Rubric: "1.2.2. Mathematical modeling, numerical methods and software packages (technical sciences)"
Rogulin R. S. (Vladivostok State University)
doi: 10.18698/2309-3684-2023-2-129154
The formation of the supply chain of raw materials is closely related to the production problems of woodworking enterprises. Construction of supply chains for raw materials and the optimal calculation of daily production have been hot topics since the beginning of the second industrial revolution. This article discusses the enterprise of the Primorsky Territory of the woodworking industry, which does not have plots for rent. The purpose of the work is to solve the problem of building a supply chain of raw materials, taking into account the daily loading of production facilities and finding the optimal solution. The source of raw materials is the commodity exchange, where lots appear daily randomly in different mining regions. In the scientific literature, there are many ways to calculate the best profit value, taking into account many restrictions, but they do not take into account many features that are important for woodworking enterprises. Based on a review of the scientific literature, this article presents a mathematical model that acts as a decisionmaking mechanism on each individual day, and it differs in that it can take into account the coefficient of useful volume of raw materials that will reach the warehouse and travel time. The model was tested on the data of the Russian Commodity and Raw Materials Exchange and a company in Primorsky Krai. The result of testing the model is the calculated optimal profit trajectory for each set of data on the volume of raw materials, the time of lots in transit, as well as many important indicators for any production: profit volume, production volume of goods. The analysis of the received solutions showed that there are difficulties in planning supply chains and production volumes. The regions are analyzed as sources of raw materials, from which regions and when it is worth buying raw materials. The shortcomings and positive aspects of the mathematical model are given
Рогулин Р.С. Математическая модель формирования цепочек поставок сырья с товарно-сырьевой биржи в условиях риска с опорой на траекторию прибыли за предыдущие периоды. Математическое моделирование и численные методы, 2023,№ 2, с. 129–154.
Valishin A. A. (Bauman Moscow State Technical University), Zaprivoda A. V. (Bauman Moscow State Technical University), Klonov A. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-1-93109
With the development of forecasting methods, the exclusion of random effects from the initial information and the studied processes becomes essential. These effects are associated not only with the impossibility of taking into account all factors, but also with the fact that some of them are often not taken into account at all. It is important not to forget about random measurement errors. In the predicted values, due to these effects, a kind of random offset or "noise" is created. Filtering (exclusion) of noise should, of course, increase the reliability and justifiability of forecasts. This article discusses the principles of real-time data filtering. The problem statement is given, as well as the main evaluation criteria that must be met to obtain a satisfactory result. In addition, the principle of operation of the two most common types of filters – absolutely optimal and conditionally optimal - is analyzed, their advantages and disadvantages are described. The application of Kalman and Pugachev filters to a model with two sensors is considered. Some conclusions and recommendations are presented on in which cases it is better to use one or another filter.
Валишин А.А., Запривода А.В., Клонов А.С. Математическое моделирование и сравнительный анализ численных методов решения задачи непрерывнодискретной фильтрации случайных процессов в реальном времени. Математическое моделирование и численные методы, 2024, № 1, с. 93–109.
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
Ruziev Z. J. (Ташкентский государственный технический университет), Sobirov O. I. (Ташкентский государственный технический университет), Koraboev K. A. (Ташкентский государственный технический университет), Sapaev U. K. (Ташкентский государственный технический университет)
doi: 10.18698/2309-3684-2022-1-314
Second harmonic generation of ultrashort laser pulses in nonlinear photonic crystals is investigated by numerical methods based on the approximation of slowly varying amplitudes and a unidirectional approximation, applicable to simplify the wave equation with nonlinear polarization in a dispersive medium. Under the same experimental conditions, the results of these approximations are compared. Comparative analysis shows that up to 10 fs of the main pulse duration, both approximate methods describe this process of frequency conversion in almost the same way, but below 10 fs, there is a discrepancy between their results. Mainly, the formation of the temporal profile of the second harmonic pulse and its efficiency are compared. A method for obtaining time profiles of the second harmonic pulse using a unidirectional approximation where the incident field is used entirely in both the spectral and time domains of the calculation is also shown. The effect of dispersion up to the third order of smallness is taken into account, during the use of the approximation of slowly varying amplitudes.
Рузиев З.Дж., Собиров О.И., Корабоев К.А., Сапаев У.К. Численное моделирование генерации второй гармоники ультракоротких лазерных импульсов в нелинейных фотонных кристаллах. Математическое моделирование и численные методы, 2022, № 1, с. 3–14.
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.
Висам Махди Абас А. (SRSPU (NPI)), Arutyunyan R. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-2-6885
The article deals with the analysis of nonlinear dynamic and stationary systems based on Volterra integro–functional series and various classes of quadrature formulas. A mathematical model of the input–output type is used, which does not take into account the specific physical nature of the dynamic process, which is commonly called a black box. The methods of the article are applicable to the main variants of the Volterra integral–functional decomposition, including for the case of stationary dynamical systems, a vector input signal. An example of an optimization problem based on the considered integrative series is given. It is noted that when analyzing and optimizing nonlinear dynamical systems by the method of integro–functional series, the problem of calculating multidimensional integrals may arise. The article considers the application of the combined method based on the Volterra integrative series and grid methods for solving the corresponding one -— and multidimensional integral equations for the analysis of nonlinear dynamic and stationary systems. This article considers the case when a certain set of implementations of input and output signals is known, which can be in principle random processes. According to these data, the kernels are found in the decomposition based on the solution of the corresponding linear multidimensional Fredholm integral equation of the first kind. The corresponding problem belongs to the incorrectly posed ones and the regularization method according to A.N. Tikhonov is used to solve it. The article proposes to apply the quasi Monte–Carlo method, characterized by satisfactory convergence, in this problem in the case of large dimensions. The computational qualities in the considered problem of a semi-statistical method for solving integral equations of large dimension, the quasi Monte–Carlo method, the method of central rectangles (cells) and the quadrature formulas of Gauss–Legendre are studied. The approaches under consideration allow us to expand the range of problems to be solved in the theory of analysis and optimization of systems, since methods are proposed that are practically acceptable for large dimensions of integral equations in conditions of limited information about the system.
Абас Висам Махди Абас, Арутюнян Р.В. Моделирование нелинейных динамических и стационарных систем на основе интегро–функциональных рядов Вольтерры и различных классов квадратурных формул. Математическое моделирование и численные методы, 2021, № 2, с. 68–85.
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.
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
Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-2-102113
Using the method of dynamics of averages, a "mixed" model of numerous groupings confrontation has been developed with linear dependencies on the time of effective speeds of striking by units of the parties. An algorithm is constructed that allows to investigate the course of the process and calculate its main indicators. It is established that the use of confrontation models with constant effective speed of strikes in many cases leads to significant errors in the calculation of the main indicators of the process. The influence of a preemptive strike by one of the opposing sides on the course of the progress and the final outcome are investigated.
Чуев В.Ю., Дубограй И.В. «Смешанная» модель противоборства многочисленных группировок при линейных зависимостях от времени эффективных скоростей воздействий единицами сторон. Математическое моделирование и численные методы, 2022, № 2, с. 104–115