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Khludnev A.,Lavrentyev Institute of Hydrodynamics
European Journal of Mechanics, A/Solids | Year: 2012

In the paper, we propose an elastic plate model with delaminated thin rigid inclusions and provide mathematical analysis of the model. Both vertical and horizontal displacements of the plate are taken into account. It is assumed that the inclusion is delaminated which leads to an appearance of a crack. To provide a mutual non-penetration between crack faces we impose non-linear boundary conditions at the crack faces with unknown set of a contact. A correct problem formulation is proposed, and an existence of solutions is proved for different locations of the rigid inclusion inside of the elastic body. © 2011 Elsevier Masson SAS. All rights reserved.

Khabakhpasheva T.I.,Lavrentyev Institute of Hydrodynamics | Korobkin A.A.,University of East Anglia
Journal of Fluids and Structures | Year: 2013

The problem of elastic wedge impact onto the free surface of an ideal incompressible liquid of infinite depth is considered. The liquid flow is two-dimensional, symmetric and potential. The side walls of the wedge are modelled as Euler beams, which are either simply supported or connected to the main structure by linear springs. The liquid flow, the deflection of wedge walls and the size of wetted region are determined simultaneously within the Wagner theory of water impact. We are concerned with the impact conditions of strong coupling between the hydrodynamic loads and the structural response. The coupling is well pronounced for elastic wedges with small deadrise angles. This is the case when the fully nonlinear models fail and approximate models based on the Wagner approach are used. In contrast to the existing approximate models, we do not use any further simplifications within the Wagner theory. Calculations of the velocity potential are reduced to analytical evaluation of the added-mass matrix. Hydrodynamic pressures are not evaluated in the present analysis. In order to estimate the maximum bending stresses, both stages when the wedge surface is partially and totally wetted are considered.Three approximate models of water impact, which are frequently used in practical computations, are examined and their predictions are tested against the present numerical solution obtained by the normal mode method within the Wagner theory. It is shown that the decoupled model of elastic wedge impact, which does not account for the beam inertia, provides a useful formula for estimating the maximum bending stress in thick wedge platings. © 2012 Elsevier Ltd.

Khludnev A.,Lavrentyev Institute of Hydrodynamics
European Journal of Mechanics, A/Solids | Year: 2010

In the paper, an optimal control problem of crack growth is considered, allowing to choose the most safe inclusions in elastic bodies from the standpoint of their influence on a crack propagation. © 2009 Elsevier Masson SAS. All rights reserved.

Karabut E.,Lavrentyev Institute of Hydrodynamics
Comptes Rendus - Mecanique | Year: 2013

Some approach to the solution of boundary value problems for finding functions that are analytical in a wedge is proposed. If the ratio of the angle at the wedge vertex to the number π is rational, then the boundary value problem is reduced to the finite system of ordinary differential equations. Such approach, applied to the problem of inertial motion of a liquid wedge, made it possible to sum the series with small denominators arising in the problem and find four exact examples of self-similar flows with a free boundary. © 2013 Académie des sciences.

Kupershtokh A.L.,Lavrentyev Institute of Hydrodynamics
Computers and Mathematics with Applications | Year: 2014

The three-dimensional simulations of an anisotropic decay of binary mixtures of a dielectric liquid with solute gas in a strong electric field are carried out. The Lattice Boltzmann Equation method (LBE) is exploited for computer simulations of the evolution of such systems with the newly arising interfaces between vapor and liquid phases. The parallel implementation of the LBE algorithm is realized on a large number of cores in the GPU. For the GPU programming, the CUDA technology is used. It is important that new regions of the low-density phase appear as thin quasi-cylindrical gas-vapor channels oriented along the electric field. The gas-vapor channels expand because of the diffusion of the solute gas from the mixture, evaporation of liquid into the channels and also due to the coalescence of channels with each other. The critical values of electric field necessary for such decay of a binary mixture are considerably lower than the critical electric field for pure dielectric liquids. Hence, if we take into account a solute gas, the electric fields for which the anisotropic mechanism of streamer channels generation and growth is operated, become considerably lower. Thus, at a breakdown of dielectric liquids in a strong electric field, the anisotropic instability is possibly the key mechanism of the generation of a gas phase, inception of conducting streamer structures, their fast growth in the form of thin filamentary channels, as well as branching of streamer structures during propagation. © 2013 Elsevier Ltd. All rights reserved.

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