Aerostatic Stability and Bifurcation for Long-Span Bridges Based on Reduced Order Modeling via Singular Value Decomposition

Abstract

The traditional nonlinear aerostatic instability of long-span bridges is based on a two-layer iteration method that accurately predicts the structural equilibrium path before the critical buckling point. Due to strong nonlinearity after buckling, this traditional method cannot easily calculate the structural equilibrium and possible bifurcation using either Newton–Raphson or arc-length methods. In this study, a reduced order modeling (ROM) method for long-span bridge aerostatic deformation is proposed to approximate the bridge aerostatic equilibrium path after the critical point. The structural deformation mode shapes are extracted through singular value decomposition performed on the deformation matrix, and the nonlinear structural stiffness matrix is determined through the indirect displacement-based method on the finite-element method (FEM) platform. The ROM method is validated through comparison against the aerostatic deformation by the traditional two-layer iteration method based on FEM. By extending to higher wind speed, the ROM method can approximate the bridge deformation after initial buckling, and pitchfork bifurcation is observed after the structure undergoes rapid deformation growth. The stability of the equilibrium paths is examined through the Jacobian of restoring force vector, and the “snap-through” phenomenon exists for the equilibrium path before the bifurcation point.