Bridge finite element real-time analysis method and system

Abstract

The invention discloses a bridge finite element real-time analysis method and system, and the method comprises the steps: constructing a finite element model of a structure, and dividing the finite element model into a plurality of finite element units through discretization processing; calculating an overall stiffness matrix K according to the established finite element model; in combination with the boundary condition of the structure, recalculating to obtain a processed total stiffness matrix K ', and carrying out serialization operation on the processed total stiffness matrix K '; selecting a position for storing the sparse matrix according to a specific computing environment; according to the load information acquired by the sensor, converting the load information into a corresponding load vector in the finite element model; and combining the cached total stiffness matrix K'with a load vector, solving node displacement and structural response, and transmitting a result to a post-processing module. According to the method, the required data are efficiently accessed according to different calculation requirements on the basis of a sparse matrix cache strategy, when the load changes, only the load vector needs to be recalculated and solved, the overall stiffness matrix does not need to be recalculated, and the calculation efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of bridge structure simulation technology, and more specifically, relates to a real-time finite element analysis method and system for bridges. Background Technology

[0002] In finite element static analysis, generating the stiffness matrix is ​​a crucial step in solving the problem. The stiffness matrix is ​​typically a sparse matrix, and this sparsity provides optimization space for matrix storage and computation. Storage formats such as Compacted Sparse Rows (CSR) and Compacted Sparse Columns (CSC) are commonly used to reduce memory requirements and improve computational efficiency. However, traditional finite element analysis methods require repeated generation and assembly of the stiffness matrix in each calculation, especially in dynamic condition analysis, leading to a large amount of redundant computation and increasing the difficulty of real-time analysis.

[0003] Real-time finite element analysis (FEM) can rapidly calculate the stress and deformation response of a structure based on real-time operating conditions. As the structural system and load distribution change at different stages, real-time analysis allows for dynamic assessment of the safety and stability of construction conditions, avoiding potential risks. Traditional solvers are typically designed for one-time global calculations, offering limited support for matrix reuse. Real-time FEM caches the stiffness matrix in CSR format to support rapid reading and reuse of the stiffness matrix. Under dynamic conditions, the sparse matrix cache needs to be partially updated to adapt to changes, rather than reassembling the entire matrix. Summary of the Invention

[0004] To address the aforementioned shortcomings or improvement needs of existing technologies, this invention provides a real-time finite element analysis method and system for bridges. By employing sparse matrix caching technology, it can efficiently handle dynamic changes in finite element analysis, ensuring the real-time nature of structural analysis. Combining local and remote cache database storage strategies, the system flexibly selects data storage locations according to different computational needs. This multi-level caching mechanism not only improves data access speed but also enhances system flexibility and response speed. When the load changes, the system does not need to recalculate the overall stiffness matrix K; it only needs to recalculate and solve the load vector. This strategy significantly reduces the overhead of redundant calculations and substantially improves computational efficiency.

[0005] To achieve the above objectives, according to one aspect of the present invention, the present invention provides a real-time finite element analysis method for bridges, comprising the following specific steps: S100: Construct a finite element model of the structure, and divide the actual structure into multiple finite element elements through discretization. S200: Based on the established finite element model, calculate the overall stiffness matrix K; S300: Based on the boundary conditions of the structure, the overall stiffness matrix K is recalculated to obtain the processed overall stiffness matrix K′, and then serialized. S400: Depending on the specific computing environment, the sparse matrix can be stored in a local storage device or a cache database; S500: Based on the load information acquired by the sensor, the load information is converted into the corresponding load vector in the finite element model; S600: Combines the cached overall stiffness matrix K′ with the load vector to solve for nodal displacements, calculates the structural response, and stores these calculation results in a structured manner or passes them to the post-processing module; S700: Perform efficient Web service post-processing on the calculation results to generate RGB color data and deformation visualization data for cloud map rendering, and then output them. If the load information changes, return to step S500. If the boundary conditions of the structure change, return to step S300. If the entire structure changes, return to step S100 to restart the entire process.

[0006] Further, step S100 includes: S110: Select the appropriate element type and define the material properties of each element based on the structural material properties and analysis requirements; S120: Determine the node position of each element, number the nodes and elements according to certain rules to ensure the uniqueness and continuity of the numbering, and define the coordinate information of the nodes, including the x, y, and z coordinates in three-dimensional space; S130: Check the integrity and accuracy of the finite element model, ensuring that all element and node connections are correct, material properties are correctly assigned, and avoiding isolated nodes or unconnected elements.

[0007] Further, step S200 includes: S210: For each finite element, calculate the element stiffness matrix ke in the local coordinate system based on its geometry, material properties, and element type. Then, using the transformation matrix T, calculate the element stiffness matrix in the global coordinate system. The element stiffness matrix equation is:

[0008] S220: Assemble the stiffness matrices of all elements into a global stiffness matrix K by arranging the stiffness matrix Ke of each element according to the node number positions. The equation of the global stiffness matrix is:

[0009] Where: i and j are the indices of the global node, K ij It is an element in the global stiffness matrix K, Ke ijIt is the contribution of the element stiffness matrix Ke to the global positions i and j.

[0010] Furthermore, the local storage device includes, but is not limited to, hard disk storage and database storage; the cache database includes, but is not limited to, in-memory database and distributed cache.

[0011] Further, step S500 includes the following: By installing sensors at key parts of the structure, structural response data under load is collected in real time. The collected sensor data is preprocessed and normalized to meet the input requirements of the finite element model. Based on the sensor data and the stress characteristics of the structure, the types of loads acting on the structure are identified. At the same time, the spatial distribution and temporal variation of the loads are analyzed. According to the location and mode of load application, the loads are distributed to the corresponding nodes of the finite element model. The load values ​​distributed to each node are arranged in a certain order to form a column vector, i.e., the load vector.

[0012] Furthermore, the data preprocessing in step S500 includes noise removal, missing value filling, and unit conversion to ensure that the data collected by the sensor matches the input requirements of the finite element model and can adapt to different types of sensor data formats.

[0013] Further, step S600 includes: S610: Load the modified global stiffness matrix K′ and load vector P from the storage medium; S620: Combine the processed global stiffness matrix K′ with the load vector P to form the structural equation K′U=P, where K′ represents the modified global stiffness matrix, U is the nodal displacement vector, and P is the load vector. S630: Solve the structural equation K′U=P linearly to obtain the nodal displacement vector U of the structure, that is, the displacement value of each node in different directions.

[0014] S640: Extract the displacement values ​​of each node in different directions from the obtained nodal displacement vector U. Based on the nodal displacements and the element information of the finite element model, calculate the internal forces, stresses, strains, deformations and support reactions of the structure, and store these calculation results in a structured manner or pass them to the post-processing module.

[0015] Furthermore, step S700 also includes: when post-processing the element stress or internal force, loading the element result data that has been calculated under the corresponding model and working condition; for the stress type of the specified element e, defining the stress result value of element e as σ and the internal force result value as F; when element e has multiple evaluation points, it is expressed by the following formula:

[0016] Where |x| represents the absolute value of the stress or internal force in element e, σ nodeI and F nodeI σ represents the resulting value of stress or internal force at endpoint i of the element. nodeJ and F nodeJ It is the result value of the stress or internal force of the element at endpoint j; Obtain all similar units and their corresponding result values ​​under the current working condition, iterate through and compare the result values ​​to determine the maximum and minimum values, and at the same time perform a small perturbation on the zero value to avoid division by zero errors in subsequent calculations;

[0017] Where, σ max and σ min F represents the maximum and minimum values ​​of the stress result. max and F min This represents the maximum and minimum values ​​of the internal force results; For each unit's result value, the corresponding RGB color value is calculated using a preset color mapping algorithm. Each color component takes values ​​in the range [0,1]. The piecewise linear color mapping algorithm includes:

[0018] Among them, (R) e G e B e ) is the RGB color value of the unit, τ e The corresponding calculated element stress or internal force values; Convert floating-point RGB values ​​to hexadecimal color codes:

[0019] Where H represents the converted hexadecimal RGB, and C... e Hexadecimal color codes; Returns the element ID, element stress σ or element internal force F, and hexadecimal color code C in JSON format. e Unit, σ max and σ min Maximum and minimum values ​​of stress results or F max and F min Post-processed data for the maximum and minimum values ​​of internal force results; When post-processing the node deformation and displacement, the original coordinates (X, Y, Z) and displacement vector (u) of node i are loaded. i,x ,u i,y ,u i,z ), calculate the displacement scalar value δ of each node according to the specified displacement type.i :

[0020] Where, δ xyz This represents the resultant displacement of node i; Calculate the 3D coordinates of node i after deformation:

[0021] Among them, P i,def Let X be the deformed three-dimensional coordinates. i,d Y i,d Z i,d These are the coordinate values ​​of (X, Y, Z) after being multiplied by the magnification factor and distorted, respectively. i,o Y i,o Z i,o These are the original coordinates of (X, Y, Z); Calculate the maximum and minimum values ​​of all nodal displacement scalar values:

[0022] For each node's displacement scalar value, the corresponding RGB color value is calculated using a preset color mapping algorithm. Each color component takes values ​​in the range [0,1]. The piecewise linear color mapping algorithm includes:

[0023] Where is the RGB color value of node i, δ i The corresponding calculated scalar value of the displacement of node i; Convert floating-point RGB values ​​to hexadecimal color codes:

[0024] Where is the converted hexadecimal RGB, and is the hexadecimal color code; Returns post-processed data in JSON format, including node ID, node displacement value, node coordinates after deformation, node color code, unit, and overall maximum / minimum displacement value.

[0025] Furthermore, the color mapping algorithm includes mapping data values ​​close to zero or within a specific reference range to a first preset color, mapping positive or stretched data values ​​to a first color system in segments according to their size, and mapping negative or compressed data values ​​to a second color system in segments according to their size. It can perform post-processing on element stress or internal force and nodal deformation or displacement, and supports receiving post-processing requests through API interface and returning visualized post-processing data in JSON format.

[0026] According to another aspect of the present invention, a real-time finite element analysis system based on sparse matrix caching is provided, comprising: Model building module: Constructs a finite element model of the structure, and divides the actual structure into multiple finite element elements through discretization. Stiffness matrix calculation module: Calculates the overall stiffness matrix K based on the established finite element model; Boundary condition processing module: Based on the boundary conditions of the structure, the overall stiffness matrix K is recalculated to obtain the processed overall stiffness matrix K′, and then serialized. Storage module: Depending on the specific computing environment, the sparse matrix can be stored on local storage devices or in a cache database; Load vector generation module: Based on the load information acquired by the sensor, the load information is converted into the corresponding load vector in the finite element model; The result calculation and transmission module combines the cached overall stiffness matrix K′ with the load vector to solve for nodal displacements, calculate the structural response, and store these calculation results in a structured manner or transmit them to the post-processing module. Post-processing module: Performs efficient web service post-processing on the calculation results, generating RGB color data and deformation visualization data for cloud map rendering, allowing users to obtain and display analysis results in real time through network interface. If the load information changes, it returns to step S500; if the boundary conditions of the structure change, it returns to step S300; if the entire structure changes, it returns to step S100 to restart the entire process.

[0027] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: 1. The finite element real-time analysis method of the present invention significantly improves the efficiency of finite element analysis under dynamic load conditions by optimizing the calculation process. In traditional finite element analysis, load changes usually require recalculation of the overall stiffness matrix K, which is computationally intensive and time-consuming. However, the present invention caches the processed overall stiffness matrix K′ and only recalculates the load vector P and solves the structural equation KU=P when the load changes, avoiding the overhead of repeatedly calculating the overall stiffness matrix, significantly reducing the calculation time, and improving the real-time performance of the analysis.

[0028] 2. The finite element real-time analysis method of the present invention adopts a multi-level caching strategy, combining local caching and remote caching databases to meet the data access needs of different computing environments. This flexible storage strategy not only improves the system's response speed but also enhances the system's scalability, enabling it to adapt to various scenarios from small-scale local computing to large-scale distributed computing, thereby improving the overall system's operating efficiency.

[0029] 3. The finite element real-time analysis method of the present invention, through sparse matrix caching technology, stores only non-zero elements and their position information, which greatly reduces the storage space occupied and improves the computational efficiency. Based on the sparse matrix caching strategy, it can process and analyze structural data more quickly, meeting the needs of real-time analysis. For computational scenarios involving multiple variables and complex dynamic changes, the combination of sparse matrix caching and efficient algorithms can ensure the accuracy and stability of the calculation results, providing a reliable basis for engineering design and decision-making.

[0030] 4. The finite element real-time analysis method of the present invention can provide detailed and accurate information for the mechanical analysis of bridge structures by accurately calculating element stress, internal force, and nodal deformation and displacement data, and understand the stress and deformation state of the structure under different working conditions. By adopting a preset color mapping algorithm, the mechanical data is displayed intuitively by color, thereby quickly distinguishing different mechanical states in the structure and enhancing the intuitiveness of the analysis. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating a real-time finite element analysis method for bridges according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating step S100 in a real-time finite element analysis method for bridges according to an embodiment of the present invention. Figure 3 This is a flowchart of step S200 in a bridge finite element real-time analysis method according to an embodiment of the present invention; Figure 4 This is a flowchart illustrating step S600 in a real-time finite element analysis method for bridges according to an embodiment of the present invention. Figure 5 This is a visualization of the analysis results in a bridge finite element real-time analysis method according to an embodiment of the present invention; Figure 6 This is a comparison chart of calculation times in a bridge finite element real-time analysis method according to an embodiment of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0033] It should be noted that the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0034] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0035] Example 1 The following describes a real-time finite element analysis system for bridges provided in this application through Example 1. In this example, the system may include: Model building module: Constructs a finite element model of the structure, and divides the actual structure into multiple finite element elements through discretization. Stiffness matrix calculation module: Calculates the overall stiffness matrix K based on the established finite element model; Boundary condition processing module: Based on the boundary conditions of the structure, the overall stiffness matrix K is recalculated to obtain the processed overall stiffness matrix K′, and then serialized. Storage module: Depending on the specific computing environment, the sparse matrix can be stored on local storage devices or in a cache database; Load vector generation module: Based on the load information acquired by the sensor, the load information is converted into the corresponding load vector in the finite element model; The result calculation and transmission module combines the cached overall stiffness matrix K′ with the load vector to solve for nodal displacements, calculate the structural response, and store these calculation results in a structured manner or transmit them to the post-processing module. Post-processing module: Performs efficient web service post-processing on the calculation results, generating RGB color data and deformation visualization data for cloud map rendering, allowing users to obtain and display analysis results in real time through network interface. If the load information changes, it returns to step S500; if the boundary conditions of the structure change, it returns to step S300; if the entire structure changes, it returns to step S100 to restart the entire process.

[0036] Example 2 In this embodiment, the above-described system is used to implement a real-time finite element analysis method for bridges. This embodiment uses a bridge construction support as an example. In this embodiment, as... Figure 1 As shown, the method includes: S100: Construct a finite element model of the structure, discretizing the actual structure into multiple elements; such as Figure 2 As shown, the specific steps include the following: S110: Select the appropriate element type and define the material properties of each element based on the structural material properties and analysis requirements; Select the appropriate element type based on the structural material properties and analysis requirements. Different materials and analysis needs require different types of elements. When defining the material properties of each element, the corresponding property values ​​need to be set according to the material's mechanical property parameters, such as elastic modulus, Poisson's ratio, and yield strength.

[0037] Choosing the appropriate element type and accurately defining material properties are crucial for ensuring the accuracy of finite element analysis results. A suitable element type can better simulate the mechanical behavior of materials, while accurate material property definitions allow the finite element model to more realistically reflect the actual stress conditions of the structure.

[0038] S120: Determine the node position of each element, number the nodes and elements according to certain rules to ensure the uniqueness and continuity of the numbering, and define the coordinate information of the nodes, including the x, y, and z coordinates in three-dimensional space; Determining the node locations of each element is a crucial step in finite element modeling. Node locations should be determined based on the structure's geometry and element division, ensuring that the nodes accurately reflect the structure's geometric characteristics and stress conditions. After determining the node locations, nodes and elements need to be numbered according to certain rules. These numbering rules should ensure uniqueness and continuity, avoiding duplicate or discontinuous numbering. Furthermore, the numbering should exhibit a certain regularity to facilitate rapid location and processing of nodes and elements in subsequent analyses.

[0039] S130: Check the integrity and accuracy of the finite element model, ensuring that all element and node connections are correct, material properties are correctly assigned, and avoiding isolated nodes or unconnected elements.

[0040] After the finite element model is completed, a comprehensive check of its integrity and accuracy is required. This can be done by reviewing the model's graphical display, checking the connection lists of nodes and elements, and verifying the material properties and boundary condition settings.

[0041] By checking the completeness and accuracy of the finite element model, the support model has a total of 116 nodes and 198 beam elements. The material is Q235 steel, and the material parameter is an elastic modulus of 2 × 10⁻⁶. 5 MPa, Poisson's ratio is taken as 0.3, and bulk density is taken as 7.698×10 -5 The load is N / mm3, which is a concentrated load added to the top. The load is obtained by a sensor installed on the winch. The boundary condition is a fixed constraint at the four bottom points.

[0042] S200: Based on the established finite element model, calculate the overall stiffness matrix K; such as Figure 3 As shown, the specific steps include the following: S210: For each finite element, calculate the element stiffness matrix ke in the local coordinate system based on its geometry, material properties, and element type. Then, using the transformation matrix T, calculate the element stiffness matrix in the global coordinate system. The element stiffness matrix equation is:

[0043] S220: Assemble the stiffness matrices of all elements into a global stiffness matrix K by arranging the stiffness matrix Ke of each element according to the node number positions. The equation of the global stiffness matrix is:

[0044] Where: i and j are the indices of the global node, K ij It is an element in the global stiffness matrix K, Ke ij It is the contribution of the element stiffness matrix Ke to the global positions i and j.

[0045] The global stiffness matrix K is global and reflects the stiffness characteristics of the entire structure. It is assembled from the stiffness matrices Ke of all elements and includes the contributions of all elements in the structure. The global stiffness matrix K is usually a sparse matrix because each element is connected to only a finite number of nodes. Sparsity makes storage and computation more efficient. The assembly of the global stiffness matrix depends on the mapping relationship of node numbers. Local node numbers need to be correctly mapped to global node numbers to ensure the correct assembly of the stiffness matrix.

[0046] S300: Based on the boundary conditions of the structure, the overall stiffness matrix K is recalculated to obtain the processed overall stiffness matrix K′, and then serialized. Based on the actual structural conditions, the boundary conditions of the structure are determined, including fixed supports, hinged supports, and elastic supports. Considering the influence of these boundary conditions on the internal forces and deformations of the structure, the overall stiffness matrix K is recalculated. Based on this modification, the processed overall stiffness matrix K′ is then obtained. For example, for fixed supports, the stiffness matrix elements of certain degrees of freedom at the corresponding nodes can be set to zero to indicate that these degrees of freedom are fully constrained. For elastic supports, the overall stiffness matrix needs to be adjusted accordingly based on the stiffness coefficients of the supports.

[0047] Choose an appropriate serialization method based on actual needs and application scenarios. Common serialization methods include text serialization and binary serialization. Text serialization is easy to read and debug, but the file size is large; binary serialization has a smaller file size, but poorer readability. Using the selected serialization method, convert the processed global stiffness matrix K′ into a serialized format. By saving the serialized global stiffness matrix K′ to a file or database, data storage and access efficiency can be improved, and the time and space costs of data storage and transmission can be reduced.

[0048] S400: Depending on the specific computing environment, the sparse matrix can be stored in a local storage device or a cache database; Furthermore, the local storage device includes, but is not limited to, hard disk storage and database storage; the sparse matrix is ​​stored on the local hard disk in the form of a file.

[0049] Specifically, the cache database includes, but is not limited to, in-memory databases and distributed caches. In-memory databases, such as Redis and Memcached, are used to store sparse matrices. In-memory databases offer advantages such as fast read / write speeds and high performance, making them suitable for scenarios with high data access speed requirements. For large-scale structural projects, distributed caches, such as Redis Cluster and Memcached Cluster, can be used to store sparse matrices. Distributed caches can provide higher storage capacity and access performance, making them suitable for distributed computing and large-scale data processing.

[0050] Storing sparse matrices on local storage devices or in a cache database can improve computational efficiency. Local storage devices offer fast data read / write speeds, while cache databases provide even faster data access, thus reducing computation time.

[0051] Sparse matrices typically have a large number of zero elements. By using sparse matrix storage techniques, significant storage space can be saved. Local storage devices and cache databases can both efficiently store sparse matrices, thereby reducing storage costs.

[0052] S500: Based on the load information acquired by the sensor, the load information is converted into the corresponding load vector in the finite element model; By installing sensors at key locations within the structure, real-time data on the structural response under load, such as strain, displacement, and acceleration, is collected. The collected sensor data undergoes preprocessing, including data cleaning, filtering, and noise reduction, to improve accuracy and reliability. Simultaneously, the data is normalized to meet the input requirements of the finite element model.

[0053] Based on sensor data and the stress characteristics of the structure, the types of loads acting on the structure are identified, such as temperature loads, concentrated loads, and distributed loads. Simultaneously, the spatial distribution and temporal variation patterns of the loads are analyzed to provide a basis for constructing load vectors.

[0054] In finite element analysis, load vectors are typically represented by a column vector, whose elements correspond to the magnitude and direction of the loads at each node in the finite element model. The method for constructing load vectors varies depending on the type and distribution of the load. For example, for concentrated loads, the load values ​​can be directly applied to the corresponding nodes; for distributed loads, methods such as numerical integration are needed to transform them into equivalent nodal loads.

[0055] The constructed load vector is then applied to the finite element model. During application, the elements of the load vector are assigned to the corresponding nodal degrees of freedom based on the load's location and direction. Simultaneously, the time history of the load is considered, and the load vector is applied to the model according to the time step to simulate the actual load application process.

[0056] When the load information changes, only the load vector needs to be recalculated, and the overall stiffness matrix does not need to be recalculated, which improves the efficiency of calculation and analysis and saves calculation time. S600: Combines the cached overall stiffness matrix K′ with the load vector to solve for nodal displacements, calculates the structural response, and stores these calculation results in a structured manner or passes them to the post-processing module; such as Figure 4 As shown, the specific steps include the following: S610: Load the modified global stiffness matrix K′ and load vector P from the storage medium; S620: Combine the processed global stiffness matrix K′ with the load vector P to form the structural equation K′U=P, where K′ represents the modified global stiffness matrix, U is the nodal displacement vector, and P is the load vector. S630: Solve the structural equation K′U=P linearly to obtain the nodal displacement vector U of the structure, that is, the displacement value of each node in different directions.

[0057] S640: Extract the displacement values ​​of each node in different directions from the obtained nodal displacement vector U. Based on the nodal displacements and the element information of the finite element model, calculate the internal forces, stresses, strains, deformations and support reactions of the structure, and store these calculation results in a structured manner or pass them to the post-processing module.

[0058] From the obtained nodal displacement vector U, the displacement values ​​of each node in different directions are extracted. Based on these displacement values ​​and the element information of the finite element model, the internal forces, stresses, strains, deformations, and support reactions of the structure can be calculated. The calculation results are then visualized in real time. Figure 5 As shown.

[0059] By extracting displacement values ​​from the nodal displacement vector U and calculating the internal forces, stresses, strains, deformations, and support reactions of the structure based on the element information of the finite element model, a comprehensive understanding of the mechanical behavior and performance of the structure under external loads can be obtained.

[0060] S700: Perform efficient Web service post-processing on the calculation results to generate RGB color data and deformation visualization data for cloud map rendering, and then output them. If the load information changes, return to step S500. If the boundary conditions of the structure change, return to step S300. If the entire structure changes, return to step S100 to restart the entire process.

[0061] Specifically, when post-processing element stress or internal force, the corresponding model and the calculated element result data under the working condition are loaded. For the stress type of a specified element e, the stress result value of element e is defined as σ, and the internal force result value is defined as F. When element e has multiple evaluation points, it is expressed by the following formula:

[0062] Where |x| represents the absolute value of the stress or internal force in element e, σ nodeI and F nodeI σ represents the resulting value of stress or internal force at endpoint i of the element. nodeJ and F nodeJ It is the result value of the stress or internal force of the element at endpoint j; Obtain all similar units and their corresponding result values ​​under the current working condition, iterate through and compare the result values ​​to determine the maximum and minimum values, and at the same time perform a small perturbation on the zero value to avoid division by zero errors in subsequent calculations;

[0063] Where, σ max and σ min F represents the maximum and minimum values ​​of the stress result. max and F minThis represents the maximum and minimum values ​​of the internal force results; For each unit's result value, the corresponding RGB color value is calculated using a preset color mapping algorithm. Each color component takes values ​​in the range [0,1]. The piecewise linear color mapping algorithm includes:

[0064] Among them, (R) e G e B e ) is the RGB color value of the unit, τ e The corresponding calculated element stress or internal force values; Convert floating-point RGB values ​​to hexadecimal color codes:

[0065] Where H represents the converted hexadecimal RGB, and C... e Hexadecimal color codes; Returns the element ID, element stress σ or element internal force F, and hexadecimal color code C in JSON format. e Unit, σ max and σ min Maximum and minimum values ​​of stress results or F max and F min Post-processed data for the maximum and minimum values ​​of internal force results; When post-processing the node deformation and displacement, the original coordinates (X, Y, Z) and displacement vector (u) of node i are loaded. i,x ,u i,y ,u i,z ), calculate the displacement scalar value δ of each node according to the specified displacement type. i :

[0066] Where, δ xyz This represents the resultant displacement of node i; Calculate the 3D coordinates of node i after deformation:

[0067] Among them, P i,def Let X be the deformed three-dimensional coordinates. i,d Y i,d Z i,d These are the coordinate values ​​of (X, Y, Z) after being multiplied by the magnification factor and distorted, respectively. i,o Y i,o Z i,o These are the original coordinates of (X, Y, Z); Calculate the maximum and minimum values ​​of all nodal displacement scalar values:

[0068] For each node's displacement scalar value, the corresponding RGB color value is calculated using a preset color mapping algorithm. Each color component takes values ​​in the range [0,1]. The piecewise linear color mapping algorithm includes:

[0069] Where is the RGB color value of node i, δ i The corresponding calculated scalar value of the displacement of node i; Convert floating-point RGB values ​​to hexadecimal color codes:

[0070] Where is the converted hexadecimal RGB, and is the hexadecimal color code; Return post-processed data in JSON format, including node ID, node displacement value, node coordinates after deformation, node color code, unit, and overall maximum / minimum displacement value. Furthermore, the color mapping algorithm includes mapping data values ​​close to zero or within a specific reference range to a first preset color, mapping positive or stretched data values ​​to a first color system in segments according to their size, and mapping negative or compressed data values ​​to a second color system in segments according to their size. It can perform post-processing on element stress or internal force and nodal deformation or displacement, and supports receiving post-processing requests through API interface and returning visualized post-processing data in JSON format.

[0071] Furthermore, if the load information changes, return to step S500, regenerate the load vector and solve it; if the boundary conditions of the structure change, return to step S300, correct the overall stiffness matrix; if the entire structure changes (such as changes in geometry or material properties), return to step S100, and rebuild the finite element model.

[0072] Normally, when the load information changes, the load vector needs to be recalculated and solved, which greatly saves calculation time and enables real-time calculation. When the boundary conditions change, only the overall stiffness matrix K needs to be reprocessed. The overall stiffness matrix needs to be recalculated and cached only when the structure changes.

[0073] This feedback mechanism ensures that finite element analysis is always based on the latest and most accurate structural information, avoiding inaccurate analysis results due to structural changes. This improves the flexibility and adaptability of finite element analysis, enabling it to better handle various complex situations and changes in practical engineering. Figure 6As shown, the present invention significantly reduces the average computation time compared to methods that do not cache the matrix.

[0074] In summary, the bridge finite element real-time analysis method and system provided by this invention, based on a sparse matrix caching strategy, better supports real-time analysis, adapts to complex dynamic calculation needs, and ensures the real-time performance of structural analysis. Employing local and remote caching database storage strategies, it can efficiently access required data according to different calculation needs, improving the flexibility and response speed of data processing. It can quickly respond and recalculate the structural response when load information or boundary conditions change. By caching the processed overall stiffness matrix K′, redundant calculations are avoided, significantly shortening the analysis time, thereby achieving real-time finite element analysis.

[0075] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A real-time finite element analysis method for bridges, characterized in that, The specific steps include the following: S100: Construct a finite element model of the structure, and divide the actual structure into multiple finite element elements through discretization. S200: Based on the established finite element model, calculate the overall stiffness matrix K; S300: Based on the boundary conditions of the structure, the overall stiffness matrix K is recalculated to obtain the processed overall stiffness matrix K′, and then serialized. S400: Depending on the specific computing environment, the sparse matrix can be stored in a local storage device or a cache database; S500: Based on the load information acquired by the sensor, the load information is converted into the corresponding load vector in the finite element model; S600: Combines the cached overall stiffness matrix K′ with the load vector to solve for nodal displacements, calculates the structural response, and stores these calculation results in a structured manner or passes them to the post-processing module; S700: Perform efficient Web service post-processing on the calculation results to generate RGB color data and deformation visualization data for cloud map rendering, and then output them. If the load information changes, return to step S500. If the boundary conditions of the structure change, return to step S300. If the entire structure changes, return to step S100 to restart the entire process.

2. The bridge finite element real-time analysis method according to claim 1, characterized in that, Step S100 includes: S110: Select the appropriate element type and define the material properties of each element based on the structural material properties and analysis requirements; S120: Determine the node position of each element, number the nodes and elements according to certain rules to ensure the uniqueness and continuity of the numbering, and define the coordinate information of the nodes, including the x, y, and z coordinates in three-dimensional space; S130: Check the integrity and accuracy of the finite element model, ensuring that all element and node connections are correct, material properties are correctly assigned, and avoiding isolated nodes or unconnected elements.

3. The bridge finite element real-time analysis method according to claim 1, characterized in that, Step S200 includes: S210: For each finite element, calculate the element stiffness matrix ke in the local coordinate system based on its geometry, material properties, and element type. Then, using the transformation matrix T, calculate the element stiffness matrix in the global coordinate system. The element stiffness matrix equation is: ； S220: Assemble the stiffness matrices of all elements into a global stiffness matrix K by arranging the stiffness matrix Ke of each element according to the node number positions. The equation of the global stiffness matrix is: ； Where: i and j are the indices of the global node, K ij It is an element in the global stiffness matrix K, Ke ij It is the contribution of the element stiffness matrix Ke to the global positions i and j.

4. The bridge finite element real-time analysis method according to claim 1, characterized in that, The local storage device includes, but is not limited to, hard disk storage and database storage; the cache database includes, but is not limited to, in-memory database and distributed cache.

5. The bridge finite element real-time analysis method according to claim 1, characterized in that, Step S500 includes the following: By installing sensors at key parts of the structure, structural response data under load is collected in real time. The collected sensor data is preprocessed and normalized to meet the input requirements of the finite element model. Based on the sensor data and the stress characteristics of the structure, the types of loads acting on the structure are identified. At the same time, the spatial distribution and temporal variation of the loads are analyzed. According to the location and mode of load application, the loads are distributed to the corresponding nodes of the finite element model. The load values ​​distributed to each node are arranged in a certain order to form a column vector, i.e., the load vector.

6. The bridge finite element real-time analysis method according to claim 5, characterized in that, The data preprocessing in step S500 includes noise removal, missing value filling, and unit conversion to ensure that the data collected by the sensor matches the input requirements of the finite element model and can adapt to different types of sensor data formats.

7. The bridge finite element real-time analysis method according to claim 1, characterized in that, Step S600 includes: S610: Load the modified global stiffness matrix K′ and load vector P from the storage medium; S620: Combine the processed global stiffness matrix K′ with the load vector P to form the structural equation K′U=P, where K′ represents the modified global stiffness matrix, U is the nodal displacement vector, and P is the load vector. S630: Solve the structural equation K′U=P linearly to obtain the nodal displacement vector U of the structure, that is, the displacement value of each node in different directions; S640: Extract the displacement values ​​of each node in different directions from the obtained nodal displacement vector U. Based on the nodal displacements and the element information of the finite element model, calculate the internal forces, stresses, strains, deformations and support reactions of the structure, and store these calculation results in a structured manner or pass them to the post-processing module.

8. The bridge finite element real-time analysis method according to claim 1, characterized in that, Step S700 further includes: when post-processing the element stress or internal force, loading the element result data that has been calculated under the corresponding model and working condition; for the stress type of the specified element e, defining the stress result value of element e as σ and the internal force result value as F; when element e has multiple evaluation points, it is expressed by the following formula: ； Where |x| represents the absolute value of the stress or internal force of element e, σ nodeI and F nodeI σ represents the resulting value of stress or internal force at endpoint i of the element. nodeJ and F nodeJ It is the result value of the stress or internal force of the element at endpoint j; Obtain all similar units and their corresponding result values ​​under the current working condition, iterate through and compare the result values ​​to determine the maximum and minimum values, and at the same time perform a small perturbation on the zero value to avoid division by zero errors in subsequent calculations; ； Where, σ max and σ min F represents the maximum and minimum values ​​of the stress result. max and F min This represents the maximum and minimum values ​​of the internal force results; For each unit's result value, the corresponding RGB color value is calculated using a preset color mapping algorithm. Each color component takes values ​​in the range [0,1]. The piecewise linear color mapping algorithm includes: ； Among them, (R) e G e B e ) is the RGB color value of the unit, τ e The corresponding calculated element stress or internal force values; Convert floating-point RGB values ​​to hexadecimal color codes: ； Where H represents the converted hexadecimal RGB, and C... e Hexadecimal color codes; Returns the element ID, element stress σ or element internal force F, and hexadecimal color code C in JSON format. e Unit, σ max and σ min Maximum and minimum values ​​of stress results or F max and F min Post-processed data for the maximum and minimum values ​​of internal force results; When post-processing the node deformation and displacement, the original coordinates (X, Y, Z) and displacement vector (u) of node i are loaded. i,x ,u i,y ,u i,z ), calculate the displacement scalar value δ of each node according to the specified displacement type. i : ； Where, δ xyz This represents the resultant displacement of node i; Calculate the 3D coordinates of node i after deformation: ； Among them, P i,def Let X be the deformed three-dimensional coordinates. i,d Y i,d Z i,d These are the coordinate values ​​of (X, Y, Z) after being multiplied by the magnification factor and distorted, respectively. i,o Y i,o Z i,o These are the original coordinates of (X, Y, Z); Calculate the maximum and minimum values ​​of all nodal displacement scalar values: ； For each node's displacement scalar value, the corresponding RGB color value is calculated using a preset color mapping algorithm. Each color component takes values ​​in the range [0,1]. The piecewise linear color mapping algorithm includes: ； Where is the RGB color value of node i, δ i The corresponding calculated scalar value of the displacement of node i; Convert floating-point RGB values ​​to hexadecimal color codes: ； Where is the converted hexadecimal RGB, and is the hexadecimal color code; Returns post-processed data in JSON format, including node ID, node displacement value, node coordinates after deformation, node color code, unit, and overall maximum / minimum displacement value.

9. The bridge finite element real-time analysis method according to claim 8, characterized in that, The color mapping algorithm includes mapping data values ​​close to zero or within a specific reference range to a first preset color, mapping positive or stretched data values ​​to a first color system in segments according to their size, and mapping negative or compressed data values ​​to a second color system in segments according to their size. It can perform post-processing on element stress or internal force and nodal deformation or displacement, and supports receiving post-processing requests through API interface and returning visualized post-processing data in JSON format.

10. A real-time finite element analysis system for bridges, characterized in that, The application implements a bridge finite element real-time analysis method as described in any one of claims 1-9, comprising: Model building module: Constructs a finite element model of the structure, and divides the actual structure into multiple finite element elements through discretization. Stiffness matrix calculation module: Calculates the overall stiffness matrix K based on the established finite element model; Boundary condition processing module: Based on the boundary conditions of the structure, the overall stiffness matrix K is recalculated to obtain the processed overall stiffness matrix K′, and then serialized. Storage module: Depending on the specific computing environment, the sparse matrix can be stored on local storage devices or in a cache database; Load vector generation module: Based on the load information acquired by the sensor, the load information is converted into the corresponding load vector in the finite element model; The result calculation and transmission module combines the cached overall stiffness matrix K′ with the load vector to solve for nodal displacements, calculate the structural response, and store these calculation results in a structured manner or transmit them to the post-processing module. Post-processing module: Performs efficient web service post-processing on the calculation results, generating RGB color data and deformation visualization data for cloud map rendering, allowing users to obtain and display analysis results in real time through network interface. If the load information changes, it returns to step S500; if the boundary conditions of the structure change, it returns to step S300; if the entire structure changes, it returns to step S100 to restart the entire process.

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