Rubric: "1.2.2. Mathematical modeling, numerical methods and software packages (technical sciences)"
519.6 Numerical solution of equations of mixed type in unlimited region on a plane
Galanin M. P. (Bauman Moscow State Technical University/Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Ukhova A. R. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2023-3-105124
The purpose of the work is to build and implement an algorithm for finding a numerical solution to a problem for mixed-type equations in an unlimited region. In this case problems are considered in which the process under study is described in some limited area by the thermal conductivity equation or wave equation, and outside it by the Laplace equation. The necessary additional conditions at zero, at infinity and the conditions for conjunction at the border of the inner region are set. There is described an algorithm for finding a numerical solution to a problem with a wave equation in a limited region in one-dimensional and two-dimensional cases, problems with a thermal conductivity equation or a wave equation in a two-dimensional case. Difference schemes are built by the integro–interpolation method. The task is solved in a limited area. Nonlocal boundary conditions are set on its border so the solution of task in limited area coincides with projection of problem in unlimited area. In this case, an artificial boundary is introduced for the solution in the part of the region in which the process is described by the Laplace equation. An iterative algorithm and an algorithm with a non-local boundary condition are built. The results of calculations for examples in various fields are presented.
Галанин М.П., Ухова А.Р. Численное решение уравнений смешанного типа в неограниченной области на плоскости. Математическое моделирование и численные методы, 2023, № 3, с. 105–124.
539.3 Finite element modeling of non-stationary thermal buckling of composite structures
Dimitrienko Y. I. (Bauman Moscow State Technical University), Bogdanov I. O. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Maremshaova A. A. (Bauman Moscow State Technical University), Anokhin D. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-1-3854
The problem of modeling for buckling analysis of the composite structures due to nonstationary thermal effects on them, taking into account the temperature dependence of the properties of the composite components, is considered. Systems of equations are formulated for calculating the basic and varied states of the structure. A classification of buckling analysis problems is proposed. The application of the finite element method to determine the critical temperature and the corresponding buckling mode of a structure is described. A local generalized eigenvalue problem was formulated and the proposed model was verified using the SMCM software package developed at the Simplex Research Center of Bauman Moscow State Technical University, as well as using ANSYS. It is shown that the results of calculating the eigenforms and eigenvalues in the test problem coincide quite well.
Димитриенко Ю.И., Богданов И.О., Юрин Ю.В., Маремшаова А.А., Анохин Д. Конечно-элементное моделирование нестационарной термоустойчивости композитных конструкций. Математическое моделирование и численные методы, 2024, № 1, с. 38–54.
004.942 Mathematical Model of Distributed Design Toolkit Architecture
Belov V. F. (МГУ им. Н.П. Огарева/АУ «Технопарк–Мордовия»), Gavryushin S. S. (Bauman Moscow State Technical University), Zankin A. I. (МГУ им. Н.П. Огарева), Isaykin V. Y. (МГУ им. Н.П. Огарева)
doi: 10.18698/2309-3684-2024-1-110123
The aim of the article is to develop a method for distributing design tasks of mechanical engineering products among a given set of task performers. These task performers are structurally and geographically connected to their respective digital platforms, collectively forming a design ecosystem. A mathematical model has been developed, which can be successfully applied to generate the architecture of a toolkit covering requirements engineering, system architecture, and testing tasks for each project assigned to one of the platforms. The use of Petri nets is justified as a modeling method. Its implementation in the form of a software application for the Product Lifecycle Management (PLM) system of the digital platform can significantly improve project and portfolio management quality.
Белов В.Ф., Гаврюшин С.С., Занкин А.И., Исайкин В.Ю. Математическая модель архитектуры комплекса средств распределенного проектирования. Математическое моделирование и численные методы, 2024, № 1, с. 110–123.
Nikitin A. D. (Institute for Computer Aided Design of the Russian Academy of Sciences), Stratula B. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2024-1-1837
A comparative analysis of the fatigue strength of hot-rolled and SLM materials was performed based on data from high-frequency cyclic tests for corset specimens made of aluminum alloy D16T and SLM alloy AlSi10Mg on piezoelectric equipment. The relatively low cyclic strength of SLM materials is shown, which is associated with their complex microstructure and is influenced by the laser scanning strategy, laser beam parameters, energy, heat transfer from the melting zone, and environmental parameters in the chamber. Mathematical modeling of the process of fatigue failure of the specified specimens was carried out for various amplitudes and mean stresses in the cycle using a multi-mode model of cyclic damage and a numerical method for calculating the kinetics of damage under high-frequency cyclic loading. The proposed model and calculation method make it possible to quickly and efficiently fatigue curves constructing for various cyclic loading modes and cycle asymmetry coefficients. It is enough to know the base points of the bi-modal fatigue curve for the reverse cycle to implement this computational procedure.
Никитин А.Д., Стратула Б.А. Моделирование циклической повреждаемости и усталостной прочности при высокочастотном нагружении 3Д-напечатанных образцов из алюминиевого сплава. Математическое моделирование и численные методы, 2024, № 1, с. 18–37.
Kreerenko S. S. (PJSC Beriev Aircraft Company), Kreerenko O. D. (PJSC Beriev Aircraft Company)
doi: 10.18698/2309-3684-2024-3-8199
The problem of modeling the longitudinal motion of a transport category aircraft and the parametric identification of the aerodynamic characteristics of the longitudinal motion: the components of the dimensionless coefficients of aerodynamic lift and pitching moment are considered. The problem is solved in a class of modular semiempirical dynamic models created by combining theoretical and neural network modeling. The performance and practical significance of the models is confirmed by the results of computational experiments. The development of a neural network model of the longitudinal movement of an aircraft was carried out in Python using the Tensorflow open software library for machine learning and the high-level Keras API as part of Tensorflow.
Крееренко С.С., Крееренко О.Д. Моделирование и параметрическая идентификация аэродинамических характеристик самолета транспортной категории с использованием нейросетей в среде Тensorflow. Математическое моделирование и численные методы, 2024, № 3, с. 81–99.
519.87 Modeling of the effects of double standards and soft power in competition by cellular
Bobrov V. A. (MPGU), Brodsky Y. I. (ФИЦ ИУ РАН)
doi: 10.18698/2309-3684-2021-4-12134
We consider a discrete analog of the classical A. Lotka – V. Volterra competition model in the environment of cellular automata. In the classical model, we know that the type of its evolution over time primarily depends on the coefficients of double standards affiliation to certain ranges of their possible values. The paper shows that the same situation holds for the discrete model either. We can see there is a soft power effect for the classical model. The classic competition model turns into a cooperative positional differential game, the limitations of which are the original system of competition equations by A. Lotka – V. Volterra. The controls are the coefficients of double standards when considering it concerning social systems. The effect of soft power is that the parties tend to compare the competitive pressure on them by the rival population with the one within the domestic population and may take the less stress of the opponent for his favorable attitude towards them, and more extensive — for the hostile manifestation. Whereas comparing the external competitive pressure with the internal pressure in this game does not give us any information — everything depends exclusively on the coefficients of double standards, which are controls and therefore are unavailable to the opponents in this game. Simulation experiments with the discrete analog of the competition model implemented in the cellular automata environment show that the effect of soft power also takes place in this case
Бобров В.А., Бродский Ю.И. Моделирование клеточными автоматами эффектов двойных стандартов и мягкой силы при конкуренции. Математическое моделирование и численные методы, 2021, № 4, с. 121–134.
Ivanov M. Y., Bushuev A. Y. (Bauman Moscow State Technical University), Shcherbakov N. S. (Bauman Moscow State Technical University), Resh G. F.
doi: 10.18698/2309-3684-2024-3-100119
In various technical systems hydraulic devices are widely used to ensure the synchronous movement of executive bodies — unregulated chokes, flow dividers, regulators and/or flow stabilizers. The latter are characterized by the fact that their functioning occurs in the range of pressure drops of liquid amounting to several hundred atmospheres. The issues related to the numerical simulation of non-stationary physical processes in the flow stabilizer the design of which is protected by a patent of the Russian Federation for the invention are considered. The results of computer modeling based on a theoretical model with concentrated parameters, the use of the finite-difference implicit Geer method for solving a system of rigid differential equations are presented. The problem of optimal improvement of the design of such flow stabilizer in accordance with the selected criterion is formulated and solved. This optimization criterion is to ensure the condition of the minimum possible positive statism of the flow-drop (static) characteristic in conditions of wide change in the pressure drop on the device and the effect of the axial component of the hydrodynamic force. The problem of optimal design improvement was solved using one of the widely used evolutionary optimization algorithms — genetic algorithm with real coding. The results of computational experiments in modeling physical processes of the analysis problem correspond to the available experimental data that were previously obtained by the authors of the work. It is shown that improvement of the existing design of the flow stabilizer is possible — the angle of inclination of the flow-drop characteristic to the horizontal axis has decreased almost twofold. At the same time, it was possible to obtain higher accuracy of maintaining volumetric flow rate of the liquid. This accuracy is on the order of ±7,5 % of the nominal (tuning) value of the flow stabilizer. For comparison, the accuracy of maintaining the volume flow rate of the liquid before performing the optimization procedure was about ±10 %.
Иванов М.Ю., Бушуев А.Ю., Щербаков Н.С., Реш Г.Ф. Компьютерное моделирование динамических процессов в гидравлическом стабилизаторе расхода и его оптимизация на основе эволюционного алгоритма. Математическое моделирование и численные методы, 2024, № 3, с. 100-119.
Isaev V. I. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS), Cherepanov A. N. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS), Shapeev V. P. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS/Новосибирский государственный университет)
doi: 10.18698/2309-3684-2023-1-8191
We proposed a self-consistent thermokinetic model of binary alloy crystallization in the weld joint modified by nanodimensional inoculators added to the welding pool during the laser weling process. This combined model of laser welding of uniform metals describes thermophysical prcesses of macroscopic properties of the weld joint and its structure depending on welding regimes and properties of nanomodifying powders (capillary angle, powder concentration). It is based on a thermophysical model of the action of the laser radiation on metal during the laser welding of metallic plates. The simulation is supplemented with a nonequilibrium model of heerogeneous nucleation and the growth of crystalline phase on nanomodifying particles added to the welding pool during the cooling and solidification of alloy in the weld joint. Numerical simulations based on the collocations and least squared methods were performed for butt weling of plates made of a binary aluminum alloy. We calculated the temperature distribution in the plates, the shape of the cross-section of the welding pool, and quantitative properties of its crystal structure. We investigated the effect of the capillary angle and nanomodifying powder concentration on the crystal grain size
Исаев В.И., Черепанов А.Н., Шапеев В.П. Исследование влияния смачиваемости и концентрации модифицирующих наночастиц на структуру шва при лазерной сварке алюминиевого сплава. Математическое моделирование и численные методы, 2023, No 1, с. 81–91.
519.63 Modification of aluminum by laser shock wave detected in atomistic modeling
Perov E. A. (JIHT), Zhakhovsky V. V. (Dukhov Automatics Research Institute/JIHT), Алимович N. A. (L.D. Landau Institute for Theoretical Physics RAS), Shepelev V. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Fortova S. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Doludenko A. N. (JIHT)
doi: 10.18698/2309-3684-2023-4-7492
Plastic deformations are the basis of such industrial technology as laser thermal hardening or laser pinning (LSP, laser shock peening). In this paper, the possibility of hardening the surface layer of an aluminum sample irradiated by a single femtosecond laser pulse is investigated by the method of classical molecular dynamics. Several initialstates of the film are simulated; three orientations of the crystal lattice are investigated — [1, 0, 0] (the first orientation of the crystal lattice), [1, 1, 0] (the second orientation of the crystal lattice), [1, 1, 1] (the third orientation of the crystal lattice). A numerical study of the effect of various values of the invested energy in the range from 120,98 J/m2 to 2540,01 J/m2 of a laser pulse on the depth of plastic deformations affecting the hardening of the material under study was carried out. The energy values were selected in such a way that the plastic front of the UV (shock wave) stopped before it reached the right boundary of the simulated film. If this condition is not observed, then the dependence cannot be considered correctly constructed, since the stretching wave reflected from the right boundary of the sample will slow down the plastic shock front, acting as an unloading wave. With the help of this dependence, the threshold value of the invested energy is determined, when exceeded, aluminum begins to deform plastically.
Перов E.А., Жаховский В.В., Иногамов Н.А., Шепелев В.В., Фортова С.В., Долуденко А.Н.. Молекулярно-динамическое моделирование модификации алюминия лазерной ударной волной. Математическое моделирование и численные методы, 2023, № 4, с. 74-92