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.

Geometric numerical integrators based on the magnus expansion in bifurcation problems for non-linear elastic solids / Castellano, Anna; Foti, Pilade; Fraddosio, Aguinaldo; Marzano, Salvatore; Piccioni, Mario Daniele. - In: FRATTURA E INTEGRITÀ STRUTTURALE. - ISSN 1971-8993. - 8:29(2014), pp. 128-138. (Intervento presentato al convegno GIMC-GMA 2014- XX Convegno nazionale di meccanica Computazionale - VII Riunione del Gruppo Materiali AIMETA tenutosi a Cassino (Italia) nel 11-13 Giugno 2014) [10.3221/IGF-ESIS.29.12].

Geometric numerical integrators based on the magnus expansion in bifurcation problems for non-linear elastic solids

CASTELLANO, ANNA;FOTI, Pilade;FRADDOSIO, Aguinaldo;MARZANO, Salvatore;PICCIONI, Mario Daniele
2014-01-01

Abstract

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.
2014
Geometric numerical integrators based on the magnus expansion in bifurcation problems for non-linear elastic solids / Castellano, Anna; Foti, Pilade; Fraddosio, Aguinaldo; Marzano, Salvatore; Piccioni, Mario Daniele. - In: FRATTURA E INTEGRITÀ STRUTTURALE. - ISSN 1971-8993. - 8:29(2014), pp. 128-138. (Intervento presentato al convegno GIMC-GMA 2014- XX Convegno nazionale di meccanica Computazionale - VII Riunione del Gruppo Materiali AIMETA tenutosi a Cassino (Italia) nel 11-13 Giugno 2014) [10.3221/IGF-ESIS.29.12].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/1293
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