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Updated Lagrangian formulation for second-order elastic analysis of space frames using beam elements

Report


Type Of Work


  • Report

Abstract


  • It has been demonstrated previously by the authors that conservative internal moments of a spatial beam are of the so-called fourth kind, and that the rotation variables which are work-conjugate with such moments are vectorial rotations. If the vectorial rotations of a spatial beam element are approximated by the corresponding transverse displacement derivatives to the first order in formulating the governing equilibrium equation, incorrect element stiffness matrices will result unless a measure is taken to account for the distinction between the two displacement parameters. The required correction naturally depends on the 'assumed' rotational behaviour of internal moments in the system. The present work derives the stiffness matrices of a spatial beam element based on the definitive knowledge of the rotational behaviour of conservative internal moments established previously by the authors. It is shown through numerical experiments that the resulting computational algorithms are robust and accurate.

Publication Date


  • 1996

Citation


  • Teh, L. H., & Clarke, M. J. (1996). Updated Lagrangian formulation for second-order elastic analysis of space frames using beam elements: Research Report - University of Sydney, School of Civil and Mining Engineering.

Scopus Eid


  • 2-s2.0-0030231755

Web Of Science Accession Number


Book Title


  • Research Report - University of Sydney, School of Civil and Mining Engineering

Start Page


  • 1

End Page


  • 44

Issue


  • 727

Type Of Work


  • Report

Abstract


  • It has been demonstrated previously by the authors that conservative internal moments of a spatial beam are of the so-called fourth kind, and that the rotation variables which are work-conjugate with such moments are vectorial rotations. If the vectorial rotations of a spatial beam element are approximated by the corresponding transverse displacement derivatives to the first order in formulating the governing equilibrium equation, incorrect element stiffness matrices will result unless a measure is taken to account for the distinction between the two displacement parameters. The required correction naturally depends on the 'assumed' rotational behaviour of internal moments in the system. The present work derives the stiffness matrices of a spatial beam element based on the definitive knowledge of the rotational behaviour of conservative internal moments established previously by the authors. It is shown through numerical experiments that the resulting computational algorithms are robust and accurate.

Publication Date


  • 1996

Citation


  • Teh, L. H., & Clarke, M. J. (1996). Updated Lagrangian formulation for second-order elastic analysis of space frames using beam elements: Research Report - University of Sydney, School of Civil and Mining Engineering.

Scopus Eid


  • 2-s2.0-0030231755

Web Of Science Accession Number


Book Title


  • Research Report - University of Sydney, School of Civil and Mining Engineering

Start Page


  • 1

End Page


  • 44

Issue


  • 727