Event-driven integration of linear structural dynamics models under unilateral elastic constraints

This paper proposes an algorithm for the numerical simulation of linear structural dynamics problems under unilateral elastic constraints, i.e., constraints with a linear force/displacement characteristic whenever active. The presented procedure relies on an event-driven strategy for the handling of the contact constraints, in combination with one-step schemes dedicated to the time integration of the second-order equations of motion. Efficiency of the procedure follows from the use of cubic Hermite interpolation to continuously extend the normal gap functions that reflect the openings of the contact interfaces. Robustness follows from the proper handling of complex numerical situations, e.g., numerical grazing or discontinuity sticking, through appropriate algorithm structure and numerical implementation. And, integration stability is guaranteed by the very nature of the algorithm and that of the one-step integration scheme. Following a detailed coverage of the integration procedure and the countermeasures to the expected numerical difficulties, three application examples are treated for illustration purposes. A MATLAB implementation of the procedure is provided online; download and usage information are given in the Appendix.