Degrading Bouc–Wen Model Parameters Identification Under Cyclic Load

Degrading Bouc–Wen Model Parameters Identification Under Cyclic Load

G. C. Marano (College of Civil Engineering Fuzhou University, Fuzhou, China), M. Pelliciari (‘Enzo Ferrari' Engineering Department, University of Modena and Reggio Emilia, Modena, Italy), T. Cuoghi (‘Enzo Ferrari' Engineering Department, University of Modena and Reggio Emilia, Modena, Italy), B. Briseghella (College of Civil Engineering Fuzhou University, Fuzhou, China), D. Lavorato (Department of Architecture, Roma Tre University, Rome, Italy) and A. M. Tarantino (‘Enzo Ferrari' Engineering Department, University of Modena and Reggio Emilia, Modena, Italy)
Copyright: © 2017 |Pages: 22
DOI: 10.4018/IJGEE.2017070104


The purpose of this article is to describe the Bouc–Wen model of hysteresis for structural engineering which is used to describe a wide range of nonlinear hysteretic systems, as a consequence of its capability to produce a variety of hysteretic patterns. This article focuses on the application of the Bouc–Wen model to predict the hysteretic behaviour of reinforced concrete bridge piers. The purpose is to identify the optimal values of the parameters so that the output of the model matches as well as possible the experimental data. Two repaired, retrofitted and reinforced concrete bridge pier specimens (in a 1:6 scale of a real bridge pier) are tested in a laboratory and used for experiments in this article. An identification of Bouc–Wen model's parameters is performed using the force–displacement experimental data obtained after cyclic loading tests on these two specimens. The original model involves many parameters and complex pinching and degrading functions. This makes the identification solution unmanageable and with numerical problems. Furthermore, from a computational point of view, the identification takes too much time. The novelty of this work is the proposal of a simplification of the model allowed by simpler pinching and degrading functions and the reduction of the number of parameters. The latter innovation is effective in reducing computational efforts and is performed after a deep study of the mechanical effects of each parameter on the pier response. This simplified model is implemented in a MATLAB code and the numerical results are well fit to the experimental results and are reliable in terms of manageability, stability, and computational time.
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1. Introduction

Reinforced concrete or steel structural systems show nonlinear behaviour of parts of the structures (plastic hinge) or devices (isolator, dissipative braces, etc.) applied on some structures to mitigate their seismic response when severe excitations occur during strong earthquakes. In that condition the restoring force becomes highly nonlinear, showing significant hysteresis. The modelling of this hysteretic behaviour is much important to analyse the structural seismic response and design properly structural details and mitigation devices.

Many engineering systems involve the hysteresis. For instance, seismic protection devices, electronic systems, mechanical components, and others (Ismail, Ikhouane, & Rodellar, 2009). In this case, memory effect appears in the behaviour of the system. This means that the nonlinear restoring force cannot be expressed as a function of the instantaneous values of displacement and velocity. For this reason, many hysteretic models are based on a set of differential equations to be integrated over the entire event, in order to include the time dependency of the force. In seismic engineering, the structural hysteresis depends on the natural mechanism of materials which produce restoring forces in function of the instantaneous deformation and the history of the deformation (memory material nature) when are subjected to great inelastic deformations.

The detailed modelling of nonlinear hysteretic systems is very complex. Moreover, practical applications require simple and effective models that can be managed and easily controlled. Thus, alternative models have been developed. They do not focus on the detailed description of the system. Instead, they view the system in terms of its input and output, without analysing its intrinsic behaviour. This kind of models are often known as ‘semi-physical’ models.

When complex loading patterns happened, such as those produced by earthquakes, the availability of smooth continuous mathematical models, able to describe realistically the time evolution of hysteresis properties, is crucial. In this way, it is possible to perform analyses about the structural capability of systems subjected to seismic actions with modest computational efforts.

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