Sessions 2010-2011

Smoothed Particle Hydrodynamics (SPH) Method for solving unsteady hydrodynamic problems is investigated.

Three models with different boundary conditions were considered:
1. Poiseuille Flow. A comparison of velocity profile for analytical solution and numerical results was presented.
2. Classical Dam Break problem (free surface flow). A comparison with experimental data was done.
3. Fluid flow between deformable plates. Qualitative flow patterns were obtained.

Also different method modifications were described. Multithreaded implementation using Nvidia CUDA were discussed.

Contact analysis of a pipeline bending in laying on a rigid seabed is carried out. The pipeline is modeled by a semi-infinite elastic beam. Length of its sagging part is not known and is defined in the result of calculations.

A formula for hydrostatic loading of a rod is derived in the paper; it is shown that in some cases simplified accounting of the loading by reduction of the rod’s weight for the weight of the liquid superseded leads to significant errors.

The analysis of pipeline stress-strain state is considered. Analytical expressions and numerical results are received by asymptotic method and finite difference method. The form of sagging part is defined and internal forces, moments, and stresses are shown depending on the angle of pipeline fixing and the distance from the seabed. The seabed reaction is found for two rod models: the classical and Timoshenko ones.

An infinite cylindrical shell supported by totally rigid cylindrical rolls is considered as a simpliest model of a shell of centrifugal ore-dressing concentrator. The dependence of natural frequencies on angular velocity of rotation and formulae for modes of nonrotating shell with arbitrary number of fixing rolls are obtained. To estimate the accuracy of the model the frequencies of a hinged shell of finite length were found for some particular cases.

Local forms of the buckling of the momentless axisymmetric stress condition of the fine elastic shells of revolution are considered. It is assumed that the shell is reinforced by two systems of fibres inclined at angles t and -t to the generatrix. The forms of the loss of stability of isotropic and orthotropic shells are regarded and the comparison of these forms is conducted. The optimum reinforcement by fibers is considered.

We consider the simulation of groundwater flowing contours recessed rectangular weir, whose corners are rounded to the curves of constant values of filtration rate, when the permeable base is underlain by a curved impermeable, which includes a horizontal Plots, characterized by a constant flow velocity. The results of numerical calculations and gives the hydrodynamic analysis of the impact of the basic physical parameters of the model on the shape and size of the underground contour of the dam.

The investigation of mechanical behavior of multilayered nanotubes is the actual and important problem. Particularly the definition of nanotubes stiffness has been studied by means of scanning probe microscopy. The stiffness is defined as a ratio the value of local load (applied to a tube) to the value of the displacement. The nanotubes made of natural chrysotile asbestos with different materials for fillings are analyzed. The experiments show that the stiffness
of a tube depends on the materials for filling. The tubes with water are softer than the tubes without filling materials and the tubes filled mercury are more rigid than tubes without filling materials. It was previously shown that the classical theory of beam bending could not explain the experimental results, but the experimental results well agree with the Timoshenko-Reisner theory (at least qualitatively), when interlaminar shear modulus of elasticity changes for different filling materials. When additional factors such as lamination of structure and cylindrical anisotropy are taken into account the theory of Rodionova-Titaev-Chernyh (RTC) permits to obtain much more reliable results. In this work the authors also applied one more nonclassical shell theory, namely the shell theory of Paliy-Spiro (PS) developed for medium-thickness shells and considered radial pressure. The comparison of nonclassical shell theories (RTC and PS) with experimental data and finite elements method calculations are presented in the report.

The report is devoted to actual problem of processing experimental researches. The purpose of the research is to construct the fluidity contours for the various constructional materials with difficult rheology. The problem, thay is a classical problem of regression analysis, is reduced to evaluation of the contour factors providing minimum to the objective function. Three fluidity contour construction methods for experimental data are considered: i) manual selection, ii) the method of coordinate descent, iii) the method of the fastest descent. On their basis the technique permitting to obtain the result with the least error is proposed. The computer code realizing the proposed technique is developed.

The paper deals with periodic wave phenomena in a thin elastic plate floating on the surface of an incompressible fluid. The plate covers its entire surface and performs flexural vibrations that accompany gravity waves in the fluid. Free vibrations of the plate are violated along an infinitely-long straight line (or several straight lines having arbitrary spacing between them). We study the transmission and reflection of flexural-gravity waves which are orthogonally incident from infinity upon the so-called “point linear” obstacles in the plate. Exact analytical expressions are found for the wave field in the fluid and flexural field in the plate. The transmission and reflection coefficients of the incident waves are determined. Analytical wave fields’ expressions are also obtained for two approximate models of water depth: infinite and shallow water. First we consider the general problem with arbitrary types of the plate’s obstacles. After that to illustrate the general solution three following types of the obstacles are used. They are rigid supports (clamps), movable supports and infinitely thin cracks. By obtained explicit formulae we numerically calculate the transmission and reflection coefficients, the plate’s deflection and the internal forces (shearing forces and bending moments) appeared in the plate’s supports. Numerical results obtained are compared to determine the validity ranges of the approximate models of water depth (infinite and shallow water).