DEVELOPMENT AND APPLICATIONS OF TIME-STEPPING METHODS FOR REAL-TIME AND PSEUDO-DYNAMIC TESTING WITH DYNAMIC SUBSTRUCTURING

摘要

Real-Time Hardware-in-the-loop (RTHIL) is a novel form of heterogeneous numerical-experimental testing capable of assessing the behaviour of structures subjected to dynamic loadings. The technique involves splitting the emulated structure being tested into two parts: the Physical Substructure (PS), which contains a key region of interest and is experimentally tested; the Numerical Substructure (NS), which contains the remainder of the structure and is numerically simulated. By imposing compatibility and equilibrium conditions at the interface between the NS and the PS, respectively, the substructures are made to interact in real-time such that they emulate the dynamic behaviour of the full structure. Running the entire process in real- time leads to the use of Real-Time Compatible (RTC) integrators; for this reason, we propose two L-stable real-time (LSRT) integrators based on Rosenbrock schemes for RTHIL testing. These algorithms are more competitive than other structural Newmark-based integrators in terms of stability and accuracy both for linear and non-linear systems. The proposed LSRT methods entail five beneficial properties: (i) they can be implemented in a real-time environment; (ii) they can deal with stiff systems relying on the L- stability property; (iii) they do not exhibit overshoot in the velocity for large time step Δt; (iv) they do not require the computation of the exponential of the system matrix and are easy to implement with few stages; (v) they predict explicit the state potentially assuring a better control of the acceleration of the transfer system. In the paper, some experimental results from a series of RTHIL tests carried out on MDoF linear and nonlinear systems using the proposed integrators are described. We present also the development and application of partitioned procedures of coupled dynamical systems in the context of pseudo-dynamic (PsD) tests with dynamic substructuring. In detail, we present the convergence analysis of a novel parallel interfield procedure for time-integrating hybrid substructures. The partitioned method conceived by Pegon and Magonette is an extension of a method originally proposed by Gravouil and Combescure which utilizes a domain decomposition enforcing the continuity of the velocity at interfaces through Lagrange multipliers. In detail. the merits of the new method, which can couple arbitrary Newmark schemes with different time steps in different subdomains and advances simultaneously all the substructure states, are analysed in terms of accuracy and stability. All theoretical results are derived for single-and two-DoF systems as a MDoF system is too difficult to analyse mathematically. Finally, the insight gained from the analysis of these coupled problems and the conclusions drawn are confirmed by means of numerical simulations.