Co-rotating rigid beam with generalized plastic hinges for the nonlinear dynamic analysis of planar framed structures subjected to impact loading

Abstract

The purpose of this paper is to model the nonlinear dynamical response of steel frame structures subjected to impact loading. A 2D co-rotational rigid beam element with generalized elasto-plastic hinges is presented. The main idea is to integrate the concept of the generalized elasto-plastic hinge into the standard co-rotational framework by performing a static condensation procedure in order to remove extra internal nodes and their corresponding degrees of freedom. In addition, impact loading is applied through a contact model that is described in the rigorous framework of non-smooth dynamics. In this framework, equations of motion are derived using a set of differential measures and convex analysis tools, whereas Newton's impact law is imposed by means of a restitution coefficient in order to accommodate energy losses. An energy and momentum conserving scheme is adopted to solve the dynamical equations. The main interest of the current model is the ability to evaluate the geometrically nonlinear inelastic behaviour of steel structures with semi-rigid connections subjected to impact in a simple and efficient way, using only a few number of elements. The accuracy of the proposed formulation is assessed in three numerical applications.