# Mechanics

## Dynamics of Multilayered Thermoviscoelastic Plates

This paper deal with laminated thin-walled structures. The laminated structures considered herein consist of three layers. The following assumptions are assumed. The thickness of inner layer is considerably greater the others.The kine matic relationsf ortheinnerlayerare examined in the form of Mindlin – Reissner shell theory, for the outer layers are in the form of membrane theory. The deformations of the whole layered structure are deﬁned by the polyline hypothesis.

## Mathematical Models of Stability Loss of Nonuniform Cylindrical Shells Because of Nonuniform Radial Loading

The circular cylindrical shell with variable thickness along the axis of elongation is considered. The axisymmetric radial pressure along the axis of shell is suggested. The one of values (for the law of pressure variation) which effects the stability loss of shell is determinated.

## Plate Braking Against the Layerof «Delayed» Viscoplastic Fluid with Regard to Wall Sliding

The paper presents the problem of unstable viscoplastic fluid flow between parallel planes, one of which is fixed, while the other one is put in motion from a standstill under the influence of constant force. Viscoplastic fluid flow develops gradually. The border of the flow is not known in advance and is to be determined in the process of solving the task. The force applied to the upper plate is chosen so as to cause the effect of sliding along the two plates in the course of time.

## Some Aspects of Applying Finite Element Method to Contact Problems Using ABAQUS System

In this paper the selection of preferred computational scheme for numerical research of a contact interaction between a rigid indentor andanelastic-plastichalf-spaceusing ABAQUS system is фdescribed. Furthermore, the critical values of the load applied to indentor which don’t cause plastic deformation in the material and subsequently don’t effect the process of a surface hardening are determined. Some peculiarities of the forming of near-surface plastic region by static loading are investigated.

## Modeling of Motion of the Complex Elastic System

The purpose of article is a receipt of mathematical model of motion of the complex elastic system. The normal modes and frequencies are searched by decomposition of vibrations on the modes of stationary elements of the system. It allows to transform partial differential equations of motion in ordinary differential equations. The motion of a space craft which consists of elastic large size elements (solar panels) is modeled.

## Mathematical Modeling of Longitudinal Blauofthe System of Homogeneous Rodsabout Rigid Barrir at Increase Long Solids

Mathematical modeling of longitudinal elastic central blow of non-homogeneous rod system about a rigid barrier is carried out, at not-holding connections. Mathematical modeling is carried out by the exact analytical decision of the wave differential equation by method of Dalamber with the setting of necessary initial and boundary conditions. The rod system consists of a step non-homogeneous rod and a homogeneous rod of constant cross section. Connections with a rigid barrier and between rods are not-holding.

## Mode Mixity Parameters for Mathematical Crack Type

A method for calculating the elastic-plastic stress intensity factors for full range of mixed mode loading from tensile to shear crack is suggested. The state of arbitrary oriented straight-line crack in form of mathematical notch under biaxial loading is considered. The solution is based on a combination of both the compatibility strain equation and the Airy stress function with its derivatives. The elastic-plastic material behavior is represented by the Ramberg – Osgood model.

## Thickness Influence of the Multylayer Corneal Shell on the Value of Intraocular Pressure

A research of changes in the stress-strain state of the corneoscleral shell of the human eye under loading by a flat base stamp is made. In this paper a three-dimentional finite-element model of contact problem under loading of multilayer corneal shell with flat base stamp is presented. This mathematical model is made in software package ANSYS. Cornea is modeled as a transversely isotropic spherical shell of variable thickness composed of four layers: epithelium, Bowman's membrane, stroma of the cornea, and Descement's membrane.

## Variable Bending of a Three-layer Rod with a Compressed Filler in the Neutron Flux

The present paper considers variable bending of a three-layer elastoplastic bar with a compressible filler in the neutron flux. To describe kinematic properties of an asymmetric through thickness pack we have accepted the hypotheses of a broken line as follows: Bernoulli’s hypothesis is true in the thin bearing layers; Timoshenko’s hypothesis is true in the compressible through thickness filler with a linear approximation of displacements through the layer thickness. The filler’s work is taken into account in the tangential direction.

## Development of Asymptotic Methods for the Analysis of Dispersion Relations for a Viscoelastic Solid Cylinder

Propagation of time-harmonic waves in a viscoelastic solid cylinder is considered. Vibrations of the cylinder are described by three-dimensional viscoelasticity equations in cylindrical coordinates. The stress-free surface boundary conditions are imposed. Viscoelastic properties are described by integral operators with a fractional-exponential kernel. For the case of a rational singularity parameter the method of asymptotic analysis of dispersion relations is proposed, which is based on the generalized power series expansion.