CC BY
9----------------------- Page 1-----------------------
Methods of computational algebra and solving mathematical physics equations 43
A combined analytical and numerical approach to solve spatial bending problems of composite beams
1,3 2 1
S. K. Golushko , G. L. Gorynin , A. G. Gorynin
1Novosibirsk State University
2Surgut State University
3Federal Research Center for Information and Computational Technologies
Email: s.k.golushko@gmail.com
DOI 10.24412/cl‐35065‐2021‐1‐00‐15
The spatial problem of the theory of elasticity with small parameter is solved in application to the bending
of composite beams. Using the asymptotic splitting method [1, 2] the problem is reduced to consecutive solv‐
ing of two and one‐dimensional problems, where two‐dimensional problems are defined on the cross‐section
of the beam and one‐dimensional problem is defined along beams length. In the general case of complex
cross‐section geometry, numerical solutions are obtained using the least‐squares collocation method [3] and
finite‐element method.
This work was supported by the Russian Foundation for Basic Research (project no. 18‐29‐ 18029).
References
1. Gorynin G. L., Nemirovsky Y. V. Deformation of Laminated Anisotropic Bars in the Three‐dimensional Statement 1.
Transverse‐longitudinal Bending and Edge Compatibility Condition // Mechanics of Composite Materials. 2009. V. 45, N.
3, P. 257‐280.
2. Golushko S. K., Gorynin G. L., Gorynin A. G. Method of Asymptotic Splitting in Dynamical Problems of the Spatial
Theory of Elasticity // Itogi Nauki i Tekhniki. Seriya" Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory".
2020. V. 188, P. 43‐53.
3. Shapeev V., Belyaev V., Golushko S., Idimeshev S. New Possibilities and Applications of the Least Squares
Collocation Method // EPJ Web of Conferences. – EDP Sciences, 2018. V. 173 (01012).
Modelling of burning coke sediment at catalyst grain
I. M. Gubaidullin1 2 2
, E. E. Peskova , O. S. Yazovtseva
1Ufa State Petroleum Technological University
2National Research Ogarev Mordovia State University, Saransk
Email: kurinaos@gmail.com
DOI 10.24412/cl‐35065‐2021‐1‐00‐16
Recovery of the catalyst activity is an essential part for industrial catalytic processes. One of the least cost‐
ly regeneration methods is oxidative regeneration – burning out coke sediments from the catalyst grain by ox‐
ygen‐containing gas [1‐3]. The formation of surface complexes on the catalyst grain is observed during oxygen
adsorption [4]. Heat exchange and the exothermic nature of the effect of coke burning inevitably leads to an
increase in the temperature of the grain. One of the undesirable consequences of the oxidative regeneration
process can be overheating of the catalyst layer, leading to its irreversible changes [1, 5]. Another issue requir‐
ing special attention is toxic carbon monoxide, which manifests itself during the decomposition of adsorption
complexes. If the permissible limit is exceeded, the using of special procedures to reduce the concentration is
required.
The article is devoted to numerical modelling of the nonlinear regeneration process, which is described by
the partial differential equations system. Modelling results are visualized. Comparison with the experiment
revealed the admissible deviation of the calculated data from the experimental data.
