Bifurcation scenarios in helical buckling of slender rods using new FE

Marcin Kapitaniak, Vahid Vaziri, Marian Wiercigroch*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We develop a new Finite Element to accurately model twisting of rods and capture the bifurcation scenarios leading to helical buckling and various further post-buckling states. Since standard nonlinear beam elements do not account for nonlinearities in torsional modes, as well as for coupling between axial, lateral and torsional modes, we derive a new beam element, which allows us to describe complex helical buckling bifurcation scenarios of a rod subjected to a twisting load. The formulated beam element is systematically tested to assess its predictive capabilities in determining critical torsional buckling loads and its sensitivity to number of elements used. Once the model is validated against commercial FE software (Abaqus), we focus our attention on computing bifurcation scenarios to observe various complex helical configurations and transitions between them. The analysis reveals co-existence between helices with multiple loops for certain values of twisting load. Additionally, we trace the transition onsets between stable helical configurations. The developed FE can be applied to study complex buckling mechanics of engineering and biological structures.

Original languageEnglish
Article number103197
Number of pages14
JournalInternational Journal of Engineering Science
Volume147
Early online date18 Dec 2019
DOIs
Publication statusPublished - Feb 2020

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Buckling
Mechanics

Keywords

  • helical buckling
  • bifurcations
  • twisted rods
  • finite element
  • post-buckling configurations

Cite this

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title = "Bifurcation scenarios in helical buckling of slender rods using new FE",
abstract = "We develop a new Finite Element to accurately model twisting of rods and capture the bifurcation scenarios leading to helical buckling and various further post-buckling states. Since standard nonlinear beam elements do not account for nonlinearities in torsional modes, as well as for coupling between axial, lateral and torsional modes, we derive a new beam element, which allows us to describe complex helical buckling bifurcation scenarios of a rod subjected to a twisting load. The formulated beam element is systematically tested to assess its predictive capabilities in determining critical torsional buckling loads and its sensitivity to number of elements used. Once the model is validated against commercial FE software (Abaqus), we focus our attention on computing bifurcation scenarios to observe various complex helical configurations and transitions between them. The analysis reveals co-existence between helices with multiple loops for certain values of twisting load. Additionally, we trace the transition onsets between stable helical configurations. The developed FE can be applied to study complex buckling mechanics of engineering and biological structures.",
keywords = "helical buckling, bifurcations, twisted rods, finite element, post-buckling configurations",
author = "Marcin Kapitaniak and Vahid Vaziri and Marian Wiercigroch",
note = "The authors would like to acknowledge the use of the Maxwell High Performance Computing Cluster of the University of Aberdeen IT Service and various industrial projects sponsored by Oil & Gas Innovation Centre (OGIC), which stipulated these studies.",
year = "2020",
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doi = "10.1016/j.ijengsci.2019.103197",
language = "English",
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T1 - Bifurcation scenarios in helical buckling of slender rods using new FE

AU - Kapitaniak, Marcin

AU - Vaziri, Vahid

AU - Wiercigroch, Marian

N1 - The authors would like to acknowledge the use of the Maxwell High Performance Computing Cluster of the University of Aberdeen IT Service and various industrial projects sponsored by Oil & Gas Innovation Centre (OGIC), which stipulated these studies.

PY - 2020/2

Y1 - 2020/2

N2 - We develop a new Finite Element to accurately model twisting of rods and capture the bifurcation scenarios leading to helical buckling and various further post-buckling states. Since standard nonlinear beam elements do not account for nonlinearities in torsional modes, as well as for coupling between axial, lateral and torsional modes, we derive a new beam element, which allows us to describe complex helical buckling bifurcation scenarios of a rod subjected to a twisting load. The formulated beam element is systematically tested to assess its predictive capabilities in determining critical torsional buckling loads and its sensitivity to number of elements used. Once the model is validated against commercial FE software (Abaqus), we focus our attention on computing bifurcation scenarios to observe various complex helical configurations and transitions between them. The analysis reveals co-existence between helices with multiple loops for certain values of twisting load. Additionally, we trace the transition onsets between stable helical configurations. The developed FE can be applied to study complex buckling mechanics of engineering and biological structures.

AB - We develop a new Finite Element to accurately model twisting of rods and capture the bifurcation scenarios leading to helical buckling and various further post-buckling states. Since standard nonlinear beam elements do not account for nonlinearities in torsional modes, as well as for coupling between axial, lateral and torsional modes, we derive a new beam element, which allows us to describe complex helical buckling bifurcation scenarios of a rod subjected to a twisting load. The formulated beam element is systematically tested to assess its predictive capabilities in determining critical torsional buckling loads and its sensitivity to number of elements used. Once the model is validated against commercial FE software (Abaqus), we focus our attention on computing bifurcation scenarios to observe various complex helical configurations and transitions between them. The analysis reveals co-existence between helices with multiple loops for certain values of twisting load. Additionally, we trace the transition onsets between stable helical configurations. The developed FE can be applied to study complex buckling mechanics of engineering and biological structures.

KW - helical buckling

KW - bifurcations

KW - twisted rods

KW - finite element

KW - post-buckling configurations

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DO - 10.1016/j.ijengsci.2019.103197

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VL - 147

JO - International Journal of Engineering Science

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