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Применения топологии в одной численной схеме решения задач механики сплошных сред
С. 164–168.
Finite element numerical schemes for solving the continuum mechanics problems are discussed. One of the authors developed a method of acceleration of calculations which uses the simplicial mesh inscribed in the original cubic cell partitioning of a three-dimensional body. In this work it is shown that the obstacle to the construction of this design may be described in terms of modulo 2 homology groups. The method of removing the obstacle is proposed.
In book
Каз.: Издательство Казанского университета, 2017.
Левенков Я. Ю., Чичекин И. В., Вдовин Д. С. et al., Труды НАМИ 2025 № 1 (300) С. 17–30
Введение (постановка задачи и актуальность). В настоящее время широкое распространение получило использование автономных мобильных беспилотных транспортно-технологических средств (БТТС) при выполнении работ в зонах с вредными и опасными факторами. Также данные машины могут быть использованы для выполнения поисково-спасательных работ, доставки грузов в труднодоступные районы и иных подобных задач. Поэтому к таким БТТС предъявляются повышенные требования к ...
Added: April 16, 2026
Mikolaenko V., Koniushenko M., Стулков Л. Д., Механическое оборудование металлургических заводов 2025 № 2(25) С. 23–30
Uniaxial tensile testing of flat specimens under superplastic conditions is widely used to determine the deformation behavior of materials. However, the standard interpretation of the results relies on the hypothesis of an ideal uniaxial stress state and often fails to account for the influence of specimen geometry and material flow from the gripping zones to ...
Added: March 5, 2026
Данилин А. Н., Yurin A., Кондратьев Н. М. et al., Компьютерная оптика 2023 Т. 47 № 4 С. 580–587
Advantages and prospects of using optical microresonators for the development of measuring instruments based on frequency combs are described. A principle of a frequency comb generator based on an optical microresonator is considered. An example of modeling the properties of microresonators used to generate optical frequency combs is considered. The influence of the nonuniformity of ...
Added: July 5, 2023
Bosboom V., Van der Vegt J. J., Kupriyanov M. Y. et al., Superconductor Science and Technology 2022 Vol. 34 No. 11 Article 115022
We develop a quantitative model describing the distribution of the supercurrent density and
density of states in SN-N-NS type Josephson junctions in three dimensions (S is a
superconductor and N is a normal metal). The model is based on the self-consistent solution of
the quasiclassical Usadel equations using the finite element method. We investigate the
influence of the proximity ...
Added: October 31, 2022
Kushnareva L., Cherniavskii D., Mikhailov V. et al., , in: Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing (EMNLP).: Association for Computational Linguistics, 2021. P. 635–649.
Added: September 27, 2021
Mikolaenko V., Journal of Physics: Conference Series 2021 Article 012022
Superplasticity is an ability of polycrystalline materials to archive extremely large deformations, which is utilized in advanced forming technologies demanded mainly in the aerospace industry. Design of such technologies needs an information of the material flow behaviour, which describes the relation of the effective stress on the strain and strain rate taking place during deformation. ...
Added: September 22, 2021
Zakhariev I., Journal of Physics: Conference Series 2021 Vol. 1740 P. 1–6
Superplastic blow forming is a technology of shell parts production. The development of these processes requires computer simulation which cannot be realized without accurate parameters of the applied material. This characterization can be based on results of free bulging tests. Characterization techniques utilize the models of the dome growth during the bulging test. This study ...
Added: January 27, 2021
Kazeev V., Oseledets I., Rakhuba M. et al., / Series math "arxiv.org". 2020.
Homogenization in terms of multiscale limits transforms a multiscale problem with n+1 asymptotically separated microscales posed on a physical domain D⊂ℝd into a one-scale problem posed on a product domain of dimension (n+1)d by introducing n so-called "fast variables". This procedure allows to convert n+1 scales in d physical dimensions into a single-scale structure in (n+1)d dimensions. We prove here that both the original, physical multiscale problem and the ...
Added: October 20, 2020
Yakovlev E., Epifanov V., Lobachevskii Journal of Mathematics 2019 Vol. 40 No. 5 P. 690–698
We solve some computational problems for triangulated closed three-dimensional manifolds
using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms
for computing intersection numbers of 1- and 2-dimensional cycles are developed. Using these
algorithms it is possible to construct a basis of the cohomology group from a given basis of the
homology group of complementary dimension. ...
Added: October 8, 2019
Borisov N., Kasatkin A., Presnyakov S., T-Comm: Телекоммуникации и транспорт 2019 Т. 13 № 2 С. 4–10
The task is to sharply reduce the complexity of analysis, multivariate analysis and parametric optimization of linear and linearized equivalent electrical circuits. The source of such schemes are not only linear electronic circuits, but also circuits formed on the basis of artificial electrical analogies. They can be formed on the basis of finite element methods ...
Added: March 1, 2019
E. I. Yakovlev, Chekmaryov D. T., Russian Mathematics (USA) 2018 Vol. 62 No. 9 P. 72–85
We discuss numerical schemes of finite element method for solving the continuum mechanics problems. Previously a method of acceleration of calculations was developed which uses the simplicial mesh inscribed in the original cubic cell partition of a three-dimensional body. In this paper we show that the obstacle to the construction of this design may be ...
Added: October 14, 2018
Sorgente D., Palumbo G., Piccininni A. et al., CIRP Journal of Manufacturing Science and Technology 2018 No. 20 P. 29–35
Mechanical performances of titanium biomedical implants manufactured by superplastic forming are strongly related to the process parameters: the thickness distribution along the formed sheet has a key role in the evaluation of post-forming characteristics of the prosthesis. In this work, a finite element model able to reliably predict the thickness distribution after the superplastic forming ...
Added: December 1, 2017
Vexler B., Zlotnik A., Trautmann P., Comptes Rendus Mathematique 2018 Vol. 356 No. 5 P. 523–531
The paper deals with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces of either measure-valued functions or vector measures. Bilinear finite element discretizations are constructed and their stability and error analysis is accomplished. ...
Added: April 8, 2017
Trautmann P., Vexler B., Zlotnik A., Mathematical Control and Related Fields 2018 Vol. 8 No. 2 P. 411–449
This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$ or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level ...
Added: April 8, 2017