Abstract
Real-time substructure testing (RST) algorithm is a newly developed integration method for real-time hybrid simulation (RTHS) which has structure-dependent and explicit formulations for both displacement and velocity. The most favourable characteristics of the RST algorithm is unconditionally stable for linear and no iterations are needed. In order to fully evaluate the performance of the RST method in solving dynamic problems for nonlinear systems, stability, numerical dispersion, energy dissipation, and overshooting properties are discussed. Stability analysis shows that the RST method is only conditionally stable when applied to nonlinear systems. The upper stability limit increases for stiffness-softening systems with an increasing value of the instantaneous degree of nonlinearity while decreases for stiffness-hardening systems when the instantaneous degree of nonlinearity becomes larger. Meanwhile, the initial damping ratio of the system has a negative impact on the upper stability limit especially for instantaneous stiffness softening systems, and a larger value of the damping ratio will significantly decrease the upper stability limit of the RST method. It is shown in the accuracy analysis that the RST method has relatively smaller period errors and numerical damping ratios for nonlinear systems when compared with other two well-developed algorithms. Three simplified engineering cases are presented to investigate the dynamic performance of the RST method, and the numerical results indicate that this method has a more desirable accuracy than other methods in solving dynamic problems for both linear and nonliner systems.
Highlights
Real-time hybrid simulation (RTHS) is an advanced technique for assessing the seismic behaviours of structures, especially large-scale and ultralimit complex systems [1,2,3,4]
E displacement-coordination and force-equilibrium are two principles for the coupling between two components at the interfaces [5]. Both the restoring force calculated from numerical substructures and the resisting force measured from experimental substructures at each time step are fed back to an integration algorithm. en, the subsequent timestep target displacement applied to the experimental substructure is calculated by solving the step-by-step equation of motion under external excitations and the reacting forces measured from experimental substructures [6]
Stability analysis indicates that the Real-time substructure testing (RST) method is only conditionally stable when applied to nonlinear systems, and the instantaneous degree of nonlinearity will exert great influence on the upper stability limit of the method
Summary
Real-time hybrid simulation (RTHS) is an advanced technique for assessing the seismic behaviours of structures, especially large-scale and ultralimit complex systems [1,2,3,4]. Is method is unconditionally stable for linear and instantaneous stiffness softening systems, and it can control the amount of numerical damping by a single parameter All these favourable attributes are achieved at the expense of degraded accuracy for general structural dynamics problems [27]. Tang and Lou [15] presented a new type of structure-dependent explicit integration algorithm for RTHS using a pole-mapping rule from the discrete domain and named it real-time substructure testing (RST) algorithm. The numerical properties of the RST method in RTHS are discussed for nonlinear structural dynamic problems and compared with other two structure-dependent integration algorithms (i.e., CEM and CRM) since they have quite similar formulations and numerical properties. The overshooting behaviour [25, 29] of the RST method in displacement is addressed as well. ree different simplified engineering structural systems are presented as numerical examples to demonstrate the computational stability and accuracy of the RST method when compared with other algorithms
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