# Mechanics

## Application of generalized functions in dynamical contact problems of wing aeroelasaticity

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

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.

## Finite Element Analysis of the Influence of the Orthodontic Appliance Design on the Maxillary Expansion

In present paper the results of the stress-strain state finite element analysis of the humanmaxillary complex after activating orthodontic appliance are performed. Skull and abutment teeth models are obtained on the basis of the tomographic data of the dry intact adult skull. Orthodontic appliance designs are differ in the arrangement of rods and screws relative to the sky. The equivalent stresses and displacements of the maxillary bones and supporting the teeth are evaluated.

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

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.

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

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.

## Modeling of the shock system motion with impacts about hard barriers

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

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.

## The asymptotic separation of variables in thermoelastic problem for anisotropic layer with inhomogeneous boundary conditions

A method for resolving a thermoelasticity problem with inhomogeneous boundary conditions is presented. Boundary conditions represent uneven surface heating of the layer. An asymptotic procedure for separation of variables based on introduction of additional dimensional scales is used. With an additional assumption that the unevenness of the heating is small enough this procedure makes it possible to obtain the solution. The method is shown for periodic heating case. After the separation of variables the solution is obtained using Fourier series.

## Calculation plainly loaded geometrically nonlinear designs on the basis of mixed FEM with tenzorno-vector approximation requires sizes

The algorithm of reception on a step of loading designs matrixes of deformation of a volume final element with cross-section section in the form of any quadrangle with central unknown persons in the form of increments of movings and increments of deformations is stated in mixed formulation FEM. For numerical realization of algorithm it is used functional, received of a condition of equality of possible and valid works of external and internal forces on a step loading.

## 3-dimentional mathematical model of blood flow with secondary heart theory

This paper presents haemodynamics of blood vessels mathematical model. There is 3-dimentional system of equations describes blood flow, where vessel motions are taking in account.