| Issue |
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 1023 - 1042 | |
| DOI | https://doi.org/10.1051/m2an/2025016 | |
| Published online | 02 April 2025 | |
The solution method and its accuracy for a nonlinear Timoshenko axisymmetric shell model
1
I. Javakhishvili Tbilisi State University, University str. 2, 0177 Tbilisi, Georgia
2
Georgian Technical University, M. Kostava str. 77, 0171 Tbilisi, Georgia
* Corresponding author: n.kachakhidze@gtu.ge
Received:
6
June
2024
Accepted:
6
March
2025
The boundary value problem of the axisymmetric displacement of a Timoshenko (cylindrical) shell in static regime was considered. From the given nonlinear system of ordinary differential equations with respect to the displacement functions u, w and ψ, using the Green functions, we obtain an integro-differential equation for the function w. This equation, together with the Dirichlet boundary condition, forms the boundary value problem. To obtain an approximate solution of the problem for w we apply the method that includes the Galerkin method and the Jacobi–Cardano iteration. Obtained values of w and of its error estimate are used for constructing the approximations for other displacement functions u and ψ and for estimation of their errors. The results of the numerical experiment are given.
Mathematics Subject Classification: 34B27 / 65L10 / 65L60 / 65L70 / 74B20 / 74K25
Key words: Timoshenko shell / approximate method / Green function / Galerkin method / Jacobi type iteration method / Cardano formula
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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