Bifurcation analysis of elastic residually-stressed circular cylindrical tubes
The theory of superimposed incremental elastic deformations is applied to a deformed configuration of a residually-stressed circular cylindrical tube. The tube is subject to internal or external pressure and an axial load that maintain its circular cylindrical shape, and then bifurcations from this...
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| Vydáno v: | International journal of solids and structures Ročník 226-227; s. 111062 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
Elsevier Ltd
01.09.2021
Elsevier BV |
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| ISSN: | 0020-7683, 1879-2146 |
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| Abstract | The theory of superimposed incremental elastic deformations is applied to a deformed configuration of a residually-stressed circular cylindrical tube. The tube is subject to internal or external pressure and an axial load that maintain its circular cylindrical shape, and then bifurcations from this shape are analysed. Detailed governing equations and boundary conditions are provided for axisymmetric, prismatic and asymmetric bifurcations for a general form of strain–energy function that incorporates radial and circumferential residual stress components. The theory is applied to a simple model strain–energy function with two material parameters and a parameter that reflects the magnitude of the residual stress. Numerical computations are used to illustrate the dependence of the results of the bifurcation analysis on these parameters and the axial and radial underlying deformation. It is shown that in general the presence of residual stress has a significant effect compared with the corresponding results without residual stress. |
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| AbstractList | The theory of superimposed incremental elastic deformations is applied to a deformed configuration of a residually-stressed circular cylindrical tube. The tube is subject to internal or external pressure and an axial load that maintain its circular cylindrical shape, and then bifurcations from this shape are analysed. Detailed governing equations and boundary conditions are provided for axisymmetric, prismatic and asymmetric bifurcations for a general form of strain–energy function that incorporates radial and circumferential residual stress components. The theory is applied to a simple model strain–energy function with two material parameters and a parameter that reflects the magnitude of the residual stress. Numerical computations are used to illustrate the dependence of the results of the bifurcation analysis on these parameters and the axial and radial underlying deformation. It is shown that in general the presence of residual stress has a significant effect compared with the corresponding results without residual stress. |
| ArticleNumber | 111062 |
| Author | Ogden, Ray W. Merodio, José Dorfmann, Luis Melnikov, Andrey |
| Author_xml | – sequence: 1 givenname: Andrey orcidid: 0000-0001-8639-0000 surname: Melnikov fullname: Melnikov, Andrey email: melnikov.andrey5@gmail.com organization: Department of Earth Sciences, Memorial University of Newfoundland, St. John’s, Canada – sequence: 2 givenname: Ray W. orcidid: 0000-0002-7002-7028 surname: Ogden fullname: Ogden, Ray W. email: raymond.ogden@glasgow.ac.uk organization: School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK – sequence: 3 givenname: Luis surname: Dorfmann fullname: Dorfmann, Luis email: Luis.Dorfmann@tufts.edu organization: Department of Civil and Environmental Engineering, Tufts University, Medford, MA 02155, USA – sequence: 4 givenname: José surname: Merodio fullname: Merodio, José email: merodioj@gmail.com organization: Department of Continuum Mechanics and Structures, E.T.S. Ing. Caminos, Canales y Puertos, Universidad Politecnica de Madrid, 28040, Madrid, Spain |
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| Cites_doi | 10.1007/BF00705801 10.1016/j.wavemoti.2011.04.004 10.1016/j.jsv.2020.115467 10.1080/14786443908562246 10.1016/0022-5096(79)90027-9 10.1088/0266-5611/14/2/007 10.1016/j.mechrescom.2009.10.006 10.1007/BF00040818 10.1023/A:1010835316564 10.1007/s00033-018-0954-5 10.1007/s10665-021-10097-4 10.1098/rsif.2009.0357 10.1114/1.191 10.1016/j.ijnonlinmec.2013.02.010 10.2140/jomms.2011.6.453 10.1016/0022-5096(79)90001-2 10.1007/BF00043022 10.1007/BF00040956 10.1016/j.jmps.2016.02.020 10.1093/imamat/hxs070 10.1007/BF00044971 10.1016/j.jmbbm.2016.01.012 10.1007/BF00752113 10.1038/s41598-019-44694-2 10.1007/s00161-015-0411-z 10.1063/1.1712807 10.1016/j.ijsolstr.2008.02.005 10.1016/j.finel.2019.04.004 10.1098/rsta.2018.0077 10.1007/BF00705803 10.1016/S0021-9290(97)00032-8 |
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| Keywords | Residual stresses Nonlinear elasticity Tube bifurcation Incremental elastic deformations |
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| SubjectTerms | Axial loads Bifurcation theory Boundary conditions Elastic analysis Elastic deformation External pressure Incremental elastic deformations Nonlinear elasticity Parameters Residual stress Residual stresses Strain Tube bifurcation Tubes |
| Title | Bifurcation analysis of elastic residually-stressed circular cylindrical tubes |
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