Cfd numerical computational method for flutter responses of long-span bridges in nonlinear geometric stiffness conditions

A CFD numerical computational method for flutter responses of long-span bridges in nonlinear geometric stiffness conditions, implemented by the following steps:

• step 1:
• establishing a three-dimensional finite element model of a bridge, and establishing a nonlinear geometric stiffness model based on computational analysis;
• and specifically:
• establishing a functional relation between lateral geometric stiffness Kx(x,t) and lateral displacement x(t), a functional relation between vertical geometric stiffness Ky(y,t) and vertical displacement y(t), and a functional relation between torsional geometric stiffness Kα(α,t) and torsional displacement α(t) of the bridge;
• step 2:
• determining dynamic parameters of a bridge girder, including equivalent mass, moment of inertia and natural frequency, and determining geometric scale ratio, vibration frequency ratio and wind velocity ratio of a girder rigid model;
• step 3:
• establishing coupling motion equations of lateral, vertical and torsional degrees of freedom of the girder rigid model in a wind field;
• and during the motion of the bridge girder, dynamically adjusting the lateral geometric stiffness Kx(x,t), the vertical geometric stiffness Ky(y,t) and the torsional geometric stiffness Kα(α,t) with changes in time and displacements;
• step 4:
• constructing a state equation to provide a computational basis for subsequent numerical integration solution and real-time update of the geometric stiffnesses varying with displacements;
• step 5:
• establishing a geometric model of the bridge girder, determining the size and boundary conditions of a flow field computational domain, dividing flow field meshes, and reading the aerodynamic forces acting on the bridge girder and the probe position of a flow field in each flow field mesh cell;
• step 6:
• importing the flow field meshes divided in step 5 into Fluent software, and embedding the state equation of nonlinear dynamic behaviors of the bridge girder and the nonlinear geometric stiffness model into the solver of the Fluent software by user defined functions (UDF) to achieve fluid-structure interaction (FSI) solution of the bridge girder and the wind field;
• step 7:
• at the initial stage of computation, keeping the bridge girder in a stationary state to ensure that the flow field is fully developed and reaches a stable distribution;
• subsequently, applying an initial displacement excitation to the bridge girder as an initial condition of a free vibration stage;
• and in the free vibration stage, repeating step 6 for the bridge girder at each time step to solve the nonlinear flutter response time history of the bridge girder after excitation, thus to achieve numerical analysis of wind-induced flutter characteristics of the nonlinear geometric stiffnesses of the bridge.