Improved Explicit Integration Algorithms with Controllable Numerical Damping for Real-Time Hybrid Simulation

Abstract

The paper proposes an improved single-step method of explicit displacement and velocity (SSMEDV) with controllable numerical damping based on the discrete control theory, which can be applied to real-time hybrid simulation (RTHS). The stability, overshoot, and numerical damping characteristics of the proposed algorithms are studied. It is shown that certain algorithms have unconditional stability for linear and softening nonlinear structures. The overshoot phenomenon is small, where the displacement is one power of the time step due to the initial velocity, whereas the velocity does not. The amount of numerical damping is adjusted by a single parameter to control the divergence of false higher-order modes. The analysis of RTHS was performed on a multiple degrees-of-freedom (MDOF) structure and complex building–damper structure to verify the theoretical analysis. The comparison with two typical algorithms of the explicit Newmark and Gui-λ demonstrates the effectiveness of the proposed algorithms in improving stability, accuracy, and computational efficiency, which can be applied to complex RTHS.