MATLAB codes for "Fast In-Plane Dynamics of a Beam with Unilateral Constraints"

Abstract

A computationally efficient technique to simulate the dynamic response of a beam colliding with rigid obstacles is described in this paper. The proposed method merges three key concepts. First, a low order discretization scheme that maximizes the number of nodes of the discrete model, where impacts are detected, at the expense of the degree of continuity of the constructed displacement field. Second, the constrained problem is transformed into an unconstrained one by formulating the impact by means of a complementarity Signorini's law involving the impulse generated by the collision and the pre- and post- impact velocity linked via a coefficient of restitution. Third, Moreau's midpoint time-stepping scheme developed within the context of colliding rigid bodies, is used to advance the solution.