Finite element based study on aerostatic post-buckling and multi-stability of long-span bridges

Abstract

Aerostatic instability is one of two vital instabilities of wind resistance design for long-span bridges. Traditionally, the aerostatic instability considering aerodynamic and structural nonlinearity is evaluated through finite element methods employing the Newton-Raphson algorithm. However, the Newton-Raphson algorithm cannot track the structural equilibrium path after the first critical wind speeds (zero stiffness point) and the potential post-buckling multi-stability. This study proposes to use the arc-length method to calculate the aerostatic structural deformation for increasing wind speeds iteratively. Arc-length can track the equilibrium force-deformation curve even after the initial critical wind speeds. This study finds out that when the pitch moment curve of the bridge deck has a” turning point” at a large angle of attack, there is possibly more than one equilibrium point (multi-stability) for the same wind speeds. Correspondingly, the bridge deck deformation shape and cable and hangers’ internal force along span direction change dramatically at the same wind speed due to aerostatic multi-stability. In the last part of this study, the bridge structure under a turbulent wind field can buckle at a lower wind speed than a smooth wind field because the material yields are caused by large instantaneous deformation.