The contact problem for two prestressed cylindrical coaxial punches and a layer with initial (residual) tension
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 78, Issue 2
Abstract
The article deals with the coaxial mixed type task of measuring pressure of prestressed two coaxial cylinder punches upon a layer with initial (residual) stresses within the framework of linear elasticity theory. We consider the cases in the absence of the friction forces. In general, the research was carried out for the theory of great initial (ultimate) deformations and different variants of the theory of small initial deformations with arbitrary structure of elastic potential. It is assumed that elastic potentials are two continuously differentiated functions of algebraic invariants of the Green tensor deformation (the initial states of the layer and of cylindrical punches remains uniform and equal). The research is carried out within the coordinates of the initial deformed state, which are interrelated with the Lagrangian coordinates (natural state). Besides, it is also assumed that the influence of the die causes small disorders of the main elastic deformed state. It is assumed that the elastic dies as well as the layer are made of different isotropous, transversely isotropic or composite materials and they are interacting on one of the dieses surfaces. The mode of deformation in elastic layer with initial (residual) stress will be defined with the help of harmonic functions as the Henkel integrals. We should note, although the Henkel-method does not provide exact solutions, but it lets us reduce the task to the Fredholm equations, which let us use the method of consecutive approximations. Consequently we got a components of potential vector and tenzor of deformations in the case of unequal roots of axis-symetrical type task. So, the received solutions are defined by lines with the help of very many constants. These constants are defined with two systems of regular linear algebraic equations. The research was carried out on the problem of the influence of initial stresses on the law of distribution of contact disorders in the elastic layer with initial (residual) stresses.
Authors and Affiliations
Diana Maksymchuk
Keywords
Related Articles
- EP ID EP571428
- DOI -
- Views 40
- Downloads 0
Load transfer from the infinite stringer to the two jammed along one edge identical stripes with initial (residual) stresses
The article is devoted to problems of contact interaction of infinite elastic stringer and two identical jammed along one edge pre-stressed stripes. The research has been conducted in the framework of linearized theory o...
Transportation research process bulk material widely universal screw conveyor
Screw transporter has been developed, which consists of the vertical tube-column, to which the horizontal loading branch is fixed rigidly in the upper part being able to revolve, and in the bottom part – the unloading br...
Forced vibrations and dissipative heating of three-dimensional piezoelectric prism
Prismatic passive and piezoactive nonelastic bodies are used wide-ly in present – day technics. Under harmonic loading the electromechanical energy in these bodies is turning in thermal energy and the body temperature is...
Method of segmentation of determined cyclic signals for the problems related to their processing and modeling
In this work the method of adaptive segmentation of determined cyclic signals has been developed. The problem of segmentation (breakdown, division of the signal into distinctive segments) of the cyclic determined signal...
Mathematical modeling of processes of nonisothermal adsorption, desorption and heat transfer of hydrocarbons in nanoporous catalysts based on zeolite ZSM-5 of exhaust gas neutralization systems
An experimental and theoretical study of the non-isothermal adsorption and desorption of gas using microporous silica beds for motor fuel technology is described. Analytical solutions to the problem of non-isothermal ads...