Light high-strength orthogonal isotropic steel bridge deck structure and parameter optimization method thereof

Abstract

The invention discloses a light high-strength orthogonal isotropic steel bridge deck structure and a parameter optimization method thereof, and belongs to the technical field of bridge engineering, the structure comprises a top layer steel plate, a lower layer steel plate, longitudinal plate ribs, a diaphragm plate and a diaphragm plate bottom plate, and the longitudinal plate ribs and the diaphragm plate are separated to form closed plate grid cavities. A flexible transition rib array composed of a plurality of independent ribs is arranged in the bridge direction in an opening area formed when a transverse partition plate penetrates through longitudinal plate ribs and is located below a top-layer steel plate, and a response surface model is coupled according to a preset multi-parameter. Through finite element analysis, Latin hypercube sampling, Kriging agent model construction and multi-target genetic algorithm global optimization, inversion optimization from a preset performance target to an optimal geometric parameter combination of each flexible transition rib is realized, the fatigue performance at the opening of the diaphragm plate is improved, and meanwhile, the lightweight and economical efficiency of the structure are realized.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically relating to a lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method. Background Technology

[0002] Orthotropic steel bridge decks (also known as orthotropic steel bridge decks) are a highly efficient structural form that integrates load-bearing and force transmission functions. With their significant advantages such as lightweight and high strength, clearly defined stress distribution, high degree of factory manufacturing, and large span capacity, they have become the preferred bridge deck structure for modern long-span bridges, especially steel box girder bridges. Their typical structure usually consists of a top plate, longitudinal U-shaped or trapezoidal ribs, and transversely arranged diaphragms, forming a plate-rib combination system with varying longitudinal and transverse stiffness.

[0003] However, the inherent structural characteristics of this type of structure also bring about significant mechanical problems. The diaphragms, which are openings through the longitudinal ribs, are the weakest points in the entire structure. Under the repeated loads of vehicles, the sudden interruption of this structural feature causes drastic changes in stiffness, resulting in high stress concentrations at the opening edges, especially at the angles where the top plate connects to the diaphragm. These localized stress peaks are often several times higher than the nominal stress of the bridge deck, becoming the initiation point for fatigue cracks. Extensive engineering practice and research have shown that the vast majority of fatigue cracks in orthotropic steel bridge decks originate around the openings in the diaphragms, seriously threatening the safe operation and durability of the structure, and sometimes even requiring costly repairs and reinforcements, disrupting traffic.

[0004] To address this technical challenge, scholars and engineers both domestically and internationally have proposed various improvement measures. Traditional methods mainly include locally increasing the thickness of the top plate or diaphragm, welding reinforcing rings or plates to the opening edges, and optimizing the geometry of the opening (such as using large-radius circular arc transitions). These methods improve stress distribution to some extent, but often have limitations: simply increasing the plate thickness significantly increases the structural self-weight and material costs, contradicting economic objectives; welding reinforcing rings and other additional components may introduce new welding hotspots and stress concentration points, posing a risk of "sacrificing one aspect for another"; and the effect of shape optimization has an upper limit, making it difficult to fundamentally solve the core contradiction of abrupt stiffness changes. In addition, these methods largely rely on engineers' experience and a large number of "trial and error" finite element analyses, resulting in long design cycles, low efficiency, and difficulty in systematically finding the global optimal solution. There is a lack of a scientific design method and corresponding refined structural form that can coordinate the complex relationship between smooth stiffness transition, effective stress control, and material economy.

[0005] Therefore, there is a need in this field for an innovative steel bridge deck structure and its corresponding optimization methods to improve the fatigue resistance and service life of orthotropic steel bridge decks. Summary of the Invention

[0006] To overcome the aforementioned deficiencies of existing technologies, this invention provides a lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method. By innovatively setting a flexible transition rib array 6 with gradually changing geometric parameters in the opening area of ​​the diaphragm 4, a gradually increasing stiffness band is constructed along the bridge direction. Combined with an intelligent inversion optimization method based on a multi-parameter coupled response surface model and a multi-objective genetic algorithm, the optimization from structural performance objectives to the optimal combination of geometric parameters is achieved, thereby reducing stress concentration at the opening edge, suppressing the generation of fatigue cracks, and ensuring structural safety and durability while taking into account the lightweight and economical use of materials.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A lightweight, high-strength orthotropic steel bridge deck structure includes a top steel plate 1, a lower steel plate 2 parallel to the top steel plate, multiple longitudinal ribs 3 disposed between the two steel plates, and transverse diaphragms 4 spaced apart along the bridge direction. A transverse diaphragm bottom plate 5 is provided below the transverse diaphragms. The longitudinal ribs 3 and the transverse diaphragms 4 separate to form closed plate-grid chambers 7. When the transverse diaphragms 4 pass through the longitudinal ribs 3 and form an opening area below the top steel plate 1, a flexible transition rib array 6 composed of multiple independent ribs is arranged along the bridge direction within the opening area. Each flexible transition rib includes, in sequence, a rib that is connected to the lower surface of the top steel plate 1. The upper bonding section, the transition section between the two bonding sections, and the side bonding section that is bonded to the side of the transverse diaphragm 4 are all bonded together. The transition section is arched or zigzag-shaped. The flexible transition rib array 6 is set along the bridge direction from the end away from the transverse diaphragm 4 to the end closer to the transverse diaphragm 4. The plate thickness increases step by step, the arch height of the transition section decreases step by step, and the bonding length of the upper bonding section and the side bonding section increases step by step. This forms a progressive stiffness band with gradually increasing equivalent vertical stiffness along the bridge direction in the opening area, so that the local deflection of the top steel plate 1 is smoothly transferred from the continuous plate area to the transverse diaphragm 4, thereby reducing the concentration of principal tensile stress at the opening edge.

[0009] A lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method, based on a pre-constructed multi-parameter coupled response surface model, includes the following steps:

[0010] Step 1: Establish a local finite element reference model including the opening and surrounding components, and analyze and obtain the maximum principal tensile stress and vertical equivalent stiffness at the opening when no flexible transition rib is set as reference values.

[0011] Step 2: Determine the target principal tensile stress and target vertical stiffness at the opening based on the bridge design parameters, and then obtain the required stiffness increment to compensate.

[0012] Step 3: Within the bridge-direction installation length of the opening, decompose the total stiffness increment into multiple sub-target stiffnesses according to the preset stiffness distribution function.

[0013] Step 4: Input the stiffness of each sub-target and its preset installation position in the bridge direction into the multi-parameter coupled response surface model to define the four-dimensional geometric parameter space of the target. Use Latin hypercube sampling technology to generate representative training samples in the parameter space. Obtain the stiffness contribution value and maximum equivalent stress of each sample through parametric finite element simulation to form a training dataset. Use Kriging method to establish stiffness contribution prediction model and stress prediction model respectively. In the inversion calculation, use a multi-objective genetic algorithm to perform global optimization in the parameter feasible region, with the goals of stiffness matching error less than 5%, minimum equivalent stress of transition ribs, and minimum material volume, and automatically output the optimal geometric parameter combination for each flexible transition rib.

[0014] Step 5: Input the results into the multi-parameter coupled response surface model for verification analysis. If the actual stress at the opening does not reach the target, adjust the sub-target stiffness of the middle transition rib and recalculate.

[0015] As a further aspect of the present invention, in step one, the local finite element model adopts shell elements, and the mesh is refined at the edge of the diaphragm opening and in the area where the diaphragm connects to the top steel plate.

[0016] As a further aspect of the present invention, in step one, the vertical equivalent stiffness is obtained by calculating the ratio of the sum of the vertical reaction forces of the nodes of the opening control section to the average vertical displacement.

[0017] As a further aspect of the present invention, in step three, the stiffness distribution function is a linear function, an exponential function, or a nonlinear function with intermediate weights.

[0018] As a further aspect of the present invention, in step four, the multi-parameter coupled response surface model is constructed using a Kriging surrogate model or a radial basis function neural network, based on sampling and finite element analysis data of the geometric parameter space of the flexible transition rib.

[0019] As a further aspect of the present invention, when performing inversion calculations using the multi-parameter coupled response surface model, the optimization algorithm employed is a multi-objective genetic algorithm, whose optimization objectives include satisfying stiffness requirements, minimizing the stress of the transition rib itself, and minimizing the material volume.

[0020] As a further aspect of the present invention, in step five, if adjustment is required, the sub-target stiffness of the flexible transition rib located in the middle third region of the stiffness gradient zone is adjusted first.

[0021] As a further aspect of the present invention, in the load analysis of step one, the longitudinal load arrangement of the bridge includes at least the two most unfavorable conditions: the wheels being located directly above the opening of the diaphragm and the mid-span area adjacent to the opening.

[0022] This invention constructs and applies a highly integrated multi-parameter coupled response surface model. This model, through systematic sample sampling and high-precision surrogate model technology, combines the complex mapping relationship between multiple geometric parameters (plate thickness, arc height, and fitting length) of the flexible transition rib and its key mechanical properties (stiffness contribution and self-stress). Based on this, combined with a multi-objective genetic algorithm, it realizes the automatic and rapid inversion from the preset structural performance objectives (sub-objective stiffness, low stress, and lightweight) to the optimal combination of geometric parameters.

[0023] The technical effects and advantages of this invention, which describes a lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method, are as follows: By setting a flexible transition rib array 6 in the opening area of ​​the diaphragm 4, a progressively increasing stiffness band is formed along the bridge direction, effectively dispersing and transferring stress caused by local loads, significantly reducing the peak value of principal tensile stress at the opening edge, and extending the fatigue life of the structure; the geometric parameters of the flexible transition ribs change gradually along the bridge direction, achieving a smooth transition of stiffness from the continuous plate area to the diaphragm 4, avoiding local stress concentration caused by abrupt stiffness changes; under the premise of ensuring stiffness and strength, the optimal material distribution is achieved by optimizing the geometric parameters of the flexible transition ribs, effectively controlling the structural self-weight and meeting the design requirements of lightweight and high strength; based on a multi-parameter coupled response surface model and a multi-objective genetic algorithm, the inverse optimization from performance objectives to optimal geometric parameters is realized, greatly improving design efficiency and accuracy, and avoiding the subjectivity and blindness of traditional trial calculation methods; under the premise of meeting structural performance, the manufacturing cost is reduced by optimizing material usage, resulting in good economic benefits. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the overall structure of the flexible transition rib steel bridge deck of the present invention;

[0025] Figure 2 This is an enlarged schematic diagram of the flexible transition rib array at the opening of the transverse diaphragm of the present invention;

[0026] Figure 3 This is the segmental local finite element analysis model of the present invention;

[0027] Figure 4 This is a schematic diagram of two transverse load arrangements for the present invention;

[0028] Figure 5 This is a schematic diagram of the longitudinal load arrangement of the bridge.

[0029] Figure 6 A schematic diagram of Pareto front optimization for multi-objectives.

[0030] In the diagram: Top steel plate 1, bottom steel plate 2, longitudinal ribs 3, transverse diaphragms 4, bottom plate of transverse diaphragms 5, flexible transition rib array 6, closed plate grid chamber 7. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Example 1

[0033] This embodiment is as follows: Figure 1 Based on a lightweight, high-strength orthotropic steel bridge deck structure, the top steel plate 1 and the lower steel plate 2 are arranged in parallel, with equally spaced longitudinal ribs 3 forming closed plate-grid chambers 7 along the bridge direction between them. Transverse diaphragms 4 are arranged along the bridge direction according to the engineering layout, and if necessary, a diaphragm base plate 5 is configured to form a transverse stiffness band. Where the diaphragm 4 passes through the longitudinal ribs 3, it forms an opening area on the underside of the top steel plate 1. The core component of this invention, the flexible transition rib array 6, is installed within this opening area and arranged along the bridge direction. Figure 2 As shown in the enlarged view, the array consists of multiple independent flexible transition ribs, which are welded to the lower surface of the top steel plate 1 and the side of the diaphragm 4. Ultimately, these transition ribs form a gradient zone in which the stiffness smoothly transitions from a continuous area of ​​the top steel plate 1 to the diaphragm 4, thereby smoothly transferring the local flexural stress caused by the vehicle load borne by the top plate.

[0034] like Figure 3 As shown, this embodiment first selects a representative local segment to establish a detailed finite element model. This segment should include a transverse diaphragm 4, the influence area of ​​longitudinal ribs 3 on each of its three spans, and the corresponding top steel plate 1 and bottom steel plate 2. The model is discretized using four-node or three-node shell elements. Without the flexible transition rib array 6, the specific geometric parameters of the model can be referenced as follows: the total length of the longitudinal bridge is 6 spans, each span is 3000mm long; the net width of the bridge deck is 4200mm. The thickness of the top steel plate 1 is 16mm, and the thickness of the bottom steel plate 2 is 14mm; the dimensions of the longitudinal ribs 3 are 10mm (thickness) × 120mm (height), with a center-to-center spacing of 350mm, totaling 12 ribs; the transverse diaphragm 4 is arranged according to the designed span.

[0035] The edges of openings and the roots of diaphragms are stress concentration areas. The mesh in these areas should be significantly refined. The principle of refinement is to ensure that the element size is no more than twice the thickness of the plate at that location. For example, at the edge of an opening in a 16mm thick top plate, the mesh size should be controlled below 32mm to ensure the accuracy of stress calculation.

[0036] The material parameters are set according to the actual properties of the steel. In this embodiment, the elastic modulus E = 2.10 × 10⁻⁶. 5MPa, Poisson's ratio ν = 0.30, the boundary conditions are usually set at the bottom plate 5 of the transverse diaphragm at both ends of the segment, restricting all translational and rotational degrees of freedom, in order to simulate the connection with the web of the main beam or other main load-bearing components, to ensure that the boundary effects of the local model are minimized and the mechanical behavior is consistent with the overall structure.

[0037] This embodiment uses standard vehicle wheel tracks for load assessment, with a single wheel static load of 70kN, a contact surface size of 200×600mm, and an equivalent surface pressure of 0.641MPa. The transverse bridge layout strictly follows the attached... Figure 4 (Load Arrangement 1, Load Arrangement 2): The center-to-center distance between the two wheels is 2000mm. For Load Arrangement 1, the margins from the outer edges of both sides to the edge of the slab are 750mm and 850mm respectively; for Load Arrangement 2, the corresponding margins are 925mm and 675mm. The two red rectangles represent wheel imprints. Static analysis is performed in the longitudinal direction by placing the two wheels directly above the opening of the transverse diaphragm 4 and in the most unfavorable position of its adjacent span to examine the lateral eccentric load effect. Meanwhile, the longitudinal direction is as shown in the attached diagram. Figure 5 As shown, two wheels were placed at two key positions: directly above the opening of the diaphragm and at the midpoint of its adjacent span, respectively, for loading. A linear static solution was performed on the above load condition using a finite element solver to obtain the displacement and stress fields of the structure. After the solution was completed, the first principal tensile stress was extracted from the lower surface of the shell element (SNEG) at the upper edge of the opening and the corner. The maximum principal tensile stress at the opening was obtained by nominalization.

[0038]

[0039] In the formula, σ0: the maximum principal tensile stress at the opening after nominalization, in megapascals (MPa); σ1: the first principal stress extracted from the lower surface of the shell element at the upper edge and corner of the opening in the finite element model, and the tensile stress component is selected, in megapascals (MPa). In this embodiment, σ0 = 215 MPa, and the vertical reaction force and vertical displacement of the nodes at the opening control section are summarized to define the equivalent vertical stiffness of the opening:

[0040]

[0041] In the formula, δ0 represents the vertical equivalent stiffness of the open region, measured in Newtons per millimeter (N / mm); ∑F z δ represents the sum of the vertical reactions at all selected nodes within the open control section under load, expressed in Newtons (N). z : This represents the average vertical displacement of the same group of nodes, in millimeters (mm). In this embodiment, k0 = 1.85 × 10 6 N / mm, where σ0 and δ0 are two indicators of the "original state".

[0042] The determination of the target principal tensile stress σ needs to be based on the durability requirements of the bridge. The design service life of this bridge is 100 years and the traffic level is heavy. According to the fatigue detail category of this opening structure detail in the bridge design code, and by applying Miner's linear cumulative damage theory to analyze the expected fatigue load spectrum, it is concluded that under the design load, in order to ensure sufficient fatigue life, the target principal tensile stress σ should be controlled within 150MPa.

[0043] In this embodiment, the target vertical stiffness K is determined based on the explicit inverse relationship between stress and stiffness in elasticity. Under constant load conditions, the structural stress σ and its stiffness K satisfy the proportional relationship σ∝1 / K. Based on the initial finite element analysis, the reference stress σ0 = 215 MPa and the reference stiffness k0 = 1.85 × 10⁻⁶ MPa are... 6 N / mm, and the set target stress σ=150MPa, through K=(σ0 / σ)×k0=(215 / 150)×1.85×10 6 The target stiffness K is calculated to be 2.65 × 10⁻⁶. 6 N / mm, thus obtaining the exact stiffness compensation amount ΔK=K-k0=0.80×10 6 N / mm.

[0044] Within the bridge-direction area of ​​the opening, an installation area with a length of L = 1200 mm is reserved according to the structural space. In this embodiment, a linear distribution function (i.e., an arithmetic progression) is used to divide the total stiffness increment ΔK into n = 6 parts on average. Then, the stiffness K of each sub-target is... i =ΔK / 6≈1.333×10 5 N / mm (i = 1 to 6), these 6 sub-target stiffnesses correspond to 6 flexible transition ribs, which will be arranged sequentially along the bridge direction, starting from the end closest to the continuous area of ​​the top steel plate 1 and ending at the end closest to the transverse diaphragm 4. Each rib is designed to bear the same share of stiffness increment, but due to their different positions, the overall equivalent stiffness formed by their combined action increases smoothly along the bridge direction, and the installation positions are evenly distributed within a length of 1200mm.

[0045] This invention discloses a lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method. It introduces a multi-parameter coupled response surface model, which is constructed based on a comprehensive analysis of four key geometric parameters of the flexible transition rib: plate thickness (t) 6-16 mm, arc height (h) 10-50 mm, and bonding length with the top steel plate 1 (L). t 80-200mm, length of contact with the transverse partition 4 (L) d For thicknesses of 80-200mm, 500 representative sample points are first generated in a four-dimensional parameter space using Latin hypercube sampling technology. Parametric finite element simulation is then performed on each sample point to obtain its stiffness contribution value (K). c) and its own maximum equivalent stress (σ r A complete training dataset was formed, and then a stiffness prediction model M was constructed using the Kriging surrogate model technique, which can instantly and accurately map geometric parameters to mechanical properties. K With stress prediction model M σ To verify the model's accuracy, 50 sets of validation samples that were not used in training were reserved. The determination coefficient R0 of the stiffness prediction model was verified. 2 The coefficient of determination R of the stress prediction model is 0.985. 2 The value of 0.972 indicates that the surrogate model has extremely high fitting accuracy to the real physical response, meeting the reliability requirements of engineering optimization design.

[0046] During the inversion calculation stage, for each sub-objective stiffness K i The algorithm employs a multi-objective genetic algorithm for computation. In this embodiment, the core parameters of the multi-objective genetic algorithm are set as follows: population size of 200, maximum number of iterations of 500 generations, crossover probability of 0.85, and mutation probability of 0.02. The algorithm initializes the population within the feasible domain of the geometric parameters and rapidly evaluates the predicted stiffness, predicted stress, and material volume of each individual using a multi-parameter coupled response surface model. With the common objectives of "highest stiffness matching accuracy," "minimum stress of the transition rib," and "minimal material volume," after hundreds of generations of selection, crossover, and mutation operations, it finally converges to the Pareto optimal solution set. The solution set that achieves the best balance between stiffness error (<5%), self-stress, and economy can be selected as the final geometric parameters of the rib.

[0047] Through inversion calculation, the multi-parameter coupled response surface model of this embodiment outputs the optimal parameter combination for the six transition ribs: the plate thickness from rib 1 to rib 6 presents an increasing sequence of 8mm, 9mm, 10mm, 11mm, 12mm, and 14mm; the arc height presents a decreasing sequence of 40mm, 35mm, 30mm, 25mm, 20mm, and 15mm; and the bonding length with the top steel plate 1 and the transverse partition 4 also increases accordingly.

[0048] The calculated geometric parameters were then matched one by one with the determined bridge-direction installation positions to obtain a complete list of flexible transition rib array processing and installation. The list clearly specifies the unique identifier of each rib, its plate thickness, arc height, bonding length with the top steel plate 1, bonding length with the transverse diaphragm 4, and its installation position in the bridge direction of the opening area.

[0049] The generated flexible transition rib array fabrication and installation list is updated into the established local segment finite element model. Then, the same load condition is applied again to this updated model. Figure 4 and Figure 5Static analysis was performed at the most unfavorable load locations 1 and 2 shown. After the analysis was completed, the actual maximum principal tensile stress σ at the opening was extracted. actual .

[0050] In the first verification of this embodiment, σ actual =158MPa. Although this value is significantly lower than the reference stress of 215MPa, it is still higher than the target value of 150MPa. This indicates that the initial design is close to but has not yet met the requirements, and fine-tuning is needed. Priority should be given to adjusting the sub-target stiffness K of the transition rib located in the middle of the stiffness gradient zone. i Because the central region is most sensitive to the smoothness of the stiffness gradient, we will use K for the two central ribs. i The values ​​were increased by approximately 10%, eliminating the need for tedious finite element recalculations. Simply input the adjusted K3 and K4 back into the multi-parameter coupled response surface model, and the model will quickly re-optimize the geometry for these two ribs. Replace these two updated transition ribs in the overall model and perform another verification analysis. The resulting σ... actual =148MPa, which meets the design target of no more than 150MPa.

[0051] At this point, the entire parametric design process is complete, resulting in a final design scheme that satisfies stress control requirements, ensures low stress in the transition ribs, and optimizes material usage.

[0052] Example 2

[0053] In the design of a large cross-river steel box girder bridge, in order to solve the potential problem of recurring fatigue cracks at the four openings of the transverse diaphragm, the parametric design method of this invention was adopted. The bridge has a large traffic flow and a high proportion of heavy-duty vehicles. This project uses a high-precision multi-parameter coupled response surface model as the core to design for this specific working condition.

[0054] In this embodiment, firstly, based on the actual design parameters of the bridge, a local reference finite element model including four openings in the transverse diaphragm was established. The analysis results show that, without the flexible transition ribs, the maximum principal tensile stress at the edge of the openings reaches as high as 245 MPa, far exceeding the fatigue detail allowable stress target of 140 MPa. In order to reduce the stress to a safe level, the calculated stiffness increment that needs to be compensated is approximately 0.90 × 10⁻⁶. 6 N / mm, it is planned to arrange 8 flexible transition ribs in the bridge-direction space of 1500 mm on both sides of the opening to jointly bear this stiffness increment, with the total stiffness increment (ΔK=0.90×10) determined. 6After calculating the stiffness (N / mm), it needs to be rationally allocated to the eight planned flexible transition ribs. To achieve a smooth transition in stiffness, this embodiment uses an intermediate weighted nonlinear distribution function to decompose the total stiffness increment into eight sub-target stiffnesses. This function ensures that the ribs located in the middle of the stiffness gradient zone bear a larger share of stiffness, thereby more effectively smoothing the stiffness gradient between the opening area and the transverse diaphragm 4. The calculated sub-target stiffness sequence of the eight transition ribs is determined as: K1 = 1.02 × 10⁻⁶. 5 N / mm, K2=1.15×10 5 N / mm, K3=1.28×10 5 N / mm, K4=1.41×10 5 N / mm, K5=1.53×10 5 N / mm, K6=1.66×10 5 N / mm, K7=1.79×105N / mm, K8=1.92×10 5 N / mm.

[0055] Before project implementation, four key geometric parameters were defined as inputs to the multi-parameter coupled response surface model: plate thickness (t), arc height (h), and contact length with the top plate (L). t The fitting length (Ld) of the diaphragm 4 varies within its feasible engineering range. To efficiently and uniformly analyze this four-dimensional parameter space, the multi-parameter coupled response surface model uses Latin hypercube sampling technology to generate 800 representative combinations of geometric parameters. The finite element software is driven by a parametric script to perform automated simulation analysis on each set of parameters, calculating the "stiffness contribution value" and its own "maximum equivalent stress" provided by each transition rib. These 800 sets of "parameter-performance" data constitute the dataset for training the multi-parameter coupled response surface model.

[0056] Based on this high-quality data, the multi-parameter coupled response surface model constructed two high-precision surrogate models using the Kriging method: one for predicting the stiffness contribution (M... K Another is used to predict the maximum equivalent stress (M) of the transition rib itself. σ After rigorous validation, the coefficients of determination (R²) of these two models were... 2 The values ​​all exceeded 0.98, thus enabling the reproduction of complex finite element analysis results with extremely high confidence. Table 1 below shows a comparison of some input parameters, predicted outputs, and finite element calculations of the multi-parameter coupled response surface model.

[0057] Table 1 Examples of prediction accuracy of multi-parameter coupled response surface model

[0058]

[0059] Based on the acquisition of a high-precision surrogate model, the multi-parameter coupled response surface model transforms the traditional experience-dependent "forward trial calculation" design process into a "reverse optimization" intelligent design based on performance objectives. For the eight pre-determined sub-objective stiffnesses, the stiffness of each sub-objective and its preset installation position are used as input conditions to start the embedded multi-objective genetic algorithm for global optimization search.

[0060] The multi-objective genetic algorithm's optimization objective function simultaneously considers three key performance indicators: the matching error of stiffness contribution values ​​must be less than 5%, the maximum equivalent stress of the transition ribs themselves must be minimized, and the structural material volume must be minimized. The algorithm performs an efficient search within a feasible region composed of four geometric parameters. Through evolutionary operations such as selection, crossover, and mutation, iteratively optimizes the population. After a set number of generations, the algorithm converges to a Pareto optimal solution set, where each non-dominated solution represents the optimal trade-off among the three objectives.

[0061] like Figure 6 The Pareto front diagram for multi-objective optimization illustrates the balance between three performance indicators in the design of flexible transition ribs. The three axes in the diagram include: the X-axis represents the percentage of stiffness error, indicating the deviation (%) between the calculated stiffness and the target stiffness; the Y-axis represents the maximum equivalent stress (N / mm) of the flexible transition rib; and the Z-axis represents the volume of structural material (in units of 10⁻⁶). 6 mm 3 (Unit: ). The orange surface represents the Pareto front formed during the algorithm optimization process, i.e., the optimal trade-off surface among the objectives; the blue dots represent a series of non-dominated solutions, which cannot further improve any of the three factors—stiffness error, stress, and material usage—without compromising other performance characteristics. From the surface morphology, it can be seen that a smaller stiffness error (to the left) often requires increasing the material volume or allowing higher stress; if low stress or material saving is pursued, stiffness matching accuracy will be slightly sacrificed. Therefore, engineers need to choose a balance point among the three, and the decision can be made according to specific engineering preferences. In this embodiment, the solution with a stiffness matching error strictly controlled within 3%, an equivalent stress below 200 MPa, and relatively economical material usage is preferentially selected as the final design scheme.

[0062] The optimal geometric parameter sequence obtained from the inversion was substituted into the complete finite element model for verification calculation. The analysis results show that the maximum principal tensile stress at the edge of the opening of the diaphragm 4 was significantly reduced from the initial 245 MPa to 138 MPa, which is lower than the allowable stress target of 140 MPa, and the structural fatigue performance was fundamentally improved. At the same time, the maximum equivalent stress of all flexible transition ribs was controlled within the safe range of below 200 MPa.

[0063] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0064] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A lightweight, high-strength orthotropic steel bridge deck structure, characterized in that, It includes a top steel plate (1), a lower steel plate (2) arranged parallel to the top steel plate, multiple longitudinal ribs (3) arranged between the two steel plates, and transverse diaphragms (4) arranged at intervals along the bridge direction. A transverse diaphragm bottom plate (5) is provided below the transverse diaphragm. The longitudinal ribs (3) and the transverse diaphragms (4) are separated to form a closed plate grid chamber (7). When the transverse diaphragm (4) passes through the longitudinal ribs (3) and forms an opening area below the top steel plate (1), a flexible transition rib array (6) composed of multiple independent ribs is arranged along the bridge direction in the opening area. Each flexible transition rib includes a rib that is attached to the lower surface of the top steel plate (1). The upper bonding section, the transition section between the two bonding sections, and the side bonding section that is bonded to the side of the transverse diaphragm (4) are combined. The transition section is arched or zigzag. The flexible transition rib array (6) is set along the bridge direction from the end away from the transverse diaphragm (4) to the end close to the transverse diaphragm (4). The plate thickness increases step by step, the arch height of the transition section decreases step by step, and the bonding length of the upper bonding section and the side bonding section increases step by step. In the opening area, a progressive stiffness zone with gradually increasing equivalent vertical stiffness along the bridge direction is formed, so that the local deflection of the top steel plate (1) is smoothly transferred from the continuous plate area to the transverse diaphragm (4), thereby reducing the concentration of principal tensile stress at the opening edge.

2. A lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method, characterized in that, Based on a pre-built multi-parameter coupled response surface model, the following steps are included: Step 1: Establish a local finite element reference model including the opening and surrounding components, and analyze and obtain the maximum principal tensile stress and vertical equivalent stiffness at the opening when no flexible transition rib is set as reference values. Step 2: Determine the target principal tensile stress and target vertical stiffness at the opening based on the bridge design parameters, and then obtain the required stiffness increment to compensate. Step 3: Within the bridge-direction installation length of the opening, decompose the total stiffness increment into multiple sub-target stiffnesses according to the preset stiffness distribution function. Step 4: Input the stiffness of each sub-target and its preset installation position in the bridge direction into the multi-parameter coupled response surface model to define the four-dimensional geometric parameter space of the target. Use Latin hypercube sampling technology to generate representative training samples in the parameter space. Obtain the stiffness contribution value and maximum equivalent stress of each sample through parametric finite element simulation to form a training dataset. Use Kriging method to establish stiffness contribution prediction model and stress prediction model respectively. In the inversion calculation, use a multi-objective genetic algorithm to perform global optimization in the parameter feasible region, with the goals of stiffness matching error less than 5%, minimum equivalent stress of transition ribs, and minimum material volume, and automatically output the optimal geometric parameter combination for each flexible transition rib. Step 5: Input the results into the multi-parameter coupled response surface model for verification analysis. If the actual stress at the opening does not reach the target, adjust the sub-target stiffness of the middle transition rib and recalculate.

3. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, In step one, the local finite element model uses shell elements, and the mesh is refined at the opening edge of the diaphragm (4) and in the connection area between the diaphragm (4) and the top steel plate (1).

4. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, In step one, the vertical equivalent stiffness is obtained by calculating the ratio of the sum of the vertical reaction forces of the nodes of the open control section to the average vertical displacement.

5. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, In step four, the multi-parameter coupled response surface model is constructed using a Kriging surrogate model or a radial basis function neural network, based on sampling and finite element analysis data of the geometric parameter space of the flexible transition rib.

6. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, In step four, the determination coefficients of the stiffness and stress prediction models of the multi-parameter coupled response surface model are both no less than 0.

97.

7. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, When performing inversion calculations on the multi-parameter coupled response surface model in step four, the optimization algorithm used is a multi-objective genetic algorithm. Its optimization objectives include meeting stiffness requirements, minimizing the stress of the transition rib itself, and minimizing the material volume.

8. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, In step five, if adjustments are needed, the sub-target stiffness of the flexible transition rib located in the middle third of the stiffness gradient zone should be adjusted first.

9. The lightweight, high-strength orthotropic steel bridge deck structure and its parameter optimization method according to claim 2, characterized in that, In the load analysis of step one, the longitudinal load arrangement of the bridge includes at least the two most unfavorable conditions: the wheels being located directly above the opening of the diaphragm and the mid-span area adjacent to the opening.

Images