a Rectangular Punch on the Porous Elastic Half-Space

The paper is concerned with a contact problem about rigid rectangular punch forced into a half-space made of a linear elastic isotropic material with voids. We use a Cowin–Nunziato model for the half-space, and reduce the problem to a double Fredholm integral equation of the first kind. Then we apply two different approaches, to solve this equation. The first one is based on a direct collocation numerical technique. The second method is asymptotic, and we use a small parameter that is the relative width of the punch. Finally, compliance of the punch is determined, and results of the two different methods are compared with each other, as well as with a Sivashinsky–Panek–Kalker solution. Mathematics Subject Classifications (2000) 74M15.