Monolithic and partitioned Rosenbrock-based time integration methods for dynamic substructure tests

Real-time testing with dynamic substructuring provides an efficient way to simulate the nonlinear dynamic behaviour of civil structures or mechanical facilities. In this technique, the test structure is divided onto two substructures: the relatively crucial substructure is tested physically and the other is modelled numerically in the computer. The key challenge is to ensure that both substructures interact in real-time, in order to simulate the behaviour of the emulated structure. This has special demands on the utilized integration methods and their implementations. Researchers have devoted significant effort to implement second-order integrators, such as Newmark integration methods, in a monolithic way where both substructures are integrated altogether. However, in view of large and complex structures, time integration methods are required to advance large-scale systems hence endowed with high-frequency components of the response or mixed first- and second- order systems like in the case of controlled systems. In this case, the monolithic implementation of a second-order time integration method becomes inefficient or inaccurate. With these promises, the thesis adopts the Rosenbrock-based time integration methods for both dynamic simulations of complex systems and substructure tests, and in particular, focuses on the development of monolithic schemes with subcycling strategies for nonlinear cases and partitioned methods with staggered and parallel solution procedures for linear and nonlinear cases. Initially, the Rosenbrock integration methods endowed with one stage to three stages are introduced and their applicabilities to second-order systems are investigated in terms of accuracy, stability and high-frequency dissipation, such as stability analysis of the Rosenbrock methods with one stage and two stages via the energy approach and numerical experiments on an uncoupled spring-pendulum system. Then, these methods are implemented in a monolithic way for real time substructure tests also considering subcycling strategies. Meanwhile, real-time substructure tests considering nonlinearities both in the numerical and physical substructures were carried out to illustrate the performances of the monolithic methods. Moreover, three types of partitioned algorithms based on the element-to-element partitioning are successively proposed. Two of them are based on acceleration continuity with a staggered solution procedure and a parallel solution procedure, respectively, and one of them is based on velocity continuity and a projection method. Both stability and accuracy properties of the proposed algorithms are examined by means of analytical techniques and numerical studies on single-, two-, three- and four-degree-of-freedom model problems and a coupled spring-pendulum system. Finally, a novel test rig conceived to perform both linear and nonlinear substructure tests with different combinations of numerical and physical substructures are presented and commented.