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.
Andrianov I. K. (Комсомольский-на-Амуре государственный технический университет), Chepurnova E. K. (Комсомольский-на-Амуре государственный технический университет)
doi: 10.18698/2309-3684-2024-2-316
The study considers the problem of optimizing the crack detection system of gas turbine blades. The shell of the capsule of the damage detection system, which is under the influence of internal pressure, is considered as an object of research. The task of the study was devoted to the mathematical modeling of optimal pressure in capsules of the damage detection system. As part of solving the research problem, a mathematical formulation of the problem of optimizing the nonlinear pressure function was carried out in the presence of restrictions on variable parameters: wall thickness and outer diameter of the cylindrical capsule shell. The construction of the optimization objective function was carried out on the basis of the equilibrium condition of the shell element in the area of crack opening of the turbine blade, the limit state criterion using the Tresk-Saint-Venant strength theory. The research methodology was based on the approximate decomposition of the function into a Taylor series, the Lagrange multiplier method, and the Kuhn-Tucker theorem. When solving the problem of conditional optimization, the cases of violation of the regularity conditions of the limiting functions are analyzed. According to the calculation results, the minimum value of the required pressure for the destruction of the capsule shell in case of opening of the crack banks of the turbine blade is achieved at the maximum value of the outer diameter of the shell and the minimum thickness of its wall. According to the test calculation data, the area of acceptable solutions to the optimization problem is graphically presented, and the lines of the level of the target function of pressure optimization are shown. The constructed mathematical model and calculation algorithm will automate the process of calculating the required pressure in the capsules of the turbine blade crack detection system and obtain an estimate of the minimum pressure value in the presence of restrictions on the absolute and relative values of the capsule shell wall thickness, the outer diameter of the capsule.
Андрианов И.К., Чепурнова Е.К. Математическая модель условной оптимизации давления в системе обнаружения трещин лопаток газовых турбин. Математическое моделирование и численные методы, 2024, № 2, с. 3–16.
Bushuev A. Y. (Bauman Moscow State Technical University), Danilov N. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-2-313
A mathematical model of functioning of synchronization systems of actuators based on a throttle flow divider was developed to solve design problem. The solution of the optimization problem of a mismatch time of movement of actuators operating under conditions of external alternating-sign force effects is given, performed using the genetic algorithm and refined using the Nelder-Mead algorithm
Бушуев А.Ю., Данилов Н.А. Математическое моделирование гидравлической системы синхронизации исполнительных органов на основе дроссельного делителя потока. Математическое моделирование и численные методы, 2022, № 2, с. 3–15
Mozzhorina T. Y. (Bauman Moscow State Technical University), Rakhmankulov D. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-3-7487
In this paper, the optimization of the transfer of a low–mass satellite from the Earth's orbit to the Mars orbit under a solar sail is considered. Optimization of the control of the pitch angle of the solar sail is carried out using the Pontryagin maximum principle while minimizing the flight time. In contrast to previous works on this topic, the solution of the boundary value problem, to the solution of which the maximum principle is reduced, was obtained by the false position method. The calculation program is written in the C++ programming language. Despite the computational difficulties arising when using the false position method, it was possible to achieve good convergence of the Newton method underlying the algorithm. The analysis of the accuracy of the results obtained is carried out and the possibility of using the false position method in solving such problems is shown. A comparison is made with the data of previously published works. Despite some assumptions used in the development of the calculation algorithm, the work has its value in terms of assessing the possibility of using the false position method, which gives the most accurate numerical optimization results.
Мозжорина Т.Ю., Рахманкулов Д.А. Моделирование и оптимизация управлением спутника малой массы при перелете с орбиты Земли на орбиту Марса под солнечным парусом. Математическое моделирование и численные методы, 2021, № 3, с. 74–87.
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.
519.6 Agent model of two competing populations taking into account their structurality
Belotelov N. V. (Bauman Moscow State Technical University/Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS), Brovko A. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-3-7183
The article describes an agent simulation model of two populations competing for one resource. In the model, it is assumed that an individual dies if its mass-energy becomes non-positive. It is assumed that individuals of each of the populations under consideration can form flocks, this allows populations to increase their competitiveness. In the model, this is formalized through the ability to organize networks connecting individuals of the same species. At the same time, individuals can form only a certain number of connections with neighbors. The concept of "valence" is introduced in the model to describe this. It is assumed that within each network there is an instantaneous redistribution of the resource available to all members of the network by each member of the pack. In addition to the model, the article describes the structure of the program with which simulation experiments were carried out. As a result of the simulation experiments, the following was obtained. If the resource is highly productive, then in the process of competitive interaction, the population wins, the agents of which have a large "valence". And in the case of a low-productive resource, individuals of a population with a lower "valence" win in competitive interaction. This is due to the fact that more complex structures require more energy to maintain the flock.
Белотелов Н.В., Бровко А.В. Агентная модель двух конкурирующих популяций с учетом их структурности. Математическое моделирование и численные методы, 2022, № 3, с. 71–83.
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
Parkhomenko V. P. (ФИЦ ИУ РАН/Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-2-3853
The aim of this work is to consider a global model of the carbon cycle. The model describes the production process of forest ecosystems taking into account the seasonal sicle of climatic factors. It is designed to simulate a long period of time as part of a global climate model of intermediate complexity. It has been established that the global characteristics of the climate system reach a steady state over a period of about 2000 years, and the model works steadily. The temporal and spatial distributions of the obtained climatic characteristics and the biogeochemical carbon cycle of terrestrial vegetation are given.
Пархоменко В.П. Глобальная климатическая модель с учетом биогеохимического углеродного цикла растительности суши. Математическое моделирование и численные методы, 2021, № 2, с. 38–53.
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.