Plastic Flow in a Thin Layer: the Theory, Formulations of the Boundary- Value Problems and the Applications

Two-dimensional, averaged over the thickness of the layer, mathematical theory of the spreading of a plastic layer on the plane has been studied. General and simplified mathematical formulations of boundary value problem were presented. The problem of plastic stretching of a strip by forces applied on its “clamped” ends was investigated. The analysis of various modes of the process was carried out, which are determined by both the total compression force of the ends and the total tensile force. Mathematical analogy between the process of the free spreading of a plastic layer on the plane and the process of heat transfer was studied. For known forms of a domain occupied by a thin plastic layer at the initial time and for a given law of convergence of the plates, the evolution of the boundary of a plastic layer spreading was described. The exact particular solutions of the aforementioned problem was obtained.

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Plastic Flow in a Thin Layer: New Formulation of the Boundary-Value Problem and Its Solution

EPJ Web of Conferences ◽

10.1051/epjconf/201922401001 ◽

2019 ◽

Vol 224 ◽

pp. 01001

Author(s):

Vagid Kadymov ◽

Eugenе Sosenushkin

Keyword(s):

Boundary Value Problem ◽

Boundary Value ◽

Thin Sheet ◽

Mathematical Formulation ◽

Contact Boundary ◽

Plastic Layer ◽

Structural Elements ◽

Sheet Rolling ◽

Thin Plastic ◽

New Formulation

The paper is dedicated to the theory of flow in a thin plastic layer that has numerous applications in calculations of technological processes of material treatment by pressure, such as stamping and pressing of thin-walled structural elements, thin-sheet rolling, and others. Two-dimensional, averaged over the thickness of the layer mathematical formulation of the contact boundary value problem of the spreading of a plastic layer on the plane has been examined. In the framework of the general “viscous liquid” model, an approximate analytical solution has been obtained and evaluated against measurements. This solution is in good agreement with the experimental results in the area far from the free boundary and the central part of the sample.

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Application of thermal potentials to the solution of the problem of heat conduction in a region degenerates at the initial moment

Filomat ◽

10.2298/fil1803825k ◽

2018 ◽

Vol 32 (3) ◽

pp. 825-836

Author(s):

Alexey Kavokin ◽

Adiya Kulakhmetova ◽

Yuriy Shpadi

Keyword(s):

Heat Transfer ◽

Integral Equation ◽

Heat Conduction ◽

Liquid Metal ◽

Boundary Value Problem ◽

Boundary Value ◽

Constructive Method ◽

Initial Time ◽

Initial Moment ◽

Electric Contacts

In this paper, the boundary value problem for the heat equation in the region which degenerates at the initial time is considered. Such problems arise in mathematical models of the processes occurring by opening of electric contacts, in particular, at the description of the heat transfer in a liquid metal bridge and electric arcing. The boundary value problem is reduced to a Volterra integral equation of the second kind which has a singular feature. The class of solutions for the integral equation is defined and the constructive method of its solution is developed.

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Semidiscrete approximations for the stationary radiative–conductive heat transfer problem in a two-dimensional system of plates

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2016-0001 ◽

2016 ◽

Vol 31 (1) ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Andrey A. Amosov ◽

Dmitry A. Maslov

Keyword(s):

Heat Transfer ◽

Boundary Value Problem ◽

Transfer Problem ◽

Boundary Value ◽

Conductive Heat Transfer ◽

Heat Transfer Problem ◽

Dimensional System ◽

Conductive Heat ◽

Two Dimensional ◽

Two Dimensional System

AbstractSpecial semidiscrete approximations, namely, basic, first, and second semidiscrete problems are proposed for a boundary value problem describing a stationary radiative–conductive heat transfer in a two-dimensional system of heat-conductive plates of width

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