Dispersion of generalized Rayleigh waves in the half-plane covered with pre-stretched two layers under complete contact

In this paper the dispersion of the generalized Rayleigh wave propagation in the non-prestressed half-plane covered with pre-stretched two layers under complete contact conditions is investigated by 3-D linearized theory of elasticity. The layers and the half-plane are assumed that elastic, homogeneous, isotropic, and the complete contact conditions are existed. The inter phase zone between the upper layer and half-plane is modeled by this second layer. The purpose of the investigation is the determination on the effect of the existence of the second layer to the considered generalized Rayleigh wave propagation velocity. For this purpose, firstly the same materials were selected for both layers and the results obtained in previous studies for a single layer in the literature were verified, the accuracy of the modeling was shown, and then the effect of the second layer on the considered problem was shown by selecting the different materials and applying different initial pre-stresses. Consequently, the present study can be considered as the investigation of the existence of the inter phase zone which is characteristic one for the composite materials to the dispersion of the generalized Rayleigh wave propagation. Numerical results obtained and discussed.

Plane contact problem on the interaction of a pre-stressed strip with an infinite inhomogeneous stringer

The article is devoted to the study of problems of contact interaction of an infinite elastic inhomogeneous stringer with a prestressed strip clamped along one edge. As a result of the research, we have obtained a resolving system of recurrent systems of integro-differential equations. In general, the studies were carried out for the theory of large initial and various versions of the theory of small initial deformations within the framework of the linearized theory of elasticity with an elastic potential of an arbitrary structure. Integral integer differential equations are obtained using the integral Fourier transform. Their solution is presented in the form of quasiregular infinite systems of algebraic equations. The article also investigates the influence of the initial (residual) stresses in strips on the distribution law of contact stresses along the line of contact with an infinite stringer. The system is solved in a closed form using the Fourier transform. The stress expressions are represented by Fourier integrals with a fairly simple structure. The influence of the initial stress on the distribution of contact stresses has been studied and mechanical effects have been found under the action of concentrated loads.

Contact interaction of prestressed annular punch and half-space

The article is devoted to the task of contact interaction of the pressure of a pre-stressed cylindrical annular punch on the half-space with initial (residual) stresses without friction. It is solved for the case of unequal roots of the characteristic equation. In general, the research was carried out for the theory of great initial (ultimate) deformations and two variants of the theory of small initial ones within the framework of linearized theory of elasticity with the elastic potential having any structure. It is assumed that the initial states of the elastic annular stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the annular stamp causes small perturbations of the basic elastic deformed state. It is assumed that the elastic annular stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials.

A flat contact problem the interaction two prestressed stripes with an infinite stringer

The article is devoted to the research of problems of contact interaction of infinite elastic stringer with two identical clamped along one edge of pre-stressed strips. In general, the research was carried out for the theory of great initial and different variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure. The integral integer-differential equations are obtained using the integral Fourier transform. Their solution is represented in the form of quasiregular infinite systems of algebraic equations. In the article alsaw was investigated the influence of the initial (residual) stresses in strips on the law of distribution of contact stresses along the line of contact with an infinite stringer. The system is solved in a closed forms using transformation of Fourier. Expressions of stresses are represented by Fourier integrals with a simple enough structure. Influence of initial stress on the distribution of contact stresses is study and discovered the mechanical effects under the influence of concentrated loads

Concentration of Stress Around the Cylindrical Hole in an Initial Stressed Rectangular Orthotropic Thick Plate

An orthotropic pre-stressed thick plate with a cylindrical hole under additional static loading on the upper face-plane of the plate have been studied within the framework of the Three-Dimensional Linearized Theory of Elasticity (TDLTE) in Initially Stressed Bodies. The corresponding problem formulation is presented and, in order to find the solution to this problem, the 3D finite element method is employed. The numerical results on the concentration of the stress around the cylindrical hole and the influence of the initial forces, geometrical and mechanical parameters on these concentrations are presented in graphical form and discussed. According to these results, in particular it is established that the stress distributions around the cylindrical hole changed significantly with the initial stretching or compressing forces.