Fabricated steel structure thermal expansion analysis and calculation method based on finite element method

Abstract

The invention relates to the field of constructional engineering and structural design, and discloses a fabricated steel structure thermal expansion analysis and calculation method based on a finite element method.The fabricated steel structure thermal expansion analysis and calculation method comprises the following steps that fractal parameters are inversely optimized by constructing a thermal-force coupling equation and introducing an adjoint equation, errors of a temperature field and a displacement field are iteratively calculated, and the fractal parameters are updated; the convergence condition is met; the adjoint equation comprises an adjoint equation of a temperature field and an adjoint equation of a displacement field, and is used for calculating the gradient of the fractal parameter and performing back propagation optimization; in each iteration, recalculating the fabricated steel structure thermal expansion analysis model based on the updated fractal parameters, and judging whether a convergence condition is met or not; and finally outputting the optimized temperature field, displacement field and fractal parameters through repeated iterative optimization. According to the method, the calculation efficiency and optimization precision of thermal expansion analysis can be improved, the safety, stability and reliability of the steel structure under the thermal action are ensured, and the method is suitable for automatic analysis and optimization of a large-scale structure.

Description

Technical Field

[0001] The present invention relates to the technical field of construction engineering and structural design, and particularly to a method for analyzing and calculating the thermal expansion of prefabricated steel structures based on the finite element method. Background Art

[0002] With the continuous development of the construction industry, prefabricated steel structures have been widely used in high-rise buildings, bridges, large industrial plants and other fields due to their excellent structural performance and fast construction characteristics. However, in practical applications, prefabricated steel structures often face the problem of thermal expansion in high-temperature environments, especially the thermo-mechanical coupling effect caused by temperature changes, which leads to significant changes in the deformation and stress distribution of steel structures, thereby affecting their safety and stability. Therefore, how to accurately and efficiently perform thermal expansion analysis has become an important issue in the design and optimization of steel structures.

[0003] In the prior art, common thermo-mechanical coupling analysis methods include the finite element analysis method, numerical integration method, etc. These methods mainly establish physical models and perform numerical solutions by combining heat conduction equations and mechanical equations. However, traditional analysis methods usually rely on simple iterative calculations, are prone to falling into local optimization, have a slow convergence speed, and a large amount of calculation, and cannot effectively handle the thermo-mechanical coupling problems of large-scale prefabricated steel structures. In addition, due to the lack of an efficient error feedback mechanism in the optimization process of these methods, a large amount of manual intervention and repeated parameter adjustment are often required, resulting in low efficiency and insufficient accuracy in the design process.

[0004] Although some improved algorithms such as optimization algorithms and inversion techniques have been applied in related fields, most methods still face problems such as the inability to accurately control the errors of the temperature field and displacement field, the lack of effective convergence criteria, and the failure to fully utilize the gradient information in numerical calculations. These defects make the prior art unable to improve the calculation efficiency while ensuring the design accuracy when dealing with the thermal expansion analysis of prefabricated steel structures, and fail to fully utilize efficient optimization techniques to automatically update design parameters.

[0005] Therefore, how to overcome the defects of low calculation efficiency, poor accuracy, and insufficient optimization in the prior art, and provide a more efficient and accurate thermal expansion analysis method has become an urgent problem to be solved. Summary of the Invention

[0006] Aiming at the deficiencies of the prior art, the present invention provides a method for analyzing and calculating the thermal expansion of prefabricated steel structures based on the finite element method, which solves the problems of low calculation efficiency, low accuracy, and insufficient optimization process in the prior art when performing thermal expansion analysis on prefabricated steel structures.

[0007] To achieve the above object, the present invention is realized by the following technical solutions: A method for analyzing and calculating the thermal expansion of prefabricated steel structures based on the finite element method, comprising the following steps:

[0008] Generate a geometric model of the prefabricated steel structure, define a fractal rough surface for the contact interface, and mark it as the key area of heat conduction;

[0009] Define the material model, and describe the interface heat conduction behavior through a non-local heat conduction equation containing fractal parameters;

[0010] Mesh the model and dynamically adjust the local mesh density based on the error criterion;

[0011] Set the thermal-mechanical coupling analysis step, dynamically divide the implicit and explicit integration regions based on the chaos stability criterion, and apply a synchronous control mechanism;

[0012] Solve the temperature field and displacement field by tensor decomposition for dimensionality reduction, and perform implicit and explicit integration calculations in different regions;

[0013] Combine the adjoint equation to inversely optimize the fractal parameters until the convergence condition is met, update the model and output the results.

[0014] Preferably, the step of generating a geometric model of the prefabricated steel structure, defining a fractal rough surface for the contact interface, and marking it as the key area of heat conduction includes:

[0015] According to the design drawings of the prefabricated steel structure, establish a three-dimensional geometric model of the steel structure;

[0016] Identify the contact interface and define a fractal rough surface, and the rough surface is generated by the Weierstrass-Mandelbrot function;

[0017] Define the heat conduction characteristics of the contact area according to the generated fractal rough surface, mark it as the key area of heat conduction, and specify the thermal conductivity parameter for this area;

[0018] In the geometric model, consider the influence of interface roughness on heat flow, and set the boundary conditions and internal and external heat source terms of the heat conduction equation;

[0019] Generate a complete geometric model of the prefabricated steel structure.

[0020] Preferably, the step of defining the material model and describing the interface heat conduction behavior through a non-local heat conduction equation containing fractal parameters includes:

[0021] Define the thermophysical properties of steel, including specific heat capacity, thermal conductivity, and density parameters;

[0022] According to the characteristics of the fractal rough surface, a non-local heat conduction equation is used to describe the interfacial heat conduction behavior, and the non-local heat conduction equation is as follows:

[0023]

[0024] where, is the temperature gradient, x and x′ are spatial positions respectively, D is the fractal dimension, Ω is the calculation region, and Q(x) is the heat source term;

[0025] Combined with the fractal dimension D, the kernel function in the heat conduction equation is adjusted to consider the influence of interface roughness on heat flux;

[0026] Boundary conditions are set for each contact interface region to ensure the reasonable transfer of the temperature field in the heat conduction analysis of the structure;

[0027] Finally, a heat conduction model with a fractal rough surface is generated, considering the heat flux characteristics of the interface.

[0028] Preferably, the steps of meshing the model and dynamically adjusting the local mesh density based on an error criterion include:

[0029] Based on the geometric model of the prefabricated steel structure, the overall structure is initially meshed using tetrahedral elements or hexahedral elements;

[0030] Calculate the temperature gradient and the heat flux density under the initial mesh, and evaluate the local mesh error according to the following error estimation formula:

[0031]

[0032] where, q h and q h / 2 are the estimated values of the heat flux density of the current mesh and the mesh with one layer of encryption respectively, and η e is the local error index;

[0033] Based on the error threshold η th , determine whether mesh encryption is required:

[0034] If η e > 1.5η th , then locally encrypt this area;

[0035] If η e <0.5η th , then coarsen the mesh;

[0036] Adopt an adaptive mesh refinement algorithm to refine the mesh in the high-error area;

[0037] After the mesh adjustment is completed, recalculate the error and check whether the overall error convergence criterion is met. If not, repeat the mesh adjustment process until the preset accuracy requirement is achieved.

[0038] Preferably, the step of setting the thermal-mechanical coupling analysis step, dynamically dividing the implicit and explicit integration regions based on the chaos stability criterion, and applying the synchronous control mechanism includes:

[0039] Establish the thermal-mechanical coupling control equation, use the heat conduction equation to describe the temperature field change, and describe the stress-strain response of the steel structure through the elasticity equation. Its basic form is:

[0040]

[0041] where ρ is the density, c p is the specific heat capacity, k is the thermal conductivity, t is the temperature field, Q is the heat source term, represents the dot product of the thermal conductivity and the temperature gradient, σ is the stress tensor, u is the displacement vector, is the displacement acceleration term, f is the body force;

[0042] Calculate the local Lyapunov exponent λ(x) to judge the system stability. Its calculation formula is:

[0043]

[0044] where T(x,t) is the temperature at point x at time t, T(x,0) is the temperature at point x at the initial time t = 0, ||·|| represents the norm of the matrix; when λ(x)>0, this region exhibits chaotic characteristics and implicit integration is used, otherwise explicit integration is used;

[0045] According to the spatial distribution of the Lyapunov exponent, dynamically divide the calculation region into implicit and explicit integration regions, and use different time steps Δt:

[0046] Implicit region: Suitable for high-gradient change regions, and the Newton-Raphson iteration method is used for solution;

[0047] Explicit region: Suitable for low Lyapunov exponent regions, and the central difference format is used for calculation;

[0048] Introduce a synchronous control mechanism to coordinate the field variable updates in the implicit and explicit regions. The temperature field synchronous control equation is:

[0049]

[0050] where, is the temperature at time step n + 1 in the explicit region, is the temperature at time step n in the explicit region, Δt is the time step size, and F(T n ) is the correlation function between the heat source term and the temperature field in the explicit region, and γ is the synchronization gain coefficient. is the temperature at time step n in the implicit region;

[0051] Perform coupled solution and use interpolation method for data transfer at the junction of the implicit and explicit regions.

[0052] Preferably, the steps of solving the temperature field and displacement field by dimensionality reduction through tensor decomposition and performing implicit and explicit integral calculations in sub-regions include:

[0053] Based on the thermo-mechanical coupling control equation, perform dimensionality reduction on the temperature field and displacement field through tensor decomposition method:

[0054] Based on the dimensionality-reduced field variables, perform implicit and explicit integral calculations on the temperature field and displacement field in each region respectively;

[0055] Between the implicit and explicit integral regions, use a smooth transition algorithm to balance the two integral methods to ensure the continuity of the temperature field and displacement field;

[0056] Through multiple iterations, adjust the time step sizes of the implicit and explicit regions to complete the solution of the temperature field and displacement field.

[0057] Preferably, the steps of combining the adjoint equation to invert and optimize the fractal parameters until the convergence condition is met, updating the model and outputting the results include:

[0058] Based on the constructed thermo-mechanical coupling equation, introduce the adjoint equation to invert and optimize the fractal parameters. The adjoint equation is expressed as:

[0059]

[0060] where λ is the adjoint temperature field, μ is the adjoint displacement field, and F T and F u are the source terms of the temperature field and displacement field respectively;

[0061] By solving the adjoint equation, calculate the gradient of the fractal parameters, and then obtain the error inversion direction. Use the inversion result to update the fractal parameters. The update formula is:

[0062]

[0063] where θ k is the fractal parameter in the k-th iteration, α is the learning rate, is the objective function, representing the measure of the errors of the temperature field and displacement field;

[0064] Based on the updated fractal parameters, recalculate the thermal expansion analysis model of the prefabricated steel structure to obtain a new temperature field and displacement field, and determine whether the convergence condition is satisfied. If it is satisfied, output the results and terminate the calculation. If not, continue the iteration. The convergence criterion is:

[0065] ||T k+1 -T k ||<∈ T

[0066] And

[0067] ||u k+1 -u k ||<∈ u

[0068] Wherein, T k and T k+1 are the results of two consecutive iterations of the temperature field respectively, and u k and u k+1 are the results of two consecutive iterations of the displacement field respectively, and ∈ T and ∈ u are the convergence precisions of the temperature field and the displacement field;

[0069] Output the optimized model results, including the temperature field, the displacement field and the optimized fractal parameters, and complete the thermal expansion analysis calculation of the prefabricated steel structure.

[0070] The present invention also provides a thermal expansion analysis calculation device for prefabricated steel structures based on the finite element method, including:

[0071] A geometric modeling module, which is used to generate a geometric model of the prefabricated steel structure, define a fractal rough surface for the contact interface, and mark it as a key area for heat conduction;

[0072] A material definition module, which is used to define a material model and describe the interface heat conduction behavior by using a non-local heat conduction equation containing fractal parameters;

[0073] A mesh generation module, which is used to mesh the geometric model and dynamically adjust the local mesh density based on an error criterion;

[0074] A thermal-mechanical coupling analysis module, which is used to set thermal-mechanical coupling analysis steps, dynamically divide the implicit and explicit integration regions based on a chaos stability criterion, and apply a synchronous control mechanism at the same time;

[0075] A calculation and solution module, which is used to solve the temperature field and the displacement field by tensor decomposition dimensionality reduction and perform implicit and explicit integration calculations in sub-regions;

[0076] An optimization and update module, which is used to inversely optimize the fractal parameters by combining adjoint equations until the convergence condition is satisfied, update the model and output the thermal expansion analysis calculation results.

[0077] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned method is implemented.

[0078] The present invention also provides a storage medium, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned method is implemented.

[0079] The present invention provides a method for analyzing and calculating the thermal expansion of prefabricated steel structures based on the finite element method.

[0080] It has the following beneficial effects:

[0081] 1. By introducing the adjoint equation for inversion optimization, the present invention can efficiently update the fractal parameters, thereby quickly converging during the thermal expansion analysis. Compared with traditional iterative methods, using adjoint equation inversion optimization can greatly reduce the computational amount and improve the model solving efficiency, and is particularly suitable for the thermo-mechanical coupling analysis of large-scale prefabricated steel structures.

[0082] 2. By continuously optimizing the fractal parameters, the present invention gradually reduces the error between the temperature field and the displacement field, thereby improving the analysis accuracy of the steel structure under thermal expansion. By finely adjusting the fractal parameters, the calculation results of the temperature field and the displacement field are closer to the actual physical situation, enhancing the reliability of the structural design.

[0083] 3. By introducing the automatic optimization mechanism of the objective function and the adjoint equation, the present invention enables the entire design process to be automatically completed by an algorithm, avoiding manual intervention, and improving the automation degree of the design and the accuracy of the optimization process. This method can achieve the adaptive optimization of the structural design without a large amount of manual adjustment.

[0084] 4. By iteratively optimizing the fractal parameters, the final optimized result output by the present invention can ensure the safety, stability, and durability of the steel structure under thermal expansion. The optimized temperature field and displacement field meet strict convergence conditions and can provide accurate thermo-mechanical coupling analysis results, providing a scientific basis for the engineering application of steel structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a schematic flowchart of the method of the present invention;

[0086] Figure 2 It is a schematic structural diagram of the device of the present invention;

[0087] Figure 3 It is a schematic structural diagram of the computer device of the present invention.

[0088] Among them, 100 is a geometric modeling module; 200 is a material definition module; 300 is a mesh generation module; 400 is a thermal-mechanical coupling analysis module; 500 is a calculation and solution module; 600 is an optimization and update module; 40 is a computer device; 41 is a processor; 42 is a memory; 43 is a storage medium. Specific implementation manners

[0089] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0090] Please refer to the attached Figure 1 The present invention provides a method for analyzing and calculating the thermal expansion of prefabricated steel structures based on the finite element method, aiming to improve the accuracy of thermal expansion analysis of prefabricated steel structures under the action of heat, fully consider the interfacial heat conduction behavior, and optimize the calculation efficiency.

[0091] As Figure 1 shown, the steps of the method for analyzing and calculating the thermal expansion of prefabricated steel structures based on the finite element method may include:

[0092] S1. Generate a geometric model of the prefabricated steel structure, define a fractal rough surface for the contact interface, and mark it as the key area of heat conduction;

[0093] S2. Define a material model, and describe the interfacial heat conduction behavior through a non-local heat conduction equation containing fractal parameters;

[0094] S3. Mesh the model and dynamically adjust the local mesh density based on an error criterion;

[0095] S4. Set the thermal-mechanical coupling analysis step, dynamically divide the implicit and explicit integration regions based on a chaos stability criterion, and apply a synchronous control mechanism;

[0096] S5. Solve the temperature field and displacement field by tensor decomposition and dimensionality reduction, and perform implicit and explicit integration calculations in different regions;

[0097] S6. Combine the adjoint equation to inversely optimize the fractal parameters until the convergence condition is met, update the model and output the results.

[0098] The following is a detailed description of each step in the method of the present invention, and a comprehensive elaboration on the specific implementation principles, technical details, and processes of each step is carried out.

[0099] For step S1, in this embodiment, step S1 is used to generate a geometric model of the prefabricated steel structure and define the contact interface as a fractal rough surface, so as to identify the key areas of heat conduction and ensure that the subsequent calculation process can accurately describe the interface heat expansion characteristics.

[0100] First, establish a geometric model of the prefabricated steel structure, use a three-dimensional modeling tool to generate components such as beams, columns, and joints, and form an overall structure through prefabricated connection methods. The geometric model includes multiple steel members, and the members are connected by bolts, welding, or plugging, etc. The contact area is defined as the interface area.

[0101] Subsequently, based on fractal theory, describe the rough characteristics of the contact interface of the prefabricated steel structure, and use the Weierstrass-Mandelbrot function to characterize the microscopic morphology of the interface. The rough surface height distribution function is expressed as:

[0102]

[0103] where H is the Hurst exponent, characterizing the surface roughness; γ is the scale parameter, determining the frequency attenuation; φ n is the random phase, simulating the surface randomness; N is the fractal order, controlling the fractal detail level.

[0104] Furthermore, by calculating the interface fractal parameters, determine the heat conduction characteristics of the key areas. Use the contact thermal conductivity k c to calculate the interface heat flux transmission ability, and the expression is as follows:

[0105] k c = k0(1 + βD f )

[0106] where k0 is the reference thermal conductivity, β is the adjustment parameter, and D f is the interface fractal dimension, obtained by calculating the fractal model. The calculation method of the fractal dimension is as follows:

[0107] D f = 2 - H

[0108] where H is obtained by fitting the Weierstrass-Mandelbrot model with the surface profile data.

[0109] Subsequently, discretize the geometric model of the prefabricated steel structure, and construct a finite element model based on the finite element mesh generation method. Use tetrahedral or hexahedral elements to mesh the structure, and apply refined meshes in the interface area to improve the calculation accuracy. The interface mesh density is controlled by the error criterion, and the calculation formula is as follows:

[0110]

[0111] When the error η is greater than the set threshold η c , a local refinement strategy is adopted to improve the mesh resolution, otherwise the original mesh density is maintained.

[0112] Finally, a finite element model of the prefabricated steel structure containing the information of the interfacial fractal rough surface is generated and output to the subsequent thermal-mechanical coupling analysis and calculation module.

[0113] For step S2, in this embodiment, step S2 is used to define the material model of the prefabricated steel structure and describe the interfacial heat conduction behavior using the non-local heat conduction equation to accurately characterize the change of the interfacial temperature field and consider the influence of the fractal rough surface on heat transfer.

[0114] First, define the thermophysical properties of the materials of the prefabricated steel structure, including specific heat capacity, thermal conductivity, and density parameters. Assume that the density of the steel is ρ, the specific heat capacity is c p , and the thermal conductivity is k0, then the material heat conduction behavior satisfies the heat diffusion equation:

[0115]

[0116] where T is the temperature field distribution, Q is the external heat source term, represents the change of heat flux in the heat conduction process.

[0117] Subsequently, for the contact interface region, the fractal theory is used to describe the interface roughness, and a heat conduction equation is established based on the non-local heat conduction theory. The non-local heat conduction equation is expressed as:

[0118]

[0119] where x and x' are the spatial positions respectively, D is the fractal dimension, Ω is the calculation region, is the temperature gradient, and the kernel function is used to describe the non-local influence of the interface heat transfer, and Q(x) is the heat source term.

[0120] Furthermore, in combination with the fractal dimension D f the kernel function is adjusted to consider the influence of the interface roughness on the heat flux, and the modified kernel function K f is set as follows:

[0121]

[0122] where β is the adjustment parameter used to correct the interface thermal conductivity to match the fractal surface effect. This kernel function is used to calculate the non-local heat conduction effect in the interface region.

[0123] Subsequently, boundary conditions are set for each contact interface region to ensure the reasonable transfer of the temperature field in the heat conduction analysis of the prefabricated steel structure. The interface boundary condition adopts the heat flux continuity condition, that is:

[0124]

[0125] where k eff,1 and k eff,2 are the effective thermal conductivities of the components on both sides of the interface respectively, is the normal temperature gradient, ensuring the continuity of heat flux on the interface.

[0126] Finally, a heat conduction model with a fractal rough surface is generated. This model combines fractal theory and the non-local heat conduction equation, and can accurately describe the heat flux characteristics of the contact interface of the prefabricated steel structure, providing an accurate temperature field input for subsequent thermo-mechanical coupling analysis.

[0127] For step S3, in this embodiment, step S3 is used to mesh the geometric model of the prefabricated steel structure and dynamically adjust the local mesh density based on an error criterion to ensure calculation accuracy and efficiency. This process combines the material model and the non-local heat conduction equation defined in the previous steps S1 and S2, aiming to achieve efficient and accurate calculations in complex heat conduction analysis.

[0128] First, based on the geometric model of the prefabricated steel structure generated in the previous step S1, the overall structure is initially meshed using tetrahedral elements or hexahedral elements. Tetrahedral elements are suitable for structures with irregular geometric shapes, while hexahedral elements are suitable for components with regular shapes. The preliminary purpose of meshing is to ensure that the geometric model can be effectively discretized in finite element analysis and provide a basis for subsequent heat conduction analysis.

[0129] After the initial meshing is completed, heat conduction analysis is carried out. According to the material properties set in step S2, the temperature gradient and heat flux density are calculated under the initial mesh. Where k is the thermal conductivity of the material, is the temperature gradient within the current mesh element, and q represents the heat flux density passing through this region. At this time, the temperature gradient and heat flux density are used to reflect the heat conduction behavior of each region in the structure, further affecting the evaluation of mesh errors.

[0130] After obtaining the preliminary temperature gradient and heat flux density, the local mesh is evaluated according to the error criterion. The local mesh error is calculated using an error estimation formula, and the formula is as follows:

[0131]

[0132] where q hand q h / 2 They represent the heat flux values ​​calculated at the current grid h and the encrypted grid h / 2 respectively. Error index η e It is used to evaluate the accuracy of the local grid and reflects the difference between the results after mesh refinement and the results of the original grid.

[0133] Next, based on the error threshold η th , to determine whether it is necessary to encrypt or coarsen the mesh in certain areas. The specific judgment criteria are as follows:

[0134] If η e >1.5η th , then the area is locally encrypted;

[0135] If η e <0.5η th , the mesh is coarsened.

[0136] When the error exceeds the threshold, the local encryption strategy is used to refine the grid to improve the calculation accuracy of these areas. Local encryption uses an adaptive grid refinement algorithm to give areas with large changes in heat flux density a higher grid density to capture the details of the heat conduction process. When the error is less than the threshold, the number of grids is reduced through grid coarsening, thereby improving calculation efficiency.

[0137] During the mesh refinement process, the mesh cell size h new According to the error η e Dynamic adjustment, the specific formula is as follows:

[0138]

[0139] Among them, h old is the size of the current grid unit, η c is the error threshold, and η is the local error value. In this way, the grid can be accurately adjusted according to the change of heat flux density, which improves the calculation accuracy of key areas in the structure (such as contact interfaces).

[0140] After the mesh refinement is completed, the local error needs to be recalculated and the overall error needs to be checked to see if it meets the set convergence criteria. If the overall error does not meet the predetermined accuracy requirements, the mesh adjustment and error calculation process is repeated until the error convergence conditions are met. The entire process continuously adjusts the local mesh density to achieve the required calculation accuracy.

[0141] This step enables accurate meshing for thermal expansion analysis of prefabricated steel structures, while dynamic mesh adjustment ensures the efficiency and accuracy of heat conduction analysis. Finally, an optimized mesh model is obtained, which is suitable for subsequent thermal-mechanical coupling analysis.

[0142] For step S4, in this embodiment, step S4 is used to set up a thermal-mechanical coupling analysis step, dynamically divide the implicit and explicit integration regions based on the chaotic stability criterion, and impose a synchronization control mechanism to ensure the effective coupling between the temperature field and the mechanical response.

[0143] First, establish a thermal-mechanical coupling control equation to describe the heat conduction and mechanical response of the prefabricated steel structure under thermal-mechanical coupling. The heat conduction equation describes the change of the temperature field, and its basic form is:

[0144]

[0145] where ρ is the density, c p is the specific heat capacity, k is the thermal conductivity, T is the temperature field, Q is the heat source term, represents the dot product of the thermal conductivity and the temperature gradient. This equation describes the heat conduction behavior inside the structure.

[0146] The mechanical part describes the stress-strain response of the steel structure through the elasticity equations, and its basic form is:

[0147]

[0148] where σ is the stress tensor, u is the displacement vector, is the displacement acceleration term, and f is the body force. This equation describes the mechanical response generated by thermal expansion.

[0149] Next, calculate the local Lyapunov exponent λ(x) to judge the system stability. The Lyapunov exponent is used to analyze the chaos and stability of the system, and its calculation formula is as follows:

[0150]

[0151] where T(x,t) is the temperature at point x at time t, and T(x,0) is the temperature at point x at the initial time t = 0. ||·|| represents the norm of the matrix. Through this formula, the Lyapunov exponent of each point is calculated to evaluate its stability. When λ(x)>0, it means that this region exhibits chaotic characteristics and the implicit integration method needs to be used; when λ(x)≤0, it means that this region exhibits stability characteristics and the explicit integration method can be used.

[0152] Based on the spatial distribution of the calculated Lyapunov exponents, the entire calculation domain is dynamically divided into an implicit integration region and an explicit integration region. Specifically, the implicit region is applicable to areas with large temperature gradient changes, where the heat flux changes violently, and the implicit integration method is used for solution. These regions usually correspond to places where the temperature changes rapidly or significant thermal expansion of the structure occurs. In these regions, the Newton-Raphson iteration method is used for solution to improve the calculation stability.

[0153] The explicit region is applicable to areas with small temperature gradient changes, where the heat flux changes gently, and the explicit integration method is used for solution. The explicit integration method usually uses the central difference scheme, which can handle the regions with lower Lyapunov exponents in the calculation and maintain high calculation efficiency in these regions.

[0154] To ensure the thermal-mechanical coupling effect between the implicit region and the explicit region, a synchronization control mechanism is introduced between the regions. The synchronization control mechanism is used to coordinate the update of the temperature field between the implicit and explicit regions to ensure the consistency between the two. Specifically, the temperature field update formula under the explicit region is as follows:

[0155]

[0156] where, is the temperature at time step n + 1 under the explicit region, is the temperature at time step n under the explicit region, Δt is the time step size, F(T n ) is the correlation function between the heat source term and the temperature field under the explicit region, γ is the synchronization gain coefficient, is the temperature at time step n under the implicit region. Through this formula, the temperature field of the explicit region is not only affected by its own heat source term but also by the feedback of the temperature field of the implicit region, ensuring the synchronization between the two.

[0157] At the junction of the implicit and explicit regions, data transfer is carried out by the interpolation method. The interpolation method is used to transfer the temperature values calculated in the implicit region to the explicit region or transfer the temperature values calculated in the explicit region to the implicit region. In this way, the continuity and consistency of the temperature field between the implicit and explicit regions are ensured, thus realizing effective thermal-mechanical coupling.

[0158] Through the above steps, it is possible to dynamically select an appropriate integration method according to the stability of the system, and at the same time ensure the coordination of the temperature field between the implicit and explicit regions through the synchronization control mechanism. This method can effectively handle the thermal expansion problem of prefabricated steel structures under the action of heat and provide accurate data support for subsequent thermal-mechanical coupling analysis.

[0159] For step S5, in this embodiment, step S5 is used for the thermal expansion analysis of prefabricated steel structures. Among them, by means of dimensionality reduction processing combined with implicit and explicit integration, the thermo-mechanical coupling problem is solved, and the continuity of the temperature field and displacement field between the implicit and explicit regions is ensured.

[0160] First, according to the thermo-mechanical coupling control equation, the temperature field T and displacement field u are processed by dimensionality reduction using the tensor decomposition method. The basic idea of tensor decomposition is to decompose high-dimensional data (such as the temperature field and displacement field) into low-dimensional subspaces, thereby reducing the computational complexity. Assuming that both the temperature field and displacement field are tensor data, after tensor decomposition, the following form is obtained:

[0161]

[0162] where T is the temperature field, u is the displacement field, r is the rank of the decomposition, λ i , μ i are the corresponding coefficients, A i , B i , C i and P i , Q i , R i are the basis matrices after tensor decomposition, represents the tensor product. In this way, the original high-dimensional temperature field and displacement field can be converted into multiple low-dimensional subspaces, greatly reducing the computational complexity.

[0163] Based on the dimensionality-reduced temperature field and displacement field, next, implicit and explicit integration calculations are performed for each region. The implicit integration method is applicable to regions with large thermal gradients and is usually used to calculate the responses of more complex structures, while the explicit integration method is applicable to regions with small thermal gradients and can improve the computational efficiency. In the implicit region, the update formulas for the temperature field and displacement field are:

[0164]

[0165] where, and are the values of the temperature field and displacement field in the implicit region at time step n + 1, respectively, and are the values at time step n, Δt is the time step size, F(T n ) and G(u n ) are the correlation functions of the heat source term with the temperature field and the mechanical equation with the displacement field in the implicit region, γ is the synchronization gain coefficient, and are the temperature field and displacement field in the explicit region, respectively.

[0166] In the explicit region, the update formulas for the temperature field and displacement field are:

[0167]

[0168] Among them, and are the values of the temperature field and displacement field in the explicit region at time step n + 1 respectively, and are the values at time step n respectively, H(T n ) and J(u n ) are the correlation functions between the heat source term and the temperature field, and the mechanical equation and the displacement field in the explicit region respectively.

[0169] Between the implicit and explicit integration regions, in order to ensure the continuity of the temperature field and displacement field, a smooth transition algorithm is adopted for balancing. Through this algorithm, a smooth transition of the temperature field and displacement field can be achieved at the junction of the implicit region and the explicit region, ensuring a smooth transition between the two integration methods, thus avoiding possible numerical discontinuity problems. The basic idea of the smooth transition algorithm is to adjust the field variables in the explicit region and the implicit region by means of weighted average, so that the two are consistent at the junction.

[0170] The specific transition formula is as follows:

[0171]

[0172] Among them, T smooth and u smooth are the temperature field and displacement field after smooth transition respectively, and α is the transition coefficient, usually taking values between 0 ≤ α ≤ 10, which is used to control the transition degree between the implicit and explicit regions.

[0173] By iteratively adjusting the time steps of the implicit and explicit regions multiple times, the calculation process can be further optimized to ensure the accuracy and efficiency of the thermo-mechanical coupling analysis. During the iteration process, according to factors such as local temperature gradient, stress distribution, and Lyapunov exponent, the time steps of each region are dynamically adjusted to ensure that the physical characteristics of different regions can be adapted during the solution process.

[0174] Through the above steps, the temperature field and displacement field of the prefabricated steel structure under thermo-mechanical coupling can be effectively solved, and the continuity and consistency of the calculation results between the implicit and explicit regions can be ensured. At the same time, the introduction of the tensor decomposition method greatly reduces the calculation complexity and improves the solution efficiency.

[0175] For step S6, in this embodiment, step S6 introduces an adjoint equation to invert and optimize the fractal parameters until the convergence condition is satisfied, thereby updating the model and outputting the optimized result.

[0176] First, based on the previously established thermo-mechanical coupling equations, the adjoint equations are introduced for the inversion optimization of the fractal parameters. The adjoint equations control the inversion process of the temperature field and displacement field errors, and the specific forms are as follows:

[0177] The adjoint equation of the temperature field is:

[0178]

[0179] where λ is the adjoint temperature field, k is the thermal conductivity, T is the temperature field, and F T is the source term of the temperature field. This equation describes the influence of the temperature field error on the fractal parameters and provides the reverse gradient information for the optimization of the fractal parameters.

[0180] The adjoint equation of the displacement field is:

[0181]

[0182] where μ is the adjoint displacement field, σ is the stress field, and F u is the source term of the displacement field. This equation describes the influence of the displacement field error on the structural displacement fractal parameters and provides the necessary update information for the inversion process.

[0183] Next, the results of solving the adjoint equations can be used to calculate the gradient of the fractal parameters. Specifically, through the solved adjoint temperature field λ and adjoint displacement field μ, the error inversion direction can be obtained. Based on this gradient, the fractal parameters are updated to optimize the temperature field and displacement field. The update formula is:

[0184]

[0185] where θ k is the fractal parameter in the k-th iteration, α is the learning rate, is the objective function, representing the measure of the temperature field and displacement field errors. The error gradient is calculated through backpropagation, and the fractal parameters are adjusted to gradually optimize the temperature field and displacement field.

[0186] With the updated fractal parameters, the thermal expansion analysis model of the prefabricated steel structure is recalculated. Specifically, based on the optimized fractal parameters, the heat conduction and mechanical response are recalculated to obtain the new temperature field and displacement field. These updated field variables will be used as the basis for the next analysis.

[0187] In each iteration process, it is necessary to judge whether the temperature field and displacement field converge. The convergence criterion is calculated based on the difference between the temperature field and displacement field in the previous and current iterations. The specific convergence condition is:

[0188] ||T k+1 -T k || < ∈ T

[0189] ||u k+1 -u k ||<∈ u

[0190] Among them, T k and T k+1 are the results of the previous and subsequent iterations of the temperature field respectively, and u k and u k+1 are the results of the previous and subsequent iterations of the displacement field respectively, and ∈ T and ∈ u are the convergence accuracies of the temperature field and the displacement field. When the above conditions are met, it indicates that the temperature field and the displacement field have converged, and the calculation ends and the optimized results are output.

[0191] If, during the iteration process, the temperature field and the displacement field have not reached the convergence accuracy, the iteration continues, and the model is recalculated and optimized using the updated fractal parameters until the convergence conditions are met. Through multiple iterations of optimization, it is ensured that the final result accurately reflects the true response of the steel structure under thermal expansion.

[0192] Finally, after multiple iterations and meeting the convergence conditions, the optimized results of the thermal expansion analysis of the prefabricated steel structure are output, including the optimized temperature field, displacement field, and optimized fractal parameters. This result can be further used for structural design optimization to ensure the safety and stability of the steel structure under thermal action.

[0193] Through this step, efficient optimization of the temperature field and the displacement field can be achieved, updating the fractal parameters by adjoint equation inversion, optimizing the steel structure design, and ensuring good performance and reliability of the structure under thermal expansion.

[0194] Generally speaking, the present invention constructs a rough surface of the contact interface through fractal geometry modeling and dynamically optimizes the mesh division, describes the interface heat transfer behavior by combining the non-local heat conduction equation, divides the implicit / explicit integration region based on the Lyapunov chaos stability criterion, and uses tensor decomposition dimensionality reduction and adjoint equation inversion technology to achieve efficient solution of the thermo-mechanical coupling field and closed-loop optimization of fractal parameters. This method establishes a multi-level collaborative mechanism of dynamic correction of the fractal dimension, adaptive encryption of the mesh, and intelligent matching of the regional integration method, and realizes quantitative characterization of the interface thermal resistance characteristics and accurate prediction of the thermal expansion response through the coupling feedback of the thermal conductivity-fractal parameters, synchronous control of the temperature field-displacement field, and gradient inversion of the fractal parameters.

[0195] The prefabricated steel structure thermal expansion analysis and calculation device based on the finite element method described below can be correspondingly referred to the prefabricated steel structure thermal expansion analysis and calculation method based on the finite element method described above.

[0196] Please refer to the appendix Figure 2, the present invention also provides a calculation device for thermal expansion analysis of prefabricated steel structures based on the finite element method, including:

[0197] A geometric modeling module 100, which is used to generate a geometric model of the prefabricated steel structure, define a fractal rough surface for the contact interface, and mark it as a key area for heat conduction;

[0198] A material definition module 200, which is used to define a material model and describe the interfacial heat conduction behavior by using a non-local heat conduction equation containing fractal parameters;

[0199] A mesh generation module 300, which is used to generate a mesh for the geometric model and dynamically adjust the local mesh density based on an error criterion;

[0200] A thermal-mechanical coupling analysis module 400, which is used to set thermal-mechanical coupling analysis steps, dynamically divide the implicit and explicit integration regions based on a chaos stability criterion, and apply a synchronous control mechanism at the same time;

[0201] A calculation and solution module 500, which is used to solve the temperature field and displacement field by tensor decomposition dimensionality reduction and perform implicit and explicit integration calculations within sub-regions;

[0202] An optimization and update module 600, which is used to inversely optimize the fractal parameters by combining the adjoint equation until the convergence condition is met, update the model, and output the calculation results of thermal expansion analysis;

[0203] The device in this embodiment can be used to execute the above method embodiment, and its principle and technical effects are similar, so they will not be elaborated here.

[0204] Please refer to the appendix Figure 3 , the present invention also provides a computer device 40, including: a processor 41 and a memory 42. The memory 42 stores a computer program executable by the processor. When the computer program is executed by the processor, it executes the above method.

[0205] The present invention also provides a storage medium 43. A computer program is stored on the storage medium 43. When the computer program is run by the processor 41, it executes the above method.

[0206] Among them, the storage medium 43 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disc.

[0207] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method, characterized in that: The following steps are involved: Generate a geometric model of the prefabricated steel structure, define a fractal rough surface for the contact interface, and mark it as a critical area for heat conduction; Define the material model and describe the interface heat conduction behavior through the non-local heat conduction equation with fractal parameters; Mesh the model and dynamically adjust the local mesh density based on error criteria; Set up the thermal-mechanical coupling analysis step, dynamically divide the implicit and explicit integration regions based on the chaos stability criterion, and apply the synchronization control mechanism; The temperature field and displacement field are solved by reducing the dimension through tensor decomposition, and implicit and explicit integral calculations are performed in different regions; The fractal parameters are optimized by inversion of the adjoint equation until the convergence conditions are met, the model is updated and the results are output.

2. The method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method according to claim 1 is characterized in that: The steps of generating a geometric model of the assembled steel structure, defining a fractal rough surface for the contact interface, and marking it as a key area for heat conduction include: Establish a 3D geometric model of the steel structure; Identifying the contact interface and defining a fractal rough surface, wherein the rough surface is generated by a Weierstrass-Mandelbrot function; Define the heat conduction characteristics of the contact area according to the generated fractal rough surface, mark it as the key area of ​​heat conduction, and specify the thermal conductivity parameters for the area; In the geometric model, the effect of interface roughness on heat flow is considered, and the boundary conditions and internal and external heat source terms of the heat conduction equation are set; Generate a complete geometric model of the prefabricated steel structure.

3. The method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method according to claim 1 is characterized in that: The step of defining a material model and describing the interface heat conduction behavior by a non-local heat conduction equation containing fractal parameters comprises: Define the thermophysical properties of steel, including specific heat capacity, thermal conductivity, and density parameters; According to the characteristics of fractal rough surface, the non-local heat conduction equation is used to describe the interface heat conduction behavior. The non-local heat conduction equation is: in, is the temperature gradient, x and x' are the spatial positions, D is the fractal dimension, Ω is the calculation area, and Q(x) is the heat source term; Combined with the fractal dimension D, the kernel function in the heat conduction equation is adjusted to consider the effect of interface roughness on heat flow; Set boundary conditions for each contact interface area to ensure that the temperature field is reasonably transferred in the heat conduction analysis of the structure; Finally, a heat conduction model with a fractal rough surface is generated, taking into account the heat flow characteristics of the interface.

4. The method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method according to claim 1 is characterized in that: The steps of meshing the model and dynamically adjusting the local mesh density based on the error criterion include: Based on the geometric model of the prefabricated steel structure, the initial meshing of the whole structure is performed using tetrahedral elements or hexahedral elements; Calculate the temperature gradient under the initial grid and heat flux And the local mesh error is evaluated according to the following error estimation formula: Among them, q h and q h / 2 are the estimated values ​​of heat flux density of the current grid and the grid with one layer of encryption, η e is the local error index, k is the thermal conductivity of the material, is the temperature gradient within the current grid cell; Based on the error threshold η th , determine whether mesh encryption is needed: If η e >1.5η th , then the area is locally encrypted; If η e <0.5η th , the grid is coarsened; Adopt adaptive mesh refinement algorithm to refine the mesh in high error areas; After completing the grid adjustment, recalculate the error and check whether it meets the overall error convergence standard. If not, repeat the grid adjustment process until the preset accuracy requirement is met.

5. The method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method according to claim 1, characterized in that: The steps of setting a thermal-mechanical coupling analysis step, dynamically dividing implicit and explicit integration regions based on a chaotic stability criterion, and applying a synchronous control mechanism include: The thermal-mechanical coupling control equation is established, the heat conduction equation is used to describe the temperature field change, and the elastic mechanics equation is used to describe the stress-strain response of the steel structure. Its basic form is: Where ρ is the density, c p is the specific heat capacity, k is the thermal conductivity, t is the temperature field, Q is the heat source term, represents the dot product of thermal conductivity and temperature gradient, σ is the stress tensor, u is the displacement vector, is the displacement acceleration term, f is the body force; Calculate the local Lyapunov exponent λ(x) to determine the stability of the system. The calculation formula is: Where, T(x),t) is the temperature of point x at time t, T(x,0) is the temperature of point x at the initial time t=0, and ||·|| represents the norm of the matrix; when λ(x)>0, the region exhibits chaotic characteristics and implicit integration is used, otherwise explicit integration is used; According to the spatial distribution of the Lyapunov exponent, the calculation area is dynamically divided into implicit integration area and explicit integration area, using different time steps Δt: Implicit region: Applicable to regions with high gradient changes, using the Newton-Raphson iteration method for solution; Explicit region: Applicable to low Lyapunov exponent regions, using central difference format for calculation; A synchronous control mechanism is introduced to coordinate the updating of field variables in implicit and explicit regions. The synchronous control equation of the temperature field is: in, is the temperature at time step n+1 in the explicit region, is the temperature at time step n in the explicit region, Δt is the time step, F(T n ) is the correlation function between the heat source term and the temperature field in the explicit region, γ is the synchronization gain coefficient, is the temperature at time step n in the implicit region; A coupled solution is performed and the interpolation method is used to transfer data at the boundary between implicit and explicit regions.

6. The method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method according to claim 1, characterized in that: The steps of solving the temperature field and the displacement field by reducing the dimension through tensor decomposition and performing implicit and explicit integral calculations in different regions include: Based on the thermal-mechanical coupling control equation, the temperature field and displacement field are reduced in dimension by the tensor decomposition method: Based on the field variables after dimension reduction, implicit and explicit integration calculations are performed on the temperature field and displacement field of each region respectively; Between the implicit and explicit integration regions, a smooth transition algorithm is used to balance the two integration methods to ensure the continuity of the temperature field and displacement field. Through multiple iterations, the time steps of implicit and explicit regions are adjusted to complete the solution of temperature field and displacement field.

7. The method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method according to claim 1, characterized in that: The steps of combining the adjoint equation to inversely optimize the fractal parameters until the convergence condition is met, updating the model and outputting the results include: Based on the constructed thermal-mechanical coupling equation, the adjoint equation is introduced to inversely optimize the fractal parameters. The adjoint equation is expressed as: Among them, λ is the accompanying temperature field, μ is the accompanying displacement field, and F T and F u are the source terms of temperature field and displacement field respectively; By solving the adjoint equation, the gradient of the fractal parameter is calculated, and then the error inversion direction is obtained. The inversion result is used to update the fractal parameter. The update formula is: Among them, θ k is the fractal parameter in the kth iteration, α is the learning rate, is the objective function, which represents the measure of the error of temperature field and displacement field; Based on the updated fractal parameters, the thermal expansion analysis model of the prefabricated steel structure is recalculated to obtain new temperature fields and displacement fields. It is judged whether the convergence conditions are met. If so, the results are output and the calculation is terminated. If not, the iteration is continued. The convergence criteria are: ||T k+1 -T k ||<∈ T and ||in k+1 -in k ||<∈ u Among them, T k and T k+1 They are the results of the previous and next iterations of the temperature field, u k and u k+1 are the results of the previous and next iterations of the displacement field, ∈ T and ∈ u is the convergence accuracy of temperature field and displacement field; Output the optimized model results, including temperature field, displacement field and optimized fractal parameters, to complete the thermal expansion analysis and calculation of prefabricated steel structures.

8. A device for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method, used to execute the method for analyzing and calculating thermal expansion of assembled steel structures based on the finite element method as claimed in any one of claims 1 to 7, characterized in that: include: The geometric modeling module is used to generate the geometric model of the prefabricated steel structure, define the fractal rough surface for the contact interface, and mark it as the key area for heat conduction; Material definition module, which is used to define the material model and use the non-local heat conduction equation with fractal parameters to describe the interface heat conduction behavior; Meshing module, used to mesh the geometric model and dynamically adjust the local mesh density based on error criteria; Thermal-mechanical coupling analysis module, which is used to set the thermal-mechanical coupling analysis step and dynamically divide the implicit and explicit integration regions based on the chaos stability criterion, while applying the synchronization control mechanism; The calculation and solution module is used to solve the temperature field and displacement field by reducing the dimension through tensor decomposition, and perform implicit and explicit integral calculations in sub-regions; The optimization update module is used to optimize the fractal parameters by combining the adjoint equation inversion until the convergence conditions are met, update the model and output the thermal expansion analysis calculation results.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the method for analyzing and calculating thermal expansion of prefabricated steel structures based on the finite element method as described in any one of claims 1 to 7.

10. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the method for analyzing and calculating thermal expansion of prefabricated steel structures based on the finite element method as described in any one of claims 1 to 7.

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