# Mechanics

## Stability of Vertical Mountain Developments in Elastic Viscous-Plastic Files with Porous Structure

The mathematical model of the basic intense-deformed condition of the vertical mountain development, considering elastic-viscousplastic properties of a file, and also porous structure of a material is constructed. Within the limits of the exact three-dimensional stability equations stability of the basic condition of vertical development in files of rocks with the compressed time is investigated. The estimation of influence on size of critical pressure of parametres of hills is given.

## Variantof the Descriptionof the Intense-Deformed Stateofthe Plane with the Semi-Infinite Flaw on the Basis of the Concept of the Stratum of Interaction at the Normal Separation

The flaw is considered as a physical slit, and a material lying on continuation of a slit, shapes an interaction stratum between its coast sides. The given approach, unlike the concept of a mathematical slit, allows to establish laws of change of voltages and strains in deadlock field. It gives the chance to specify the values of exterior loadings corresponding to transition of a stratum in a plastic state.

## The Problem of Lift Maximization for Circle with a Vortex in a Stream

The key part of the problem lies in finding of vortex position in a stream which would provide the maximum lift of circle. It has been shown that at approaching of a vortex to circle the lift unrestrictedly increases.

## Spline-Collocation Method and its Modification in the Problems of Static Bending of Thin Orthotropic Rectangular Plate

A numerical method for determining the stress-strain state (SSS) of a bended thin rectangular plate with non-classical boundary conditions is presented. Numerical results for three different materials can be used to estimate the influence of the material anisotropy and boundary conditions on its SSS.

## On the Steady Transverse Vibrations of a Rectangular Orthotropic Plate

The problem of the steady transverse vibrations of a rectangular orthotropic plate under the classical Kirchhoff theory assumptions is considered. Two-dimensional problem is reduced to one-dimensional via the modified spline-collocation method. One-dimensional problem is numerically solved with the stable discrete orthogonalization method. Numerical results for three resonance frequencies and plots for deformed middle-surface are presented for three types of boundary conditions on the edges.

## Numerical Investigation of Spectrums of Three-Dimensional Turbulent Convection

The three-dimensional turbulent convectional ﬂows of viscous and incompressible ﬂuid in a rectangular parallelepiped numerically is simulated at heating from below. The horizontal boundaries are stress-free and isothermal. The calculated time spectrum of temperature pulsations at supercriticality is equal to 410 in centre of convective cell has a good agreement with experimental data for convection in cryogenic He. The Obukhov – Bolgiano spectra k−11/5, k−3 and k−5 have been found for velocity pulsations.

## Wave Propagation in Fibre-Reinforced Cylinders

Non-stationary wave propagation in cylindrical composite shell is considered. The shell consists of isotropic matrix reinforced by two families of symmetrically wound spiral ﬁbres. These families have the same mechanical properties and the cylinder is considered to be incompressible. Solutions of coupled equations of motion are represented in the form of Frobenius power series. Approximate dispersion relation derived is analyzed numerically for different shell thicknesses and ﬁbre winding angles.

## Calculation of Outgoing Shock Waves in The Empty Cavity Collapse Problem

The self-similar problem about a collapse of an empty cylindrical or spherical cavity in compressible ﬂuid with adiabatic exponent γ is considered. Two possible variants of the ﬂow after collapse are discussed. The variants are connected with the entropy behavior through the outgoing shock. The calculations show that the main difference in the ﬂow quantities behavior at reﬂection stage have a quantitative character. Outgoing shock compression ratio, characterized by relation ρ2/ρ1, decreases for both variants of the reﬂection when γ is increase.

## Bend of Composite Anisotropic Slab Under Normal Loading

In this contribution, deﬂected mode of a thin slab under bending is investigated by the Lehnicky method of complex potential. The slab is composed of two elliptical rings; they are embedded in each other without tension. Material of the rings is anisotropic and different.

## Analysis of Healthy and Pathological Human Willis Circle Arteries

The aim of this research is to explain initiation, growth and rupture processes of intracranial aneurysms from the mechanical point of view. Results of mechanical testing experiments of intracranial arteries segments are presented, method of obtaining hyperelastic material constants is described. Several boundary problems which simulate blood flow through the arteries were solved with the help of finite element method.