On a representation of the solution of the linear elasticity equations

A new representation of the stress tensor in the linear theory of elasticity is proposed. The representation satisfies the equilibrium equations and the compatibility conditions for strains. In this representation, the stress tensor is expressed in terms of a harmonic vector. The second boundary-value problem for an elastic half-space and elastic layer is considered as an example.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 85–91, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

Boussinesq indentation of a transversely isotropic half-space reinforced by a buried inextensible membrane

The normal indentation of a rigid circular disk into the surface of a transversely isotropic half-space reinforced by a buried inextensible thin film is addressed. By virtue of a displacement potential function and the Hankel transform, the governing equations of this axisymmetric mixed boundary value problem are represented as a dual integral equation, which is subsequently reduced to a Fredholm integral equation of the second kind. Two important results of the contact stress distribution beneath the disk region as well as the equivalent stiffness of the system are expressed in terms of the solution of the Fredholm integral equation. When the membrane is located on the surface or at the remote boundary, exact closed-form solutions are presented. For the limiting case of an isotropic half-space the results are verified with those available in the literature. As a special case, the elastic fields of a reinforced transversely isotropic half-space under the action of surface axisymmetric patch loads are also given. The effects of anisotropy, embedment depth of the membrane, and material incompressibility on both the contact stress and the normal stiffness factor are depicted in some plots.     

On the possibility of local buckling of the surface of an elastic half-space under compression

The possibility of local buckling of the free surface of the lower half-plane under compression is studied in a static formulation within the framework of plane deformation. It is shown that in some media small subcritical strains can lead to local buckling of the half-plane surface. It is found that two forms of local surface buckling correspond to one critical compression load. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 149–152, May–June, 2005.     

Mixed Antiplane Problem of Electroelasticity for a Piezoceramic Half-Space with a Tunnel Hole

Harmonic vibrations of a piezoceramic half-space weakened by a tunnel hole with a system of active surface electrodes are investigated. Based on integral representations for solutions to two types of conditions on the boundary of the half-space, the boundary-value problem of electroelasticity is reduced to a system of singular integrodifferential equations of the second kind. The results of parametric investigations characterizing the behavior of the electroelastic field components on the boundary and in the region of a piecewise-homogeneous half-space are presented.     

Indentation on one-dimensional hexagonal quasicrystals: general theory and complete exact solutions

This paper presents a general account of the indentation responses of a one-dimensional hexagonal quasicrystal half-space pressed by an axisymmetric rigid punch. Based on Green's functions of the half-space subjected to point sources on the surface, the mixed boundary value problem is transformed to integral equations and solved exactly using the results of the potential theory method. Explicit expressions for the generalised pressures and indentation forces are derived for three common indenters (cylinder, cone and approximate sphere) in a systematic manner. For conical and spherical indenters, relations between the contact radius and indentation loads are determined. The coupling phonon–phason fields in the half-space under indentation are accurately expressed in terms of elementary functions. Numerical calculations are performed and discussions on related physical phenomena are given. The present exact solutions can serve as benchmarks for approximate or numerical analyses and can guide the experimental characterisation of material properties of quasicrystals.     

基于弹性半空间Green函数的明置条形基础阻抗解答

基于弹性半空间理论,在Lamb解的基础上推导了非轴对称的简谐线激振荷载及条形均布激振荷载作用下的地基Green函数。然后将明置条形基础与地基的接触面分割成若干个条形单元,根据刚体位移所决定的各单元位移,运用上述Green函数求解各单元的接触力,将所求得的力叠加即为地基阻抗函数。通过分段积分法及Cauchy主值积分对涉及的多值广义积分进行数值处理,计算了明置条形基础的垂直阻抗,观察了其收敛性,亦计算了其水平和回转动柔度,并与半解析半数值的薄层法的结果进行了比较,表现出很好的一致性。最后通过算例讨论了土体泊松比对明置条形基础阻抗的影响。     

半空间电大涂敷目标散射的高频分析方法

研究了半空间内(海面,地面)电大尺寸涂敷目标散射的高频求解方法.将半空间并矢格林函数引入物理光学方法中,对半空间复杂环境影响进行考虑,并利用阻抗边界条件考虑涂敷目标表面的复杂电磁散射,推导出半空间物理光学分析方法,同时结合图形电磁学,对半空间电大涂敷目标进行消隐判断,提取像素面元法矢量和深度缓存等有效信息,快速有效地计算了半空间电大涂敷目标的雷达散射截面.数值结果证明了方法的有效性和准确性. 关键词： 半空间物理光学方法 半空间并矢格林函数 图形电磁学 雷达散射截面     

A note on the dispersion of Love waves in layered monoclinic elastic media

The dispersion equation for Love waves in a monoclinic elastic layer of uniform thickness overlying a monoclinic elastic half-space is derived by applying the traction-free boundary condition at the surface and continuity conditions at the interface. The dispersion curves showing the effect of anisotropy on the calculated phase velocity are presented. The special cases of orthotropic and transversely isotropic media are also considered. It is shown that the well-known dispersion equation for Love waves in an isotropic layer overlying an isotropic half-space follows as a particular case.     

弹性半空间地基上预应力中厚矩形板的弯曲

基于Reissner-Mindlin一阶剪切变形理论,讨论在预加面内机械荷载或预加温度场作用下,弹性半空间地基上四边自由中厚矩形板的弯曲问题。把地基看作三维弹性半空间体,考虑地基变形的衰减。用一组数学上完备的二元多项式作为位形函数,采用pb-2 Rayleigh-Ritz法求得四边自由中厚矩形板的挠度和弯矩,并讨论了初应力对板的挠度和弯矩的影响。     

非均匀法向荷载下半空间的二阶弹性效应问题

本文提供各向同性弹性半空间，在非均匀分布法向荷载下，二阶弹性效应的一个封闭形式解，运用积分变换方法，讨论了按Ｈｅｒｔｚ规律分布的荷载情形；导出了不可压缩各向同性弹性材料的极限解；算出了上述二阶弹性材料问题在ｚ方向的位移和法向应力数值。我们发现，与线弹性情形相比较，在二阶弹性材料中相应位移增大而法向应力减小。