Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence

A geometrically and physically nonlinear model of a membrane cylindrical shell, which has been built and tested, describes the behavior of a airbag made of fabric material. Based on the geometrically accurate relations of "strain-displacement", it has been shown that the equilibrium equati...

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Autor principal:	Vitalii Myntiuk
Formato:	article
Lenguaje:	EN RU UK
Publicado:	PC Technology Center 2021
Materias:	axisymmetric cylindrical shell geometric nonlinearity physical nonlinearity spectral method Technology (General) T1-995 Industry HD2321-4730.9
Acceso en línea:	https://doaj.org/article/022b9153f44c4076a5111f82f8bd3e2f
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spelling	oai:doaj.org-article:022b9153f44c4076a5111f82f8bd3e2f2021-11-04T14:08:24ZSpectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence1729-37741729-406110.15587/1729-4061.2021.242372https://doaj.org/article/022b9153f44c4076a5111f82f8bd3e2f2021-10-01T00:00:00Zhttp://journals.uran.ua/eejet/article/view/242372https://doaj.org/toc/1729-3774https://doaj.org/toc/1729-4061A geometrically and physically nonlinear model of a membrane cylindrical shell, which has been built and tested, describes the behavior of a airbag made of fabric material. Based on the geometrically accurate relations of "strain-displacement", it has been shown that the equilibrium equations of the shell, written in terms of Biot stresses, together with boundary conditions acquire a natural physical meaning and are the consequences of the principle of virtual work. The physical properties of the shell were described by Fung’s hyper-elastic biological material because its behavior is similar to that of textiles. For comparison, simpler hyper-elastic non-compressible Varga and Neo-Hookean materials, the zero-, first-, and second-order materials were also considered. The shell was loaded with internal pressure and convergence of edges. The approximate solution was constructed by an spectral method; the exponential convergence and high accuracy of the equilibrium equations inherent in this method have been demonstrated. Since the error does not exceed 1 % when keeping ten terms in the approximations of displacement functions, the solution can be considered almost accurate. Similar calculations were performed using a finite element method implemented in ANSYS WB in order to verify the results. Differences in determining the displacements have been shown to not exceed 0.2 %, stresses – 4 %. The study result has established that the use of Fung, Varga, Neo-Hookean materials, as well as a zero-order material, lead to similar values of displacements and stresses, from which displacements of shells from the materials of the first and second orders significantly differ. This finding makes it possible, instead of the Fung material whose setting requires a significant amount of experimental data, to use simpler ones – a zero-order material and the Varga materialVitalii MyntiukPC Technology Centerarticleaxisymmetric cylindrical shellgeometric nonlinearityphysical nonlinearityspectral methodTechnology (General)T1-995IndustryHD2321-4730.9ENRUUKEastern-European Journal of Enterprise Technologies, Vol 5, Iss 7 (113), Pp 6-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN RU UK
topic	axisymmetric cylindrical shell geometric nonlinearity physical nonlinearity spectral method Technology (General) T1-995 Industry HD2321-4730.9
spellingShingle	axisymmetric cylindrical shell geometric nonlinearity physical nonlinearity spectral method Technology (General) T1-995 Industry HD2321-4730.9 Vitalii Myntiuk Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
description	A geometrically and physically nonlinear model of a membrane cylindrical shell, which has been built and tested, describes the behavior of a airbag made of fabric material. Based on the geometrically accurate relations of "strain-displacement", it has been shown that the equilibrium equations of the shell, written in terms of Biot stresses, together with boundary conditions acquire a natural physical meaning and are the consequences of the principle of virtual work. The physical properties of the shell were described by Fung’s hyper-elastic biological material because its behavior is similar to that of textiles. For comparison, simpler hyper-elastic non-compressible Varga and Neo-Hookean materials, the zero-, first-, and second-order materials were also considered. The shell was loaded with internal pressure and convergence of edges. The approximate solution was constructed by an spectral method; the exponential convergence and high accuracy of the equilibrium equations inherent in this method have been demonstrated. Since the error does not exceed 1 % when keeping ten terms in the approximations of displacement functions, the solution can be considered almost accurate. Similar calculations were performed using a finite element method implemented in ANSYS WB in order to verify the results. Differences in determining the displacements have been shown to not exceed 0.2 %, stresses – 4 %. The study result has established that the use of Fung, Varga, Neo-Hookean materials, as well as a zero-order material, lead to similar values of displacements and stresses, from which displacements of shells from the materials of the first and second orders significantly differ. This finding makes it possible, instead of the Fung material whose setting requires a significant amount of experimental data, to use simpler ones – a zero-order material and the Varga material
format	article
author	Vitalii Myntiuk
author_facet	Vitalii Myntiuk
author_sort	Vitalii Myntiuk
title	Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
title_short	Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
title_full	Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
title_fullStr	Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
title_full_unstemmed	Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
title_sort	spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence
publisher	PC Technology Center
publishDate	2021
url	https://doaj.org/article/022b9153f44c4076a5111f82f8bd3e2f
work_keys_str_mv	AT vitaliimyntiuk spectralsolutiontoaproblemontheaxisymmetricnonlineardeformationofacylindricalmembraneshellduetopressureandedgesconvergence
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Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence

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