Numerical implementation of Richardson extrapolation for dynamic problems of multilayer cylindrical shells

Authors

DOI:

https://doi.org/10.15587/1729-4061.2025.345897

Keywords:

multilayer shells, forced vibrations, unsteady loading, numerical methods, Richardson extrapolation

Abstract

This study considers forced vibrations of a heterogeneous elastic structure in the form of a multilayer cylindrical shell consisting of rigidly connected layers and reinforced with discrete ring elements.

A mathematical model of vibrations of an elastic heterogeneous structure under the action of a non-stationary load has been constructed. The stressed-strained state of a multilayer cylindrical shell with discrete ring ribs was investigated using the geometrically nonlinear theory of Timoshenko-type shells and rods. The presence of a complex right-hand side and discontinuous coefficients in the spatial coordinates in the hyperbolic equations of vibrations of a heterogeneous elastic cylindrical shell (at the locations of the reinforcing ribs) necessitated the use of numerical methods for solving them. A numerical algorithm using Richardson extrapolations has been proposed for studying the constructed model.

For example, a three-layer reinforced cylindrical shell is considered, taking into account the discreteness of the ribs' placement under dynamic loading with rigidly clamped ribs. The proposed numerical algorithm has made it possible to investigate the stressed-strained state of a three-layer reinforced elastic structure of a cylindrical type at any given moment in time. A comparative analysis of the numerical results of the calculations revealed that, according to the standard approach, the discrepancy in the deflection values for n = 40 and n = 160 reached 31%, for n = 80 and n = 160 it was about 5%, according to Richardson's approach for n = 40 ÷ 80 and the standard approach for n = 160, this difference was about 1%.

A distinctive feature of this study is the use of Richardson extrapolation to identify the stressed-strained state of a three-layer reinforced cylindrical shell, which made it possible to increase the accuracy of the solution to the dynamic problem without reducing the calculation step.

The study's results reported in this work could be used for investigating unsteady vibrations of shell structures at research and engineering organizations

Author Biographies

Yuliia Meish, National University of Life and Environmental Sciences of Ukraine

Doctor of Technical Sciences, Professor

Department of Higher and Applied Mathematics

Maryna Belova, State University of Trade and Economics

PhD, Associate Professor

Department of Digital Economy and System Analysis

Nataliia Arnauta, National University of Life and Environmental Sciences of Ukraine

PhD, Associate Professor

Department of Higher and Applied Mathematics

Nataliia Maiborodina, National University of Life and Environmental Sciences of Ukraine

PhD, Associate Professor

Department of Natural Sciences, Mathematics and General Engineering Disciplines

Vіacheslav Gerasymenko, National University of Life and Environmental Sciences of Ukraine

PhD, Associate Professor

Department of Electric Power Engineering, Electrical Engineering and Electromechanics

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Numerical implementation of Richardson extrapolation for dynamic problems of multilayer cylindrical shells

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Published

2025-12-31

How to Cite

Meish, Y., Belova, M., Arnauta, N., Maiborodina, N., & Gerasymenko, V. (2025). Numerical implementation of Richardson extrapolation for dynamic problems of multilayer cylindrical shells. Eastern-European Journal of Enterprise Technologies, 6(7 (138), 16–29. https://doi.org/10.15587/1729-4061.2025.345897

Issue

Vol. 6 No. 7 (138) (2025): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2025 Yuliia Meish, Maryna Belova, Nataliia Arnauta, Nataliia Maiborodina, Vіacheslav Gerasymenko

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