Rosenbrock-based algorithms and subcycling strategies for real-time non-linear substructure testing

In this paper, Rosenbrock-based algorithms originally developed for real-time testing of linear systems with dynamic substructuring are extended for use on nonlinear systems. With this objective in mind and for minimal overhead, both two- and three-stages linearly implicit real-time compatible algorithms were endowed with the Jacobian matrices requiring only one evaluation at the beginning of each time step. Moreover, these algorithms were improved with subcycling strategies. In detail, the paper briefly introduces Rosenbrock-based L-Stable Real-Time (LSRT) algorithms together with linearly implicit and explicit structural integrators, which are now commonly used to perform real-time tests. Then, the LSRT algorithms are analysed in terms of linearized stability with reference to an emulated spring pendulum, which was chosen as a nonlinear test problem, because it is able to exhibit a large and relatively slow nonlinear circular motion coupled to an axial motion that can be set to be stiff. The accuracy analysis on this system was performed for all the algorithms described. Following this, a coupled spring-pendulum example typical of real-time testing is analysed with respect to both stability and accuracy issues. Finally, the results of representative numerical simulations and real-time substructure tests, considering nonlinearities both in the numerical and the physical substructure, are explored. These tests were used to demonstrate how the LSRT algorithms can be used for substructuring tests with strongly nonlinear components. Copyright © 2010 John Wiley & Sons, Ltd.