A simplified model for nonlinear dynamic analysis of steel column subjected to impact

• A new simplified model of a steel column subjected to impact.
• The 4 DOF model captures the geometrical and material nonlinearities.
• A new generalized yield criterion describes the plastic behaviour of the hinge.
• Rigorous non-smooth mechanics framework is used to describe impact.
• Multiples examples show the effectiveness of the model.

This paper presents a new simplified model of the nonlinear dynamic behavior of a steel column subjected to impact loading. In this model, the impacted column, which undergoes large displacement, consists of two rigid bars connected by generalized elastic–plastic hinges where the deformation of the entire steel column as well as the connections is concentrated. The effect of the rest of the structure on the column is modeled by an elastic spring and a point masse both attached to the top end of the column which is also loaded by a compressive force. The plastification of the hinges follows the normality rule with a yield surface that accounts for the interaction between M and N. The latter is described by a super-elliptic yield surface that allows ones to consider a wide range of convex yield criterion by simply varying the roundness factor that affects the shape of the limit surface. By including these features, the model captures both geometry and material nonlinearities. Both the flow rule and the equations of motion are integrated using the midpoint scheme that conserves energy. The non-smooth nature of impact is considered by writing the equations of motion of colliding masses using differential measures. Contact conditions are written in terms of velocity and combined with Newton's law to provide the constitutive law describing interactions between masses during impact. Numerical applications show that the model is able to capture the behavior of a column subjected to impact.