Heterogeneous Time Integration Algorithm for Structural Dynamics with Localized Hysteretic Nonlinearities

Abstract

This paper proposes a heterogeneous time integration algorithm to analyze the dynamic response of structures with localized hysteretic nonlinearities. The critical point is to treat the whole structure as a combination of a linear substructure governed by the second-order dynamic equation and a nonlinear substructure controlled by the first-order differential formulation. With this partitioning, tailored numerical integration algorithms with heterogeneous time steps are applied directly to calculate the displacements and hysteretic forces from the linear and the nonlinear substructures, respectively. Subsequently, the dynamic responses of the whole structure are solved by a predictor–corrector procedure, where the hysteretic forces and displacement responses are coupled and exchanged to update the partitioning solutions. Furthermore, the energy balance method is derived to verify the stability of the proposed heterogeneous time integration algorithm. Dynamic responses of structures with friction damper, hysteretic models, and bolted joint models are studied to demonstrate the accuracy and efficiency of the proposed algorithm.