CFD numerical calculation method for flutter response of long-span bridges under nonlinear geometric stiffness conditions

Abstract

The present application belongs to the technical field of bridge wind vibration analysis, and discloses a flutter response CFD numerical calculation method under the condition of nonlinear geometric stiffness of large-span bridge. In view of the problem that the existing response CFD numerical calculation method all assumes constant structure geometric stiffness, and it is difficult to accurately simulate the flutter response of super-long-span bridge under large static wind displacement and large amplitude, a flutter response CFD numerical calculation method under the condition of nonlinear geometric stiffness of large-span bridge is provided. The method real-time embeds nonlinear geometric stiffness into the main beam motion equation, and carries out fluid-structure coupling calculation with the flow field, realizes the dynamic correlation of the main beam displacement and the geometric stiffness, and high-precision solves the nonlinear flutter response of the bridge under wind-induced excitation. Compared with the traditional CFD simulation constant geometric stiffness assumption, the calculation mode is more reasonable and the precision is higher; compared with the wind tunnel test, the present application can flexibly regulate and control the geometric nonlinear stiffness parameters of any form without complex nonlinear simulation device.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge wind-induced vibration analysis, and relates to the fluid-structure coupling of a bridge main beam and a wind field, structural geometric stiffness nonlinearity, and a flutter stability analysis method of aerodynamic nonlinearity, in particular to a bridge wind-induced nonlinear flutter dynamic response CFD calculation method considering that the structural geometric stiffness changes with displacement. BACKGROUND

[0002] The existing flutter analysis of long-span bridges generally considers that the geometric stiffness of the structure remains unchanged during vibration, which has certain applicability under small displacement and amplitude conditions. However, when the bridge structure is subjected to strong wind excitation to generate large static wind displacement and amplitude, the geometric stiffness of the structure is no longer constant. If a constant stiffness model is still used, it will be difficult to accurately simulate the actual flutter critical wind speed and aerodynamic response of the bridge structure.

[0003] The existing computational fluid dynamics (CFD) method for studying bridge flutter response is based on the assumption of constant geometric stiffness, which does not conform to the actual geometric stiffness nonlinearity. This simulation method meets the engineering requirements for small-span bridges and hard flutter precision, but for super-long-span flexible bridges that generate very large static wind displacement and amplitude, the simulation error is unacceptable.

[0004] Therefore, the application proposes to consider the change of geometric stiffness with displacement in CFD flutter calculation, introduce relevant nonlinear stiffness characteristics, realize the real-time correlation of structural geometric stiffness and displacement, and truly simulate the wind-induced large displacement and large amplitude vibration behavior of the bridge structure. Compared with the traditional constant geometric stiffness assumption, this method can describe the influence of the softening or hardening effect of the structural geometric stiffness on the vibration frequency, response amplitude and stability boundary, thereby improving the accuracy of the flutter analysis results. SUMMARY

[0005] The application proposes a flutter CFD numerical calculation method under the condition of simulating the non-constant geometric stiffness of long-span bridges. This method introduces the nonlinear characteristics of the change of structural geometric stiffness with displacement in bridge wind-induced flutter numerical calculation, which can truly reflect the change law of the overall geometric stiffness of the structure with displacement compared with the traditional simulation method assuming that the geometric stiffness is constant, and is close to the real dynamic characteristics of the bridge, providing a more reliable and accurate numerical analysis means for bridge flutter mechanism research and wind-resistant design.

[0006] The technical scheme of the application is as follows:

[0007] A flutter response CFD numerical calculation method under the condition of nonlinear geometric stiffness of long-span bridges, taking two-dimensional simulation as an example, the steps are as follows:

[0008] Step one: Establish the three-dimensional finite element model of the bridge, and based on the calculation and analysis, establish the nonlinear geometric stiffness model, specifically: Establish the lateral bending geometric stiffness K x (x,t) and the function relationship of the lateral bending displacement x(t), the vertical bending geometric stiffness K y (y,t) and the function relationship of the vertical bending displacement y(t), the torsional geometric stiffness K α (α,t) and the function relationship of the torsional displacement α(t);

[0009] Step two: Determine the dynamic parameters of the bridge girder, including equivalent mass, moment of inertia and natural frequency, determine the geometric scale ratio, vibration frequency ratio and wind speed ratio of the rigid model of the main girder;

[0010] Step three: Establish the lateral bending, vertical bending and torsional free degree coupling motion equation of the rigid model of the main girder in the wind field; During the movement of the bridge girder, the lateral bending geometric stiffness K x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsional geometric stiffness K α (α,t) dynamically adjust with time and displacement changes;

[0011] Step four: Construct the state equation to provide the calculation basis for subsequent numerical integral solution and real-time updating of the geometric stiffness with displacement changes;

[0012] Step five: Establish the geometric model of the bridge girder, determine the calculation domain size and boundary conditions of the flow field, divide the flow field grid, and read the aerodynamic force acting on the bridge girder and the probe position of the flow field in each flow field grid unit;

[0013] Step six: Import the flow field grid divided in step five into Fluent software, embed the state equation and nonlinear geometric stiffness model of the nonlinear dynamic behavior of the bridge girder into the Fluent software solver using user-defined functions (User Defined Functions, UDF), and realize the fluid-structure coupling solution of the bridge girder and the wind field;

[0014] The specific process is as follows:

[0015] 1) At the beginning of each time step, the lateral bending geometric stiffness K x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsional geometric stiffness K α (α,t) are calculated according to the displacement and velocity of the bridge girder at the current time t, the state equation (13) is updated, and the updated lateral bending displacement, vertical bending displacement and torsional displacement of the bridge are read to realize the real-time change of the nonlinear geometric stiffness with displacement;

[0016] 2) The state equation of the bridge girder is solved using the updated lateral bending geometric stiffness, vertical bending geometric stiffness, torsional geometric stiffness and aerodynamic force, and the fourth-order Runge-Kutta method is used to perform time-domain promotion on the displacement and velocity;

[0017] 3) The position of the bridge girder is updated and the wind field calculation domain grid is automatically adjusted to maintain the consistency of the fluid-structure coupling;

[0018] Step seven: At the beginning of the calculation, the bridge girder is kept in a static state to ensure that the flow field is fully developed and reaches a stable distribution; then an initial displacement excitation is applied to the bridge girder as the initial condition of the free vibration stage; in the free vibration stage, the bridge girder repeatedly performs step six in each time step to solve the nonlinear flutter response time history of the bridge girder after excitation, and the wind-induced flutter characteristics of the bridge geometric stiffness nonlinearity are numerically analyzed.

[0019] Further, step three: the lateral bending, vertical bending and torsional free degree coupling motion equation of the rigid model of the main girder in the wind field is established, which is expressed as:

[0020] (1)

[0021] (2)

[0022] (3)

[0023] In the formula, m and I are the equivalent mass and moment of inertia of the main girder rigid model respectively; x(t), y(t) and a(t) are the lateral bending displacement, vertical bending displacement and torsional displacement respectively; 、 、 are the lateral bending velocity, vertical bending velocity and torsional angular velocity respectively; 、 、 are the lateral bending acceleration, vertical bending acceleration and torsional angular acceleration respectively; F x (t), F y (t) and M(t) are the aerodynamic force in the lateral bending, vertical bending and torsional direction respectively; C x0 , C y0 , C α0 are the damping coefficients in the lateral bending, vertical bending and torsional direction respectively; K x0 , K y0 , K α0 are the reference stiffness in the lateral bending, vertical bending and torsional direction respectively; the expressions are as follows:

[0024] (4)

[0025] (5)

[0026] (6)

[0027] (7)

[0028] (8)

[0029] (9)

[0030] where ω x0 , ω y0 , ω α0 are the natural frequencies of lateral bending, vertical bending and torsion respectively; ξ x0 , ξ y0 , ξ α0 are the mechanical damping ratios of lateral bending, vertical bending and torsion respectively;

[0031] The lateral bending geometric stiffness K x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsion geometric stiffness K α (α,t) of the bridge girder dynamically adjust with time and displacement during the motion of the bridge girder;

[0032] The lateral bending displacement x(t), the vertical bending displacement y(t) and the torsion displacement α(t) are calculated in real time in the user-defined function (UDF), and the lateral bending geometric stiffness K x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsion geometric stiffness K α (α,t) are dynamically updated, so as to realize real-time adjustment of the geometric stiffness with displacement;

[0033] The reference stiffnesses K x0 , K y0 and K α0 of the lateral bending, the vertical bending and the torsion in the formula (1), the formula (2) and the formula (3) are replaced by the nonlinear lateral bending geometric stiffness K x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsion geometric stiffness K α (α,t) considering the change of the geometric stiffness with time and displacement, and the formula (1), the formula (2) and the formula (3) are arranged as follows:

[0034] (10)

[0035] (11)

[0036] (12)

[0037] Further, the specific method of constructing the state equation in step four is as follows:

[0038] Let =[x(t),y(t),α(t), , , ] T That is, the second-order differential equations (10), (11) and (12) are arranged into the following first-order differential equation form:

[0039] (13)

[0040] Equation (13) is a state equation describing the nonlinear dynamic behavior of the bridge girder in the wind field; in the numerical simulation process, when the aerodynamic force and aerodynamic torque acting on the bridge girder at each time step are obtained, the time-domain evolution of the system state is solved based on the state equation using the fourth-order Runge-Kutta numerical integration algorithm, and the displacement response x(t), y(t), α(t) and velocity response 、 、 of the bridge girder under wind-induced excitation are obtained.

[0041] Further, the calculation domain used in step five is a rectangular wind field region set around the bridge girder, and the boundary conditions are set, including setting a velocity inlet boundary, setting a pressure outlet boundary, setting the upper and lower boundaries of the calculation domain as symmetric boundary conditions, and setting the surface of the bridge girder as a no-slip wall boundary, to ensure the physical closure of the flow field solution; the grid of the calculation domain adopts a grid structure containing a near-wall encryption boundary layer region and a dynamic grid region whose position or shape is updated with the movement of the bridge girder, to ensure that the changes in the flow field caused by the movement of the bridge girder can be effectively captured; the update of the dynamic grid region is realized by the grid fairing method; the above parameter settings are adjustable, and can be reasonably selected and corrected according to the characteristics of the bridge structure, the wind field conditions and the calculation accuracy requirements.

[0042] In practical applications, the method of the present application can use both a two-dimensional rigid girder model and a three-dimensional rigid girder model to carry out CFD numerical simulation. Compared with the two-dimensional case, three-dimensional calculation needs to construct a three-dimensional calculation domain containing the length direction of the girder, and arrange the grid in the axial direction of the girder, while setting the corresponding three-dimensional boundary conditions and turbulence models, and combining three-dimensional dynamic grid technology to realize real-time update of the spatial movement of the girder. Due to the need to handle larger-scale grids and more complex flow structures, the calculation amount and resource demand of three-dimensional simulation are significantly higher than that of the two-dimensional case.

[0043] The beneficial effects of the present application: compared with the traditional CFD calculation method based on the assumption of constant geometric stiffness, the present application has the following beneficial effects: ① Realize the adjustment of geometric stiffness under fluid-structure coupling with displacement dynamics, which can more truly reflect the actual nonlinear dynamic characteristics of the bridge structure and improve the accuracy of the flutter analysis; ② Compared with the wind tunnel test method, the present application method can flexibly regulate and control the geometric nonlinear stiffness parameters of any form without complex nonlinear simulation devices. ③ It has wide engineering applicability, which can not only be used for post-flutter analysis of bridges, but also can be extended to other engineering wind-induced response analysis with obvious geometric stiffness nonlinearity. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The method flow of the embodiment of the present application.

[0045] Figure 2 The mechanical model diagram of the main beam system in the wind field in the embodiment of the present application.

[0046] Figure 3 The main beam model diagram of the embodiment of the present application.

[0047] Figure 4 The wind field calculation domain and boundary condition diagram of the embodiment of the present application.

[0048] Figure 5 The wind field calculation domain flow field grid division diagram of the embodiment of the present application: (a) the overall region of the calculation domain; (b) the main beam and its surrounding region; (c) the central guardrail of the bridge; (d) the side guardrail of the bridge; (e) the wind nozzle.

[0049] Figure 6 The main beam vibration numerical simulation process diagram of the embodiment of the present application.

[0050] Figure 7 The vertical bending flutter displacement time history curve diagram of the constant geometric stiffness main beam and the displacement-varying geometric stiffness main beam in the embodiment of the present application.

[0051] Figure 8 The torsional flutter displacement time history curve diagram of the constant geometric stiffness main beam and the displacement-varying geometric stiffness main beam in the embodiment of the present application. DETAILED DESCRIPTION

[0052] The specific embodiments of the present application are further described below in combination with the drawings and technical solutions.

[0053] Embodiment

[0054] For the two-dimensional streamline section main beam, the model parameters are: the main beam width is 0.2485m, the scale ratio with the actual bridge is 1:200, m = 1.07696kg / m, I = 0.00645kg·m 2 / m, ωy0 = 1.42Hz, ω α0 = 3.14Hz, ξ y0 = 0.002, ξ α0 = 0.002. Since the sensitivity of the bridge in this embodiment to the change of the lateral bending stiffness under the action of wind is low, the influence on the overall flutter characteristics is limited, therefore, the nonlinear analysis of the lateral bending stiffness is not carried out in this embodiment, only the nonlinear vertical bending and torsional geometric stiffness are considered. The nonlinear vertical bending and torsional geometric stiffness K y (y, t), K α (α, t) are respectively represented as:

[0055] (10)

[0056] (11)

[0057] In the formula, β y , β α is a nonlinear coefficient for regulating the change of the geometric stiffness with the vertical displacement and the torsional displacement; y ref is a reference vertical bending displacement, α ref is a reference torsional angle; n y , n α is a nonlinear order, in this embodiment, n y = 1, n α = 2. The above form is only used for illustration in this embodiment, in actual engineering, other mathematical forms or fitting functions can also be used to represent the change characteristics of the geometric stiffness of the structure with the vibration response, so as to meet the design requirements of different bridge structures. In order to facilitate the illustration, two different working conditions are designed in this embodiment, and the geometric stiffness nonlinear parameter settings are shown in Table 1:

[0058] Table 1 Geometric stiffness nonlinear parameter working condition setting

[0059]

[0060] The flutter response of the bridge girder under different conditions is obtained by using the method of the present application, and the flowchart is shown in Figure 1 , and the specific operation steps are as follows:

[0061] Step 1: Establish a three-dimensional finite element model of a two-dimensional streamline section girder, analyze the geometric stiffness characteristics of the bridge girder in the vertical and torsional directions, and determine the overall law of the change of the stiffness with the displacement and the angle.

[0062] Step 2: Determine the dynamic parameters of the bridge girder, including the equivalent mass, the moment of inertia and the natural frequency, determine the geometric scale ratio, the vibration frequency ratio and the wind speed ratio of the rigid model of the girder.

[0063] Step three: Establish the vertical bending and torsion free degree coupling motion equation of the rigid model of the main beam in the wind field, wherein the geometric stiffness is no longer constant, but a function of displacement.

[0064] Step four: Build the state equation to convert the vertical bending and torsion second order motion equation into state space form for numerical integration solution, and provide calculation basis for real-time updating of nonlinear geometric stiffness varying with displacement.

[0065] Step five: Establish the calculation domain and boundary conditions of the two-dimensional streamline bridge two-dimensional model, as shown in Figure 4 The calculation domain is a two-dimensional rectangular wind field area, with a length of 3.75m in the flow direction and a length of 2.5m in the vertical direction. The origin of the coordinate system is located at one-third of the upstream of the flow domain, 1.25m away from the inlet, and 1.25m away from the bottom and top. The center of gravity of the two-dimensional streamline bridge two-dimensional model coincides with the origin, and the blockage rate is less than 1%. The left side of the calculation domain is set as the velocity inlet boundary, and the right side is set as the pressure outlet boundary. The upper and lower boundaries of the calculation domain are set as symmetric boundary conditions, and the surface of the main beam of the bridge is set as a no-slip wall boundary. The grid division of the wind field calculation domain includes three parts: the near-wall boundary layer region, the rigid dynamic grid region and the deformed dynamic grid region, as shown in Figure 5 The boundary layer region grid is divided into 25 layers, and the first layer grid height of the boundary layer region grid is set to 0.00005m, which increases layer by layer along the normal direction with an expansion rate of 1.1. Outside the boundary layer region grid, the dynamic grid region changes position with the movement of the main beam of the bridge and the boundary layer region grid; and outside the dynamic grid region, the dynamic grid region realizes the position and shape update of the grid with the movement of the structure through the grid smoothing algorithm. The Interface interface realizes the bidirectional transmission of velocity field and pressure field information between the regions.

[0066] Step six: Import the flow field grid divided in step five into Fluent software, embed the state equation and nonlinear geometric stiffness model of the nonlinear dynamics behavior of the bridge main beam into the Fluent software solver through user-defined function (UDF), and realize the fluid-structure coupling solution of the main beam and the wind field. The specific process is as follows: (1) At the beginning of each time step, the nonlinear vertical bending geometric stiffness K y (y, t) and the torsion geometric stiffness K α (α, t) of the bridge main beam are calculated according to the displacement and velocity of the bridge main beam at the current time t, the state equation is updated, and the vertical bending displacement and torsion displacement of the bridge main beam at the current time t are read; according to the read vertical bending displacement and torsion displacement of the bridge main beam at the current time, the nonlinear vertical bending geometric stiffness K y (y, t) and the torsion geometric stiffness K α(α, t) calculates the effective stiffness of vertical bending and torsional freedom, and realizes the real-time change of nonlinear geometric stiffness with displacement; (3) using the updated nonlinear geometric stiffness, aerodynamic force F y (t), aerodynamic moment M(t) to solve the state equation of the nonlinear dynamic behavior of the bridge girder, and to use the fourth-order Runge-Kutta method to carry out time-domain promotion on displacement and velocity to obtain the displacement and velocity response of the bridge girder at the current time step. The updated bridge girder position is fed back to the wind field calculation domain through the dynamic mesh method, and the smoothing algorithm based on the diffusion equation is used for mesh updating, in which the displacement of the mesh node is inversely proportional to the 1.5 power of the nearest distance from the mesh node to the surface of the main beam, so as to maintain the grid quality and numerical stability.

[0067] Step seven: At the beginning of the calculation, the main beam is kept in an approximately static state to ensure that the incoming flow field is fully developed and reaches a stable distribution. Then, an initial excitation (torsional angle 2°) is applied to the main beam, and after the excitation is completed, the structure free vibration response is solved by repeating step six. As the calculation proceeds, the vertical and torsional displacement time histories of the main beam under the condition of nonlinear geometric stiffness can be obtained. Figure 7 and Figure 8 Comparing the vertical bending and torsional flutter displacement time histories of the constant stiffness main beam and the main beam using different nonlinear geometric stiffness functions at a wind speed of 5.9 m / s, it can be seen that the nonlinear geometric stiffness has a significant influence on the model response amplitude and the flutter critical wind speed.

[0068] The protection scope of the present application is not limited to the above-mentioned embodiments. For those skilled in the art, equivalent replacement, improvement or deformation of part of the technical features according to the disclosed technical content of the present application can be made without departing from the technical concept of the present application, and these equivalent replacement, improvement or deformation should be considered to fall within the protection scope of the present application.

Claims

1. A CFD numerical calculation method for flutter response of a long-span bridge under a nonlinear geometric stiffness condition, characterized in that, The following steps are taken: Step one: establish the three-dimensional finite element model of the bridge, and based on the calculation and analysis, establish the nonlinear geometric stiffness model, specifically: establish the lateral bending geometric stiffness K x (x,t) and the function relationship of lateral bending displacement x(t), vertical bending geometric stiffness K y (y,t) and the function relationship of vertical bending displacement y(t), torsional geometric stiffness K α (α,t) and the function relationship of torsional displacement α(t); Step two: Determine the dynamic parameters of the bridge girder, including equivalent mass, moment of inertia and natural frequency, determine the geometric scale ratio, vibration frequency ratio and wind speed ratio of the rigid model of the main girder; Step three: Establish the side bending, vertical bending and torsion free degree coupling motion equation of the rigid model of the main beam in the wind field; the side bending geometric stiffness K x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsion geometric stiffness K α (α,t) dynamically adjust with time and displacement changes; Step four: Construct the state equation, which provides the calculation basis for subsequent numerical integration and real-time updating of the geometric stiffness with displacement changes; Step five: Establish the geometric model of the bridge girder, determine the size of the calculation domain and the boundary conditions of the flow field, divide the flow field grid, and read the aerodynamic force acting on the bridge girder and the probe position in each flow field grid element; Step six: Import the flow field grid divided in step five into Fluent software, use user-defined function UDF to embed the state equation and nonlinear geometric stiffness model of the nonlinear dynamic behavior of the bridge girder into the Fluent software solver, and realize the fluid-structure coupling solution of the bridge girder and the wind field; Step seven: At the beginning of the calculation, keep the bridge girder stationary to ensure that the flow field is fully developed and reaches a stable distribution; then apply an initial displacement excitation to the bridge girder as the initial condition of the free vibration stage; in the free vibration stage, the bridge girder repeats step six in each time step to solve the nonlinear flutter response time history of the bridge girder after excitation, and realize the numerical analysis of the wind-induced flutter characteristics of the bridge geometric stiffness nonlinearity.

2. The flutter response CFD numerical calculation method for long-span bridges under nonlinear geometric stiffness conditions according to claim 1, characterized in that, Step three: Establish the lateral bending, vertical bending and torsional free degree coupling motion equation of the rigid model of the main girder in the wind field, which is expressed as: (1) (2) (3) In the formula, m, I are the equivalent mass and moment of inertia of the main beam rigid model respectively; x(t), y(t), a(t) are the lateral bending displacement, vertical bending displacement and torsional displacement respectively; 、 、 are the lateral bending velocity, vertical bending velocity and torsional angular velocity respectively; 、 、 are the lateral bending acceleration, vertical bending acceleration and torsional angular acceleration respectively; F x (t), F y (t), M(t) are the aerodynamic force in the lateral bending, vertical bending direction and the aerodynamic moment in the torsional direction respectively; C x0 , C y0 , C α0 are the damping coefficients in the lateral bending, vertical bending and torsional direction respectively; K x0 , K y0 , K α0 are the reference stiffness in the lateral bending, vertical bending and torsional direction respectively; the expressions are as follows: (4) (5) (6) (7) (8) (9) where ω x0 , ω y0 , and ω α0 are the natural frequencies of lateral bending, vertical bending, and torsion, respectively; and ξ x0 , ξ y0 , and ξ α0 are the mechanical damping ratios of lateral bending, vertical bending, and torsion, respectively. The lateral bending geometric stiffness K x (x, t), the vertical bending geometric stiffness K y (y, t), and the torsional geometric stiffness K α (α, t) are dynamically adjusted as a function of time and displacement. The lateral bending displacement x(t), the vertical bending displacement y(t) and the torsional displacement a(t) are calculated in real time in a user-defined function (UDF), and the lateral bending geometric stiffness K is dynamically updated x (x,t), the vertical bending geometric stiffness K y (y,t) and the torsional geometric stiffness K α (a,t) are dynamically updated, so that the real-time adjustment of the geometric stiffness with displacement is realized. The lateral, vertical and torsional stiffnesses K x0 , K y0 and K α0 in equations (1), (2) and (3) are replaced by the nonlinear lateral, vertical and torsional stiffnesses K x (x, t), K y (y, t) and K α (a, t) that take into account the time and displacement dependence of the geometric stiffnesses, and equations (1), (2) and (3) are rearranged as: (10) (11) (12)。 3. The flutter response CFD numerical calculation method for long-span bridges under nonlinear geometric stiffness conditions according to claim 2, characterized in that, Step four of constructing the state equation is as follows: Let = [x(t), y(t), a(t), , , ] T i.e., the second-order differential equations (10), (11), and (12) are arranged in the form of the following first-order differential equations: (13) Equation (13) is a state equation for describing the nonlinear dynamic behavior of the bridge girder in the wind field; in the numerical simulation process, after the aerodynamic force and aerodynamic torque acting on the bridge girder at each time step are obtained, the time-domain evolution solution of the system state is realized based on the state equation by using the fourth-order Runge-Kutta numerical integral algorithm, and the displacement responses x(t), y(t), a(t) and the velocity responses , , of the bridge girder under the wind-induced excitation are obtained.

4. The flutter response CFD numerical calculation method for long-span bridges under nonlinear geometric stiffness conditions according to claim 3, characterized in that, The specific implementation process of step five is as follows: The calculation domain used is a rectangular wind field area set around the bridge girder, and the boundary conditions are set, including setting the velocity inlet boundary, setting the pressure outlet boundary, setting the upper and lower boundaries of the calculation domain as symmetric boundary conditions, and setting the bridge girder surface as a no-slip wall boundary; The grid of the calculation domain uses a grid structure that includes a boundary layer region with near-wall encryption and a dynamic grid region that updates its position or shape with the movement of the bridge girder; The update of the dynamic grid region is realized by the grid smoothing method.

5. The flutter response CFD numerical calculation method for long-span bridges under nonlinear geometric stiffness conditions according to claim 4, characterized in that, The specific implementation process of step six is as follows: 1) At the beginning of each time step, the lateral geometric stiffness K x (x,t), the vertical geometric stiffness K y (y,t) and the torsional geometric stiffness K α (α,t) are calculated according to the current displacement and velocity of the bridge main beam at time t, the state equation (13) is updated, and the updated lateral displacement, vertical displacement and torsional displacement of the bridge are read to realize the real-time change of the nonlinear geometric stiffness with displacement. 2) Use the updated lateral bending geometric stiffness, vertical bending geometric stiffness and torsional geometric stiffness and aerodynamic force to solve the state equation of the bridge girder, and use the fourth-order Runge-Kutta method to perform time-domain advancement on displacement and velocity; 3) Update the position of the bridge girder and automatically adjust the grid of the wind field calculation domain to maintain the consistency of fluid-structure coupling.

Images