Mechanics

Influence of slipping on viscosimetric flow of a elastoviscoplastic material between rigid coaxial cylinders

Authors: Ustinova A. S.

 The viscoplastic flow of an incompressible elastoviscoplastic material between two rigid coaxial cylindrical surfaces is considered when slipping of a material is possible at one of them. The solution is constructed using the model of large elastoviscoplastic deformations. Reversible deformation, development and braking of a viscoplastic flow, unloading and deformation under rotation in the opposite direction are considered. Laws of movement of elastic-plastic boundaries are received. 

The heat conductivity in the infinite solid of the convection in a cylindrical cavity

Authors: Dudar E. S., Dudar O. I., Osipenko M. A.

The problem of heat conductivity in the infinite solid from gas moving in a cylindrical cavity is solved by the combination of the Green function method and the Laplace transformation. 

Flow of Slibar–Paslay material in a flat channel

Authors: Okulov N. A.

The question of the numerical simulation of unstable flow of a viscoplastic material in a flat channel is considered. Defining relations are taken in the form of Slibar–Paslay. The problem is solved in stresses. Theorem about the weak discontinuity at the interfaces between rigid and viscoplastic zones is proved. The original numerical method for solving the problem is offered. Numerical simulation results are presented. 

Application of generalized functions in dynamical contact problems of wing aeroelasaticity

Authors: Lukashchik E. P.

The range of problems dealing with analysis of deformed state of thin elastic wing at the oscillations in limited acoustic medium is considered in this article. The theory of generalized functions was chosen as an instrument for the mathematical research. By results of performed numerical experiment the existence of damp forces in the acoustic medium and resonance effects caused by elastic properties of the wing was confirmed. 

Analysis of algorithms study of stability of thin-walled shells

Authors: Karpov V. V.

We consider three variants of algorithms for studying the stability of thin-shell: An algorithm based on the Ritz method and iterative processes, an algorithm based on the method of steepest descent, the algorithm based on a method of extending the solution to the parameter. Analyzes the results of the study of shells produced using these algorithms. 

Mathematical modelling of critical speed of the multistage core at longitudinal blow

Authors: Bityurin A. A.

Mathematical modeling of longitudinal elastic central blow of a multistage core about a rigid barrier is carried out, at not keeping communications. Mathematical modeling is carried out by the exact analytical decision of the wave differential equation by a method of Dalamber with the task of necessary initial and boundary conditions. With application of the formula of Euler analytical expression for calculation of critical pretonic speed at which there comes loss of stability of a step core is received. 

Stress-strain State of an Elliptical Cylinder with an Ellipsoidal Bottoms of Dissimilar Materials Based FEM

Authors: Klochkov Y. V., Nikolaev A. P., Kiseleva T. A.

The algorithm of calculating the construction in the form of an elliptical cylinder with ellipsoidal bottom of different materials based

on the finite element method with the use of scalar and vector fields interpolating movements is described. As part of the sampling

using rectangular curved finite elements with eighteen degrees of freedom in the node. Calculations of a circular cylinder with an

articulated ellipsoid of rotation the verification of the algorithm and shows its effectiveness.

Optimal filtration of matrix gaussian random processes in planes lateral motion problem

Authors: Pristavko V. T., Litvin A. Y.

 In practice, observation problem is more complex because of random influences (noises): wind effects plane course, sensor errors distort object position view. In order to reduce noise filters are used. Proposed to carry out a simultaneous filtering of identical objects motion by defining problem in matrix variables. To achieve phisical realizability controlled matrix filter was proposed. Statements that allow to find the optimal solution was proved. 

Investigation of surface roughness at micro-scale and mechanical response in the contemporary bio-polimer sutures by the nanoindentation

Authors: Kuchumov A. G., Solod'ko V. N., Gavrilov V. A., Samartsev V. A., Chaikina E. S.

An investigation of properties of contemporary suture materials (surgical threads) is the state-of-art challenge in biomechanics. To improve an effectiveness of sutures application, an analysis of structure and elastic properties by the atomic force microscopy and scanning electron microscopy is necessary to be performed.

Covariant field equations and d-tensors of hyperbolic thermoelastic continuum with fine microstructure

Authors: Kovalev V. A., Radaev Y. N.

A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained. Constitutive equations of microstructural hyperbolic thermoelasticity are discussed.

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