About one solving method of the contact problem for an elastic semi-infinite layer
Journal Title: Дослідження в математиці і механіці - Year 2014, Vol 19, Issue 3
Abstract
It is solved the contact problem on the action of a circular stamp with an extra-central power on the elastic semi-infinite layer. On the lateral and lower side of the layer the conditions of the smooth contact are given. The problem was solved with the decomposition to the slightest parameter. The singular integral equation with respect to unknown contact pressure was obtained. The problem was reduced to the system of recurrent integral equations which were solved by the method of the orthogonal polynomials and were reduced to the infinite one-dimensional systems of algebraic equations. These equations were solved by the reduction method. As a result the eccentricity and precipitation of the stamp that provide its forward movement were determined.
Authors and Affiliations
A. A. Fesenko
Hyperbolic equation with singular coefficient
Dedicated to research existence conditions of quasi-linear differential equations with measurable coefficients, ie the study limitations imposed by the non linearity in which the system will have to research a solution a...
STABILITY OF UNIFORM ATTRACTORS FOR ONE CLASS OF IMPULSIVE PARABOLIC SYSTEMS
In this paper we consider weakly non-linear two-dimensional parabolic systems, whose solutions have jumps at moments of intersection with fixed (impulsive) subset of the phase space. It generates impulsive dynamical syst...
Axisymmetric torsion problem for the finite length multilayered cylinder
The exact solution of the axysimmetric elasticity problem on the torsion of the multilayered massive and hollow cylinder under an influence of the torsion loading at the lateral cylinder’ surface. The layers are in the c...
About the characteristic polynomial of product Frobenius’ matrix
The formula for calculating characteristic polynomials of product Frobenius’ matrix was obtained. The opportunity of using this formula by the tasks of control of nonlinear discret systems was shown.
T. The problem of stress concentration in the band-shaped plate, weakened by crack, which is parallel to the side edges
The solution to the problem about hinged band-shaped plate, weakened by the crack has been found. The crack is parallel to the bearings. Relation between stress intencity factor at the crack end and crack’s location and...