Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids
We illustrate a procedure based on the Magnus expansion for studying mechanical problems which lead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by the analysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In...
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| Format: | Article |
| Language: | English |
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Gruppo Italiano Frattura
2014-07-01
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| Series: | Fracture and Structural Integrity |
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| Online Access: | https://www.fracturae.com/index.php/fis/article/view/1244 |
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| author | A. Castellano P. Foti A. Fraddosio S. Marzano M. D. Piccioni |
| author_facet | A. Castellano P. Foti A. Fraddosio S. Marzano M. D. Piccioni |
| author_sort | A. Castellano |
| collection | DOAJ |
| description | We illustrate a procedure based on the Magnus expansion for studying mechanical problems which lead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by the analysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In particular, for an isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study the possibility of axially periodic twist-like bifurcations. The approximate matricant of the resulting differential problem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation are determined by employing a simplified version of the Magnus method, characterized by a truncation of the Magnus series after the second term. |
| format | Article |
| id | doaj-art-8100296b6faf499db2c1c560afd727e9 |
| institution | Kabale University |
| issn | 1971-8993 |
| language | English |
| publishDate | 2014-07-01 |
| publisher | Gruppo Italiano Frattura |
| record_format | Article |
| series | Fracture and Structural Integrity |
| spelling | doaj-art-8100296b6faf499db2c1c560afd727e92025-01-03T01:03:08ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89932014-07-01829Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solidsA. Castellano0P. Foti1A. Fraddosio2S. Marzano3M. D. Piccioni4Politecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’ArchitetturaPolitecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’ArchitetturaPolitecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’ArchitetturaPolitecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’ArchitetturaPolitecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’ArchitetturaWe illustrate a procedure based on the Magnus expansion for studying mechanical problems which lead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by the analysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In particular, for an isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study the possibility of axially periodic twist-like bifurcations. The approximate matricant of the resulting differential problem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation are determined by employing a simplified version of the Magnus method, characterized by a truncation of the Magnus series after the second term.https://www.fracturae.com/index.php/fis/article/view/1244Nonlinear elasticity |
| spellingShingle | A. Castellano P. Foti A. Fraddosio S. Marzano M. D. Piccioni Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids Fracture and Structural Integrity Nonlinear elasticity |
| title | Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids |
| title_full | Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids |
| title_fullStr | Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids |
| title_full_unstemmed | Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids |
| title_short | Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids |
| title_sort | geometric numerical integrators based on the magnus expansion in bifurcation problems for non linear elastic solids |
| topic | Nonlinear elasticity |
| url | https://www.fracturae.com/index.php/fis/article/view/1244 |
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