PROPOSAL OF HYSTERESIS MODEL USING DIFFERENTIAL EQUATION

Abstract

 This paper describes a new type of hysteresis model that is capable of generating various hysteresis loops. The seismic responses for structures depend on their force-displacement relationships. To improve the accuracy of seismic response prediction for the structures, the hysteresis models which are capable of calculating a force-displacement relationships closed to an actual phenomenon are essential.

 The seismic fragility assessment has been performed to clarify the seismic performance. The fragility curves are calculated using the results of seismic response analysis obtained by incremental input ground motions. Their seismic responses contain the hysteresis loops that have the ultimate neighborhood of the structures. These seismic response analyses require the hysteresis models which can capture the hysteresis loops having strongly nonlinear characteristics. In general, modeling the hysteresis loops to be able to capture the ultimate state results in difficult because the hysteresis rules and the programing code to calculate their hysteresis loops are complex.

 To overcome these problems, this paper proposes a newly hysteresis model which can capture the various nonlinear behaviors as a differential equation type. This hysteresis model can generate the hysteresis loops with strongly nonlinear skeleton-curves without the hysteresis law such as Masing’s laws because the hysteresis model can treat the any skeleton curves which are identified using an approximate polynomial based on the test results and so on. The feature will lead to improving the accuracy of seismic response prediction and the applicability of the seismic response including probabilistic assessment.

 This paper is divided into three main groups. The first is to describe the constitutive equations of the proposed hysteresis model. The second is to demonstrate the validity of the hysteresis model by generating the various hysteresis loops and compares with the measured hysteresis loops. The third is to show the applicability of the hysteresis model into the seismic response analysis using a simple analytical model. The primary results are summarized as follows:

 The proposed hysteresis model can:

 1) Express the typical hysteresis loops which are generated by the previous hysteresis models consisting of the differential equation type.

 2) Easily generate the various hysteresis loops, which contain the hysteresis loops that are varied due to the number of cyclic loading and the experienced maximum displacement.

 3) Accurately capture the measured hysteresis loops having strongly nonlinear characteristics.

 4) Easily apply to the seismic response analysis as an initial problem even if the target skeleton curve has nonlinear characteristics.