Stress State of an Inhomogeneous Elastic Layer Made of Heterogeneous Materials with a Coin-Like Rigid Inclusion under Torsion

Problems on cracks and inclusions closely relate to problems of determination of the stress-strain state of homogeneous and inhomogeneous elastic solids that contain stress concentrators. Due to their theoretical and practical importance to the issues of construction structures, machines and their parts in machinery, in the calculation of hydro-technical structures as well as in various other spheres of applied mechanics, these problems have become a subject of investigation for many authors. This paper studies the problem of determination of the stress-strain state of a piecewise homogeneous elastic layer under torsion. The upper and lower surfaces of the compound layer are loaded with tangential forces and the interface of the heterogeneous layers contains a thin absolutely rigid coin-like inclusion. It is required to determine stress jumps on the boundary of the inclusion as well as intensity coefficients of the stresses (ICS).

Torsional Surface Waves in an Inhomogeneous Layer over a Fluid Saturated Porous Half-Space

ABSTRACTIn the present paper the propagation of torsional surface waves is discussed in an inhomogeneous elastic layer lying over a fluid saturated porous half space. The inhomogeneity in rigidity and density in the inhomogeneous layer plays an important role in the propagation of torsional surface waves. The presence of fluid in the pores diminishes the velocity. Further, it is seen that if the layer becomes homogeneous and the porous half space is replaced by a homogeneous half space, the velocity of the torsional surface waves coincides with that of Love wave. The effect of inhomogeneity factors and porosity factor on the phase velocity of torsional surface wave is delimitated by means of graphs.

An approximate secular equation of Rayleigh waves in an elastic half-space coated by a thin weakly inhomogeneous elastic layer

In this paper, the propagation of Rayleigh waves in a homogeneous isotropic elastic half-space coated with a thin weakly inhomogeneous isotropic elastic layer is investigated. The material parameters of the layer is assumed to depend arbitrarily continuously on the thickness variable. The contact between the layer and the half space is perfectly bonded. The main purpose of the paper is to establish an approximate secular equation of the wave. By applying the effective boundary condition method an approximate secular equation of second order in terms of the dimensionless thickness of the layer is derived. It is shown that the obtained approximate secular equation has good accuracy.

Two-Dimensional Thermal Stresses and Displacements in an Arbitrarily Inhomogeneous Elastic Layer

This paper presents an analytical approach for solution of the plane-strain problem on elastic equilibrium of a layer whose material properties are arbitrary functions of the transversal coordinate. The layer is stressed by distributed temperature field under given displacement of its limiting surfaces. By making use of the explicit solution of the relevant problem in terms of stresses, the boundary tractions are determined by the given boundary displacements and temperature field on the basis of established one-to-one relations. In such manner, the original problem is reduced to the problem with boundary conditions in terms of stresses.