An Explicit Quadratic Alpha Numerical Integration Algorithm for Force-Based Hybrid Simulation

Abstract eng:
Hybrid simulation is a combination of physical testing and numerical simulation, which provides a powerful technique for dynamic testing of large and complex structural systems. While the hybrid simulation has been used in various applications, it has some limitations. One of the limitations is that force equilibrium is not always guaranteed because the conventional hybrid simulation is displacement based; the formulation is based on the displacement, which ensures only displacement compatibilities of unless an iterative approach is used. In some cases, displacement-based approach is not suitable and even applicable (e.g., testing of rigid specimen). This study presents an explicit numerical integration algorithm for force-based hybrid simulation. In the force-based hybrid simulation, the formulation/governing equation is calculated in terms of force first. The calculated force is then applied to the test specimen through a force control technique and the corresponding displacement is measured. The measured displacement is sent back to the numerical algorithm and the responses at the next step are updated based on the measured displacement and the responses at the previous steps. This paper presents a new force-based explicit numerical integration algorithm, so-called quadratic-alpha method. The proposed method is based on the quadratic interpolation of the equation of motion and consists of pre-experimental, experimental, and post-experimental processes to enable hybrid simulation. Formulation and background theories of the quadratic alpha method as well as the implementation flowchart are presented in the paper. Then, dynamic characteristics and stability of the method are discussed using discrete transfer functions. The stability assessment shows that the quadratic alpha method provides stable simulation for systems with different natural frequencies. The numerical simulation of the quadratic alpha method is performed for earthquake, wind and coastal storm surge loads with three restoring force models. While some discrepancies are found between the quadratic alpha method and the reference nonlinear dynamic analysis for highly nonlinear hysteresis models, the method is proven to be stable and provide reasonable accuracy for all of the considered scenarios.

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