Plane waves in a hypoplastic half-space under periodic boundary conditions

The paper presents a numerical study of the propagation of plane waves in a half-space occupied by a granular material, with periodic boundary conditions for velocity or stresses prescribed at the boundary of the half-space. The constitutive behaviour of the material is described by a simplified hypoplastic equation which takes into account different values of the stiffness for different directions of deformation, and the coupling between shear and volumetric strains owing to dilatancy. These two features are responsible for a nonlinear character of longitudinal waves and for the generation of longitudinal motion by transverse disturbances. It is shown that longitudinal and transverse boundary disturbances produce qualitatively the same longitudinal waves at large distances from the boundary. As a longitudinal wave propagates, the amplitude of oscillations decreases and eventually vanishes, resulting in a single non-oscillating wave.Received: 10 September 2002, Accepted: 31 March 2003 Correspondence to: Y. A. Berezin     

Axisymmetric contact problem for a layer on an elastic half-space with initial stresses

International Applied Mechanics -     

Plane problem of filtration consolidation for an elastic half-space with discontinuous initial conditions

The plane consolidation problem for an elastic half-space under an instantaneously applied vertical load is solved in the general case assuming that the Terzaghi hypothesis holds.     

Axisymmetric contact problem for an elastic half-space and a circular cover plate

The contact interaction problem for a thin circular rigid cover plate and an elastic half-space loaded at infinity by a tensile force directed in parallel to the boundary of the half-space is considered. It is assumed that the cover plate is not resistant to bending deformations. The problem can be reduced to an integral equation of the first kind whose kernel has a logarithmic singularity. The equation is solved approximately by the Multhopp-Kalandia method. The resulting approximate solution is compared with the previously obtained asymptotic solution.     

Stokes’ first problem for a second grade fluid in a porous half-space with heated boundary

Based on a modified Darcy's law, Stokes’ first problem was investigated for a second grade fluid in a porous half-space with a heated flat plate. Exact solutions of the velocity and temperature fields were obtained using Fourier sine transforms. In contrast to the classical Stokes’ first problem, there is a steady-state solution for the second grade fluid in the porous half-space, which is a damping exponential function with respect to the distance from the flat plate. The well-known solutions for Newtonian fluids in non-porous or porous half-space appear in limiting cases of our solutions.     

Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

Summary  The following mixed boundary-value problem for a transversely isotropic elastic half-space is considered. Arbitrary tangential displacements are prescribed at the exterior of a circle, while the interior of the circle is free of tangential stress, and the normal stress vanishes all over the boundary. The governing integral equation is solved exactly, in closed form, and in terms of elementary functions. The method of continuation of solutions previously published by the author has been used here. Several examples are considered. No similar results has been reported before, even in the case of an isotropic body. Received 8 May 2000; accepted for publication 20 July 2000     

Plane contact problem for an elastic rectangular punch and a half-plane with initial stresses

International Applied Mechanics -     

The contact problem of a rubber half-space dented by a rigid cone apex

Summary  The smooth contact of a rubber half-space dented by a rigid cone apex is analyzed based on the large deformation theory. The problem is treated as an axially symmetric case, and the material is assumed to be incompressible. The asymptotic equations for the domain near the apex are derived. They are solved analytically for the shrinking domain, while a numerical solution is found for the expanding domain in the vicinity of the stress singularity. The purpose of this paper is not only to solve a typical problem but also to provide an analytical method to solve a large-strain problem with a singular point. Received 10 July 2001; accepted for publication 24 January 2002     

The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space

In this article, we study the axisymmetric tor-sional contact problem of a half-space coated with func-tionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thick-ness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral trans-form technique and reduce the problem to a singular integral equation, and then numerically determine the unknown con-tact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.     

Plane contact problem for periodic laminated composite involving frictional heating

Summary The stationary problem of a rigid thermally insulated punch sliding over the boundary surface of a periodic two-layered thermoelastic half-space is considered. The heat generated in the contact area is assumed to be caused by frictional forces. The problem is formulated within the framework of thermoelasticity with microlocal parameters, and it is reduced to a system of two integral equations, which is solved numerically. The effects connected with the composite structure are analyzed.