Approximate resolving equations of mathematical model of a curved thin-walled cylinder

Viktor A. Rukavishnikov and Oleg P. Tkachenko

Applied Mathematics and Computation, 2022, vol. 422, issue C

Abstract: The resolving equations for mathematical model of the stress-strain state of a curved thin-walled cylinder were derived. This model is based on Koiter’s–Vlasov’s theory of moment shells. A method was proposed for approximate solution of a mathematical model equations on the basis of a sequential asymptotic expansion of unknown functions into a small parameter series and representation of the expansion coefficients in the form of Fourier series. Using this method, a one-dimensional statement of the problem was obtained. Limitations on parameters in the shell equations are indicated for which such problem transformation is possible. For the mathematical model of the curved thin-walled cylinder one-dimensional equations in two different formulations were obtained. Conditions determining applicability limits of the constructed one-dimensional mathematical models were proved. Numerical experiments were carried out and it was found that the constructed one-dimensional mathematical model approximates the original problem with high accuracy. From an applied point of view, curved thin-walled cylinder simulates a pipeline section.

Keywords: Bent thin-walled cylinder; Shell theory; Asymptotic series; Numerical experiment (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000479

DOI: 10.1016/j.amc.2022.126961

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