Mechanics

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.

Modeling of the shock system motion with impacts about hard barriers

Authors: Dozorov A. A., Manzhosov V. K.

Abstract: We have developed a model of a shock system with a resilient member under periodic force action including impacts about hard barriers. In order to model the shock system we have developed a program providing a computational solution for differential equations of a subject motion taking into account conditions of periodicity and collision, graphical and numerical reproduction of motion parameters in the simulation process. We have performed simulation of modes of the shock system.

The equilibrium equations of shells in the coordinates of the general form

Authors: Baryshev A. A., Lychev S. A., Manzhirov A. V.

A mathematical model of homogeneous elastic shells is consider under kinematics Reissner–Mindlin type. Through direct (coordinateless) methods of the tensor calculus equations of equilibrium are obtained in terms of displacements in an arbitrary (not necessarily orthogonal) coordinate system, taking into account the asymmetry of the location of the front surface. For a spherical shells proposed procedure for constructing solutions, based on the method of spectral decomposition, which describes the stress-strain state at the potential power and torque static loads.