Sessions 2021-2022

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Man is a slow, sloppy, and brilliant thinker;
computers are fast, accurate, and stupid.

March 29, 2022

N.P. Dorofeev, D.N. Ivanov, N.V. Naumova (SPbSU)
DEFORMATION OF A CIRCULAR THREE-LAYER PLATE WITH A SURFACE CHARGE
Currently, the change in the characteristics of the Solar sail is being actively investigated. The sail is usually presented as a thin film stretched over the frame. During the flight, this film undergoes deformation under the influence of a number of factors, which affects the efficiency and trajectory.

In the report, a model of the Solar sail is proposed in the form of a circular plate with a radius of 50 to 600 meters, consisting of three layers (aluminum, mylar, aluminum). A 2 ?m thick Mylar film is enclosed between two thinner aluminum films, 0.2 ?m thick. As a result of numerical calculations in the FEM package ANSYS, the values of the maximum deflections of the plate depending on its radius were obtained. In the future, it is planned to obtain an analytical solution of the problem and to compare analytical and numerical results. The proposed model can help in predicting the motion of real Solar sails and controlling their orientation in space.
Dorofeev Nikita Pavlovich – 4th year student of the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University. Area of scientific interests - deformation of multilayer plates. Scientific Advisor - Assoc. Prof. N.V. Naumova.
Naumova Natalia Vladimirovna – Associate Professor of the Department of Theoretical and Applied Mechanics of St. Petersburg State University. Research interests: mechanics of solids, vibrations and buckling of shells, asymptotic methods for solving systems of differential equations.
Ivanov Denis Nikolaevich – the leading engineer of the Department of Educational Process Support at St. Petersburg State University. Research interests: mechanics and mathematical modeling.

March 22, 2022

E.A. Ivanov, G.V. Pavilainen (SPbSU)
PLASTIC ANISOTROPY IN BENDING BEAMS AND PLATES BEHIND THE ELASTIC LIMIT
The possibility of numerical and analytical solution of the problems of bending of horizontal and vertical beams, as well as circular plates made of modern structural materials with the effect of plastic anisotropy (SD effect) is analyzed. Beams and plates are subject to hydrostatic pressure and concentrated forces.

The SD effect on the symmetry breaking in the development of plasticity in bending beyond the elastic limit is shown, and the curvature of the neutral axis of the beam and the neutral surface of the plate is estimated. The comparison of analytical and numerical solutions obtained with the help of FEM in ANSYS and COMSOL packages is carried out.
Ivanov Evgeniy Alexandrovich – 2nd year Master's student of the Department of Theoretical Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University. Area of ??expertise: studies of stress-strain state of beams and plates under bending beyond the limits of elasticity.
Pavilainen Galina Voldemarovna – Associate Professor of the Department of Theoretical and Applied Mechanics, St. Petersburg State University. Research interests - hydroelasticity, non-linear problems of bending of beams and plates made of materials with the SD effect, the effect of ice on the strength of hydraulic structures supports

March 1, 2022

I. K. Patel (SPbSU)
CONTACTLESS CAPTURE AND REMOVAL USING ELECTROMAGNETIC INDUCTION
A new method of contactless removal of space debris using electromagnetic induction is considered. The possibility to clean near-Earth space off of metallic space debris objects with the help of magnetically assisted spacecraft (also called collector) is considered. The proposed active debris removal method is classified as contactless. In order to capture a heavy satellite from high Earth orbit and subsequently, transferring it to a target point in low Earth orbit where it can be safely injected into the Earth’s atmosphere its motion should be accurately predicted. In addition, it is necessary for the success of any mission to optimize the fuel consumption in the presence of gravitational perturbation. Therefore, the need to consider the influence of perturbing forces such as Earth’s oblateness is necessary. In this model, the perturbation due to J2 zonal harmonics is taken into account. The orbital dynamics of space debris is studied using numerical simulations. The applicability of the idea is discussed based on simulations, and strategies for improvement and further study are considered.
Patel Ishan Kirankumar – PhD student at St. Petersburg State University, Department of Theoretical and Applied Mechanics, Faculty of Mathematics and Mechanics. Research interests: Methods of active debris removal. Scientific adviser – Prof. A.A. Tikhonov

February 22, 2022

A.H. Gabrielyan (SPbSU)
Peculiarities of deformational behavior of shape memory alloys
The problem of deformational behavior of shape memory alloys is discussed In the report. The research intends to study the effect of pseudoelasticity during isothermal holding under pressure, as well as the effect of martensite stabilization in quenched Ti49Ni51 alloy samples. A number of experimental data has been obtained on strain variation and temperatures transition in the studied alloy. It is shown that strain variation increases during isothermal holding and the effect of strain growth reaches a plato with cycles. The hypothesis about the influence of boundary damage on the effect of martensite stabilization was put forward.
Artur H. Gabrielyan – master's student at St. Petersburg State University, Department of Elasticity Theory, Faculty of Mathematics and Mechanics. Research interests: deformation behavior of shape memory alloys. Scientific adviser – Doctor of Physics and Mathematics S.P. Belyaev.

February 15, 2022

Degilevich E. A., Smirnov A. S. (SPbPU)
The modeling and optimization of the catenary and its modifications
The report discusses the modeling and optimization of a catenary and its several modifications, namely: an inextensible catenary in a homogeneous gravitational field, an extensible catenary in a homogeneous gravitational field, and also an inextensible catenary in a Newtonian gravitational field. An exact analytical solution is given for the catenary models under consideration, during which the optimal values of the length of the catenary are determined, ensuring minimum tension forces on the suspension points. Creation of discrete models with concentrated parameters is carried out in the ADAMS software package. The results of numerical experiments are compared with analytical solutions for continuous catenary models with distributed parameters. As a result of the study, graphs of the force characteristic are constructed depending on the length of the catenary, on the basis of which the correctness of discrete models is confirmed.
Degilevich Egor A. – Second year graduate student of the Higher school of mechanics and control processes, Peter the Great St. Petersburg Polytechnic University. Research interests: analytical mechanics, theory of oscillations, stability theory, optimization in mechanics.
Smirnov Alexey S. – Assistant Professor of the Higher school of mechanics and control processes, Peter the Great St. Petersburg Polytechnic University. Research interests: analytical mechanics, theory of oscillations, stability theory, optimization in mechanics.

November 23, 2021

S.N. Burian (SPbSU)
Dynamics of mechanisms with singularities
Configuration space of mechanical system in holonomic mechanics is a smooth manifold. Smooth structure gets us a possibility to define motion equations and corresponding vector field on the phase space of the system. In the case that there are singular points in the configuration space, only particular methods are applied. We consider several theories of singular space geometries which generalize base terms of differential calculus: (co)tangent vector, (co)tangent space and vector field, integral curves of vector fields, etc. In order to study the application of these theories to the problems of analytical dynamics, some particular examples of mechanical systems with singularities are considered. Configuration spaces, smooth motion types and reaction forces are studied. Dynamics, which is constructed in the frames of geometric theories, is compared with the observed dynamics of model examples of mechanisms. This comparison could help up to formulate the conditions which generalized geometric theory of motion must satisfy.
Sergey N. Burian – PhD student of the Department of Higher Geometry of Faculty of Mathematics and Mechanics at St. Petersburg State University. Research area – analytical mechanics, geometry of singular spaces. Scientific supervisor – Asso. Prof. V.S. Kalnitsky.

November 9, 2021

M.A. Bushmakova (SPbSU)
Evaluation of relaxation terms in state-to-state approachment problems using machine learning methods
Relaxation terms characterize the variation of vibrational level populations of molecules and molar fractions of atoms as a result of various types of energy exchange and chemical reactions. They are the right-hand sides of the set of differential equations for macroscopic gas parameters, describing the flows of multicomponent reacting gas mixtures under conditions of strong vibrational and chemical non-equilibrium. Conventional methods for calculating relaxation terms are computationally expensive, since they imply multiple summations, as well as the calculation of a large number of the rate coefficients of vibrational energy transitions and chemical reactions. In this work, a possibility of evaluating the relaxation terms by machine learning methods is assessed, and the efficiency of two models learned on datasets calculated with SSH and FHO methods is compared for the case of VT and VV relaxation in the mixture of O2-O. Then the solution of zero-dimensional problem obtained by ML algorithms is compared to solution with SSH and FHO methods. It is shown that the k-nearest neighbours algorithm provides the best accuracy/efficiency ratio and can be recommended for further studies. It is also possible to decrease computational time by using ML algorithms.
Mariia A. Bushmakova – first year master student of the Department of Hydroaeromechanics at St. Petersburg State University. Project supervisor - Prof. E.V. Kustova.

October 12, 2021

E.P. Nosov (SPbSU)
Study of the diffraction problem by the ray method for reflection of a plane wave from a parabolic surface
One of the methods for analysis of the diffraction problem is the ray method, the current concept of which was formed at the end of the last century. Nowadays, there is no general formula describing the reflection of a wave from an arbitrary surface. Therefore, special cases are considered. An example of such a case is the problem of external reflection from a parabolic surface. The purpose of this paper is a detailed study of that problem. In the current research the first two terms of the formal asymptotic series for the reflected plane monochromatic wave with constant velocity were found; the asymptotics and the residual were also calculated. It appears that the first term of the formal expansion gives sufficient accuracy for a number of problems.
Evgeny P. Nosov – first year master student of the Department of theoretical and applied mechanics at St. Petersburg State University. Project supervisor - Prof. I.V. Andronov.

October 5, 2021

S.O. Bondarenko (SPbSU)
Motion of a horizontal dynamically unbalanced rotor in gravitational field.
A horizontal dynamically unbalanced rotor motion is considered. The motion equations of two systems are obtained: with two-plane automatic ball balancer and without it. Two rotor models are designed in MATLAB Simulink base on simplyfied equation systems for numerical solution. The whirling amplitude equations are obtained analytically for a rotor rotating at constant angular speed. The gravity is taken into account. Numerical and analytical results are compared.
Sergei O. Bondarenko – first year master student of the Department of theoretical and applied mechanics at St. Petersburg State University. Research area - rotordynamics. Scientific supervisior - Asso.Prof. A. S. Kovachev.