Sessions 2018-2019

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Computers make
very fast,
very accurate
mistakes.

April 23, 2019

D.V. Franus (SPbSU)
Features of finite-element modeling of eye biomechanic's problems in COMSOL
The features of finite-element modeling of the corneoscleral shell of human eye under the pressure of applied vacuum compression ring on the example of the COMSOL software package are considered. The aspects of building the geometry of an elastic multilayer thin-walled shell consisting of two spherical parts: 1) the corneal and 2) the scleral shell are considered in detail. The features of the use of a curvilinear coordinate system, parameters and variables, contact pair settings are described.

As a result of modeling, the nonlinear relation between modulus of elasticity of the sclera and both displacement and stress of the scleral shell under the load of a vacuum compression ring is revealed.
Dmitry V. Franus – PhD

April 9, 2019

I.A. Zakharov (SPbSU)
ollision integrals of charged particles
In the modern molecular-kinetic theory of gases, the calculation of transport c oefficients (such as thermal conductivity, viscosity, diffusion coefficients) requires the calculation of Ω-integrals. The coefficients of the systems of equations are expressed with Ω-integrals, with the help of which the above-mentioned transfer coefficients are calculated. The aim of the work was to write a software module within the framework of the Kappa chair project, which calculates collision integrals (Ω-integrals) for collisions of charged and neutral particles. The main field of application of the developed module is the calculation of heat fluxes near the surface of high-speed aircraft.
Ilya A. Zakharov – the 1st Master student of Department of Hydroaeromechanics of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: molecular-kinetic theory of gases, calculation of heat fluxes. Scientific supervisor – Prof. E.V. Kustova.

March 12, 2019

A.V. Dementyev (SPbSU)
Specific features of the reflection by the radiation of a compact highly focused rotating source
The location is based on the fact that the analysis of the properties of the reflected signal provides opportunity to get information about the surface of the studied or revealed object. In the case of the location of farther objects and in larger solid angle two methods can be used: 1) to send the high energetic flux of the radiant energy (electromagnetic, acoustic etc.) at once on all possible directions by the short impulses; 2) to concentrate this flux in the narrow ray and scan different directions by it. Given the finite value of the speed of propagation of the signals the irradiation of one and the same object by these two methods may result in the appearance of the reflected impulses with different parameters.

In this research the reflection by the screen of the spherical and ellipsoidal form of the electromagnetic radiation of the compact source uniformly rotating about its axis and radiating in the limited solid angle is considered. The profiles of the reflected impulses are calculated, as well as the moments of their arrival at the remote observer. The conditions are determined under which the above methods of the irradiation of the screen give the reflected impulses with substantially different parameters.
Dementyev Andrei Viktorovich – Associate Professor of the Department of Astrophysics, Faculty of Mathematics and Mechanics, SPbSU. Research interests: Theory of Radiative Transfer, Physical Kinetics.

February 26, 2019

V.V. Komarov (SPbSU)
INVESTIGATION OF THE HYDROACOUSTIC IN A PIPE WITH A RING-SHAPED OBSTACLE WITH THE WATER FLOW
When fluid flows in various channels and valves, hydrodynamic noise, vibration and noise near the device may occur. The process of hydrodynamic noise in the liquid itself is complex and is associated with the presence of vorticity. When the flow is detached from the wall, vortices and an uneven pressure field are formed, but this field is not a sound as the disturbances propagate with the flow velocity. The existing vortices hit the elastic walls of the channel, causing their oscillations, which will be the source of the sound and propagate with the speed of sound in the liquid. In this regard, the complex problem of determining hydrodynamic noise and vibration-noise characteristics can be considered separately.

In this work, a non-stationary hydrodynamic field is investigated when water flows in a circular pipe with a spacer. As a result of the hydrodynamic calculation, nonstationary pressure distributions along the pipe walls and nonstationary flow patterns of the beam are determined. The Fourier transform of the unsteady pressure field on the walls is performed and these data are sources for the calculation of the vibro-acoustic problem.
Vladislav V. Komarov – the 1st Master student of Department of Hydroaeromechanics of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: computational hydrodynamics, hydroacoustics. Scientific supervisor – Asso.Prof. A.G. Karpenko.

February 12, 2019

A.A. Morshchinina, D.A. Morshchinina (Radioavionica orporation)
Analysis of reliability and safety of the Control omputer System produced by Radioavionica Corporation
The structure of the Control omputer System produced by Radioavionica Corporation is considered. The mathematical models of its functioning are developed. The parameters of reliability and safety of the system and its elements are determined. The analysis of reservation influence on their values is carried out. On the basis of the obtained results the reliability and safety of the Control omputer System of various configurations are estimated.
Diana A. Morshchinina – PhD, head of the Department of technological and mathematical support of scientific and technical center of perspective development of Radioavionica Corporation. Scientific interests: theory of elasticity, theory of reliability.
Alina A. Morshchinina – PhD, leading specialist of scientific and technical center of perspective development of Radioavionica Corporation. Scientific interests: theory of elasticity, theory of reliability.

December 4, 2018

Fazlyeva K.M. (SPbSU)
Control of vibration damping of a three-mass system in horizontal motion.
The research concerns one of the central problems of the control theory. An incompletely controlled mechanical system with a finite number of degrees of freedom is considered. The system motion may be affected by the control force acting on one of its generalized coordinates. The problem of vibration damping, i.e. finding the control force that moves the system at the specified distance from the initial resting state to the final resting state for a finite time period. To solve this problem we apply the methods of nonholonomic mechanics with higher-order constraints. It was also shown how the generalization of Gauss's principle of least constraint allows to construct the control function that is significantly different from solutions obtained by classical methods.
Camilla M. Fazlyeva – the 2nd year Master student of the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: nonholonomic mechanics, control theory. Scientific supervisor – Prof. M.P. Yushkov.

November 27, 2018

V.S. Federyaeva (SPbSU, JSCNIIEFA), I.V. Vitkovsky, M.M. Golovanov, I.R. Kirillov, K.A. Komov, S.A. Krizhanovsky, D.M. Obukhov,G.V. Preslitsky (JSCNIIEFA).
New methods and approaches to development of electromagnetic pumps for liquid metal fast breeder reactors
New methods and approaches to development of electromagnetic pumps for liquid metal fast breeder reactors are considered based on the design of immersed EMP of BN-1200 cold trap. Results of complex research of novel high temperature resistant electrical engineering materials to meet service life requirements at high temperature are shown. Main issues on improvement of manufacturing technology of those materials are stated. Computational results aimed to optimize EMP design, fulfill stated above requirements and confirm specified parameters are presented
Valeriya S. Federyaeva – the 1st year Master student of Department of Hydroaeromechanics of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: computational fluid dynamics, high temperature resistant inorganic materials.

October 30, 2018

Yu. M. Dahl (SPbSU), A. A. Morshchinina (Radioavionica orporation), D. A. Morshchinina (Radioavionica orporation)
SOME OF THE PROBLEMS OF BENDING AND STABILITY OF ELASTIC BEAMS AND PLATES
The problem of the stress-strain state of a curved beam loaded with an arbitrary transverse load was considered. The integration of the differential bending equation was made by using the operating method. The connection of this method with the method of initial parameters was determined.

The stability of prismatic bars was investigated by the operational method. The physical meaning of the "completely indefinite" numerical factor in the theoretical works of the authors describing the forms of stability loss of bars was determined. The local loss of stability of thin-walled elements of engineering structures was analyzed. The results of some theoretical and experimental studies of this problem were presented.

The features of deformation of thick plates and thin plates with elliptical cut were presented. It was noted that the stress concentration coefficient is a function which depends on the deformed cut configuration.

The results of laboratory experiments on stretched polymer films with a system of rectilinear cuts were presented. The solution of the plane problem of the theory of elasticity about the stretching of a plane with a lattice of rectilinear cuts was presented.
Yuriy M. Dahl – Doctor of Science (Physics&Math), professor. Scientific area: theory of elasticity.
Alina A. Morshchinina – PhD, lead engineer of scientific and technical center of perspective development of Radioavionica orporation. Scientific area: theory of elasticity.
Diana A. Morshchinina – PhD, lead specialist of scientific and technical center of perspective development of Radioavionica orporation. Scientific area: theory of elasticity.

October 23, 2018

L.A. Igusheva (SPbSU)
Rod dynamic fracture in the Klein-Gordon field
The interaction model of a constant cross-section rod with an elastic environment is considered. The directly proportional to the displacement resistance forces impacted on the rod. The equation of longitudinal vibrations of the rod interacting with the elastic medium is obtained. This equation is well-known Klein-Gordon equation. The solution of this equation is found. Displacements and stresses arising in the rod under dynamic loading are calculated. The wave propagation and reflection from the free boundary of a finite-length rod are considered. The possibility of the effect of spall fracture is shown. Fracture phenomenon is predicted by the incubation time criterion. In several special cases, the dependence of the threshold value of the load amplitude on the critical time of the rod fracture and on the duration of the load is found. With a small coefficient of environment resistance, a range of optimal frequencies load for rod fracture is found. With an increase in the resistance coefficient of the environment, it is noted that the rod fracture occurred with the direct propagation of the wave along the rod. It is shown that there are optimal frequencies of load when the rod fracture occurred.
Liudmila A. Igusheva – the 1st year Master student of Department of Theory of Elasticity of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: fracture dynamics. Scientific supervisor - Corresponding Member of the Russian Academy of Science, Professor, Dr. of Science Y.V. Petrov.

October 16, 2018

V.N. Kylev (SPbSU)
Prediction of some types of failure in the main parts and nodes of special heat engines.
Reliable design, ensuring operability (performance of specified functions) at the whole stage of the product life cycle, is a complex technical task. During operation, parametric and functional failures may occur.

Parametric failure - change of the specified operating parameters in unacceptable limits. This failure leads to an emergency mode of operation, in which it is important to ensure that the machine is not destroyed.

Functional failure is equivalent to fatigue failure. It can be associated with the preservation of the overall cyclic strength, or with its loss during the onset of high load dynamics. In addition, fatigue failure can lead to the formation and development of fatigue cracks, leading to the complete destruction of metal structures. Therefore, the main task of predicting the failure of products is the analysis of metal fatigue.
Valentin N. Kylev – the 1st Master student of Department of Theory of Elasticity of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: fatigue and fracture mechanics. Project supervisor – Asso.Prof. S.A. Meshkov. Scientific supervisor – Asso.Prof. B.N. Semenov.

October 2, 2018

A.I. Bechina (SPbSU)
Rotational energy relaxation time of vibrationally excited molecules
Simulation of nonequilibrium gas flows is important for aerospace applications, studies of the atmospheres of planets, and the solution of environmental problems. When constructing a description of nonequilibrium flows, it becomes necessary to calculate the thermal and diffusion fluxes, the stress tensor. In the kinetic theory of gases, it is necessary to know the relaxation time of the rotational energy in order to calculate the transport coefficients (the coefficients of thermal conductivity, diffusion, shear and bulk viscosity, relaxation pressure). The influence of the molecular vibrational state on the rotational energy relaxation time is studied in the state-to-state approach. The rotational levels of the molecules are described by the nonrigid rotator model; their interaction is described by the variable soft sphere model.

According to this model, collision cross sections for N2-N, O2-O, NO-O interactions are calculated for different vibrational and rotational levels of molecules. On the basis of the kinetic theory of nonequilibrium processes, the rotational relaxation time is introduced for each vibrational level. Relaxation times are calculated numerically in the wide temperature range, and a comparison with the relaxation time obtained by the well-known Parker formula is carried out. The influence of various multi-quantum rotational transitions on the accuracy of the calculation of the rotational relaxation time is analyzed.
Anna I. Bechina – the 1st Master student of Department of HydroAero-Mechanics of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: Molucular Kinetic Theory of Fluids and Gases. Scientific supervisor – Prof. E.V.Kustova

September 25, 2018

T.Yu. Chernysheva (SPbSU)
Modeling functional and mechanical behavior of CuAlNi-based shape memory alloys
Shape memory alloys based on Cu (for example, CuAlNi), which have a narrow temperature hysteresis and demonstrate a complete deformation recovery, are used in the actuators and vibration protection devices. However, little is known about the models describing their mechanical behavior. This determines the relevance of this study. Modeling of functionaland mechanical properties of shape memory alloys based on CuAlNi is performed in this work. The anisotropy of elastic constants in the austenite phase is taken into account, matrices of elastic constants and elastic compliances are recorded. The deformation matrix for the martensitic transformation β1(DO3)-β1(18R) is calculated and the crystallographic resource is determined. Modeling of isothermal deformation of single crystals of different orientations in the austenite state is performed when the shape memory alloy demonstrates the effect of pseudoelasticity. The results which obtained are in good agreement with available data in the literature.
Tatiana Yu. Chernysheva – the 1st year Master student of Department of Theory of Elasticity of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: researchng and mathematical modeling of the functional properties of alloys with shape memory. Scientific supervisor - Associate Prof. M.E. Evard.

September 11, 2018

T.A. Lapina (SPbSU)
Investigation of the possibilities of COMSOL software package for solving the problems of deformation of shape memory alloy bodies
Practical application of shape memory alloys (SMA) is often associated with the need to solve problems of deformation of complex shape bodies experiencing large deformations, as well as under difficult boundary conditions. Such problems in most cases do not have an analytical solution. The way out of this situation is the use of numerical methods. One of the most used is the finite element method, which allows to solve a large range of engineering problems.

In this work, the following possibilities of software package COMSOL Multiphysics are investigated:

• Internal material models for solving the problems of deformation of shape memory alloy bodies
• Adding external material
• Built-in SMA model in the latest version of COMSOL Multiphysics 5.3a
Tatiana A. Lapina – the 1st year Master student of Department of Theory of Elasticity of the Faculty of Mathematics and Mechanics at St. Petersburg State University. Scientific area: mathematical modeling, SMA, boundary value problems. Scientific supervisor - Associate Prof. M.E. Evard.

September4, 2018

A.L. Smirnov (SPbSU)
Free vibrations of annular plates.
Thin plates of different shapes are used as structural components in almost all engineering applications, where high strength, stiffness and light weight materials are highly needed. The aim of this research is to study free transverse vibrations of an annular thin plate. Plates of such shape are widely used not only in engineering but also in biomechanical modeling.

Analytical, asymptotic and numerical (FEM) methods are used to examine the problem. The main purpose of the research is to find simple asymptotic formulas describing the effect of small central hole on vibrational spectrum of a plate.
Andrei L. Smirnov – PhD, Associate Prof. at the Department of Theoretical and Applied Mechanics SPbSU. Author papers on mechanics of thin-walled structures.