Multiaxial softening hinge model for tubular vehicle roll-over protective structures

T. H. Kim, S. R. Reid

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


The purpose of the work described in this paper is to provide a computational tool for the design of roll-over protective structures (ROPS) comprised of thin-walled rectangular tubes. This tool simulates the multi-stage, regulatory quasi-static loading test (SAE Standard, SAE J1040 APR88) that new designs must pass. These tests are claimed to be indications of the performance of a ROPS under real (dynamic) roll-over conditions. The collapse of the framework involves large, three-dimensional deformation, which results mainly from large rotations in each member due to bending and torsion. To establish constitutive relationships for a framework model, biaxial bending collapse behaviour of thin-walled rectangular tubes was investigated using a kinematic approach to generate the bending interaction curves. The interaction between bending and torsion was examined separately using extensive finite element analyses of cantilevers modelled by the commercial finite element code ABAQUS. Approximate constitutive relationships were then formulated for a 'hinge super-element' to be implemented via the user-defined element subroutine UEL in ABAQUS. The hinge element consists of two nodes separated by a small distance. Each node has six degrees of freedom and the components of stiffness at each node are initially set to sufficiently large values to provide rigid response in the pre-collapse stage. When the collapse criterion is satisfied for the first time, the hinge element is switched to 'softening' hinge response and thereafter follows the local softening behaviour of a closed-section tube by modifying the stiffness of the three rotational components according to the constitutive relationships. To test the validity of the hinge model, the response of a simple, scaled ROPS to a simulated prescribed regulatory test load history (SAE Standard) was compared with the results from the analysis of an equivalent shell element model. Good agreement is demonstrated between the two models.

Original languageEnglish
Pages (from-to)2147-2170
Number of pages24
JournalInternational Journal of Mechanical Sciences
Issue number9
Publication statusPublished - 1 Jan 2001


  • Bending-torsion interaction
  • Biaxial bending
  • Hinge super-element
  • Normality rule
  • ROPS
  • Simplified crash analysis
  • Softening


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