Oles Honchar Dnepropetrovsk National
University
Department of Mathematics and mechanics
Dean Alexander Haminich
e-mail: dekan_mmf@ukr.net
Chairs:
Theoretical and applied mechanics
Aero-hydrodynamic and energy mass transfer
fax: +(38056) 776-82-41
Program coordinator
Deputy Dean on Research
Andriy Siasev
e-mail: dekan_mmf@ukr.net
DESCRIPTION OF COURSES
for M.S. programs in Mechanics
(duration of study – 1 year, amount of credits –60, 1 credit equals to 36 hours)
The course proposed is focused on the basic topics of modern mechanics. 1
year of study (60 credits) provides a wide range of theoretical and practical training in
general and special disciplines in mechanics. The highly qualified staff (professors
and doctors) teaches up to date courses using the latest international scientific
achievements.
The list of courses offered provides a basic training in various fields of
mechanics, from strength materials, theory of plasticity, theory of elasticity, aerohydrodynamics, heat and mass transfer. A number of courses devoted to the methods
of numerical calculation processes in mechanics, the flow of liquids and gases and
heat and mass transfer.
Obtained there theoretical and practical skills could be applied further for study,
research or industry.
Student could select either courses set close to one of topic or from
different topics depending on courses taught at their Home University.
One of the components of the program is the individual performing of
research under the guidance of a professor, which finalized by the defense of
research project.
№
1.
Course
Description (prerequisite is given in parentheses if
Credit
necessary)
s
7
Mathema- Following mathematical methods are studies in this
course: basics of differential geometry, differential
tical
equations which appear in mechanical problems, tensor
Methods
algebra, tensor calculus, Fourier and Laplace integral
of
Mechanics transforms and their application to solving differential
equations, basic theory of the generalized functions.
2.
Selected
sections of
the
strength of
materials
On the basis of the standard simplifying hypotheses
engineering methods calculation of strength, rigidity and
stability of typical, widespread elements of designs,
including thin-walled bars, plates and shells are studied.
Questions of an assessment of their working capacity and
rational design are considered.
6
3.
Numerical
methods
of
Mechanics
Methods of finite differences for solving boundary value
problems for equations of elliptic, parabolic and
hyperbolic types. Methods of finite and boundary
elements for solving of potential theory problems and
mechanics of deformable bodies problems.
5
4.
Theory of
elasticity
Theory of stresses. Theory of deformations. Generalized
Hook’s law. Basic equations of theory elasticity and
general theorems. Space problems of the theory of
elasticity. Plane problem of elasticity theory. Saint-Venant
problem. Dynamic problems of theory of elasticity..
Theory of Basic and advanced chapters of the theory of plasticity are
studied in this course. It starts from introducing initial
plasticity
plasticity conditions for different types of materials, like
polycrystalline metals, geo-materials, quasi-brittle
materials and shape memory alloys. Then emphasize is
made on the deformational and flow theories. Following
concepts are taken into account: Druker`s postulate,
associated and non-associated flow rules, kinematical and
isotropic hardening. Basics of the physical theories of
plasticity are also covered. Course ends with studying
6
5.
5
numerical stress update algorithms.
6.
Defects in elastic rigid solids. Stress concentration factor
Fracture
Mechanics and stress intensity factor. Fracture criteria of solids.
Consideration of plastic deformation before the crack tip.
Crack model with a thin plastic strip. A crack between two
different materials. Problems of fracture of composite
materials.
6
7.
Mechanics Piezoelectric materials, their structure and properties. A
of Smart full system of equations of the theory electro-elasticity.
Materials Exact solutions of some electro-elasticity problems. Plane
problem of the theory electro-elasticity. Dynamic
problems for piezoelectric materials. Some features of
deformation of shape memory alloys.
5
8.
Aerodynamic theory
of
wind
turbines
Introduction. Atmospheric circulations and wind
characteristics: atmospheric circulations, the main wind
systems, atmospheric turbulence and boundary layer, wind
characteristics. Wind energetics: the history of windmills,
present situation and future prospect, main types and
categories of the wind turbines, the principles of wind
energy extraction, technical, economical and ecological
aspects. Basic laws and concepts of aerodynamics:
introductory remarks and definitions, fluid motion
description, the main theorems and their interpretation,
potential flow patterns, the application of the complex
variables, the fundamental equations of inviscid and
viscous flows, the boundary layer concept, basic features
of compressible gas flows, applied aerodynamics of the
simple body shapes. Aerodynamics of horizontal-axis
wind turbines (HAWT): physical aspects, general
momentum theory, blade element theory, other methods.
Aerodynamics of vertical-axis wind turbines (VAWT):
physical aspects, theoretical methods, single stream-tube
approach, other methods. Optimization of wind turbine
parameters: optimization of horizontal-axis wind turbines,
optimization of vertical-axis wind turbines. Simplified
procedure of the wind turbine design: general
consideration and approximate relations, design of
horizontal-axis wind turbines, design of vertical-axis wind
4
turbines.
9.
Numerical
methods
in fluid
dynamics
and
thermal
physics
Conception of the numerical methods. Statement of the
boundary problems in the fluid dynamics and thermals
physics. Fundamentals of the finite differents and finite
volumes, building of the numerical algorithms and
schemes for calculation of the energy equation and fluid
dynamic equations. Mathematical modelling of the fluid
mechanics and heat transfer processes by CFD programs.
4
10. Methods
of
calculation
of solar
energy
systems
The methods of heat transfer. The laws of radiant heat
transfer. Low-temperature solar energy systems. A
mathematical model of the solar collector. Heat loss
coefficient of solar collector. Energy performance of solar
collector. High-temperature solar energy systems. The
intensity of the radiation. Indicatrix of radiation. Types of
solar concentrators. Mathematical model of solar radiation
concentration. Methods for calculating the concentration
systems.
3
11. Heat and
mass
transfer in
the heat
exchange
apparatus
Types of heat exchangers. The fundamental equations of
calculation of heat exchangers. Calculation of recuperative
heat exchanger. The temperature difference between heat
transfer fluids. The calculation of the final temperature of
the coolant. Comparison of forward flow and backflow.
Laminar heat transfer in a round channel. Types of heat
transfer fluids depending on the Prandtl number.
Numerical and analytical calculation. The turbulent heat
transfer in a round channel. Dynamics and heat transfer in
channels of different geometries.
3
12. Hydrodynamics
of
Multiphase Media
Continuous and disperse phases. Hydrodynamic
interaction. Motion equation for solitary particle. Particle
in cell. Examples of problems: separation, sedimentation,
bubbling, mixing. Thermal physical processes in
multiphase media. Heat conduction and diffusion near
solitary particle. Eulerian models of hydrodynamics and
heat and mass transfer in multiphase media. Numerical
methods of calculation. Combustion processes of coal
particles or fuel oil drops in boiler furnaces of
thermoelectric plants.
3
13. Heat and
Mass
Transfer
in Porous
Media
Review of processes in porous media. Main mathematical
models of filtration. Examples of filtration flows. Finite
difference method. Boundary element method. General
equations of heat and mass transfer in porous media. Heat
and mass transfer with phase transitions. Drying process.
3
14. Environm
ental Heat
and Mass
Transfer
Structures of atmosphere, hydrosphere and soils. Thermal
processes on the Earth surface. Thermal processes in soils,
irrigation and amelioration. Pollutions of soils. Free
convection in porous media. Water turnover in nature.
Circulation of World Ocean. Pollution of water resources.
Global atmospheric circulation. Local atmospheric flows.
Free convection in atmosphere. Air flows in towns. Local
and global pollution of atmosphere. Thermal pollution of
atmosphere. Transformations of water in atmosphere.
Global warming.
5
15. Fluid
Flows and
Heat and
Mass
Transfer
in Microgravity
Conditions
Weightlessness and microgravity conditions. Asymptotic
mathematical model of viscous fluid flows and heat and
mass transfer in microgravity conditions. Stokes flows.
Marangoni convection. Weak free convection. Motion of
multiphase
media
in
microgravity
conditions.
Sedimentation and flotation. Thermophoresis and
diffusiophoresis. Thermodiffusion and coupled diffusion.
Hydrodynamic effects of phase transitions. Technologies
of space industry.
5
16. Research
Individual laboratory or theoretical work under the
supervision of a professor finalized with project defense.
(Amount of credits is subject to discussion during
adjustment of plan of education)