This paper addresses the following issues:
Construction of a unified computational scheme for solving boundary value problems of dynamic calculation of flexible circular plates under the action of axisymmetric loads using nonlinear Lyave theory, development of an automated system, study of the nature of convergence of the applied numerical methods, study of the stress-strain state of flexible plates.
This work consists of an introduction, three sections and a conclusion. In the first section, in Lyave's formulation, boundary value problems of the motion of flexible circular plates in displacements are formulated. The corresponding system of two nonlinear partial differential equations is reduced to a system of two quasilinear partial differential equations.
Solution domains with initial and boundary conditions are given.
In the second section, integration with the help of central difference schemes is considered, approximating derivatives with second-order accuracy in place of quasilinear differential equations, a system of quasilinear and boundary conditions is obtained, the system of difference equations is written in matrix form.
The sweep methods are applied to the solution of a system of quasilinear algebraic equations.
In the third section, the stress-strain state of flexible round plates exposed to instantly applied loads is investigated.
This paper addresses the following issues:
Construction of a unified computational scheme for solving boundary value problems of dynamic calculation of flexible circular plates under the action of axisymmetric loads using nonlinear Lyave theory, development of an automated system, study of the nature of convergence of the applied numerical methods, study of the stress-strain state of flexible plates.
This work consists of an introduction, three sections and a conclusion. In the first section, in Lyave's formulation, boundary value problems of the motion of flexible circular plates in displacements are formulated. The corresponding system of two nonlinear partial differential equations is reduced to a system of two quasilinear partial differential equations.
Solution domains with initial and boundary conditions are given.
In the second section, integration with the help of central difference schemes is considered, approximating derivatives with second-order accuracy in place of quasilinear differential equations, a system of quasilinear and boundary conditions is obtained, the system of difference equations is written in matrix form.
The sweep methods are applied to the solution of a system of quasilinear algebraic equations.
In the third section, the stress-strain state of flexible round plates exposed to instantly applied loads is investigated.
| № | Имя автора | Должность | Наименование организации |
|---|---|---|---|
| 1 | Yuldashev A.. | dotsent | TDTU, |
| 2 | Bekchonov S.E. | катта ўқитувчиси | TDTU |
| 3 | Ahralov H.. | Assistant | TDTU |
| № | Название ссылки |
|---|---|
| 1 | 1. A. Lyav "Mathematical Theory of Elasticity". M.-L. ONTI, CF. 1935 (in Russian). |
| 2 | 2. Berezin I.S., Zhidkov N.P. "Methods of computation". T.I.II., M., Fizmatgiz, 1959 (in Russian). |
| 3 | 3. Kildibekov I.G. Investigation of Nonlinear Vibrations of Plates, Coll. "Theory of Plates and Shells", M., Publishing House "Science", 1971 (in Russian). |
| 4 | 4. Kornishin, I.S. Some questions of application of the finite difference method for the solution of boundary problems of the plate theory. "Applied Mechanics", 1963, 9, No. 3 (in Russian). |
| 5 | 5. Theory of Flexible Round Plates. Edited by Prof. A.S.Volmir, M.S.Sh, 1957 (in Chinese). |
| 6 | 6. Timoschenko, S.P. Plates and Shells, M., Gostekhizdat, 1948 (in Russian). |
| 7 | 7. A. Yuldashev, T. Buriyev, M., Gostekhizdat, 1948. 7. A. Yuldashev, T. Buriyev Statistical Calculation of Flexible Round Plates Using the Computer Grid Method. DAN UzSSR, No 4, 1973 (in Russian). |
| 8 | 8. A.Alibayev, A.Yuldashev. Effects of Uniformly Distributed Loads on a Round Ring Plate. Technology of Material Processing and Machine Design. Collection of scientific and technical papers. 1983 y (in Russian). |
| 9 | 9. A.Yuldashev, A.Alibayev. Statistical Calculation of Flexible Circular Ring Plates Crushed on the Inner Circuit and Hinged on the Outer Circuit. Differential Equations and Applied Mathematical Questions. S.A. Tashkent 1996 (in Russian). |
| 10 | Yuldashev A. "Bending of flexible round ring plates". Topical issues in the region of technical and social economic sciences, Tashkent, 2012 (in Russian). |
| 11 | 11. Yuldashev A., Bekchanov Sh.E., Mardonov A.P. Statistical calculation of flexible round solid and ring plates. Scientific Journal "Internauka", part I, №9 (91), Moscow 2019 (in Russian). |
| 12 | 12. A.Yuldashev, Z.Sadritdinova, Sh.Bekchanov, H.Akhrolov. Mathematical Modelling in Calculation of Flexible Round Plates. Journal of critical reviews. Vol 7, ISSUE 15, 2020. p.1807-1814 (in Russian). |
| 13 | 13. Kabulov V.K. Algorithmization in the theory of elasticity and deformation theory of plasticity. Tash.Izd v "Fan", UzSSR.1966 (in Russian). |
| 14 | 14. Yuldashev A., Bekchanov Sh.E., Akhralov H.Z. Investigation of the convergence of the finite difference method in the calculation of flexible circular plates. Bulletin of Science and Education. Vol 9 (87), 2020.p.17-21. |
| 15 | 15. Yuldashev A., Pirmatov Sh.T. Algorithmization of solving dynamic edge problems of the theory of flexible rectangular plates. Bulletin of Tomsk State University. Mathematiks and mekhaniks. №66. 2020, pp. 143-157. |