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Bazelyan E.M.,Moscow Power Engineering Institute | Raizer Y.,Institute for Problems in Mechanics | Aleksandrov N.L.,Moscow Institute of Physics and Technology
Journal of Atmospheric and Solar-Terrestrial Physics | Year: 2014

The properties of a non-stationary glow corona maintained near the tips of a multi-point ground system in a time-varying thundercloud electric field have been studied numerically and analytically. Computer and analytical models were developed to simulate the corona discharge initiated from a system of identical vertical conductive electrodes distributed uniformly over a grounded plane surface. The simulation was based on a solution of the electrostatic equation for electric field and continuity equations for light and aerosol ions. The development of individual corona space charge layers from different points and the formation of a united plane layer were considered. The effect of system dimensions and that of the distance between electrodes on the external electric field corresponding to corona onset near the rod tips was investigated. The evolution in time of the corona current was calculated for systems with various numbers of coronating rods in time-varying atmospheric electric field. In the limit of infinite number of coronating rods, reasonable agreement was obtained between numerical calculations and analytical theory considering the effect of surrounding rods on the corona discharge from a given rod in a simplified integral way. Conditions were determined under which the corona properties of a multi-point system are similar to the properties of a plane surface emitting ions into the atmosphere. In this case, the corona current density is governed by the time derivative of the thundercloud electric field and is independent of the ion mobility and of the coronating system dimensions. The total corona space charge injected into the atmosphere per unit area by a given instant is controlled by the thundercloud electric field at this instant and depends on the geometrical parameters of the system only indirectly, through the corona onset atmospheric electric field. This simple model could be used to simulate a corona discharge during thunderstorms at the earth's surface covered with dense vegetation. In particular, according to the model of an emitting plane, the current densities in the range 1-10nA/m2 are expected when the thundercloud electric field increases by ~50kV/m over time interval in the range 30-300s, in qualitative agreement with the analysis of available field observations. © 2013 Elsevier Ltd. Source

Alexandrov S.,Institute for Problems in Mechanics
Materials Science Forum | Year: 2010

The limit load is an essential input parameter of flaw assessment procedures. The present paper deals with an effect of plastic anisotropy on its value. An upper bound solution for threedimensional deformation of a highly under-matched welded specimen subject to tension is proposed. The base material is assumed to be rigid, and the weld material obeys Hill's quadratic yield criterion for orthotropic materials. It is demonstrated that it is crucial to account for both plastic anisotropy and three dimensionality of deformation in limit load calculations for flaw assessment procedures. © (2010) Trans Tech Publications. Source

Kuznetsov S.V.,Institute for Problems in Mechanics
Advances in Mathematical Physics | Year: 2014

Necessity for the periodic fundamental solutions arises when the periodic boundary value problems should be analyzed. The latter are naturally related to problems of finding the homogenized properties of the dispersed composites, porous media, and media with uniformly distributed microcracks or dislocations. Construction of the periodic fundamental solutions is done in terms of the convergent series in harmonic polynomials. An example of the periodic fundamental solution for the anisotropic porous medium is constructed, along with the simplified lower bound estimate. © 2014 Sergey V. Kuznetsov. Source

Alexandrov S.,Institute for Problems in Mechanics | Miszuris W.,Aberystwyth University
Acta Mechanica | Year: 2015

This paper presents a theoretical investigation into heat generation in the continued quasi-static plane strain compression of a thin metal strip between two rigid, parallel perfectly rough dies. The strip material is rigid perfectly plastic. The length of the dies is supposed to be much larger than the current strip thickness. The plastic work rate approaches infinity in the vicinity of perfectly rough friction surfaces. Since the plastic work rate is involved in the heat conduction equation, this significantly adds to the difficulties of solutions of this equation. In particular, commercial finite element packages are not capable of solving such boundary value problems. The present approximate solution is given in Lagrangian coordinates. In this case, the original initial/boundary value problem reduces to the standard second initial/boundary value problem for the nonhomogeneous heat conduction equation. Therefore, the Green’s function is available in the literature. An example is presented to illustrate the general solution. © 2015 Springer-Verlag Wien Source

Manzhirov A.V.,Institute for Problems in Mechanics
ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) | Year: 2014

A vast majority of objects around us arise from some growth processes. Many natural phenomena such as growth of biological tissues, glaciers, blocks of sedimentary and volcanic rocks, and space objects may serve as examples. Similar processes determine specific features of many industrial processes which include crystal growth, laser deposition, melt solidification, electrolytic formation, pyrolytic deposition, polymerization and concreting technologies. Recent researches indicates that growing solids exhibit properties dramatically different from those of conventional solids, and the classical solid mechanics cannot be used to model their behavior. The old approaches should be replaced by new ideas and methods of modern mechanics, mathematics, physics, and engineering sciences.Thus, there is a new track in solid mechanic that deals with the construction of adequate models for solid growth processes. The fundamentals of the mathematical theory of growing solids are under consideration. We focus on the surface growth when deposition of a new material occurs at the boundary of a growing solid. Two approaches are discussed. The first one deals with the direct formulation of the mathematical theory of continuous growth in the case of small deformations. The second one is designed for the solution of nonlinear problems in the case of finite deformations. It is based on the ideas of the theory of inhomogeneous solids and regards continuous growth as the limit case of discrete growth. The constitutive equations and boundary conditions for growing solids are presented. Non-classical boundary value problems are formulated. Methods for solving these problems are proposed. Copyright © 2014 by ASME. Source

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