Fracture and Structural Integrity e-ISSN 1971-8993 Open access
Miscellanea Vol. 8, No. 29 (2014)

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

Author and affiliation details
  • A. Castellano Corresponding author Politecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura anna.castellano@poliba.it
  • P. Foti Politecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura
  • A. Fraddosio Politecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura
  • S. Marzano Politecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura
  • M. D. Piccioni Politecnico di Bari – Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura
DOI
10.3221/IGF-ESIS.29.12
Pages
pages 128-138
Published
Published inVol. 8, No. 29 (2014)Go to the issue

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.

Keywords

Article history

  1. ReceivedUntil the next stage: 0 days
  2. AcceptedUntil the next stage: 0 days
  3. Published

How to cite

APA

Castellano, A., Foti, P., Fraddosio, A., Marzano, S., & Piccioni, M. D. (2014). Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids. Fracture and Structural Integrity, 8(29), pages 128–138. https://doi.org/10.3221/IGF-ESIS.29.12

IEEE

A. Castellano, P. Foti, A. Fraddosio, S. Marzano, and M. D. Piccioni, “Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids,” Fracture and Structural Integrity, vol. 8, no. 29, pp. pages 128–138, 2014, doi: 10.3221/IGF-ESIS.29.12.

MLA

Castellano, A., et al. “Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids.” Fracture and Structural Integrity, vol. 8, no. 29, 2014, pp. pages 128–138. https://doi.org/10.3221/IGF-ESIS.29.12.

Chicago

Castellano, A., P. Foti, A. Fraddosio, S. Marzano, and M. D. Piccioni. 2014. “Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids.” Fracture and Structural Integrity 8 (29): pages 128–138. https://doi.org/10.3221/IGF-ESIS.29.12.

Harvard

Castellano, A., Foti, P., Fraddosio, A., Marzano, S. and Piccioni, M.D. (2014) ‘Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids’, Fracture and Structural Integrity, 8(29), pp. pages 128–138. doi: 10.3221/IGF-ESIS.29.12.

Vancouver

Castellano A, Foti P, Fraddosio A, Marzano S, Piccioni MD. Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids. Fracture and Structural Integrity. 2014;8(29):pages 128-138. doi:10.3221/IGF-ESIS.29.12

BibTeX

@article{castellano2014, author = {Castellano, A. and Foti, P. and Fraddosio, A. and Marzano, S. and Piccioni, M. D.}, title = {Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids}, journal = {Fracture and Structural Integrity}, year = {2014}, volume = {8}, number = {29}, pages = {pages 128--138}, doi = {10.3221/IGF-ESIS.29.12}, url = {https://doi.org/10.3221/IGF-ESIS.29.12}, issn = {1971-8993} }

RIS

TY - JOUR AU - Castellano, A. AU - Foti, P. AU - Fraddosio, A. AU - Marzano, S. AU - Piccioni, M. D. TI - Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids JO - Fracture and Structural Integrity T2 - Fracture and Structural Integrity PY - 2014 DA - 2014/07/09 VL - 8 IS - 29 SP - pages 128 EP - 138 DO - 10.3221/IGF-ESIS.29.12 UR - https://doi.org/10.3221/IGF-ESIS.29.12 SN - 1971-8993 ER -

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