896 IV International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2011 M. Papadrakakis, E. Oñate and B. Schrefler (Eds) PARTITIONED TIME INTEGRATION METHODS FOR HARDWARE IN THE LOOP BASED ON LINEARLY IMPLICIT L-STABLE ROSENBROCK METHODS ORESTE S. BURSI * , CHUANGUO JIA † ， ZHEN WANG * * Department of Mechanical and Structural Engineering University of Trento Via Mesiano 77, 38123 Trento, Italy e-mail: oreste.bursi@ing.unitn.it, www.ing.unitn.it/~bursi/ † School of Civil Engineering, Chongqing University, Chongqing, China Key words: Real-time, Rosenbrock integration methods, Interfield partitioned methods, Hardware-in-the-loop test. Abstract. Hardware in the loop based on dynamic substructuring was conceived to be a hybrid numerical-experimental technique to simulate the non-linear behaviour of an emulated structure. Its challenge is to ensure that both numerical and physical substructures interact in real time by means of actuators –transfer systems-. With this objective in mind, the development and implementation of partitioned real-time compatible Rosenbrock algorithms are presented in this paper. In detail, we shortly introduce monolithic linearly implicit L-stable algorithms with two stages; and in view of the analysis of complex emulated structures, we present a novel interfield partitioned algorithm. Both the stability and accuracy properties of the proposed algorithm are examined through analytical and numerical studies carried out on Single-DoF model problems. Moreover, a novel test rig conceived to perform both linear and nonlinear substructure tests is introduced, and tests on a two-DoF split-mass system are illustrated. The drawbacks of this algorithm are underlined and improvements are introduced on a companion solution procedure. 1 INTRODUCTION In recent years real-time hybrid testing techniques, as depicted in Figure 1, like the Hardware-in-the-Loop (HiL) technique with Dynamic Substructuring (DS), became more and more popular in order to study the performance of components and structures subject to dynamic loads [1,2]. With regard to relevant time-stepping methods, they can be broadly classified in monolithic and partitioned. In a monolithic approach, the method integrates: i) the Numerical Substructure (NS) only, whilst the Physical Substructure (PS) is considered a black box [2]; ii) both the NS and the PS by means of stiffness estimates [3], like in a typical pseudo-dynamic (PsD) test [2]. Conversely, a partitioned approach solves both NS and PS through different integrators and takes into account the interface problem, for instance by prediction, substitution and synchronization of Lagrange multipliers. In detail, partitioned