### March 30, 2021

E.A. Vasilieva (SPbSU)

ANALYSIS OF ONE POSSIBLE APPROACH TO THE DESIGN OF INTELLIGENT MATERIALS AND STRUCTURES

An assessment of the "viability" of an idea based on combining components with different “smart” properties into a single structure is presented. Some components convert, store and/or transfer the energy of external influence, which is used to operate other components of the internal structure of the intelligent material.

The main focus is on the fact that due to the optimal choice of anisotropy, geometric, physical nonlinearity and "smart" properties in different components of the internal structure, as well as taking into account the particularity of the interaction of such components with each other, it is possible to effectively transform the external influence into “useful work” exclusively on account of the resources of the material itself without attracting additional external energy sources (batteries, accumulators, etc.) and means of information processing and decision-making (controllers, processors, etc.).

On the example of basic models of materials in a stationary formulation, the effectiveness of the ideas of combining components into a single structure, exhibiting different "smart" properties, is demonstrated. In the conclusion, the ways of further research in this direction are described.

**
Ekaterina A. Vasilieva ** – PhD student of the Department of
Elasticity at St. Petersburg State University. Scientific
supervisor - Prof. A.E. Volkov

### March 2, 2020

E.A. Ivanov (SPbSU)

The application of the method of molecular dynamic to study the energy
stability of a column graphene.

The application of the method of molecular dynamic to study the energy
stability of a column graphene (CG) under absorption of phospholipids is discussed in the report.
A column graphene can be used for water filtration or as a transfer of the active substance into living body. In a number of papers it was shown that carbon nanostructures had a tendency to aggregate in the water. Surfactants are used to overcome this problem and phospholipids is one of such surfactants.

The computer model of a column graphene’s elementary cell with different geometric parameters is developed and numerical modeling of the system “column graphene-phospholipids-water” is performed. The curve of dependency of the energy stability of the system on concentration of phospholipids is plotted.

**
Eugeny A. Ivanov ** – master student of the Department of
theoretical and applied mechanics at St. Petersburg State University. Scientific
supervisor - Associate Prof. G.V. Pavilainen. Scientific supervisor of the
project conducted at Saratov State University - PhD Anna S. Kolesnikova.

### November 24, 2020

M.K. Skalina, A.S. Smirnov (SPbPU)

Stability of a rectangular barge in a fluid

Stability of a barge, modelled by a long beam of rectangular cross-section, which
is wholly or partly immersed in a fluid, is discussed in the report.
The main goal of the work is to find all possible equilibrium states of the system and analyze their stability. Bars with different cross-section types (which affect the problem qualitatively) with respect to waterline (diving of one, two or three nodes) are analyzed. The results show that equilibrium positions are determioned by two key dimensionless parameters – the ratio of the sides of a beam and the ratio of density of a beam and fluid. The plots of the curves of equilibrium states illustrate the obtained relations. Their qualitative and quantitative verification is carried out by plotting the graph of the potential energy. In conclusion, the problem of floating of a rectangular bar with a displaced center of gravity is considered and the influence of this offset on the equilibrium positions of the system is discussed.

**
Marina K. Skalina
** – second-year master student at the Institute of Advanced Manufacturing Technologies, Peter the Great Saint Petersburg Polytechnic University. Research interests: analytical mechanics, stability theory, computational mechanics, computer engineering.

**
Alexey S. Smirnov ** –
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 17, 2020

A.A. Glushkova (SPbSU), A.A. Papin (ASU)

Filtration of two immiscible liquids in a poroelastic medium

A mathematical model of the joint motion of two immiscible fluids in a poroelastic medium is developed. The model is a generalization of the classical Musket-Leverett model, in which porosity is assumed to be a given function of the spatial coordinate. Taking into account the compressibility of a porous medium is a fundamental point.

The aim of the study is the analysis of a quasilinear system of composite equations describing one-dimensional unsteady motion of a two-phase mixture in a deformable porous medium. The problem of stability of a stationary solution is examined and the exact solution of the filtration problem of two immiscible incompressible fluids in a deformable porous medium is found.

**
Ann A. Glushkova
** –
the first-year master student at the Department of Theory of Elasticity of
St. Petersburg State University, graduate of Altai State University (Barnaul), specialty - applied mathematics and computer science.

**
Alexandr A.Papin ** –
Dr.Sc.(Math), Professor of the Department of Differential Equations, Altai State University.

### November 10, 2020

D.V. Chepela (SPbSU), Yu.N. Bukharev (MEPhI)

Numerical modeling of high-speed impact problems using the LOGOS software package.

Numerical modeling of high-speed impact problems is necessary to substantiate the durability of spacecrafts exposed to fast moving solid particles.

The LOGOS software package developed at FSUE RFNC-VNIIEF (Sarov) is designed to calculate the problems of heat and mass transfer, turbulent hydro-, aerodynamics and heat propagation on a supercomputer with massive parallelism. In 2017 - 2018, SarFTI employees and students, together with the developers of the LOGOS software, performed research work on the verification and development of models and methods of the LOGOS software for solving the problems of high-speed (up to 10 km / s) impact. The results obtained were introduced into the modernized version of the LOGOS software, which was used in this work.

The aim of this work is to study the processes of formation and development of fragmentation streams beyond the barrier when piercing thin aluminum plates when exposed to a spherical aluminum striker using numerical modeling using SPH-3D, 2D PP LOGOS, analysis and generalization of the data obtained in comparison with experimental results, other calculated data.

**
Daniil V. Chepela
** –
the first-year master student at the Department of Theory of Elasticity of
St. Petersburg State University, a graduate of SarFTI NRNU MEPhI, specialty - applied mechanics.

**
Yuri N. Bukharev ** – Doctor of Engineering, Professor of the Department of General Engineeging and Electronics, SarFTI NRNU MEPhI.

### October 27, 2020

Serebryakov D.A. (SPbPU)

The study of the stress-strain state of aluminum billets under deep punching.

The stress-strain state of aluminum billets in the production of refractive lens elements by deep-pressing methods was studied by the finite element method. The mathematical model of elastic-plastic behavior at high degrees of deformation of technically pure aluminum alloy A0 is developed. In the computational experiment one-sided and two-sided punching of parabolic-shaped voids in aluminum blanks in the shape of washers was modeled. As a result of the study, the effectiveness of the production method was evaluated, the equipment and technological modes were evaluated and the degrees of plastic deformation during processing were estimated. It reached tens of percent in the local zones of workpieces. Large degrees of deformations under compression conditions can cause recrystallization in the areas of localization of deformations.

**
Denis A. Serebryakov
** –
1st year Master student of the Department of Theoretical and Applied Mechanics
at the St. Petersburg State University. Graduated Tomsk State University. Area of research - elasto-plastic stress-strain states.

### October 20, 2020

Anokhin D.A. (SPbPU)

Mathematical modelling of the rocket prototype.

The aim of this research is to study dynamics of rocket motion. Areas of application of the study are: launch vehicles, private space, meteorological rockets.

The work optimizes the aerodynamic characteristics (ADC) of the aircraft. This increases the controllability of the rocket, its ability to more quickly change its trajectory during flight. Initially, the purpose of the research was to study dynamics of rocket motion and the accuracy of guidance. But the results of the first simulation showed that the initial aerodynamic characteristics do not allow effective control of the rocket. The problem was to obtain such ADC Aircraft, which would allow successfully performing the task, creating an algorithm that allows to consciously change the ADC.

Another result of the study is an increase in the rocket’s target accuracy. Modeling the motion of objects and analyzing the results obtained allowed us to put forward a hypothesis, which made it possible to obtain a formula for the dynamic change of one of the two coefficients of the guidance system. In particular, under certain initial conditions, this formula can significantly reduce the minimum miss of a rocket.

**
Dmitry A. Anokhin
** –
1st year Master student of the Department of Hydroaeromechanics at the St. Petersburg State University. Graduated from BSTU "VOENMEH". Area of research - ballistics and hydroaerodynamics.

### October 6, 2020

Muravyov A. S., Smirnov A. S. (SPbPU)

The stability of the movement of a tractor with a trailer (and other issues).

The report discusses the dynamics and stability of the movement of a tractor with a uniaxial trailer, which is pivotally attached to it using an elastic element. The Appel equations are used to derive a nonlinear equation of system motion. The analysis of the linear model is given taking into account the introduction of dimensionless parameters and the area of motion stability is plotted. This area is divided into sub-areas with different qualitative character of the system movement. With the help of Ferrers equations, the viscous resistance forces are taken into account, first in the articulated joint, and then in the elastic element. As a result of the analysis of dissipative models, a stability region is plotted in each of the cases. It is shown that in these two models the stability regions are qualitatively different and may differ from the analogous area plotted in the absence of friction. In conclusion, the problem of optimization the parameters of the system is discussed, where the criterion based on maximization of degree of stability is used.

**
Alexander S.Muravyov
** –
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.

**
Alexey S. Smirnov
** –
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

### September 29, 2020

G.V. Pavilainen (SPbPU)

Mathematical models of hydraulic supports made of structural materials with the effect of plastic anisotropy (SD effect).

Two approaches for analysis of vertical supports of offshore drilling rigs taking into account the lateral pressure of ice and hydrostatic pressure of water are discussed
in the report. The material of the supports is assumed to have the effect of plastic anisotropy. In the case of an elastic formulation, the problem is solved analytically using special Airy functions. In the case of an elastic-plastic formulation
the problem may be solved numerically. Some results of numerical analysis with the ANSYS package are presented.

**
Galina V. Pavilainen
** –
Associate Professor of the Department of Theoretical and Applied Mechanics, Saint-Petersburg State University. Scientific interests: plasticity theory.

### September 15, 2020

D.V. Matias (SPbPU)

Spatial description approach in the problems of hyperbolic thermoelasticity and dynamics of deformable bodies.

In this work, different types of problems are studied using the spatial description. In particular, hyperbolic thermoelastic waves in solids and gases are considered. Hyperbolic waves are described by mathematical model that takes into account the relaxation of the heat flux, due to which the thermal disturbance has a finite velocity. Integral systems are formulated for both solid and gas that allows the employment of the finite volume method. Besides that, the work studies the process of a crack opening in rock medium under internal pressure. In the spatial description, the pressure is modeled through the volumetric force moving together with the crack edges. The integrated formulation of the connection between strain and velocity fields leads to the possibility to use the finite volume method. The process of wave propagation at the interface of two media with different stiffness in a continuum with rotational degrees of freedom is also examined. The angle of incidence and wave type (torsional, bending) are varied.

**
Dmitrii V. Matias
** –
PhD student of the Higher School of Theoretical Mechanics at the Institute of Applied Mechanics and Mathematics of Peter the Great St. Petersburg Polytechnic University. Scientific interests: geomechanics, solid dynamics, thermal wave conductivity. Scientific adviser – Prof. E.A. Ivanova.

### September 8, 2020

S.V. Kashtanova (IPME), A.V. Rzhonsnitskiy (SPbSIT)

On Analytical Study of Stress-Strain State of Cylindrical Shell with the Circular Hole under Axial Tension

A new analytical approach to the deriving of the stress state of a cylindrical shell with a circular hole under axial tension is proposed. The problem statement and first idea of the method to solve this problem belongs to A.I. Lurie (40s of the XX century). It was method of expansion by a small parameter β, which characterizes the ratio of the hole radius, the shell thickness and the radius of curvature. Further, a surge of interest was observed in the mid-60s and early 70s among foreign scientists who found an error in the boundary conditions of the pioneer and revised this problem either in the same way (Murthy, Naghdi, Eringen), or by numerical collocation method (Lekkerkerker, Eringen, Naghdi, VanDyke). Subsequently, interest died down, because this problem has exhausted itself, but there is no solution in explicit form, only an algorithm without rigid mathematical justification or data tables for specific values obtained by collocation procedure.

The authors were able to find a solution in a different form when boundary conditions is satisfied exactly and a qualitatively different new analytical approach without using the expansion by a small parameter β. That way allows doing the separation of variables. The system is beautifully solved by algebraic methods, and allows you to find a solution in the range for β set by mechanical restrictions, namely from 0 to 4, while the analytics of the last century allowed you to use a solution only up to β approximately equal to 0.2 due to mathematical features.

**
Stanislava V. Kashtanova
** –
researcher at IPME RAS, Associate Prof. at Saint-Petersburg State Institute of Technology, PhD in Mechanical Engineering. Scientific interests: shells and plates with holes and inclusions, shell buckling, elasticity theory.

**
Rzhonsnitskiy Alexey
** –
senior lecturer of the Department of Bioinformatics at Saint Petersburg National Research Academic University of RAS, Saint-Petersburg State Institute of Technology. Scientific interests: commutative algebra