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

The purpose of the work described in this paper is to provide a computation al tool for the design of roll-over protective structures (ROPS) comprised of thin-walled rectangular tubes. This tool simulates the multi-stage, regu latory quasi-static loading test (SAE Standard, SAE J1040 APR88) that new d esigns must pass. These tests are claimed to be indications of the performa nce of a ROPS under real (dynamic) roll-over conditions. The collapse of th e framework involves large, three-dimensional deformation, which results ma inly from large rotations in each member due to bending and torsion. To est ablish constitutive relationships for a framework model, biaxial bending co llapse behaviour of thin-walled rectangular tubes was investigated using a kinematic approach to generate the bending interaction curves. The interact ion between bending and torsion was examined separately using extensive fin ite element analyses of cantilevers modelled by the commercial finite eleme nt 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 separate d by a small distance. Each node has six degrees of freedom and the compone nts of stiffness at each node are initially set to sufficiently large value s to provide rigid response in the pre-collapse stage. When the collapse cr iterion is satisfied for the first time, the hinge element is switched to ' softening' hinge response and thereafter follows the local softening behavi our of a closed-section tube by modifying the stiffness of the three rotati onal components according to the constitutive relationships. To test the va lidity of the hinge model, the response of a simple, scaled ROPS to a simul ated prescribed regulatory test load history (SAE Standard) was compared wi th the results from the analysis of an equivalent shell element model. Good agreement is demonstrated between the two models. (C) 2001 Elsevier Scienc e Ltd. All rights reserved.