Secondary design method for topologically optimized bridges

Abstract

The application discloses a kind of secondary design methods of topologically optimized bridge, comprising: the shape profile and size of bridge are preliminarily designed;The grid structure of bridge is generated to determine the material distribution and geometry of bridge;The grid structure is generated 3D structure with cavity by scaling and stretching;3D structure is divided into multiple segmented structures to facilitate the 3D printing of segmented structure;Determine the reinforcement of bridge and its arrangement to improve the tensile and crack resistance of bridge;Finite element analysis is carried out on the bridge after secondary design;Judge the strength, deformation and whether reasonable of bridge, if reasonable, then proceed to the next step, if not reasonable, then repeat the foregoing steps;Based on 3D structure, multiple segmented structures and the reinforcement of bridge and its arrangement, generate secondary design structure and generate the 3D printing file of bridge.The application solves the problem of insufficient structural performance, high manufacturing complexity and high cost of topologically optimized design bridge.

Description

Technical Field

[0001] This invention relates to the field of bridge design technology, and more specifically to a secondary design method for topology-optimized bridges. Background Technology

[0002] In the fields of civil engineering and architectural design, the optimization and fabrication of bridge structures is a crucial task. Topology optimization design methods enable the optimal allocation of materials while meeting engineering performance requirements, thereby improving the structural performance and material utilization of bridges. However, despite the significant importance of topology-optimized bridge design, which can substantially improve the efficiency and quality of bridge design, some undeniable shortcomings remain in practical applications.

[0003] Bridges designed with topology optimization often face the following problems due to their complex geometry and unique design requirements: the optimized structure may not possess sufficient engineering applicability and stability in certain situations, particularly in terms of tensile and crack resistance. Furthermore, the complexity of the optimized structure makes it difficult to achieve precise manufacturing using traditional processing and manufacturing methods, resulting in high manufacturing costs and long lead times. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, a secondary design method for topology-optimized bridges is provided to address the problems of insufficient structural performance, high manufacturing complexity, and high cost associated with topology-optimized bridges.

[0005] To achieve the above objectives, a secondary design method for topology-optimized bridges is provided, comprising the following steps:

[0006] a. Preliminary design of the bridge's shape and dimensions;

[0007] b. Calculate and generate the mesh structure of the bridge using a topology optimization algorithm to determine the material distribution and geometry of the bridge;

[0008] c. The mesh structure is scaled and stretched to generate a 3D structure with cavities;

[0009] d. Divide the 3D structure into multiple segments along the length of the bridge to facilitate the 3D printing of the segments;

[0010] e. Based on the stress distribution and stress conditions of the segmented bridge, determine the reinforcement materials and their arrangement to improve the tensile and crack resistance of the bridge.

[0011] f. Perform finite element analysis on the bridge after secondary design;

[0012] g. Based on the finite element analysis of the structure, determine whether the strength, deformation and rationality of the bridge are reasonable. If they are reasonable, proceed to the next step. If they are not reasonable, repeat steps b to f.

[0013] h. Based on the 3D structure, the multiple segmented structures, and the reinforcement of the bridge and its arrangement, a secondary design structure is generated;

[0014] i. Based on the secondary design structure, generate the 3D printing file of the bridge.

[0015] Furthermore, the step of generating a 3D structure with cavities by scaling and stretching the mesh structure includes:

[0016] The outer contour of the mesh structure is scaled inward by a first preset distance to form the inner contour of the 3D structure;

[0017] The outer contour of the mesh structure is stretched by a second preset distance to form a first 3D model;

[0018] The inner contour of the mesh structure is stretched by a third preset distance to form a second 3D model;

[0019] The first 3D model and the second 3D model are overlapped and aligned, and then subtracted by Boolean operation to obtain the 3D structure.

[0020] Furthermore, the step of dividing the 3D structure into multiple segmented structures along the length of the bridge to facilitate the 3D printing of the segmented structures includes:

[0021] Based on the grid structure of the bridge, the grid structure is divided into multiple segmented structures using a plane to ensure that each segmented structure can be 3D printed and transported independently;

[0022] The connection method of the multiple segmented structures is designed to ensure that the multiple segmented structures are tightly connected;

[0023] Mechanical analysis was performed on each of the multiple segmented structures.

[0024] Furthermore, the step of determining the reinforcement materials and their arrangement for the bridge based on the stress distribution and stress conditions of the segmented bridge includes:

[0025] Determine the material of the reinforcing bars;

[0026] Perform reinforcement design and determine the quantity, diameter, and arrangement of the reinforcement materials;

[0027] The grouting design of the cavity of the 3D structure is carried out to determine the type of cement mortar to be injected into the cavity and the pipe section method.

[0028] Furthermore, the step of performing finite element analysis on the bridge after secondary design includes analyzing the static and dynamic performance of the bridge after secondary design.

[0029] The beneficial effects of this invention lie in its topology-optimized secondary design method for bridges, which improves the structural performance and material utilization of bridges. By employing topology optimization and secondary design methods during the design process, optimal material configuration can be achieved while ensuring the overall mechanical performance of the bridge. This optimized design method not only reduces the amount of material used but also improves the strength and stability of the bridge.

[0030] The topology-optimized secondary design method for bridges in this invention enhances the engineering applicability of bridges. Through the hollow design of the bridge body, space is provided for prestressing tendons, steel reinforcement, and grouting, enabling the bridge to adapt to more complex engineering environments and mechanical requirements. The implementation of the reinforcement design significantly enhances the tensile and crack resistance of the bridge, improving its adaptability and durability in complex engineering environments.

[0031] The secondary design method for topology-optimized bridges in this invention reduces manufacturing complexity and cost. Through segmented design and 3D printing technology, this invention simplifies the manufacturing process, allowing each module to be printed and assembled individually. This not only improves manufacturing accuracy and efficiency but also significantly reduces manufacturing costs and labor expenses.

[0032] The secondary design method for topology-optimized bridges of this invention shortens the design and manufacturing cycle. Based on initial design and topology optimization design, this invention incorporates secondary design steps, making the entire design process more systematic and efficient. The application of segmented design and 3D printing technology further accelerates the manufacturing process. Therefore, the overall design and manufacturing cycle is significantly shortened. Attached Figure Description

[0033] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0034] Figure 1 This is a flowchart of a secondary design method for a topology-optimized bridge according to an embodiment of the present invention.

[0035] Figure 2 This is a flowchart of the variable density topology optimization design method according to an embodiment of the present invention.

[0036] Figure 3 This is a flowchart of a cavity design method according to an embodiment of the present invention.

[0037] Figure 4 This is an example diagram of the segmented design method according to an embodiment of the present invention.

[0038] Figure 5This is an example diagram of the reinforcement design method according to an embodiment of the present invention. Detailed Implementation

[0039] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0040] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0041] This invention provides a secondary design method for topology-optimized bridges, comprising the following steps:

[0042] a. Preliminary design of the bridge's shape, outline, and dimensions.

[0043] b. Calculate and generate the bridge's mesh structure using a topology optimization algorithm to determine the bridge's material distribution and geometry.

[0044] c. Generate a 3D structure with cavities by scaling and stretching the mesh structure.

[0045] Step c, the step of generating a 3D structure with cavities from the mesh structure by scaling and stretching, includes:

[0046] The outer contour of the mesh structure is scaled inward by a first preset distance to form the inner contour of the 3D structure.

[0047] The outer contour of the mesh structure is stretched by a second preset distance to form the first 3D model;

[0048] The inner contour of the mesh structure is stretched by a third preset distance to form a second 3D model;

[0049] The first 3D model and the second 3D model are overlapped and aligned, and then subtracted using Boolean operations to obtain the 3D structure.

[0050] d. Divide the 3D structure into multiple segments along the length of the bridge to facilitate the 3D printing of the segments.

[0051] Step d, which involves dividing the 3D structure into multiple segments along the length of the bridge to facilitate the 3D printing of these segments, includes:

[0052] Based on the bridge-like grid structure, the grid structure is divided into multiple segments using a plane to ensure that each segment can be 3D printed and transported independently;

[0053] Design a connection method for multiple segmented structures to ensure that the multiple segmented structures are tightly connected;

[0054] Mechanical analysis was performed on multiple segmented structures.

[0055] e. Based on the stress distribution and stress conditions of the segmented bridge, determine the reinforcement materials and their arrangement to improve the tensile and crack resistance of the bridge.

[0056] Step e, which involves determining the reinforcement materials and their arrangement based on the stress distribution and stress conditions of the segmented bridge, includes:

[0057] Determine the material of the reinforcing bars;

[0058] Perform reinforcement design and determine the quantity, diameter, and arrangement of the reinforcement;

[0059] Grouting design is carried out for the cavity of the 3D structure to determine the type of cement mortar to be injected into the cavity and the pipe section method.

[0060] f. Perform finite element analysis on the bridge after secondary design.

[0061] Step f, the step of performing finite element analysis on the bridge after secondary design, includes analyzing the static and dynamic performance of the bridge after secondary design.

[0062] g. Based on the finite element analysis of the structure, determine the strength, deformation and rationality of the bridge. If rational, proceed to the next step; if not rational, repeat steps b to f.

[0063] h. Based on the 3D structure, multiple segmented structures, and the reinforcement materials and their arrangement of the bridge, a secondary design structure is generated.

[0064] i. Based on the secondary design structure, generate the 3D printing file of the bridge.

[0065] One important direction of the secondary design of bridges in this invention is to hollow out the bridge body to facilitate the later placement of prestressing tendons, steel bars, and grouting.

[0066] The hollow bridge design of this invention not only effectively reduces the bridge's self-weight but also facilitates subsequent enhancements to structural performance. By creating cavities within the bridge structure, prestressed tendons and reinforcing bars can be rationally arranged, thereby enhancing the bridge's tensile and crack resistance, and improving the overall structural stability and durability.

[0067] Furthermore, the segmented design of the bridge in this invention is also an important aspect of secondary design. As 3D printing technology is increasingly widely used in bridge manufacturing, segmented design makes 3D printing more efficient and economical. Dividing the bridge structure into several independent modules, each of which can be printed and assembled separately, not only improves manufacturing precision but also shortens the manufacturing cycle and reduces manufacturing costs.

[0068] Finally, the bridge reinforcement design of this invention plays a crucial role in the secondary design process. By adding a reasonable arrangement of reinforcement materials to the bridge structure, the tensile and crack resistance of the bridge can be significantly improved. The reinforcement design not only enhances the structural performance of the bridge but also extends its service life and reduces the frequency and cost of later maintenance.

[0069] Therefore, this invention proposes a secondary design method for bridges with topology optimization. This method, through bridge body hollowing, segmented design, and reinforcement design, solves the problems of insufficient structural performance, high manufacturing complexity, excessive manufacturing cost, long design and manufacturing cycle, and insufficient engineering applicability in existing technologies. It facilitates the design and manufacture of safe, reliable, efficient, and economical bridge structures. This method can significantly improve the overall performance of bridges and meet the needs of use in complex engineering environments.

[0070] Reference Figures 1 to 5 As shown, in order to further illustrate the secondary design method of the topology-optimized bridge of the present invention, a single-span beam bridge with an arc-shaped lower edge is used as an example for detailed explanation.

[0071] The secondary design method for topology-optimized bridges of the present invention includes eight steps: initial design, bridge topology optimization design, bridge cavity design, bridge segment design, bridge reinforcement design, bridge finite element analysis, judgment on the rationality of bridge mechanical performance, and final design.

[0072] The specific implementation steps of the topology optimization bridge secondary design method of the present invention are as follows:

[0073] Step 1: Initial Design. Based on existing information, conduct a preliminary design of the bridge's shape and dimensions, such as... Figure 2 As shown, the initial design of the bridge 101 is a single-span beam bridge with an arc-shaped lower edge.

[0074] Step 2: Bridge topology optimization design, including defining the design region, finite element modeling, establishing a mathematical model, finite element simulation, sensitivity analysis, mathematical optimization algorithm, convergence condition judgment, and final design. See [link to relevant documentation]. Figure 2 .

[0075] Step 2.1: Define the design area 101 and determine its geometry, dimensions, loads, and boundary conditions.

[0076] Step 2.2: Finite element modeling, divide the design area into finite element mesh 102, determine the non-design area 1021 and the design area 1022, and apply loads and boundary conditions.

[0077] Design region 1021 refers to the spatial range that the topology optimization algorithm cannot modify during the iteration process. This spatial range is usually set as a solid or hollow region.

[0078] Hollow areas refer to portions of the design area that contain no material. These areas are completely empty and provide no structural strength. They are often used to reduce structural weight and decrease material usage.

[0079] Solid regions refer to areas within the design area that are completely filled with material. These regions have full material density and are typically used to bear the main structural loads and stresses during the optimization process.

[0080] Design region 1022 refers to the spatial range that the topology optimization algorithm can modify during the iteration process. In other words, within this region, the algorithm can adjust the material distribution according to the optimization objective and constraints to achieve the optimal design.

[0081] The mesh should be fine enough to provide a reasonable resolution for the structure. The mesh can be of any shape, not limited to squares. Once the mesh is generated, it remains unchanged throughout the design process, providing a fixed finite element space for the displacement and density fields during iterations.

[0082] Step 2.3: Establish a mathematical model, define the optimization objective and constraints, in the form shown below:

[0083] objective function

[0084] Constraints

[0085] The optimization objective can be written as an objective function f0, which is a function of the density field ρ. The objective function can be to minimize the structural weight, maximize the stiffness, etc.

[0086] Constraints can be equality constraints R, inequality constraints G, and density constraints ρ, etc.

[0087] An equality constraint R is a condition that requires strict equality between design variables, and can be written as a function of the density field ρ and the displacement field u(ρ). For example, in some designs, the displacements of two or more nodes must be equal, or certain geometric parameters must remain equal.

[0088] Inequality constraints G refer to the range or restrictions that must be satisfied between design variables, and can also be written as functions of the density field ρ and the displacement field u(ρ). For example, the total volume of material within the design area must be controlled within a predetermined range to ensure the economy and manufacturability of the design.

[0089] Density constraint ρ refers to the restriction conditions set on the density field ρ during the topology optimization process. It is usually stipulated that 0≤ρ≤1, where 0 represents hollow elements, 1 represents solid elements, and 0 to 1 represents transition elements.

[0090] Step 2.4: Initial design, which is to set the initial estimate of the topology optimization algorithm, for example, assuming that the material is uniformly distributed in the design area and that each cell has the same density ρ = 0.5.

[0091] Initial design is the starting point of the topology optimization process. A reasonable initial design can improve the convergence speed and effectiveness of the optimization algorithm.

[0092] Step 2.5: Finite element simulation, which involves obtaining the structural response of the initial design through finite element simulation, such as the displacement field u(ρ). o And further obtain the corresponding objective function value f0(ρ). o ) and constraint function values ​​R(ρ,u(ρ)) and G(ρ,u(ρ)).

[0093] Step 2.6: Sensitivity analysis. Calculate the derivative of the objective function f0 with respect to the design variable ρ. Through sensitivity analysis, identify which regions have the greatest impact on the objective function, thereby guiding the redistribution and optimization of materials within the design region.

[0094] Step 2.7: Mathematical optimization algorithm. Update the design variable ρ using a mathematical optimization algorithm to form the intermediate topology design 103, and calculate the corresponding objective function f0(ρ) and constraint functions R(ρ,u(ρ)) and G(ρ,u(ρ)). The mathematical optimization algorithm can use the Moving Asymptote Method (MMA), which iteratively optimizes the design variables to gradually approach the optimization objective.

[0095] The MMA algorithm dynamically adjusts the asymptote range of each variable at each step based on the current design variable value and gradient information. These asymptotes limit the magnitude of variable changes, thus avoiding excessively large or small adjustments and gradually approaching the optimal design. This is similar to setting a controllable range for each variable during the optimization process, allowing each adjustment to move more precisely towards the optimal solution.

[0096] Mathematical optimization algorithms can also employ other methods, including but not limited to Sequential Linear Programming (SLP), Sequential Quadratic Programming (SQP), and Genetic Algorithm (GA).

[0097] Step 2.8: Convergence condition judgment, that is, to determine whether the convergence condition (such as the change of the objective function) is met. If it is met, the iteration stops; otherwise, the iteration continues.

[0098] Convergence conditions typically include the following aspects:

[0099] 1) Objective function change: The change in the objective function value f0(ρ) over a series of iterations is less than a set threshold. For example, when the relative rate of change of the objective function value is less than a very small value (such as 10). -4 When the algorithm has converged, it can be considered that the algorithm has converged.

[0100] 2) Design variable change: The change of the design variable over several consecutive iterations is less than a set threshold. For example, when the relative rate of change of the design variable ρ is less than a very small value (such as 10). -3 When the algorithm has converged, it can be considered that the algorithm has converged.

[0101] 3) Constraints are satisfied: All constraints are satisfied during the iteration process, meaning the constraint function values ​​are within the allowable range;

[0102] 4) Iteration limit: Reach the preset maximum number of iterations. Although this is not an ideal convergence criterion, in practical applications, setting a maximum number of iterations can prevent the algorithm from getting stuck in an infinite loop.

[0103] Step 2.9: Final Design. Generate the final optimized design 104, which includes a defined material distribution and geometry. This design is typically a mesh structure, explicitly indicating which regions should be filled with material (ρ = 1), which regions should be empty (ρ = 0), and which regions are intermediate states. The optimized design must satisfy all set constraints and achieve the optimization objective (0 ≤ ρ ≤ 1).

[0104] Step 3: Cavity design of the bridge grid structure. This involves designing cavities within the bridge structure to provide space for the later placement of prestressing tendons, reinforcing bars, and grouting. (See [link / reference]). Figure 3 The specific steps are as follows:

[0105] Step 3.1: Filter and smooth the final topology optimization design 201 to generate a smoother, more manufacturable bridge outer contour structure 202. For example, by using spline curve fitting or other smoothing techniques, rough edges and irregular shapes in the optimization results are eliminated, thereby improving the manufacturability and aesthetics of the structure.

[0106] Step 3.2: Scale the outer contour 202 of the bridge body inward by a first preset distance to form the inner contour 203. Place the outer contour 202 and the inner contour 203 of the bridge body together. The two are similar in shape and the distance between them is equal to D at all points.

[0107] Step 3.3: Stretch the two-dimensional outer contour 202 of the bridge body by a second preset distance (i.e., the bridge width) to form a 3D model 204 (i.e., the first 3D model).

[0108] Step 3.4: Stretch the two-dimensional bridge body contour 203 by a third preset distance (i.e., bridge width) to form a 3D model 205 (i.e., the second 3D model).

[0109] Step 3.5: Overlap and align the 3D model of the outer contour of the bridge body 204 and the 3D model of the inner contour of the bridge body 205, and then subtract them through Boolean operation to obtain the 3D model 206 (i.e., 3D structure) of the hollow bridge body with a certain thickness D.

[0110] Step 4: Segmented design of the bridge structure, see [link / reference] Figure 4 The 3D model of the hollow bridge was divided into six independent modules (301, 302, 303, 304, 305, and 306) using planar segmentation (i.e., multiple segmented structures). Each module can be 3D printed and transported separately, and then assembled into the bridge structure on-site. The specific steps are as follows:

[0111] Step 4.1: Determine the segmentation scheme. Based on the overall structure and geometry of the topology-optimized bridge, divide it into 6 parts (301, 302, 303, 304, 305, and 306) using a plane. The dividing plane should not pass through the hollow parts of the topology-optimized structure (except for the middle part of the bridge) as much as possible, to ensure that each part can be 3D printed and transported independently.

[0112] Step 4.2: Design a segmented connection method to ensure that all modules can be tightly connected after installation, guaranteeing the continuity and stability of the overall structure. Common connection methods include bolted connections, welding, and mortise and tenon joints.

[0113] Step 4.3: Perform segmented mechanical analysis on modules 301, 302, 303, 304, 305 and 306 to ensure that each module will not be deformed or damaged during individual printing and transportation, while ensuring the mechanical performance of the overall structure after connection.

[0114] Step 5: Bridge reinforcement design, see Figure 5 By adding a reasonable reinforcement arrangement to the bridge structure, the tensile and crack resistance of the bridge can be significantly improved. The specific steps are as follows:

[0115] Step 5.1: Determine the reinforcement location. Based on the stress distribution and stress conditions of the bridge, determine the areas that need reinforcement, focusing on stress concentration areas and weak points to ensure that the reinforcement can significantly improve the tensile and crack resistance of the bridge.

[0116] Step 5.2: Select appropriate reinforcement materials. Commonly used reinforcement materials include steel bars, carbon fiber, and glass fiber. Select the appropriate material according to the specific requirements of the bridge.

[0117] Step 5.3: Conduct reinforcement design, determining the quantity, diameter, and arrangement of the reinforcement bars to ensure they effectively improve the structural performance of the bridge. For example... Figure 5 As shown, the designed reinforcement includes longitudinal reinforcement 401, prestressed reinforcement 402, diagonal stirrups 403, and stirrups 404.

[0118] Step 5.4: Design the grouting process, determining the type and method of cement mortar 405 to be injected into the hollow bridge body, ensuring that the injected mortar 405 can evenly fill the space surrounded by the concrete shell 406 in the cavity. Additionally, the connection 407 between the reinforced and grouted modules is fixed using bolts, welding, or adhesive materials.

[0119] Step 6: Finite element analysis of the bridge structure. A finite element analysis is performed on the bridge structure after the secondary design to analyze its static and dynamic performance. The specific steps are as follows:

[0120] Step 6.1: Establish a finite element model, divide the bridge structure after secondary design into finite element meshes, and apply loads and boundary conditions.

[0121] Step 6.2: Perform static analysis to calculate the displacement, stress, and strain distribution of the bridge, focusing on key parts and weak points of the structure.

[0122] Step 6.3: Perform dynamic analysis, calculate the natural frequency and mode shape of the bridge, and analyze the internal force and displacement response characteristics of the bridge.

[0123] Step 7: Determine if the bridge's mechanical properties are reasonable. Using finite element analysis results, determine if the bridge's strength, deformation, and stability are reasonable. If reasonable, formulate the final design scheme; otherwise, repeat steps 2 to 7 until the requirements are met.

[0124] Step 8: Final Design. Generate the final optimized secondary design model (including the cavity design, segment design, and reinforcement design of the bridge structure), and generate design drawings and construction plans. Specific steps are as follows:

[0125] Step 8.1: Organize and improve the design documents, including detailed design drawings, technical specifications and construction plans.

[0126] Step 8.2: Prepare a list of materials and tools required for manufacturing and construction, ensuring that all materials and equipment meet the design requirements.

[0127] Step 8.3: Generate 3D printing files. Generate a file format suitable for 3D printing based on the final design model to ensure printing accuracy and quality.

[0128] Step 8.4: Develop a construction plan, detailing the construction steps and schedule for each stage to ensure the orderly progress of the construction process.

[0129] Step 8.5: Conduct a final review, comprehensively review the design and construction plan to ensure that all details have been considered in order to facilitate the actual construction later.

[0130] The topology optimization method for secondary design of bridges in this invention improves the structural performance and material utilization of bridges. By employing topology optimization and secondary design methods during the design process, optimal material allocation can be achieved while ensuring the overall mechanical performance of the bridge. This optimized design method not only reduces the amount of material used but also improves the strength and stability of the bridge.

[0131] The topology-optimized secondary design method for bridges in this invention enhances the engineering applicability of bridges. Through the hollow design of the bridge body, space is provided for prestressing tendons, steel reinforcement, and grouting, enabling the bridge to adapt to more complex engineering environments and mechanical requirements. The implementation of the reinforcement design significantly enhances the tensile and crack resistance of the bridge, improving its adaptability and durability in complex engineering environments.

[0132] The secondary design method for topology-optimized bridges in this invention reduces manufacturing complexity and cost. Through segmented design and 3D printing technology, this invention simplifies the manufacturing process, allowing each module to be printed and assembled individually. This not only improves manufacturing accuracy and efficiency but also significantly reduces manufacturing costs and labor expenses.

[0133] The secondary design method for topology-optimized bridges of this invention shortens the design and manufacturing cycle. Based on initial design and topology optimization design, this invention incorporates secondary design steps, making the entire design process more systematic and efficient. The application of segmented design and 3D printing technology further accelerates the manufacturing process. Therefore, the overall design and manufacturing cycle is significantly shortened.

[0134] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A secondary design method for bridges with topology optimization, characterized in that, Includes the following steps: a. Preliminary design of the bridge's shape and dimensions; b. Calculate and generate the mesh structure of the bridge using a topology optimization algorithm to determine the material distribution and geometry of the bridge; c. The mesh structure is scaled and stretched to generate a 3D structure with cavities; d. Divide the 3D structure into multiple segments along the length of the bridge to facilitate the 3D printing of the segments; e. Based on the stress distribution and stress conditions of the segmented bridge, determine the reinforcement materials and their arrangement to improve the tensile and crack resistance of the bridge. f. Perform finite element analysis on the bridge after secondary design; g. Based on the finite element analysis of the structure, determine whether the strength, deformation and stability of the bridge are reasonable. If reasonable, proceed to the next step; if not, repeat steps b to f. h. Based on the 3D structure, the multiple segmented structures, and the reinforcement of the bridge and its arrangement, a secondary design structure is generated; i. Based on the aforementioned secondary design structure, generate the 3D printing file for the bridge; The steps for generating the mesh structure of the bridge using a topology optimization algorithm include: Define the design area, and determine its geometry, dimensions, loads, and boundary conditions; Finite element modeling involves dividing the design region into finite element meshes, defining the non-design region and the design region, and applying loads and boundary conditions. A mathematical model is established, defining the optimization objective and constraints, as shown in the following formula: The optimization objective is written as the objective function f0, which is a function of the density field ρ. The objective function is to minimize the structural weight and maximize the stiffness. The constraints are equality constraint R, inequality constraint G, and density constraint ρ. Initial design, i.e., setting the initial estimates for the topology optimization algorithm; Finite element simulation, that is, obtaining the structural response of the initial design through finite element simulation; Sensitivity analysis calculates the derivative of the objective function f0 with respect to the design variable ρ. Through sensitivity analysis, it identifies which regions have the greatest impact on the objective function, thereby guiding the redistribution and optimization of materials within the design region. Mathematical optimization algorithm is used to update the design variable ρ, form the intermediate design of topology optimization, and calculate the corresponding objective function f0(ρ) and constraint functions R(ρ,u(ρ)) and G(ρ,u(ρ)). Convergence condition judgment, that is, to determine whether the convergence condition is met. If it is met, the iteration stops; otherwise, the iteration continues. The final design generates the final optimized design, which includes the determined material distribution and geometry.

2. The secondary design method for topology-optimized bridges according to claim 1, characterized in that, The step of generating a 3D structure with cavities by scaling and stretching the mesh structure includes: The outer contour of the mesh structure is scaled inward by a first preset distance to form the inner contour of the 3D structure; The outer contour of the mesh structure is stretched by a second preset distance to form a first 3D model; The inner contour of the mesh structure is stretched by a third preset distance to form a second 3D model; The first 3D model and the second 3D model are overlapped and aligned, and then subtracted by Boolean operation to obtain the 3D structure.

3. The secondary design method for topology-optimized bridges according to claim 1, characterized in that, The step of dividing the 3D structure into multiple segmented structures along the length of the bridge to facilitate the 3D printing of the segmented structures includes: Based on the grid structure of the bridge, the grid structure is divided into multiple segmented structures using a plane to ensure that each segmented structure can be 3D printed and transported independently; The connection method of the multiple segmented structures is designed to ensure that the multiple segmented structures are tightly connected; Mechanical analysis was performed on each of the multiple segmented structures.

4. The secondary design method for topology-optimized bridges according to claim 1, characterized in that, The steps for determining the reinforcement and its arrangement of the bridge based on the stress distribution and stress conditions of the segmented bridge include: Determine the material of the reinforcing bars; Perform reinforcement design and determine the quantity, diameter, and arrangement of the reinforcement materials; The grouting design of the cavity of the 3D structure is carried out to determine the type of cement mortar to be injected into the cavity and the pipe section method.

5. The secondary design method for topology-optimized bridges according to claim 1, characterized in that, The steps of performing finite element analysis on the bridge after secondary design include analyzing the static and dynamic performance of the bridge after secondary design.

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