The inter-history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

Abstract

In seismic response analysis of seismically isolated structures (SISs), the nonlinearity is concentrated in the isolation layer while the upper structure behaves linearly, making SISs locally nonlinear systems. This paper proposed a novel seismic analysis method based on equivalent linearization (EL) and iterative solution for SISs. In this method, the equilibrium equations of an SIS are expressed by the second-order ordinary differential equations of the structural system as well as the hysteretic force of seismic isolation bearings (SIBs). Based on EL theory, the linearized equilibrium equations of the overall system were reconstructed in which the EL parameters are derived theoretically. The inter-history iteration (IHI) method was proposed to solve the linearized equation system and calculate the EL parameters in sequence iteratively for seismic response analysis of SISs, thus reducing computational cost without excessive loss of accuracy. In addition, the secondary development of the proposed method was programmed in ABAQUS for ease of engineering applications. Finally, the convergence and accuracy of the method were investigated through numerical simulation of an SIS case study. As the numerical investigation indicates, the proposed method considers the coupling between structural response and the EL parameters, achieving a high convergence rate and satisfactory solution accuracy. The ABAQUS secondary development program utilizes the powerful pre-processor, post-processor, and solvers of ABAQUS, making the IHI method more appropriate for engineering applications.