DOI
10.34229/KCA2522-9664.24.3.16
UDC 519.6, 539.3
1 Odesa I.I. Mechnykov National University, Odesa, Ukraine
 pr-bob@ukr.net
|
2 State University of Intellectual Technologies and Communications, Odesa, Ukraine
kovalev@ukr.net
|
|
|
4 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
igor.sayko1988@gmail.com
|
5 State University of Intellectual Technologies and Communications, Odesa, Ukraine
ygrikluda@gmail.com
|
|
MATHEMATICAL MODELING OF A SYMMETRIC BOUNDARY-VALUE
PROBLEM FOR A LAYER WEAKENED BY A THROUGH HOLE
WITH THE ENDS COVERED WITH A DIAPHRAGM
Abstract. The paper presents a new mathematical model for the solution of a static symmetric boundary-value problem for a layer weakened by a through hole with ends covered with a diaphragm. A new method based on a system of three singular integral equations has been developed and tested numerically. As a result of a high-precision numerical study, it was found that with an increase in the thickness of the layer, an increase in the relative circumferential stress occurs. With a decrease in one of the radii of the elliptical hole, an increase in the relative circumferential stress is also observed. The paper presents the respective dependency graphs.
Keywords: three-dimensional boundary-value problems, singular integral equations, numerical experiment, static stretching–compression, a through hole.
full text
REFERENCES
- Panchenko B.E., Kovalev Yu.D., Bukata L.M., Zhironkina O.S. Mathematical modeling of a symmetric boundary value problem for a layer with diaphragm-covered ends weakened by two through holes. Problemy keruvannya ta informatyky. 2023. N 2. P. 18–29. https://doi.org/10.34229/1028-0979-2023-2-2.
- B.E. Panchenko, Yu.D. Kovalev, T.O. Kalinina, I.M. Saiko, L.M. Bukata. Mathematical modeling in static three-dimensional boundary-value problems — a skew-symmetric problem for a layer weakened by a through hole and sliding pinching of the ends. Kibernetyka ta systemnyi analiz. 2024. Vol. 60, N 1. P. 182–195. https://doi.org/10.34229/KCA2522-9664.24.1.16.
- Data Mining. https://en.wikipedia.org/wiki/Data_mining .
- Bock F.E., Aydin R.C., Cyron C.J., Huber N., Kalidindi S.R., Klusemann B.A. Review of the application of machine learning and data mining approaches in continuum materials mechanics. Frontiers Materials. 2019. Vol. 6. https://doi.org/10.3389/fmats.2019.00110.
- Karapiperis K., Stainier L., Ortiz M., Andrade J.E. Data-driven multiscale modeling in mechanics. Journal of the Mechanics and Physics of Solids. 2021. Vol. 147. 104239. https://doi.org/10.1016/j.jmps.2020.104239.
- Farid A.F., Rashed Y.F. BEM for thick plates on unilateral Winkler springs. Innov. Infrastruct. Solut. 2018. Vol. 3. 26. https://doi.org/10.1007/s41062-018-0128-5.
- Katsikadelis J.T., Baboukos N.G. Flutter instability of laminated thick anisotropic plates using BEM. Acta Mechanica. 2018. Vol. 229. P. 613–628. https://doi.org/10.1007/s00707-017-1988-z .
- Karpilovsky V.S. Finite-element method and problems of elasticity theory [in Russian]. Kyiv: Sofia A, 2022. 275 p.
- Jiang W., Woo W., Wan Y., Luo Y., Xie X., Tu S.T. Evaluation of through-thickness residual stresses by neutron diffraction and finite-element method in thick weld plates. J. Pressure Vessel Technol. 2017. Vol. 139, N 3. 031401. https://doi.org/10.1115/1.4034676.
- Filshtinsky L.A. Kovalev Yu.D., Khvorost V.A. Study of the influence of the boundary surface on the SIF distribution in the vicinity of stress concentrators in an elastic half-layer. Applied problems of mathematical modeling: Special Issue Bulletin of Kherson State Technical University. Kherson: KhSTU, 1999. P. 81–83.
- Alexandrov A.Ya., Soloviev Yu.I. On the generalization of the method for solving axisymmetric problems of the theory of elasticity using analytical functions to spatial problems without axial symmetry. DAN USSR. 1964. Vol. 154, N 2. P. 294–297.
- Alexandrovich A.I. Application of the theory of functions of two complex variables to solve spatial problems in the theory of elasticity. Izv. AN SSSR. Mekhanika tverdogo tela. 1977. N 2. P. 164–168.
- Panchenko B.E., Kovalev Yu.D., Saiko I.N. Numerical study of systems of singular integral equations of the first kind and with an indeterminate index in the problem of diffraction of plane waves by a fixed inclusion. Kibernetika i sistemnyi analiz. 2020. Vol. 56, N 4. P. 3–17.
