Thermal-mechanical coupling response analysis method and system for fiber unit of concrete structure

The fiber element thermo-mechanical coupling response analysis method solves the problems of high cost and low efficiency in the existing technology of thermo-mechanical coupling response analysis of concrete structures, and realizes rapid and accurate assessment of large building complexes under multi-hazard scenarios, which is applicable to complex scenarios combining fire and earthquake.

CN121809073APending Publication Date: 2026-04-07TONGJI UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-29
Publication Date
2026-04-07

AI Technical Summary

Technical Problem

Existing technologies for analyzing the thermo-mechanical coupling response of concrete structures suffer from high computational costs, low efficiency, complex modeling, and difficulty in meeting the rapid assessment needs of large building complexes under multi-hazard scenarios. In particular, when fire and earthquake are combined, the prediction results are biased.

Method used

The fiber element thermo-mechanical coupling response analysis method is adopted. By establishing a fiber element numerical model of the concrete structure, heat conduction analysis and mechanical response analysis are separated. An improved constitutive model and object-oriented programming are used, combined with the Galerkin method and implicit finite difference method to calculate the temperature field. The temperature data is then mapped through an inverse distance weighted interpolation algorithm to build an integrated analysis system.

Benefits of technology

It enables rapid and accurate analysis of large structures in multi-hazard scenarios, reduces computational load, improves analysis efficiency, accurately reflects the physical differences between the protective layer and the core area, reduces human error, and is suitable for simple fire or complex multi-hazard scenarios.

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Abstract

The invention relates to a concrete structure fiber unit thermal-mechanical coupling response analysis method and system. Firstly, a fiber unit numerical model of a concrete structure is established according to a required analysis structure; secondly, creating a concrete section heat transfer analysis object, and calculating and outputting section temperature field data based on the concrete section heat transfer analysis object; then carrying out stress or disaster working condition simulation processing on the fiber unit numerical model of the concrete structure to obtain a processed fiber unit numerical model; finally, section temperature field data are read and mapped to the processed fiber unit numerical model, coupling calculation of a temperature field and a mechanical field is carried out, and a thermal-mechanical coupling response analysis result of the concrete structure is obtained and output. Compared with the prior art, the method has the advantages of high precision, high efficiency and the like.
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Description

Technical Field

[0001] This invention relates to the field of concrete structure technology, and in particular to a method and system for analyzing the thermo-mechanical coupling response of fiber units in concrete structures. Background Technology

[0002] Thermo-mechanical coupling response analysis of concrete structures is one of the key technologies for studying the performance of concrete structures under high-temperature environments. Rapid prediction and evaluation of their performance under fire and related multi-hazard effects (such as earthquake-fire) are of great strategic significance for disaster prevention and mitigation of urban infrastructure and for improving structural safety and toughness.

[0003] Currently, the main analytical methods used in academia and engineering are experimental research and numerical simulation. 1. Experimental Research Methods The experimental research primarily focuses on beams, columns, or small structures (such as a single, independent concrete frame or a small concrete structure). The procedure typically involves applying static, cyclic, or seismic time-history loads to the specimen, then placing it in a high-temperature furnace and applying a pre-set heating program to create a high-temperature environment. During the experiment, the structure's deformation and stress behavior are monitored, and its residual displacement and bearing capacity are measured after the experiment to evaluate its residual performance.

[0004] However, this method is costly and limited in size. Analyzing through testing is often expensive, and existing laboratory conditions only support fire load application on small components. For example, a university's engineering structure fire resistance laboratory only supports components or structures smaller than 4.5m × 3.0m × 2.2m, while actual engineering scenarios and needs often involve large buildings or even large-scale building complexes, which existing testing methods cannot cover.

[0005] 2. Numerical simulation methods Numerical simulation analysis mainly uses the finite element or discrete element method. A solid finite element / discrete element model of the real structure is established by computer, and constitutive relation curves that consider temperature degradation are used to simulate the stress-strain relationship of concrete and steel materials under the combined action of force and high temperature.

[0006] However, this method generally requires high computing power and is time-consuming. Numerical simulation using the solid finite element / discrete element method has significant drawbacks, such as high modeling requirements, high computing power requirements, and long computation time. Under mainstream computing environments (such as 12th generation Intel i7 processors), the computation time for a single concrete structure can even reach up to 3 days, which greatly limits the analysis efficiency.

[0007] Furthermore, these methods are difficult to model and have poor convergence. They require a very high level of modeling skill and are prone to non-convergence of calculation results when dealing with complex nonlinear thermo-mechanical coupling problems.

[0008] For example, the invention patent with publication number CN116975986A discloses a method for analyzing the fire resistance response of concrete beam bridge structures. This method determines the thermal performance indicators of materials in the temperature field analysis of box girder bridge sections, performs transient temperature field analysis, and uses a thermal-structural coupling analysis method to analyze the high-temperature mechanical properties of prestressed concrete box girder bridges. Although this method solves the problem of parameter uncertainty in the fire resistance analysis of prestressed box girder bridges to a certain extent and simplifies some modeling processes, it still has shortcomings when dealing with "multi-hazard" scenarios: First, such methods are usually based on detailed solid modeling, which is computationally expensive and difficult to meet the timeliness requirements of rapid post-disaster assessment of large building complexes; second, it is often limited to a single fire condition and fails to effectively consider the cumulative destructive effect of earthquake damage (such as cracking and spalling) coupled with high temperature on the structure, resulting in deviations in the prediction results under cascading disaster scenarios.

[0009] In summary, existing methods generally suffer from problems such as difficulty in balancing accuracy and efficiency in computational models, neglect of the difference mechanism between protective layer peeling and core area constraints in cross-sectional analysis, lack of flexibility in mesh generation, and fragmented multi-hazard simulation processes. These issues make it difficult for current technologies to meet the needs of rapid, accurate, and full-process multi-hazard performance assessment of large and complex structures in resilient city construction. Summary of the Invention

[0010] The purpose of this invention is to overcome the defects of the prior art by providing a method and system for analyzing the thermo-mechanical coupling response of fiber units in concrete structures.

[0011] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures is provided, characterized in that the method includes the following steps: S1. Based on the required analysis structure, establish a fiber element numerical model of the concrete structure; S2. Create a concrete section heat transfer analysis object, and calculate and output the section temperature field data based on the concrete section heat transfer analysis object; S3. Perform stress or disaster-induced working condition simulation on the fiber element numerical model of the concrete structure to obtain the processed fiber element numerical model. S4. Read and map the cross-sectional temperature field data to the processed fiber element numerical model, perform coupled calculations of the temperature field and mechanical field, and obtain and output the thermo-mechanical coupling response analysis results of the concrete structure.

[0012] As a preferred technical solution, the specific steps for S1 to establish a fiber element numerical model of a concrete structure include: Define node coordinates, and based on these coordinates, create concrete material objects, reinforcement material objects, and concrete section objects using object-oriented programming methods. The concrete material objects include protective layer concrete material objects and core area concrete material objects. Create a parent class for concrete sections and a subclass for mesh generation, and combine the geometric parameters and reinforcement information of the concrete section objects to generate a fiber mesh for the sections. Assign the concrete material objects and reinforcement material objects to the fiber mesh, and connect the nodes to generate fiber elements, thereby establishing a fiber element numerical model of the concrete structure.

[0013] As a preferred technical solution, the improved Kent-Scott-Park constitutive model is used when creating concrete material objects, and the improved Giuffre-Menegotto-Pinto constitutive model is used when creating steel reinforcement material objects. Improved Kent-Scott-Park and Giuffre-Menegotto-Pinto constitutive models are introduced, and a standardized mesh generation interface is provided. Specific stress-strain algorithms are embedded in material objects, taking into account hysteresis rules; rectangular or linear fiber meshes are automatically generated through preset interfaces, achieving accurate description of cyclic stress behavior and automated modeling.

[0014] The specific process of generating the fiber mesh of the cross section includes: designing the parent class of the cross section mesh, calculating the coordinates of the key positioning points of the cross section based on the input cross section geometry, protective layer thickness and reinforcement information, and providing method interfaces for generating rectangular concrete fiber mesh, linear batch generation of steel reinforcement fibers and single generation of steel reinforcement fibers.

[0015] As a preferred technical solution, when creating a concrete material object, the restraining effect of stirrups on the core area concrete is considered. The specific process includes: Obtain the stirrup ratio, yield strength, spacing, and core area cross-sectional dimensions; Calculate the constraint enhancement factor and the descent slope reduction factor; Using the aforementioned constraint enhancement coefficient and descent slope reduction coefficient, the compressive strength, peak compressive strain, and ultimate compressive strain parameters of the core area concrete are corrected to generate the core area concrete material object.

[0016] As a preferred technical solution, the specific steps of S2 include: A concrete section heat transfer analysis object is created based on object-oriented programming. The material thermal properties and external fire conditions of the heat transfer analysis object are defined. The section boundary conditions are set and temperature interpolation monitoring points are selected. The two-dimensional transient heat transfer differential equation is solved using the Galerkin method and the implicit finite difference method. The section temperature field data of the specified monitoring points changing with time are calculated and output.

[0017] Combining the Galerkin method (spatial discretization) and the implicit finite difference method (temporal discretization) to solve the heat conduction equation results in high numerical stability and improved computation speed; it also adapts to nonlinear boundaries and can well handle convection and radiation boundary conditions that change drastically with temperature in fires.

[0018] As a preferred technical solution, in S2, the solution of the two-dimensional transient heat transfer differential equation is based on the following assumptions: the three-dimensional heat transfer problem is simplified into a two-dimensional plane problem, the axial heat transfer inside the structure is ignored, and the influence of steel bars on heat transfer is not considered. The cross section is analyzed as a plain concrete cross section. The boundary condition adopts the convective heat transfer boundary condition. Based on the principle of energy conservation, the sum of the thermal radiation energy and thermal convection energy received by the surface of the structure is calculated as the external heat load.

[0019] As a preferred technical solution, the specific process of defining the material thermal properties of the heat transfer analysis object includes: real-time calculation of the thermal conductivity, specific heat capacity and density of concrete material as temperature changes; the calculation formulas for thermal conductivity, specific heat capacity and density are based on the European standard Eurocode2, and the effect of heat absorption by evaporation of water inside the concrete on the inhibition of temperature rise is considered, and the peak value of specific heat capacity is corrected by setting the moisture content parameter.

[0020] By employing nonlinear thermal parameters that vary with temperature and introducing moisture content-corrected specific heat capacity, the thermal conductivity and density are updated in real time. Particularly in the 100℃-200℃ range, the specific heat capacity of concrete is artificially increased to simulate the heat absorption due to moisture evaporation. This method accurately captures the temperature plateau formed by moisture evaporation within the concrete, preventing overestimation of the internal temperature of the structure in the initial stages of analysis. The Eurocode 2-based parameter settings ensure that the analysis results have internationally recognized engineering acceptance.

[0021] As a preferred technical solution, the stress or disaster-affected condition simulation processing of the fiber element numerical model of the concrete structure in S3 includes: Determine if seismic action exists in the current working condition: if not, apply only static load to obtain the processed fiber element numerical model; if yes, apply static load and seismic motion time history load, and unload the seismic action after the seismic action ends, retaining the residual deformation and damage state of the structure to obtain the processed fiber element numerical model.

[0022] As a preferred technical solution, in S4, the specific implementation scheme for mapping the cross-sectional temperature field data to the processed fiber element numerical model includes: When creating the concrete section heat transfer analysis object in step S2, n×n grid interpolation monitoring points are defined, where n is an integer between 9 and 50; In step S4, the thermo-coupling analysis object receives an external file containing temperature data from the n×n monitoring points, and calculates the temperature of the fiber at any position within the cross-section of the fiber unit at any time using inverse distance weighted interpolation.

[0023] According to another aspect of the present invention, a system for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures is provided, the system comprising: The fiber element modeling module creates a fiber element numerical model of the concrete structure based on the required analysis structure. The heat transfer analysis module is used to create a heat transfer analysis object, calculate the cross-sectional temperature field considering the nonlinear thermal parameters of the material and the equivalent boundary conditions, and automatically export the temperature data file of the monitoring point. The thermo-coupling analysis module is used to read temperature data files, map the temperature field to fiber units, and perform thermo-coupling analysis calculations. The evaluation module is used to monitor the force, displacement, and stress-strain response of the structure under multi-field coupling, assess the residual function of the structure to be analyzed, and output the thermo-mechanical coupling response analysis results of the concrete structure.

[0024] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention employs a fiber element analysis framework based on sequential coupling, decoupling thermal conduction analysis from mechanical response analysis and re-linking them through data mapping. In this method, a fiber model is first established, then the cross-sectional temperature field is calculated independently, followed by simulation of stress and disaster, and finally, the temperature field is mapped back to the mechanical model for coupled calculation. Compared to solid elements, fiber elements significantly reduce computational load; compared to macroscopic beam-column elements, they can accurately consider non-uniform temperature gradients and material nonlinearities within the cross-section, making them suitable for the overall analysis of large structures, thus balancing accuracy and efficiency. Decoupling thermal and mechanical analysis makes this method applicable to both simple fire analysis and complex post-earthquake fire and other multi-hazard scenario simulations, demonstrating strong versatility.

[0025] 2. In this invention, by employing object-oriented programming principles, concrete is divided into two independent objects: the protective layer and the core area. A parent / child class architecture is used to generate a mesh. Different material properties are encapsulated at the code level, and at the physical level, different material labels are assigned to the edges (protective layer) and the center (core area) during cross-sectional mesh generation. This allows the method to accurately reflect the physical fact that the protective layer concrete is prone to spalling and peeling under high temperatures during a fire, while the core area has better confinement due to the stirrups, avoiding errors caused by homogenization. The object-oriented hierarchical structure means that subsequent modifications to the material model or mesh algorithm do not require a complete system reconstruction, resulting in good program scalability.

[0026] Furthermore, this method calculates the constraint enhancement coefficient based on stirrup parameters to correct the peak parameters of the core area concrete. The algorithm automatically reads parameters such as the stirrup ratio, increases the compressive strength and ultimate compressive strain of the core area concrete, and decreases the slope of the descending segment. The constraint gain is quantified, and the corrected model can more accurately predict the ultimate bearing capacity and failure mode of the component, avoiding underestimation of the fire resistance and seismic performance of the structure due to neglecting the constraint effect.

[0027] 3. In this invention, a two-dimensional planar heat transfer assumption is adopted, and the radiative and convective heat fluxes are calculated comprehensively based on the principle of energy conservation. Furthermore, the temperature difference along the length of the component is ignored, and only the heat flow within the cross-section is calculated; the complex environmental thermal effects are simplified to an equivalent heat load input. The three-dimensional thermal analysis is simplified to two dimensions, reducing the calculation time by an order of magnitude while ensuring the accuracy of the beam-column component analysis, significantly improving computational efficiency; and the physical meaning is clear, with the boundary conditions of combined radiation and convection accurately reproducing the heating mechanism of the structural surface in a real fire.

[0028] 4. In this invention, an n×n grid interpolation monitoring point is used in conjunction with an inverse distance weighted interpolation algorithm. The heat transfer module outputs the temperature at fixed grid points, while the mechanical module calculates the temperature at any fiber location using the inverse distance weighted interpolation algorithm. This solves the grid mismatch problem, allowing the thermal analysis grid and the mechanical fiber grid to have different densities and partitioning methods, without requiring a one-to-one correspondence, greatly improving the flexibility of grid partitioning; moreover, data transmission is smooth, and the inverse distance weighted interpolation ensures the continuity of the temperature field within the cross-section, avoiding abrupt changes or distortions in temperature data during transmission.

[0029] 5. This invention constructs an integrated system comprising four functional modules: modeling, heat transfer, coupling, and evaluation. By encapsulating each functional module, an automated data flow and processing workflow is formed. Users no longer need to manually transfer data between different software programs, reducing human error and enabling one-click analysis; furthermore, the evaluation module can integrate data from multiple fields and directly output structural safety indicators, lowering the barrier to professional analysis. Attached Figure Description

[0030] Figure 1This is a schematic diagram illustrating the steps of a method for analyzing the thermo-mechanical coupling response of fiber units in a concrete structure according to the present invention. Figure 2 This is a flowchart illustrating the specific process of analyzing the thermo-mechanical coupling response of fiber units in a concrete structure in this embodiment. Figure 3 This is a schematic diagram illustrating the operation and running principle of OpenSees in the embodiment; Figure 4 This is a design framework diagram of the fiber unit modeling steps in the embodiment; Figure 5 This is a schematic diagram illustrating the principle of fiber cross-section generation in the concrete structure in the embodiment; Figure 6 This is a schematic diagram of the cross-sectional mesh generation parameters in the embodiment; Figure 7 A cross-sectional view is drawn for the embodiment; Figure 8 This is a design framework diagram of the heat transfer analysis step class in the embodiment; Figure 9a This is a schematic diagram of one-dimensional interpolation input in the embodiment; Figure 9b This is a schematic diagram of a two-dimensional H-beam in the embodiment; Figure 9c This is a schematic diagram of the two-dimensional grid interpolation input in the embodiment; Figure 9d This is a schematic diagram of the two-dimensional encrypted grid interpolation input in the embodiment; Figure 10 The graph shows a comparison between the column top displacement versus time curve obtained from the process calculation in the embodiment and the experimental results. 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, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0032] In this embodiment The detailed implementation flowchart of this method is as follows: Figure 2 As shown.

[0033] The fiber element modeling process consists of geometric modeling, concrete and steel reinforcement material property modeling, cross-sectional fiber element division, and element connection, used to establish numerical models at the component or structural scale. Subsequently, the heat transfer analysis applies the set fire load to the surface of the fire-affected component through thermal radiation and convection, automatically generating the temperature field input file and loading instructions required for subsequent analysis. Finally, while maintaining the static load on the structure or component, the cyclic load or seismic time history is unloaded, and the temperature field data is input and transferred to the heat analysis step (flow). This step (flow) is responsible for monitoring and recording parameters such as force and displacement of the concrete structure under subsequent fire exposure to assess the final residual function of the concrete structure.

[0034] The material property objects, concrete section heat transfer analysis objects, and concrete structure thermo-mechanical coupling analysis objects were created using Python and C++, with OpenSees used as the solver for the fiber element method. OpenSees supports both Tcl (Tool Command Language, a lightweight scripting language) and Python for command operations. The operation and running principles of OpenSees are as follows: Figure 3 As shown.

[0035] I. Fiber Unit Modeling Modeling fiber elements for concrete structures involves five steps: node definition, material property definition, fiber section definition, section integration, and element generation. While the material property and section definition processes are relatively fixed, determining their parameters is cumbersome, often requiring manual calculation or auxiliary tools like Excel in existing methods. This solution utilizes object-oriented programming to create material property and fiber section objects, enabling rapid assignment of reinforced concrete properties and rapid section division. The method establishes a design framework for relevant classes in the fiber element modeling step, such as… Figure 4 As shown in the diagram, the items in bold in the properties and methods are private properties (methods), meaning they cannot be accessed or modified outside the class and are automatically calculated and generated within the class. When designing the class, to protect the properties of subsequently created objects from being arbitrarily modified outside the class, all object properties are protected as private, with only basic instructions such as constructors and some methods available for user operation.

[0036] First, material objects are created. For the material properties of concrete and reinforcing steel, the improved Kent-Scott-Park constitutive model, which considers constitutive relation degradation at high temperatures, and the improved Giuffre-Menegotto-Pinto constitutive model are used to define various properties in the concrete and reinforcing steel material objects, respectively. Furthermore, since fiber elements cannot model stirrups, the improved Kent-Scott-Park constitutive model is used to enhance the compressive strength of the core concrete to account for the influence of stirrups. The material parameters of the core concrete are calculated using the following formula: ; ; ; ; ; In the formula, f c , ε c0 , ε u , f cu These are the concrete's compressive strength, peak compressive strain, ultimate compressive strain, and ultimate compressive strength, respectively. f c ' , ε c0 ' , ε u ' , f cu ' These are the compressive strength, peak compressive strain, ultimate compressive strain, and ultimate compressive strength of the reinforced core concrete. K To account for the reinforcement factor of the stirrups' confinement effect, ; Z The reduction factor for the slope of the descending segment considering the restraining effect of stirrups; ρ s The stirrup ratio is used for the stirrups. f ys The yield strength of the stirrup; b cor The cross-sectional width of the core area concrete. s str This refers to the spacing between the stirrups.

[0037] Based on the above constitutive model, and following object-oriented programming methods, a parent class for materials and three subclasses for concrete cover material, core concrete material, and reinforcing steel material are designed, allowing users to create corresponding concrete and reinforcing steel material objects. The parent class has two methods: one for displaying material parameter information and the other for quickly adding material properties to the fiber element numerical model. The subclasses are used to calculate key parameters of the concrete cover, core concrete, and reinforcing steel material properties, respectively. Python is used to implement the creation of material objects, and the process for creating material objects is described in detail below: First, create a concrete section object (variable name Sec) based on the set concrete section height h, width w, and protective layer thickness c.

[0038] Subsequently, a specific material object (variable name Mat) is created according to actual needs. The creation methods include the following three scenarios: First, create a protective concrete material object that is independent of the cross-sectional dimensions. This process requires inputting the material number, the 28-day compressive strength of the concrete, the corresponding strain when the strength is reached, the ultimate compressive strength of the concrete, and the corresponding strain when it is crushed. Second, based on the aforementioned concrete section object, a core area concrete material object is created. In addition to inputting the aforementioned concrete constitutive parameters and material number, this process also requires setting stirrup parameters, including stirrup yield strength, stirrup diameter, stirrup spacing, and the number of stirrup legs along the local coordinate axes z and y (the default value is 2 for both). Third, create a steel reinforcement material object. This process requires inputting the material number, steel yield strength, elastic modulus in the elastic stage, and strain hardening ratio.

[0039] Finally, after the material object is constructed, the specific parameter information of the object is obtained by querying the command, and the material object is quickly added to the fiber element numerical model by executing the command, and finally handed over to the OpenSees program for calculation.

[0040] In existing technologies (taking the OpenSees analysis framework as an example), the generation of concrete fiber sections typically consists of multiple independent steps, the specific process and parameter definitions of which are as follows: Step 1: Define the overall section properties. First, use the `section` command to create a section object. In this step, you need to specify the section number (secTag) and the linear elastic torsional stiffness (GJ). For concrete members where torsion is not usually considered, this torsional stiffness GJ is often set to a very large value.

[0041] Step 2: Generate the concrete fiber mesh. For the concrete material in the section, define the fibers using the `patch` command to generate a rectangular mesh. This command requires defining the following parameters: Material label (matTag): Specifies the material number corresponding to the concrete in this area; Number of mesh elements (numSubdivY, numSubdivZ): Specifies the number of elements to be divided along the local coordinate axes y-axis and z-axis, respectively; Region coordinates (*crdsI, *crdsJ): Specifies the lower left vertex of the rectangular fiber region respectively. y i , z i ) and the coordinates (yj, zj) of the top right vertex.

[0042] Step 3: Generate reinforcing steel fibers: For reinforcing steel materials in the cross section, the layer command is usually used to generate a group of fibers along a straight line, or the fiber command is used to generate a single fiber.

[0043] The layer command parameters require defining the material label, the number of rebars generated (numFiber), the cross-sectional area of ​​a single rebar (areaFiber), and the coordinates of the starting point (*start) and ending point (*end) of the generated line.

[0044] The fiber command parameters require defining the location coordinates (yloc, zloc), area (A), and material label of a single rebar.

[0045] A typical example of generating a reinforced concrete section is as follows: For a typical rectangular reinforced concrete section (such as...) Figure 5 As shown in the figure, when using the above method for discretization modeling, the code logic is usually quite cumbersome, requiring the handling of the following parts separately: Core area concrete: A core area rectangular mesh is generated by calling a patch command once.

[0046] Protective concrete layer (four corners): The patch command needs to be called four times to independently generate the protective concrete blocks for the top left, top right, bottom left, and bottom right corners.

[0047] Protective concrete (four sides): The patch command needs to be called four times to independently generate the protective concrete strips on the top, bottom, left and right sides.

[0048] Longitudinal reinforcement: Based on the reinforcement layout, the layer command needs to be called multiple times to generate the upper, lower and side (such as column members) reinforcement layers respectively.

[0049] In summary, existing methods require repeatedly calling generation commands more than ten times or even more times based on the geometric partitions of the section when defining a complete reinforced concrete fiber section, and manually calculating the coordinate parameters of each partition and its vertices.

[0050] The above-mentioned instructions for generating reinforced concrete fiber sections are quite complex, requiring at least 12 steps if strict mesh alignment is followed; according to Figure 5 It can be seen that at least 14 positioning points need to be calculated and strictly matched with the instructions, which results in a high error rate in engineering applications.

[0051] Therefore, this solution uses object-oriented programming to design a mesh generation class for generating cross-section objects. The constructor of this class calculates the 14 positioning points based on user-input parameters and assigns them to the object's attributes. Furthermore, this class should support three methods: concrete fiber mesh generation, linear batch generation of reinforcing bars, and single-bar generation, to meet basic concrete cross-section generation requirements. The class should also support a method for visualizing cross-sectional views, allowing users to check for errors, and a method for quickly adding them to the fiber element numerical model. In this embodiment, Python is used to specifically implement the creation of fiber cross-section objects. This method simplifies the fiber cross-section creation process through encapsulated instructions. The core process and basic instruction functions are described below: Step 1: Initialize the fiber cross-section mesh object. First, call the initialization command `mesh` to create a fiber cross-section mesh object (the variable name in this text is `Mesh`). This command requires two parameters: the defined concrete cross-section object (`Sec`) and the unique number of that cross-section (`secTag`).

[0052] Step 2: Generate the concrete mesh. This is done by calling the object's `concrete` method to mesh the concrete portion. This method accepts the following two types of parameters: Material object parameters: You need to pass in the cover concrete object and the core concrete object, which are usually created in the previous steps.

[0053] Mesh generation parameters: The width and height of the core area and the number of grid cells (numCoreWid, numCoreHig) need to be defined, as well as the mesh generation details of the protection layer (numCovLR, numCovUD, numCovDepth).

[0054] All the above mesh generation parameters are integer variables, with the last three having a default value of 0. This means that by default, a concrete section considering seismic damage without a protective layer is generated. To generate a complete section, these parameters can be customized.

[0055] Step 3: Generate rebar fibers. Rebar generation offers two methods: linear batch generation and single-strand generation. Both require calling the rebar material object (steel) created in the previous steps and defining the rebar diameter (ds). Linear batch generation (steelLinear): Suitable for generating steel bars arranged in a straight line. Users only need to define the number of steel bars (numSteel) and the coordinates of the group of steel bars on the local coordinate system z-axis (locz).

[0056] Automation advantages: Unlike traditional methods, this method does not require manual calculation of the start and end coordinates of the reinforcing bars in the y-axis direction. The program defaults to setting the start and end points of the y-axis to the junction of the protective layer and the core concrete.

[0057] Single-strand generation (steelSingle): Applicable to generating a single steel bar at a specific location. The specific coordinates (loc) of the steel bar must be defined.

[0058] Step 4: Visualization and Model Execution Visualization (view): Calling the view method can graphically display the fiber cross-section object created in the above steps for verification.

[0059] Execute: Calling the execute method quickly loads the created fiber section object into the fiber element numerical model and finally submits it to the OpenSees program for calculation execution.

[0060] This example demonstrates the complete process of constructing a specific reinforced concrete fiber section using the aforementioned encapsulation instructions: First, instantiate a fiber section object (mesh1) with the number 1. This object is created based on predefined concrete section attribute variables (s).

[0061] The `concrete` method is called to define the discretization method for the concrete portion, generating the concrete mesh. Predefined material objects `c2` and `c1` are specified for the protective layer and core region, respectively. For mesh generation, the core region is set to 16×16 elements, and the mesh generation parameters for the protective layer are set to 2 (left / right), 16 (top / bottom), and 16 (thickness direction).

[0062] The reinforcement bars are arranged using a combination of batch and individual generation. All reinforcement bars use material object s1 with a diameter of 8. The steelLinear command is invoked to generate a row of longitudinal reinforcement layers containing 3 steel bars at local coordinates z=-165.0 (bottom of the section) and z=165.0 (top of the section).

[0063] Call the steelSingle command to precisely locate and generate a single side longitudinal reinforcement (waist reinforcement) at coordinates (-165, 0) and (165, 0) respectively.

[0064] Finally, the `execute` command is called to automatically convert the predefined cross-sectional mesh information into OpenSees commands and load them into the model. Then, the `view` command is called to draw and output a schematic diagram of the fiber cross-section. The resulting cross-sectional diagram is shown below. Figure 7 As shown.

[0065] II. Heat Transfer Analysis Heat transfer analysis is a crucial step in the thermo-mechanical coupling response analysis of concrete. However, existing methods rely on third-party tools such as ABAQUS and MATLAB for implementation, or require data acquisition through experiments, making it difficult to quickly add data to subsequent thermo-mechanical coupling analysis objects. Furthermore, when the temperature of concrete is between 100 and 200°C, the capillary water inside the concrete evaporates, absorbing heat and thus inhibiting temperature rise, resulting in a distinct "plateau" in the temperature curve. This macroscopically reflects the changes in the material's thermodynamic parameters with temperature. Existing methods also require manual pre-calculation when considering these thermodynamic characteristics of concrete. Based on the above analysis, using the object-oriented programming method, a heat transfer analysis class is designed to support the creation of heat transfer analysis objects for concrete sections. This class includes the following methods: 1) Calculate the specific values ​​of thermal conductivity, specific heat capacity and density of concrete material in real time; 2) Visualize the cross-sectional temperature distribution using cloud maps to allow users to initially check for errors; 3) The heat transfer analysis results are automatically added to the subsequent thermo-mechanical coupling analysis objects without manual intervention; 4) Other necessary methods for heat transfer analysis, such as solving governing equations, applying boundary conditions, etc.

[0066] The method includes a design framework for heat transfer analysis classes in the heat transfer analysis step, such as... Figure 8 As shown. With Figure 4 Similarly, the attribute (method) for bolding the font is a private attribute (method).

[0067] To achieve rapid, accurate, and batch-based heat transfer analysis of concrete structure sections, the heat transfer analysis steps make the following assumptions during the calculation and solution process: 1) Using a two-dimensional concrete structure cross-section as the analysis object, and neglecting axial heat transfer within the structure, the three-dimensional heat transfer problem is simplified to a two-dimensional plane problem. Existing research shows that in non-localized fire scenarios, axial heat transfer within the concrete structure is significantly lower than in the other two directions; and calculation results from multiple real-world cases indicate that the two-dimensional analysis results are in good agreement with experimental results; furthermore, since axial heat conduction is not considered, the calculated cross-sectional temperature field will be slightly higher than the actual temperature field, making the results more conservative.

[0068] 2) The influence of steel reinforcement on heat transfer is not considered; the analysis is performed as if it were plain concrete. The thermal conductivity of steel reinforcement is approximately 40 times that of concrete, and the reinforcement ratio is typically less than 3%. This means that when steel reinforcement receives heat, it almost instantly transfers it to the surrounding concrete, and its own temperature will always remain consistent with the temperature of the surrounding concrete.

[0069] The theoretical governing equation for the heat transfer analysis step is a two-dimensional transient heat transfer differential equation, the specific formula of which is: ; In the formula, k x and k y The materials are respectively in x and y The thermal conductivity in the direction of concrete can be considered as... k x = k y = λ c ; The heat applied externally per unit time; c p The specific heat capacity of the material; ρ The density of the material.

[0070] For computer-based solutions, shape functions are used to represent the temperature at any point within a rectangular element by the temperatures at the four corners of that element. The Galerkin method is then employed, which considers the trial function to be the numerical solution of the equation when the inner product of the trial function and the residual is zero. In other words, for any element, the residual of the equation... R e The following relationship exists between shape functions and shape functions: ; In the formula, Ω represents the computational domain of the unit.

[0071] Among them, temperature versus time t The partial derivatives can be approximated using the finite difference method. For the entire cross-section, the theoretical governing equations for the heat transfer analysis can ultimately be simplified to the following linear equation form: ; In the formula, T n+1 and T n The first n +1 time step and the n At each time step, this represents the temperature matrix of each node across the entire cross section; Δ t F is the step size of a time step; n+1 For the first n +1 step external heat load vector; K is the heat conduction matrix; M is the heat absorption matrix.

[0072] Thermodynamic parameters of concrete materials: To account for the evaporation of capillary water inside concrete at high temperatures and to suppress temperature rise, the heat transfer analysis procedure referenced the specific heat capacity of concrete as explicitly defined in the European standard Eurocode 2 when defining the thermodynamic parameters of the concrete material. c p thermal conductivity λ c and density ρ With temperature T The formula for calculating the change is shown below: Specific heat capacity ( u =0): ; Thermal conductivity: ; density: ; In the formula, u This represents the moisture content of the concrete. When the moisture content of the concrete is 3%, the peak specific heat capacity at 100~110℃ is... c p,peak =2020 J / (kg∙K), the peak specific heat capacity corresponding to other moisture contents. c p,peak Based on the above formula and u The data at 3% were determined by linear interpolation. ρ 0 represents the density of concrete at 20℃, which can be taken as 2200~2500 kg / m³. 3 .

[0073] Thermal boundary conditions for concrete sections: Common boundary conditions for heat transfer analysis include Dirichlet boundary conditions, Neumann boundary conditions, and convective heat transfer boundary conditions. Dirichlet boundary conditions assume the temperature of each boundary is known; Neumann boundary conditions assume the heat flux of each boundary is known. However, in real-world scenarios, it is difficult to directly measure the temperature or heat flux of the concrete surface under fire conditions. Therefore, the heat transfer analysis step employs convective heat transfer boundary conditions, assuming the convective heat transfer coefficient of each boundary is known. The thermal effect of a fire on a structure is primarily through thermal radiation; however, under large-scale regional fires, the heat plume generated by the flow of high-temperature gases will also exert heat on the structural surface. Therefore, according to the principle of energy conservation, the structural surface... Γ The heat received is the sum of the energy from thermal radiation and thermal plumes (which are forms of convection). q Γ for: ; In the formula,q rad For thermal radiation energy, according to the Stefan-Boltzmann law, the specific formula for calculating thermal radiation energy is: ; In the formula, T amb Indicates ambient temperature; T Γ The surface temperature of the structure; ε The emissivity of concrete can be taken as 0.5~0.7; σ This is the Stefan-Boltzmann constant. q cov For heat convection energy, according to the convection heat transfer formula, the specific formula for calculating heat convection energy is: ; In the formula, h cov The convective heat transfer coefficient is given; the convective heat transfer coefficient of air is known to be 25 W / (m²). 2 •K). Transforming the specific formula for calculating thermal radiation energy into the same form as the specific formula for calculating thermal convection energy, we have: ; ; Then the structural surface Γ The heat received is the sum of the energy from thermal radiation and thermal plumes (which are convection), and can be expressed in the form of convective heat transfer. ; In this method, an object-oriented heat transfer analysis module—HTops (HeatTransfer for OpenSees)—was implemented using the Python language. Compared with traditional methods that use third-party general-purpose software such as ABAQUS for heat transfer analysis, HTops is specifically customized for concrete fiber element models, has parametric modeling capabilities, eliminates the need to manually import complex thermodynamic parameters that vary with temperature, and can automatically generate temperature field files or instructions required for subsequent calculations in OpenSees.

[0074] The specific implementation process and command functions of this module are described below: Step 1: Create a heat transfer analysis section object. First, create a heat transfer analysis section object using the initialization command. In this step, you need to define the geometric dimensions of the section and the thickness of the protective layer; at the same time, you need to set the mesh density, that is, the number of elements in the y-axis and z-axis directions in the local coordinate system; in addition, you need to specify the section type, which can be either "Full" (complete section) or "Seismic" (seismic damaged section) mode.

[0075] Step 2: Define material properties and fire conditions: Material property definition: The `material` method is called to set the thermodynamic parameters of concrete, specifically including density (rho), moisture content (u), and emissivity (e) at room temperature. The module automatically handles the nonlinear changes in material properties with temperature.

[0076] Fire curve setting: Call the fire method to introduce the fire condition. You need to pass in a fire function (fire) that describes the change of ambient temperature over time.

[0077] Step 3: Specify the data monitoring points. Use the `targetPoints` method to specify the exact location of the temperature field data output. This method accepts two list-type parameters (`ycoords` and `zcoords`), which correspond to the y-axis and z-axis coordinates of the monitoring points on the cross-section, respectively, and are used to generate the discrete temperature field data file required for subsequent analysis.

[0078] Step 4: Perform analysis and visualization: Perform analysis: Call the analysis method to start the heat transfer calculation. You need to set the total analysis duration and the time increment step.

[0079] Results visualization: After the analysis is completed, the figure method can be called to draw and output the temperature field distribution cloud map of the cross section, so as to intuitively evaluate the heat transfer effect.

[0080] Application Case Description of Heat Transfer Analysis Module (HTops) This case study selects the shear-critical fiber-reinforced lightweight aggregate concrete beam from the research of Christopher Kevinly et al. (2025) as the analysis object. The HTops module was used to numerically simulate the cross-sectional temperature field distribution under high temperature conditions. The specific implementation process is as follows: First, a custom function `Chris_fire` was written to define the fire temperature rise curve, using a piecewise function to simulate the change of ambient temperature over time. Then, the cross-section object `ChrisBeam` was initialized, setting the beam cross-section height to 370mm, width to 200mm, and protective layer thickness to 30mm. For numerical discretization, the cross-section was divided into 20 elements along the width (y-axis) and 37 elements along the height (z-axis).

[0081] The thermal parameters of lightweight aggregate concrete are defined using the material command, setting its density to 1774 kg / m³. 3The moisture content is 3% and the emissivity is 0.7. Next, the boundary heat transfer conditions are set using the boundaryCondition command, specifying the top surface of the beam as the insulating boundary (not directly exposed to fire, with a convective heat transfer coefficient of 10.0), while the other three surfaces are exposed to a high-temperature environment, and the fire curve defined above is loaded.

[0082] The `targetPoints` command specifies a series of specific y-axis and z-axis coordinate points within the cross-section to record temperature data at key locations. The `analysis` command is then invoked to initiate heat transfer analysis, setting the initial ambient temperature to 25°C, the time increment to 10 seconds, and the total simulation duration to 10,000 seconds.

[0083] After the analysis was completed, the `figure` command was used to plot and output the cross-sectional temperature field distribution cloud map at 10000s. Simultaneously, the program automatically generated a temperature field data file named `temp_0.37x0.2.txt` in the current working directory. This file records the temperature data for the entire process and can be automatically retrieved by OpenSees for subsequent structural thermo-mechanical coupling analysis.

[0084] The module returns a cross-sectional temperature field distribution cloud map at t=10000s, as shown below. Figure 8 As shown, Figure 8 In the text, the temperature ranges from 240 to 780°C, with dark blue representing low temperature and red representing high temperature. A temperature field file named "temp_0.37x0.2.txt" is generated in the current folder, which can be automatically loaded and called by OpenSees later.

[0085] III. Thermo-coupling analysis In this solution, the OpenSees fiber element solver uses cross-sectional temperature interpolation technology to input and load the temperature field, currently supporting both one-dimensional and two-dimensional temperature interpolation modes. The specific implementation method when operating through the Python interface is described below: One-dimensional temperature field loading method: A one-dimensional temperature field primarily describes the temperature variation along the cross-sectional height (Z-axis), providing two command formats: The direct definition method generates a temperature field by setting the ordinates of a series of interpolation lines and their corresponding peak temperatures, assuming that the temperature increases linearly with time. If only the first and last interpolation points are specified in the command, the system defaults to positioning them as the bottom and top surfaces of the cross-section, while the remaining seven interpolation lines are uniformly distributed within the height of the cross-section. Figure 9a As shown.

[0086] The file reading method defines a complex temperature field that changes over time by referencing an external text file (.txt or .dat). The command requires specifying the filename and the y-axis of the interpolation line. The temperature file format has strict requirements: each line represents a time step, the first column is the current time, and subsequent columns are the temperature values ​​of each interpolation point at that time, and the order of the temperature values ​​must strictly match the numbering order of the interpolation lines.

[0087] Two-dimensional temperature field loading method: Two-dimensional temperature fields are used to describe working conditions with complex cross-sections or bidirectional temperature gradients, supporting both H-shaped and rectangular cross-section modes: The rectangular section mode is defined using a 5×5 grid of interpolation points. It requires inputting 5 coordinate positions along the width (Y-axis) and height (Z-axis), as well as the corresponding 25 temperature values.

[0088] The H-section mode also supports directly defining temperature values ​​(linear heating) or reading them from an external file. When using an external file, the geometric symmetry of the section simplifies the input; only key coordinates (such as Z1, Z2 and Y1, Y2) need to be defined. The program will fix Z3 and Y3 at the axis of symmetry and automatically generate the coordinates of the remaining symmetrical points accordingly.

[0089] The coordinates of the interpolation lines / points for the H-section and the rectangular section are Z1~Z5 and Y1~Y5, respectively. Figure 9b and 9c As shown; the requirements for external files are basically the same as those for one-dimensional linear temperature interpolation, but 15 temperature values ​​must be entered per line. When defined through an external file, the remaining points are generated symmetrically along the Z1, Z2, Y1, and Y2 axes, while Z3 and Y3 are fixed at the positions of the axes of symmetry.

[0090] Preliminary calculations showed that the one-dimensional temperature input method could not account for the actual two-dimensional temperature distribution of the concrete cross-section, resulting in a significant error compared to the actual results. While the two-dimensional temperature input method only formally met the requirements with its 5×5 grid interpolation command, its coarse grid division and support for only linear heating time histories also led to substantial errors in calculations. Therefore, using the aforementioned object-oriented programming method, a user-defined grid interpolation (from 9×9 to a maximum of 50×50, such as...) was added. Figure 9d (As shown) A constructor is created to create the thermal coupling analysis object. In this mesh interpolation method, the user only needs to input the local starting point of the mesh. y shaft and z Axis coordinates y 1. y n , z 1. z n and the number of grid divisions in each direction. n(Any integer between 9 and 50), this class will automatically generate the remaining grid points: Simultaneously, the class associated with creating the thermo-coupled analysis object should add the functionality to calculate the real-time temperature of each fiber of the thermo-coupled analysis object using inverse distance weighted interpolation based on real-time temperature data from custom grid points. In the formula, T ( y , z The coordinates of the center point are () y , z ) fiber units, y k and z k These represent the coordinates of the four grid points adjacent to the fiber unit. T k Real-time temperature data for grid points. d k From the four grid points to the center point of the fiber unit ( y , z The Euclidean distance of ).

[0091] In summary, the thermo-coupling analysis module creates a thermo-coupling analysis object with custom mesh interpolation functionality for a two-dimensional temperature field. The specific operations include: calling the element loading command (eleLoad), specifying one or more beam-column element tags (eleTag) to be analyzed, and setting the loading type to beam thermal mode (-beamThermal); simultaneously, specifying the external filename containing the temperature time history data through the source parameter (-source), and defining the boundary coordinate range of the cross-sectional thermal analysis mesh (i.e., the height coordinates Y1 to Yn and the width coordinates Z1 to Zn of the cross-section in the local coordinate system); finally, inputting the mesh interpolation parameter n to specify the number or density of monitoring points to be interpolated within the boundary coordinate range, thereby mapping the external temperature field data onto the fiber model of the beam-column element.

[0092] Where Y1, Yn, Z1, and Zn are the starting points of the differences in the local area. y shaft and z The coordinates of the axis; HTObject.fileName is the file attribute of the concrete section heat transfer analysis object, and is an attribute member variable in this object. Its format requirements are basically the same as those for one-dimensional linear temperature interpolation, but each line must have n 2 A temperature value.

[0093] The specific implementation process and case demonstration of this method are described below: In this embodiment, the fire resistance performance test of a full-scale vibration-damaged reinforced concrete column conducted by Wen Bo et al. is selected as the verification object. The specimen is a reinforced concrete column with a height of 3000mm and a cross-section of 400mm×400mm, equipped with 8 longitudinal bars of 20mm diameter and stirrups of 8mm diameter (with increased reinforcement at the ends). Under the condition of maintaining an axial compression ratio of 0.45, it is subjected to four-sided fire exposure according to the ISO834 standard temperature rise curve. This embodiment aims to verify the accuracy and efficiency of this method in simulating the fire resistance performance of structures through an automated modeling and analysis process.

[0094] Step 1: Establish a fiber beam-column element structural model; First, initialize the OpenSees model space (3D, 6 degrees of freedom). Define the column cross-section geometric parameters (400mm×400mm) and reinforcement layout information. Establish 9 nodes along the column height direction, apply fully consolidated constraints to the column base (node ​​1), and apply constraints other than axial displacement to the column top (node ​​9) to simulate the experimental boundary conditions.

[0095] Subsequently, the constitutive models of the protective concrete, core concrete, and reinforcing steel are quickly defined using the material class objects (`cover`, `core`, `steel`) encapsulated in this solution. Based on the different stirrup spacings, core concrete materials are created for both the reinforced and unreinforced zones.

[0096] Then, using the mesh generation function (`mesh`), the cross-section is discretized into fine fiber bundles (such as a 16×16 mesh), automatically generating cross-sectional objects containing concrete fibers and steel fibers with different constraint effects. Finally, fiber beam-column elements considering temperature effects are constructed using the `dispBeamColumnThermal` command, completing the assembly of the structural model.

[0097] Step 2: Cross-sectional heat transfer analysis and temperature field generation; Call the thermal analysis module (`HTops`) of this solution to create a two-dimensional heat transfer analysis object with a grid density of 40mm×40mm.

[0098] Define parameters: Input concrete thermal parameters (density 2300 kg / m³) 3 (Moisture content 3%, emissivity 0.7) and ISO 834 heating function.

[0099] Boundary and Target: Set the fire-affected boundary conditions on all four sides of the cross section, and specify the coordinates of the 9×9 grid target points (`ycoords`, `zcoords`) for subsequent thermo-coupling interpolation.

[0100] Solution and Output: Set the analysis duration to 12000s and execute the transient heat conduction analysis. The program will automatically calculate and generate an external data file containing the temperature time histories of all target points.

[0101] Step 3: Loading and thermodynamic coupling analysis; Static loading: Apply the corresponding axial pressure (axial pressure ratio 0.45) to the top of the column, perform static nonlinear analysis until the structure reaches equilibrium under gravity load, and then reset the analysis time.

[0102] Applying a temperature field: Read the temperature field file generated in step two. Using the `eleLoad` command and the `-beamThermal` type, map the temperature data to the 9×9 interpolation points of the fiber unit cross-section through file input mode. Coordinate transformation is automatically completed during this process.

[0103] Coupled solution: Set the time step and convergence criterion for thermo-mechanical coupling analysis, and perform 1000 incremental iterative calculations to simulate the structural response throughout the fire process.

[0104] Results analysis: The program outputs real-time time history data of the column top axial displacement via a recorder. This data is then compared with the ABAQUS solid element finite element analysis results and experimentally measured data. Figure 10 As shown, the peak displacement and fire resistance limit calculated by this method are in excellent agreement with the experimental results. Furthermore, thanks to the high efficiency of the fiber unit and the optimization of the automated instructions, the entire calculation process in this case takes only about 10 seconds, verifying that this method combines high precision and high efficiency. Figure 10 In the diagram, the blue lines represent the experimental results, the orange lines represent the results obtained using this method, and the gray lines represent the results obtained using the solid finite element method.

[0105] In summary, this method includes fiber element modeling, heat transfer analysis, and thermo-mechanical coupling analysis. The fiber element modeling step is used to create concrete structural material and cross-sectional objects and assign relevant properties to these objects. The heat transfer analysis step is used to create and calculate the heat transfer analysis object of the concrete cross-section. The thermo-mechanical coupling analysis step is used to create and calculate the thermo-mechanical coupling response analysis object of the concrete structure. This method can achieve rapid and accurate prediction and evaluation of the performance of concrete structures under fire and related multiple disasters, balancing accuracy and efficiency, and providing an efficient technical tool for disaster prevention, mitigation, and safety assessment of resilient cities.

[0106] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures, characterized in that, The method steps include: S1. Based on the required analysis structure, establish a fiber element numerical model of the concrete structure; S2. Create a concrete section heat transfer analysis object, and calculate and output the section temperature field data based on the concrete section heat transfer analysis object; S3. Perform stress or disaster-induced working condition simulation on the fiber element numerical model of the concrete structure to obtain the processed fiber element numerical model. S4. Read and map the cross-sectional temperature field data to the processed fiber element numerical model, perform coupled calculations of the temperature field and mechanical field, and obtain and output the thermo-mechanical coupling response analysis results of the concrete structure.

2. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 1, characterized in that, The specific steps for establishing the fiber element numerical model of the concrete structure in S1 include: Define node coordinates, and based on these coordinates, create concrete material objects, reinforcement material objects, and concrete section objects using object-oriented programming methods. The concrete material objects include protective layer concrete material objects and core area concrete material objects. Create a parent class for concrete sections and a subclass for mesh generation, and combine the geometric parameters and reinforcement information of the concrete section objects to generate a fiber mesh for the sections. Assign the concrete material objects and reinforcement material objects to the fiber mesh, and connect the nodes to generate fiber elements, thereby establishing a fiber element numerical model of the concrete structure.

3. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 2, characterized in that, The improved Kent-Scott-Park constitutive model is used when creating concrete material objects, and the improved Giuffre-Menegotto-Pinto constitutive model is used when creating steel reinforcement material objects. The specific process of generating the fiber mesh of the cross section includes: designing the parent class of the cross section mesh, calculating the coordinates of the key positioning points of the cross section based on the input cross section geometry, protective layer thickness and reinforcement information, and providing method interfaces for generating rectangular concrete fiber mesh, linear batch generation of steel reinforcement fibers and single generation of steel reinforcement fibers.

4. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 2, characterized in that, When creating the concrete material object, the restraining effect of the stirrups on the core area concrete is considered. The specific process includes: Obtain the stirrup ratio, yield strength, spacing, and core area cross-sectional dimensions; Calculate the constraint enhancement factor and the descent slope reduction factor; Using the aforementioned constraint enhancement coefficient and descent slope reduction coefficient, the compressive strength, peak compressive strain, and ultimate compressive strain parameters of the core area concrete are corrected to generate the core area concrete material object.

5. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 1, characterized in that, The specific steps of S2 include: A concrete section heat transfer analysis object is created based on object-oriented programming. The material thermal properties and external fire conditions of the heat transfer analysis object are defined. The section boundary conditions are set and temperature interpolation monitoring points are selected. The two-dimensional transient heat transfer differential equation is solved using the Galerkin method and the implicit finite difference method. The section temperature field data of the specified monitoring points changing with time are calculated and output.

6. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 5, characterized in that, In S2, the solution of the two-dimensional transient heat transfer differential equation is based on the following assumptions: the three-dimensional heat transfer problem is simplified to a two-dimensional plane problem, the axial heat transfer inside the structure is ignored, and the influence of steel bars on heat transfer is not considered. The cross section is analyzed as a plain concrete cross section. The boundary condition adopts the convective heat transfer boundary condition. Based on the principle of energy conservation, the sum of the thermal radiation energy and thermal convection energy received by the surface of the structure is calculated as the external heat load.

7. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 5, characterized in that, The specific process for defining the thermal properties of the material in the heat transfer analysis includes: real-time calculation of the thermal conductivity, specific heat capacity, and density of the concrete material as temperature changes; the calculation formulas for the thermal conductivity, specific heat capacity, and density are based on the European standard Eurocode 2, and the effect of heat absorption by the evaporation of water inside the concrete on the suppression of temperature rise is considered, and the peak value of specific heat capacity is corrected by setting the moisture content parameter.

8. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 1, characterized in that, The stress or disaster-affected condition simulation processing of the fiber element numerical model of the concrete structure in S3 includes: Determine if seismic action exists in the current working condition: if not, apply only static load to obtain the processed fiber element numerical model; if yes, apply static load and seismic motion time history load, and unload the seismic action after the seismic action ends, retaining the residual deformation and damage state of the structure to obtain the processed fiber element numerical model.

9. The method for analyzing the thermo-mechanical coupling response of fiber-reinforced concrete structures according to claim 1, characterized in that, In step S4, the specific implementation scheme for mapping the cross-sectional temperature field data to the processed fiber unit numerical model includes: When creating the concrete section heat transfer analysis object in step S2, n×n grid interpolation monitoring points are defined, where n is an integer between 9 and 50; In step S4, the thermo-coupling analysis object receives an external file containing temperature data from n×n monitoring points, and calculates the temperature of the fiber at any position within the cross-section of the fiber unit at any time using inverse distance weighted interpolation.

10. A thermo-mechanical coupling response analysis system for fiber-reinforced concrete structures, characterized in that, The system operates using the thermal-mechanical coupling response analysis method for fiber-reinforced concrete structures as described in any one of claims 1-9, and the system comprises: The fiber element modeling module creates a fiber element numerical model of the concrete structure based on the required analysis structure. The heat transfer analysis module is used to create a heat transfer analysis object, calculate the cross-sectional temperature field considering the nonlinear thermal parameters of the material and the equivalent boundary conditions, and automatically export the temperature data file of the monitoring point. The thermo-coupling analysis module is used to read temperature data files, map the temperature field to fiber units, and perform thermo-coupling analysis calculations. The evaluation module is used to monitor the force, displacement, and stress-strain response of the structure under multi-field coupling, assess the residual function of the structure to be analyzed, and output the thermo-mechanical coupling response analysis results of the concrete structure.

Citation Information

Patent Citations

  • Fire resistance response analysis method based on concrete beam bridge structure

    CN116975986A