Self-Centering Beam Element for Computationally Efficient Dynamic Analysis Using Standard Time Integration Schemes

Abstract

Dynamic simulation of self-centering systems can be computationally challenging due to the opening and closing mechanisms that cause a rapid change in stiffness. In addition, the current modeling of self-centering connections requires several degrees-of-freedom per connection. This paper presents a new element for the analysis of self-centering systems to address this issue. The element formulation includes its self-centering end connections. It relies on an analytical formulation, where the elongation due to openings is considered. Furthermore, to overcome the highly nonlinear behavior of such systems, mainly due to the opening and closing of the self-centering connections, the proposed element relies on an algorithm with multiple linear brunches to define the deformation state. The proposed element can be used with standard time integration schemes with small modifications, where in this paper the well-known Newmark Beta method is adopted. The reliability of the presented element was demonstrated through two numerical examples of a wall with multiple rocking sections and a five-story self-centering moment-resisting frame (SC-MRF). The numerical results show good agreement compared to a finite-element explicit gap model for the self-centering connections, while the proposed element requires a significantly reduced number of nodes and degrees-of-freedom. Therefore, the computational effort required using the proposed element is considerably smaller. This is demonstrated using a five-story SC-MRF example.