Geometric numerical integrators based on the Magnus expansion inbifurcation problems for non-linear elastic solids
Journal Title: Frattura ed Integrità Strutturale - Year 2014, Vol 8, Issue 29
Abstract
We illustrate a procedure based on the Magnus expansion for studying mechanical problems whichlead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by theanalysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In particular, foran isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study thepossibility of axially periodic twist-like bifurcations. The approximate matricant of the resulting differentialproblem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation aredetermined by employing a simplified version of the Magnus method, characterized by a truncation of theMagnus series after the second term.
Authors and Affiliations
A. Castellano, P. Foi, S. Marzano, M. D. Piccioni
Keywords
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- EP ID EP88631
- DOI 10.3221/IGF-ESIS.29.12
- Views 86
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