A double-scale finite element analysis method and system for a steel-concrete composite bridge

Abstract

This invention relates to a dual-scale finite element analysis method and system for steel-concrete composite bridges, belonging to the field of civil engineering technology. The method includes the following steps: S1, establishing the length division of large-scale (macro-element) and small-scale (fine-element) regions in the steel-concrete composite bridge model, clarifying the focus of local stress analysis; S2, establishing components in both large and small scale regions and selecting element types for each component, simplifying the dual-scale model; S3, defining the material constitutive models of both large and small scale components to achieve consistency in material scale between macro-element and fine-element models; S4, assembling the spatial positions of each component and connecting the large and small scale regions to achieve consistency in deformation between the macro and fine models; S5, defining the internal contacts of each component and completing mesh generation; S6, applying actual loads and arranging actual boundary conditions to perform dual-scale finite element analysis. The technical solution of this invention has advantages such as high accuracy, high computational efficiency, and fast modeling speed.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering technology and relates to a dual-scale finite element analysis method and system for steel-concrete composite bridges. Background Technology

[0002] Currently, based on the different scales of the research objects, there are three main finite element modeling and analysis methods in the field of bridge engineering: ① establishing a large-scale macroscopic model of the entire bridge using tie-beam elements; ② establishing a small-scale microscopic model of local structures using solid elements and shell elements; ③ establishing a small-scale refined model of the entire bridge using solid elements and shell elements. 1) The macroscopic model of the entire bridge using tie-beam elements is a highly simplified overall structural model that can reflect the overall stress performance of the bridge under dead and live loads, but cannot reflect the stress at the structural details; 2) The refined model using shell elements and solid elements first establishes a large-scale macroscopic model of the entire bridge for overall analysis by treating local components as isolated bodies, extracting their internal forces and displacements, and then applying displacement and load boundary conditions to the isolated bodies for equilibrium, thereby analyzing the stress on the isolated bodies. This modeling method has the advantages of fast modeling speed, high computational efficiency, and can meet the needs of stress analysis of small-scale local micro-components. However, it has the disadvantages of complex boundary conditions of the extracted isolated body or difficulty in determining the boundary conditions of the model. 3) The full-bridge refined finite element model using solid and shell elements applies real boundary conditions and loads to the finite element model. There is no simulation of local structural boundaries. Its analysis results are accurate and reliable. However, the disadvantages of this modeling method are also very obvious. As the spatial scale of the structure increases, the modeling speed is slow, the computational efficiency is low, and the computational data is huge.

[0003] It is evident that for actual large and complex three-dimensional bridge structures, it is necessary to consider both the local structural stress and the overall macroscopic stress analysis of the entire bridge. The above modeling methods can no longer meet the needs of actual engineering.

[0004] In recent years, multi-scale structural simulation methods have been widely used in engineering structures. Originating in materials science, these methods were subsequently applied to structural engineering as engineers sought a balance between computational accuracy and time cost in their calculations. In multi-scale structural simulation, under load, local components often fail due to stress concentration, leading to overall structural instability. Local component failure represents a small-scale microscopic event, while overall structural instability represents a large-scale macroscopic event, belonging to different scales. The core idea of ​​multi-scale simulation is to combine a small-scale refined model with a large-scale frame model. A reasonable interface connection method replaces the original boundary conditions of the small-scale refined model, and then realistic boundary conditions are added to the large-scale model. This allows the multi-scale model to possess the advantages of both large-scale and small-scale models while eliminating their disadvantages, resulting in low computational cost and high accuracy.

[0005] Currently, multi-scale finite element simulation methods are mostly focused on applications in concrete or steel bridges, with limited research on steel-concrete composite bridges. Steel-concrete composite bridges involve two materials, steel and concrete, connected by shear connectors, and there is also incomplete discontinuous slippage at the interface between the steel and concrete. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a dual-scale finite element analysis method and system for steel-concrete composite bridges, involving the material nonlinearity of reinforced concrete bridge decks and steel beams, as well as the prominent slip problem at the steel-concrete interface. That is, the same calculation model includes both high-computation-efficiency macroscopic beam elements and high-precision fine solid elements. The different elements are coupled and connected to achieve a balance between the calculation time and accuracy of the structure. This solution has the characteristics of high accuracy, high calculation efficiency, and fast modeling speed.

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

[0008] A two-scale finite element analysis method for steel-concrete composite bridges, comprising the following steps:

[0009] S1. In the steel-concrete composite bridge model, establish the division of large-scale (macro-unit) and small-scale (fine-unit) regions to clarify the focus of local stress analysis;

[0010] S2. Establish large-scale and small-scale regional components and select the unit types for each component to simplify the dual-scale model;

[0011] S3. Define the material constitutive model of large-scale and small-scale components to achieve consistency in the material scale between macroscopic and fine-scale units;

[0012] S4. Complete the assembly of the spatial positions of each component and the connection of large and small scale areas to achieve consistency between macroscopic and fine model deformation;

[0013] S5. Define the internal contact of each component and complete the mesh generation;

[0014] S6. Apply actual loads and set actual boundary conditions to perform two-scale finite element analysis.

[0015] Furthermore, in step S1, the large-scale region reflects the macroscopic stress and deformation of the structure, while the small-scale region reflects local damage. When determining the small-scale refined region, locations prone to local failure are selected. Additionally, according to Saint-Venant's principle, the nodal stresses near the boundary are inaccurate or even erroneous, while the calculation results for the studied area tend to approach the true calculated values ​​as the length of the small-scale refined region increases. Therefore, to avoid the influence of boundary conditions on the results of the main analysis areas and to focus on the stress analysis of the main local structures, the length of the small-scale refined region, which is 1 to 2 times the beam height, is selected for locations prone to local failure.

[0016] Furthermore, in step S2, the model simplification includes model simplification in large-scale regions and model simplification in small-scale regions; the model simplification in large-scale regions includes simplification of bridge decks, steel beams, and shear members, specifically including:

[0017] Bridge deck:

[0018] 1) Bridge deck simplification: In the macroscopic truss model, it is simplified into beam elements of concrete slab sections, and each segment is combined separately in the dual-scale model; for the macroscopic truss model, the concrete slab uses beam elements. In addition, to ensure that the model accurately reflects the actual situation, the effect of the embedded reinforcement in the concrete slab is considered, and the elastic modulus of the concrete slab truss part is calculated according to the converted elastic modulus E. s A s +E c A c =E0A0, perform conversion, convert the elastic modulus E0 = (E s A s +E c A c ) / A0, where E s A s These represent the elastic modulus and cross-sectional area of ​​the reinforcing steel, E. c A c These are the elastic modulus and cross-sectional area of ​​concrete, respectively, with A0 being the converted cross-sectional area.

[0019] 2) Material Constitutive Structure: For the macroscopic concrete beam model, since it is not possible to directly define the concrete damage plasticity (CDP) constitutive structure for the beam elements, and the loss of the beam elements themselves is not the primary concern, an ideal elastic-plastic stress-strain relationship is adopted for the concrete beam elements to achieve overall macroscopic deformation consistency. The stress-strain calculation of the concrete beam elements is as follows:

[0020]

[0021] In the above formula: f c ε is the compressive strength of concrete. c =fc / E0 represents the strain corresponding to the compressive strength; E0 is the converted elastic modulus ε. i Equivalent strain of concrete; σ i Equivalent stress in concrete;

[0022] Steel beams:

[0023] 1) Simplification of steel beams: In the macroscopic truss model, the steel beams are simplified into beam elements of steel beam sections, and each segment is combined in the dual-scale model. For the macroscopic truss model, the steel beams are represented by beam elements.

[0024] 2) Material Constitutive Model: The constitutive model can well reflect the stress-strain relationship of steel during the stress process. For steel beams, a two-segment model is used, and the stress-strain relationship calculation formula is as follows:

[0025]

[0026] Among them, E s For the elastic modulus of the steel beam, σ s ε s These represent the stress and strain of the steel beam, respectively. y ε y For the yield strength and yield strain of the steel beam, f u ε u The ultimate strength and ultimate strain of steel;

[0027] Shear components:

[0028] 1) Simplification of Shear Components: In actual bridge structures, there are a large number of shear components. Modeling them using solid elements would lead to complex contact issues, high nonlinearity, and significant computational costs. Therefore, spring elements are used to simulate the mechanical behavior of shear components. The basic idea is to use two-node spring elements to establish a connection between the bottom of the concrete slab and the upper flange of the steel beam, and to describe the mechanical behavior of the shear components in translational and rotational directions by defining combined connection properties.

[0029] 2) Shear member constitutive model: The stress process of a shear member mainly includes the friction stage, slip stage, elastic stage and elastoplastic stage. By defining the load-slip curve constitutive relationship of the connection element, the mechanical behavior of the actual shear member is simulated.

[0030] Furthermore, the model simplification of the small-scale region includes:

[0031] Bridge deck: In the detailed model, the bridge deck is arranged in the same position as in reality and uses solid elements, while the reinforcement uses truss elements; Material constitutive: For the detailed model part, the solid elements of the concrete slab adopt nonlinear constitutive relations; such as the constitutive relations in Appendix C.2 of the Code for Design of Concrete Structures.

[0032] ③Constituent of concrete under uniaxial compression

[0033] σ=(1-d c E c ε

[0034]

[0035] in,

[0036] ④ Concrete uniaxial tension constitutive model

[0037] σ=(1-d t E c ε

[0038]

[0039] in,

[0040] The stress-strain calculation formula for ordinary steel reinforcement is as follows:

[0041]

[0042] Where: σ j E represents the equivalent stress of ordinary steel reinforcement. s ε is the elastic modulus of ordinary steel reinforcement; j The equivalent strain of ordinary steel reinforcement; f y The yield strength of ordinary steel bars;

[0043] Steel beams: In the refined model, the steel beams are arranged in the same positions as in reality and use thin-walled shell elements; Material constitutive model: The steel beams adopt a two-segmented model, and the stress-strain calculation formula for the steel beams is as follows:

[0044]

[0045] Among them, E s For the elastic modulus of the steel beam, σ s ε s These represent the stress and strain of the steel beam, respectively. y ε y For the yield strength and yield strain of the steel beam, f u ε u These represent the ultimate strength and ultimate strain of steel.

[0046] Furthermore, in step S4, since the spatial degrees of freedom are different between different elements, rigid connections are used to couple the elements in order to achieve force balance and deformation coordination among the three. The beam element nodes are the master nodes, and the points on the solid and shell elements are the slave nodes. The master nodes are connected to the beam element nodes in the refined model through rigid arms, which ensures the deformation coordination between the master and slave nodes.

[0047] Furthermore, in step S5, after assembling all components, it is necessary to define the contact surface relationships of each component. This mainly includes the contact relationship between the concrete slab and the steel beam, and the contact relationship between the reinforcing mesh and the concrete slab in the refined model. Additionally, for the macroscopic model, since the steel beam and bridge deck are connected by spring units, it is not necessary to set contact relationships. Specifically, this includes:

[0048] 1) Interface contact between concrete slab and steel beam: Considering that the bond force between the steel beam and the concrete slab can be ignored, the steel-concrete interface is set to a normal "hard contact" and a tangential "frictionless" contact relationship; 2) Interface contact between steel mesh and concrete slab: The steel mesh is subjected to stress in the concrete. In order to ensure that the concrete does not crack prematurely, the bond slip effect between the steel mesh and the concrete slab is ignored. The steel mesh is embedded in the concrete slab to simulate the contact relationship between the two.

[0049] Furthermore, in step S5, after the interfaces come into contact, the components need to be meshed. The appropriateness of the meshing has a significant impact on the model's computational time and accuracy. If the mesh size is coarse, the computational accuracy may be insufficient, contradicting the actual force conditions. If the mesh size is too fine, the computational results will be more accurate, but the computational efficiency will be significantly reduced. Therefore, for different types of models, the mesh size should be determined according to the different forces acting on the components to ensure more accurate force transmission simulation at special locations.

[0050] This invention also provides a dual-scale finite element analysis system for steel-concrete composite bridges.

[0051] The beneficial effects of this invention are as follows:

[0052] This invention proposes a dual-scale finite element analysis method and system for steel-concrete composite bridges, which involves the material nonlinearity of reinforced concrete bridge decks and steel beams, as well as the prominent slippage problem at the steel-concrete interface. This solution features high accuracy, high computational efficiency, and fast modeling speed.

[0053] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0054] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0055] Figure 1 This invention provides a dual-scale modeling process for steel-concrete composite beams.

[0056] Figure 2 A simplified schematic diagram of the two-scale model;

[0057] Figure 3 A simplified flowchart for concrete bridge decks;

[0058] Figure 4 Elastic-plastic stress-strain diagram of a concrete beam element;

[0059] Figure 5 Simplified flowchart for steel beams;

[0060] Figure 6 This is a stress-strain diagram of a steel beam.

[0061] Figure 7 Simplified flowchart for shear components;

[0062] Figure 8 This is a simulation diagram of the shear force component.

[0063] Figure 9 This is a stress-strain diagram of concrete under compressive stress.

[0064] Figure 10 This is a tensile stress-strain diagram of concrete.

[0065] Figure 11 This is a stress-strain diagram of reinforcing steel.

[0066] Figure 12 This is a stress-strain diagram of a steel beam.

[0067] Figure 13 The dimensions and reinforcement details are shown in the embodiment.

[0068] Figure 14 This is a schematic diagram of finite element mesh generation;

[0069] Figure 15 A comparison diagram of bridge deck stress and deflection;

[0070] Figure 16 This is a comparison diagram of stress and deflection in a steel beam. Detailed Implementation

[0071] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0072] Figure 1 This invention provides a dual-scale modeling process for steel-concrete composite beams. Figure 2 A simplified schematic diagram of the dual-scale model is shown in the figure. The dual-scale finite element analysis method for steel-concrete composite bridges provided by this invention includes the following steps: S1. Establishing the length division of large-scale (macro-unit) and small-scale (fine-unit) regions in the steel-concrete composite bridge model, clarifying the focus of local stress analysis; S2. Establishing components in large-scale and small-scale regions and selecting the element types for each component to complete the simplification of the dual-scale model; S3. Defining the material constitutive models of large-scale and small-scale components to achieve consistency in the material scale of macro-units and fine-units; S4. Completing the assembly of the spatial positions of each component and the connection of large-scale and small-scale regions to achieve consistency in the deformation of macro- and fine-scale models; S5. Defining the internal contact of each component and completing the mesh generation; S6. Applying actual loads and arranging actual boundary conditions to perform dual-scale finite element analysis.

[0073] Specifically, the following technical solutions are included:

[0074] Large- and small-scale regional division:

[0075] Since large-scale regions reflect the macroscopic stress and deformation of the structure, while small-scale regions reflect localized damage, the small-scale refined region is often selected at locations prone to localized failure. Furthermore, according to Saint-Venant's principle, the nodal stresses near the boundary are inaccurate or even erroneous, while the calculation results for the studied area tend to approach the actual calculated values ​​as the length of the small-scale refined region increases. Therefore, to avoid the influence of boundary conditions on the results of the main analysis areas and to focus on the stress analysis of the main local structures, the length of the small-scale refined region, which is 1 to 2 times the beam height, is selected at locations prone to localized failure.

[0076] Model simplification for large-scale regions:

[0077] Due to differences in element types and material properties during the modeling process, the steel beams, bridge decks, and shear members are simplified as follows.

[0078] 1. Bridge deck

[0079] (1) Simplification of bridge deck

[0080] In the macroscopic truss model, it is simplified into beam elements with concrete slab sections, and each segment is combined separately in the dual-scale model. The simplification process is as follows: Figure 3 As shown. For the macroscopic truss model, beam elements are used for the concrete slab. Furthermore, to ensure the model accurately reflects the actual situation, the effect of the internal reinforcement in the concrete slab is considered; the elastic modulus of the truss portion of the concrete slab is calculated using the converted elastic modulus E. s A s +E c Ac =E0A0, perform conversion, convert the elastic modulus E0 = (E s A s +E c A c ) / A0, where E s A s These represent the elastic modulus and cross-sectional area of ​​the reinforcing steel, E. c A c These are the elastic modulus and cross-sectional area of ​​concrete, respectively, with A0 being the converted cross-sectional area.

[0081] (2) Material constitutive

[0082] For the macroscopic concrete beam model, since it's impossible to directly define the concrete damage plasticity (CDP) constitutive model for the beam elements, and since the loss of the beam elements themselves is not the primary concern, an ideal elastoplastic stress-strain relationship is adopted for the concrete beam elements to achieve overall macroscopic deformation consistency. The stress-strain calculation for the concrete beam elements is as follows:

[0083]

[0084] In the above formula: f c ε is the compressive strength of concrete. c =f c / E0 represents the strain corresponding to the compressive strength; E0 is the converted elastic modulus ε. i Equivalent strain of concrete; σ i This refers to the equivalent stress in concrete. Figure 4 This is the elastoplastic stress-strain diagram for a concrete beam element.

[0085] 2. Steel beams

[0086] (1) Simplification of steel beams

[0087] In the macroscopic truss model, it is simplified into beam elements with steel beam sections, and each segment is combined separately in the dual-scale model. The simplification process is as follows: Figure 5 As shown. For the macroscopic truss model, the steel beams are represented by beam elements.

[0088] (2) Material constitutive

[0089] Through extensive experimental and theoretical research on the constitutive model of steel by scholars both domestically and internationally, the constitutive model has gradually matured and can well reflect the stress-strain relationship of steel during the stress process. For steel beams, a two-segmented model is used, and its stress-strain relationship is as follows: Figure 6 As shown.

[0090] The formula for calculating the stress-strain of a steel beam is as follows:

[0091]

[0092] Among them, E s For the elastic modulus of the steel beam, σ s ε s These represent the stress and strain of the steel beam, respectively. y ε y For the yield strength and yield strain of the steel beam, f u ε u These represent the ultimate strength and ultimate strain of steel.

[0093] 3. Shear members

[0094] (1) Simplification of shear members

[0095] In actual bridge structures, the number of shear keys is enormous. Modeling them using solid elements presents challenges such as complex contact issues, high nonlinearity, and significant computational costs. Therefore, spring elements are used to simulate the mechanical behavior of shear members. The basic idea is to use two-node spring elements to establish a connection between the bottom of the concrete slab and the upper flange of the steel beam. By defining combined connection properties, the mechanical behavior of the shear members in translational and rotational directions is described. The simplified process is as follows: Figure 7 As shown.

[0096] (2) Constitutive model of shear member

[0097] The stress process of a shear member mainly includes the friction stage, slip stage, elastic stage, and elastoplastic stage, and its load-slip curve is as follows: Figure 8 As shown, (a) represents the actual load-slip of the shear member, and (b) represents the simplified load-slip of the shear member. The mechanical behavior of the actual shear member is simulated by defining the constitutive relation of the load-slip curves of the connection elements.

[0098] Model simplification in small-scale regions:

[0099] 1. Bridge deck

[0100] In the detailed model, the bridge deck is arranged in the same position as in reality and uses solid elements, while the reinforcing bars are represented by truss elements.

[0101] (1) Material constitutive model

[0102] For the refined model part, the concrete slab solid elements adopt nonlinear constitutive relations, such as the constitutive relations in Appendix C.2 of the Code for Design of Concrete Structures. Figure 9 This is a stress-strain diagram of concrete under compressive stress. Figure 10 This is a tensile stress-strain diagram of concrete.

[0103] ①Constituent of concrete under uniaxial compression

[0104] σ=(1-d cE c ε

[0105]

[0106] in,

[0107] ②Concrete uniaxial tension constitutive model

[0108] σ=(1-d t E c ε

[0109]

[0110] in,

[0111] The stress-strain relationship of the reinforcing steel using an ideal elastic-plastic constitutive model is as follows: Figure 11 As shown.

[0112] The stress-strain calculation formula for ordinary steel reinforcement is as follows:

[0113]

[0114] Where: σ j E represents the equivalent stress of ordinary steel reinforcement. s ε is the elastic modulus of ordinary steel reinforcement; j The equivalent strain of ordinary steel reinforcement; f y This represents the yield strength of ordinary steel reinforcement.

[0115] 2. Steel beams

[0116] In the refined model, the steel beams are arranged in the same positions as in reality and thin-walled shell elements are used.

[0117] (1) Material constitutive model

[0118] The steel beam is modeled using a two-segmented line, and its stress-strain relationship is as follows: Figure 12 As shown.

[0119] The formula for calculating the stress-strain of a steel beam is as follows:

[0120]

[0121] Among them, E s For the elastic modulus of the steel beam, σ s ε s These represent the stress and strain of the steel beam, respectively. y ε y For the yield strength and yield strain of the steel beam, f u ε u These represent the ultimate strength and ultimate strain of steel.

[0122] Connecting regions at different scales:

[0123] Because different elements have different degrees of spatial freedom, rigid connections are used to couple them in order to achieve force balance and deformation coordination. Beam element nodes are designated as master nodes, while points on solid and shell elements are designated as slave nodes. Master nodes are connected to beam element nodes in the refined model via rigid arms, ensuring deformation coordination between master and slave nodes.

[0124] interaction:

[0125] After assembling all components, it is necessary to define the contact relationships between them. This mainly includes the contact relationship between the concrete slab and the steel beam, and the contact relationship between the steel mesh and the concrete slab in the detailed model. Furthermore, for the macroscopic model, since the steel beam and bridge deck are connected by spring elements, it is not necessary to set contact relationships.

[0126] 1. Interface contact between concrete slab and steel beam

[0127] Considering that the bond force between the steel beam and the concrete slab is negligible, a normal "hard contact" and a tangential "frictionless" contact relationship is set for the steel-concrete interface.

[0128] 2. Interface contact between steel mesh and concrete slab

[0129] The reinforcing mesh shares the load with the concrete. To prevent premature cracking of the concrete, the bond slip between the reinforcing mesh and the concrete slab is ignored. Instead, the reinforcing mesh is embedded in the concrete slab to simulate the contact relationship between the two.

[0130] Loads and boundary conditions: Arranged according to actual conditions.

[0131] Grid generation:

[0132] After the interfaces are in contact, the components need to be meshed. The appropriateness of the mesh generation has a significant impact on the model's computation time and accuracy. If the mesh size is coarse, the calculation accuracy may be insufficient, contradicting the actual force conditions. If the mesh size is too fine, the calculation results will be more accurate, but the computational efficiency will be significantly reduced. Therefore, for different types of models, the mesh size should be determined according to the different forces acting on the components to ensure more accurate force transmission simulation at specific locations.

[0133] Example:

[0134] To verify the correctness of the dual-scale model, a fully prefabricated composite beam was selected as the research object. Specific geometric dimensions and reinforcement configuration are as follows: Figure 13As shown, the composite beam bridge deck is composed of three precast concrete slabs glued together. Bolted shear connectors are used in the middle to transfer the shear force between the precast concrete slabs and the steel beams. These connectors are arranged in two rows along the beam, with two bolts forming a group. Within each group, the bolts are spaced 100mm laterally and 330mm longitudinally. The test beam is 3000mm long with a clear span of 2800mm. The precast concrete slabs are 600mm wide and 100mm high.

[0135] Dual-scale modeling was performed using the large-scale finite element software ABAQUS, and compared with a full solid model. The specific model is as follows: Figure 14 As shown.

[0136] Comparing the full-solid model and the two-scale model under self-weight, the results are as follows: Figure 15 , Figure 16 As shown.

[0137] As shown in the figure, the stress and deflection deformation trends of the two-scale model and the refined model of the full-solid model are basically consistent. Regarding stress, the maximum compressive stress at the upper flange of the bridge deck at mid-span in the full-solid model and the two-scale model are 0.147 MPa and 0.162 MPa, respectively, while the maximum tensile stress at the lower flange of the steel beam at mid-span is 1.815 MPa and 1.869 MPa, respectively, differing by 10.2% and 3.0%. The stress difference along the beam length direction at the upper flange of the bridge deck in the two-scale model is mainly due to material simplification. Regarding deflection, the maximum deflection at mid-span of the bridge deck in the full-solid model and the two-scale model is 4.04 × 10⁻⁴ MPa, respectively. -2 mm, 3.79×10 -2 mm, the maximum deflection at mid-span of the steel beam is 4.0×10 mm. -2 mm, 3.79×10 -2 The differences are 6.2% and 5.3% respectively, in mm.

[0138] Table 1 Comparison of Calculation Results between Full Solid Model and Two-Scale Model

[0139]

[0140] In summary, the dual-scale model, while sacrificing some accuracy, can better reflect the mechanical behavior of structures at both the macroscopic and microscopic scales, and has higher computational efficiency, making it suitable for calculations of large composite bridge structures.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications should be covered within the scope of the claims of the present invention.

Claims

1. A dual-scale finite element analysis method for steel-concrete composite bridges, characterized in that: The method includes the following steps: S1. In the steel-concrete composite bridge model, establish the division of large-scale and small-scale regions to clarify the focus of local stress analysis; S2. Establish large-scale and small-scale regional components and select the unit types for each component to simplify the dual-scale model; S3. Define the material constitutive model of large-scale and small-scale components to achieve consistency in the material scale between macroscopic and fine-scale units; S4. Complete the assembly of the spatial positions of each component and the connection of large and small scale areas to achieve consistency between macroscopic and fine model deformation; S5. Define the internal contact of each component and complete the mesh generation; S6. Apply actual loads and set actual boundary conditions to perform dual-scale finite element analysis; In step S1, the large-scale region reflects the macroscopic stress and deformation of the structure, while the small-scale region reflects the local damage of the structure. When determining the small-scale refined region, the area where the structure is prone to local failure is selected. In order to avoid the influence of boundary conditions on the results of the main analysis parts and to focus on the stress analysis of the main local structure, the length of the small-scale refined region where the structure is prone to local failure is selected as 1 to 2 times the beam height. In step S2, model simplification includes model simplification in large-scale regions and model simplification in small-scale regions; the model simplification in large-scale regions includes simplification of bridge decks, steel beams, and shear members, specifically including: Bridge deck: 1) Bridge deck simplification: In the macroscopic frame model, it is simplified into beam elements of concrete slab sections, and each segment is combined separately in the dual-scale model; for the macroscopic frame model, the concrete slab is represented by beam elements, and the elastic modulus of the concrete slab frame part is based on the converted elastic modulus E. s A s +E c A c =E0A0, perform conversion, convert the elastic modulus E0 = (E s A s +E c A c ) / A0, where E s A s These represent the elastic modulus and cross-sectional area of ​​the reinforcing steel, E. c A c These are the elastic modulus and cross-sectional area of ​​concrete, respectively, with A0 being the converted cross-sectional area. 2) Material Constitutive Mechanism: An ideal elastic-plastic stress-strain relationship is adopted for the concrete beam element. The stress-strain calculation for the concrete beam element is as follows: In the above formula: f c ε is the compressive strength of concrete. c =f c / E0 represents the strain corresponding to the compressive strength; E0 represents the converted elastic modulus ε. i Equivalent strain of concrete; σ i Equivalent stress in concrete; Steel beams: 1) Simplification of steel beams: In the macroscopic truss model, the steel beams are simplified into beam elements of steel beam sections, and each segment is combined in the dual-scale model. For the macroscopic truss model, the steel beams are represented by beam elements. 2) Material Constitutive Model: The constitutive model can well reflect the stress-strain relationship of steel during the stress process. For steel beams, a two-segment model is used, and the stress-strain relationship calculation formula is as follows: Among them, E s For the elastic modulus of the steel beam, σ s ε s These represent the stress and strain of the steel beam, respectively. y ε y For the yield strength and yield strain of the steel beam, f u ε u The ultimate strength and ultimate strain of steel; Shear components: 1) Simplification of shear members: Spring elements are used to simulate the mechanical behavior of shear members. A connection is established between the bottom of the concrete slab and the upper flange of the steel beam using a 2-node spring element. The mechanical behavior of the translational and rotational directions of the shear members is described by defining the combined connection properties. 2) Shear member constitutive model: The stress process of a shear member mainly includes the friction stage, slip stage, elastic stage and elastoplastic stage. By defining the load-slip curve constitutive relationship of the connection element, the mechanical behavior of the actual shear member is simulated.

2. The dual-scale finite element analysis method for steel-concrete composite bridges according to claim 1, characterized in that: The model simplification for the small-scale region includes: Bridge deck: In the detailed model, the bridge deck is arranged in the same positions as in reality and uses solid elements, while the reinforcing steel uses truss elements; Material constitutive model: For the detailed model part, the concrete slab solid elements use nonlinear constitutive relations; ①Constituent of concrete under uniaxial compression σ=(1-d c )E c e in, ②Concrete uniaxial tension constitutive model σ=(1-d t )E c e in, The stress-strain calculation formula for ordinary steel reinforcement is as follows: Where: σ j E represents the equivalent stress of ordinary steel reinforcement. s ε is the elastic modulus of ordinary steel reinforcement; j The equivalent strain of ordinary steel reinforcement; f y The yield strength of ordinary steel bars; Steel beams: In the refined model, the steel beams are arranged in the same positions as in reality and use thin-walled shell elements; Material constitutive model: The steel beams adopt a two-segmented model, and the stress-strain calculation formula for the steel beams is as follows: Among them, E s For the elastic modulus of the steel beam, σ s ε s These represent the stress and strain of the steel beam, respectively. y ε y For the yield strength and yield strain of the steel beam, f u ε u These represent the ultimate strength and ultimate strain of steel.

3. The dual-scale finite element analysis method for steel-concrete composite bridges according to claim 2, characterized in that: In step S4, since the spatial degrees of freedom are different between different elements, rigid connections are used to couple the elements in order to achieve force balance and deformation coordination among the three. The beam element nodes are the master nodes, and the points on the solid and shell elements are the slave nodes. The master nodes are connected to the beam element nodes in the refined model through rigid arms, which ensures the deformation coordination between the master and slave nodes.

4. The dual-scale finite element analysis method for steel-concrete composite bridges according to claim 3, characterized in that: In step S5, after assembling all components, it is necessary to define the contact surface relationships of each component. This mainly includes the contact relationship between the concrete slab and the steel beam, and the contact relationship between the reinforcing mesh and the concrete slab in the refined model. Furthermore, for the macroscopic model, since the steel beam and the bridge deck are connected by spring units, it is not necessary to set contact relationships. Specifically, this includes: 1) Interface contact between concrete slab and steel beam: Considering that the bond force between the steel beam and the concrete slab can be ignored, the steel-concrete interface is set to a normal "hard contact" and a tangential "frictionless" contact relationship; 2) Interface contact between steel mesh and concrete slab: The steel mesh is subjected to stress in the concrete. In order to ensure that the concrete does not crack prematurely, the bond slip effect between the steel mesh and the concrete slab is ignored. The steel mesh is embedded in the concrete slab to simulate the contact relationship between the two.

5. The dual-scale finite element analysis method for steel-concrete composite bridges according to claim 4, characterized in that: In step S5, after the interfaces come into contact, the components need to be meshed. For different types of models, the mesh size should be divided according to the different forces acting on the components to ensure more accurate force transmission simulation at special locations.

6. A dual-scale finite element analysis system for steel-concrete composite bridges, characterized in that: The system employs the method described in any one of claims 1 to 5.

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