Modeling of Disc Spring Self-Centering Energy Dissipation Braces from Inactive State to Design Limit State

This paper focuses on modeling the hysteretic behavior of disc spring self-centering energy dissipation braces (DS-SCEDBs) from the inactive state to the design limit state, and proposes two restoring force models for structural design. A logistic function is used in the modified nonlinear mechanical model to represent the behavior of the self-centering system, and the Bouc–Wen model is employed to represent the performance of the energy dissipation system. In the modified model, the logistic function improves the numerical convergence and reduces the computational cost, but the Bouc–Wen model must be solved by numerical algorithms. The modified model does not reproduce accurately the hysteretic response at small displacements. Therefore, a flag-shaped hysteretic variable model formulated using the primitive functions of the logistic function is proposed to address the shortcomings of the modified nonlinear mechanical model. The flag-shaped hysteretic variable model can be solved directly using the brace design parameters, and the hysteretic law is consistent with the theory. The hysteretic response of the DS-SCEDBs at the displacement exceeding the desired stroke also can be simulated by the primitive function of the logistic function. The dominant parameters of the proposed models are related to the design parameters, which is convenient for use in structural design and simulation. Comparisons of the prediction and test results indicated that both models can replicate the restoring forces and hysteretic responses of the DS-SCEDBs during normal operation or when the disc springs are compressed fully. The flag-shaped hysteretic variable model has higher calculation accuracy and better programmability than the modified nonlinear mechanical model.