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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Gruppo Italiano Frattura
2014-07-01
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| Series: | Frattura ed Integrità Strutturale |
| Subjects: | |
| Online Access: | https://www.fracturae.com/index.php/fis/article/view/1244 |
| Summary: | 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.
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| ISSN: | 1971-8993 |