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.

中文翻译：

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隔震结构地震响应分析的跨历史迭代方法及其基于ABAQUS的二次开发

在隔震结构（SIS）的地震响应分析中，非线性集中在隔震层，而上部结构呈线性，使得SIS系统局部非线性。本文提出了一种基于等效线性化（EL）和 SIS 迭代求解的新型地震分析方法。在该方法中，SIS的平衡方程由结构系统的二阶常微分方程以及隔震支座（SIB）的滞回力来表达。基于EL理论，重建了整个系统的线性化平衡方程，并从理论上推导了EL参数。提出了历史间迭代（IHI）方法来求解线性化方程组并按顺序迭代计算EL参数，以进行SIS的地震响应分析，从而在不过度损失精度的情况下降低计算成本。此外，为了便于工程应用，在ABAQUS中对该方法进行了二次开发。最后，通过SIS案例研究的数值模拟研究了该方法的收敛性和准确性。数值研究表明，该方法考虑了结构响应与EL参数之间的耦合，具有较高的收敛速度和满意的求解精度。ABAQUS二次开发程序利用ABAQUS强大的预处理器、后处理器和求解器，使得IHI方法更适合工程应用。