# Mechanics

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

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.

## Synthesis of Asymptotically Stable Motion of a Robot Arm Manipulator

The paper is about an active control problem. It solves the inverse problem of dynamics and concerns with construction of program motions of non-autonomous mechanical systems. This study is important and necessary in software design of automated systems for control of mechanisms. In particular, it is used in various modeling problems of robot-manipulators. Here, we construct all possible asymptotically stable program motions for a model of robots arm-manipulator, which is simulated by a mechanical system with three degrees of freedom.

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

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

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

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

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.

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

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.

## 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.