Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

[1]  Victor E. Saouma,et al.  A computational finite‐element program for hybrid simulation , 2012 .

[2]  Feng Jin,et al.  Comparison of explicit integration algorithms for real-time hybrid simulation , 2015, Bulletin of Earthquake Engineering.

[3]  Shirley J. Dyke,et al.  Next Generation Bench-mark Control Problems for Seismically Excited Buildings , 1999 .

[4]  Amin Maghareh,et al.  Evaluation of the 9-Story Benchmark Building Shear Model , 2012 .

[5]  J. Ricles,et al.  Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory , 2008 .

[6]  Shuenn-Yih Chang,et al.  A family of explicit algorithms for general pseudodynamic testing , 2011 .

[7]  Masayoshi Nakashima,et al.  Real-time on-line test for MDOF systems , 1999 .

[8]  Masayoshi Nakashima,et al.  Development of real‐time pseudo dynamic testing , 1992 .

[9]  Shirley J. Dyke,et al.  Benchmark Control Problems for Seismically Excited Nonlinear Buildings , 2004 .

[10]  Shuenn-Yih Chang,et al.  Explicit Pseudodynamic Algorithm with Unconditional Stability , 2002 .

[11]  James M. Ricles,et al.  Adaptive time series compensator for delay compensation of servo‐hydraulic actuator systems for real‐time hybrid simulation , 2013 .

[12]  James M. Ricles,et al.  Large‐scale real‐time hybrid simulation involving multiple experimental substructures and adaptive actuator delay compensation , 2012 .

[13]  Meng-Xia Zhou,et al.  Development of a family of explicit algorithms for structural dynamics with unconditional stability , 2014 .

[14]  Shuenn-Yih Chang,et al.  Explicit Pseudodynamic Algorithm with Improved Stability Properties , 2010 .

[15]  Feng Jin,et al.  Simulation of large-scale numerical substructure in real-time dynamic hybrid testing , 2014, Earthquake Engineering and Engineering Vibration.

[16]  Khalid M. Mosalam,et al.  Towards Faster Computations and Accurate Execution of Real-Time Hybrid Simulation , 2015 .

[17]  Sergio Pissanetzky,et al.  Sparse Matrix Technology , 1984 .

[18]  Martin S. Williams,et al.  Evaluation of numerical time‐integration schemes for real‐time hybrid testing , 2008 .

[19]  Richard Rosen.  Matrix bandwidth minimization , 1968, ACM National Conference.

[20]  Feng Jin,et al.  Real-Time Dynamic Hybrid Testing Coupling Finite Element and Shaking Table , 2014 .