Novel Coupling Rosenbrock-based Algorithms for Real-time Dynamic Substructure Testing

Real-time testing with dynamic substructuring is a novel experimental technique capable of assessing the behaviour of structures subjected to dynamic loadings including earthquakes. The technique involves recreating the dynamics of the entire structure by combining an experimental test piece consisting of part of the structure with a numerical model simulating the remainder of the structure. These substructures interact in real time to emulate the behaviour of the entire structure. Time integration is the most versatile ethod for analysing the general case of linear and non-linear semi-discretized equations of motion. In this paper we propose for substructure testing, L-stable real-time (LSRT) compatible integrators with two and three stages derived from the Rosenbrock methods. These algorithms are unconditionally stable for uncoupled problems and entail a moderate computational cost for real-time performance. They can also effectively deal with stiff problems, i.e. complex emulated structures for which solutions can change on a time scale that is very short compared with the interval of time integration, but where the solution of interest changes on a much longer time scale. Stability conditions of the coupled substructures are analysed by means of the zero-stability approach, and the accuracy of the novel algorithms in the coupled case is assessed in both the unforced and forced conditions. LSRT algorithms are shown to be more competitive than popular Runge–Kutta methods in terms of stability, accuracy and ease of implementation. Numerical simulations and real-time substructure tests are used to demonstrate the favourable properties of the proposed algorithms.