A two-dimensional friction-decoupling method based on numerical integration method and momentum theorem

Abstract

This article introduces a simplified Two-Dimensional Friction-Coupling Model (TDFC) designed for typical surface-to-surface contact friction systems in engineering structures. With the assumption of a constant friction force magnitude within each calculation time step, the alteration of the friction direction of TDFC within each calculation time step can be visualized as the rotation of a circular radius under horizontal bidirectional dynamic loads. This dynamic force analysis approach is referred to as the “Circular making”. It is noteworthy that the friction direction change in each calculation time step demonstrates unidirectional rotatability. Leveraging this rotatability and assuming uniform rotation, the momentum theorem accurately determines the direction of the plane friction acting on the TDFC model at the end of each calculation time step. This allows for the decoupled calculation of plane friction and precise response calculation of the TDFC model. The study verifies the reliability of theoretical assumptions, such as constant friction force magnitude and uniform rotation, with a time step of 0.01 s. Additionally, by introducing an equivalent spring effect to modify the TDFC model, it is observed that the modified TDFC effectively simulates the behavior of the Friction Pendulum Bearing (FPB) under horizontal bidirectional seismic loads. Compared to the ABAQUS finite element model of FPB, the modified TDFC model provides a more efficient approach for rapidly and accurately calculating the response of various FPB types under horizontal bidirectional seismic loads by adjusting parameter values of the modified TDFC model.