An Efficient Method for Time Integration of Dynamic Equations Including Bouc-Wen Model and Its Application to Damped Structures

The Bouc-Wen model is widely used because it can capture complex nonlinear behaviors like structural degradation and the pinching effect. However, its lack of an explicit force-deformation relation complicates the numerical integration of dynamic equations. To overcome this issue, this study proposes an efficient approach termed the Monolithic Integration of Structure and its Hysteresis (MISH). In this method, a first-order differential equation system is constructed by combining the structural dynamic equations with the hysteretic equations, and the Rosenbrock method is adopted for its numerical integration. To validate the effectiveness of MISH, simulations are performed on both Single-Degree-of-Freedom (SDoF) and Multiple-Degree-of-Freedom (MDoF) systems equipped with metal dampers. Results demonstrate that MISH offers superior accuracy, efficiency, and robustness under strongly nonlinear conditions compared with conventional partitioned integration methods. Furthermore, the method is extended to planar frames with inter-story metal dampers, confirming its applicability and reliability for practical structural dynamic analysis.