An enhanced SDOF model to predict the behaviour of a steel column impacted by a rigid body
Résumé
The transient dynamic response of a steel beam-column subjected to impact loading is a complex phenomenon involving large localized plastic deformations and non-smooth contact interactions. Exposed to high intensity of the contact force generated from impact, the beam-column may undergo large displacement and inelastic deformation. Previous research has shown that a calibrated elasto-plastic single degree of freedom system is able to reproduce both the displacement and the force time-history of a steel beam subjected to non-impulsive loading or low-velocity impact. In these models, the static force-displacement curve is derived from either experiments or detailed 3D nonlinear analysis. Tri-linear resistance function has been extensively used to reproduce the different stages of the response including catenary effects. A rigorous treatment of such a complex problem calls for the use of non-smooth analysis tools to handle the impulsive nature of the impact force, the unilateral constraint, the impenetrability condition and the discontinuity of the velocity in a rigorous manner. In this paper, we present a non-smooth elasto-plastic single degree of freedom model under impact loading that permits the use of arbitrary resistance function. Adopting the non-smooth framework offers tools such as differential measures and convex analysis concepts to deal with unilateral contact incorporating Newton's impact law. The mid-point scheme is adopted to avoid numerical unrealistic energy decay or blowup. Furthermore, the non-penetration condition is numerically satisfied by imposing the constraint at only the velocity level to guarantee energy momentum conservation [1]. The explicit expression of resistance functions of the beam that are used in the SDOF model are obtained from a simplified nonlinear static analysis of two beam-column models. In the analysis, a linear relation between normal force and bending moment is assumed for the plastification of the hinges. Two proposals to simplify the explicit expressions of the model's response behavior are given. Performing an energy-based analysis, we predict maximum displacement that is needed to absorb the kinetic energy arising from the impact for different coefficient of restitution. The numerical examples underline the validity of the model by showing good agreement with the predictions of reference models. (C) 2017 Published by Elsevier Ltd.