Bridge finite element real-time analysis method and system

Abstract

The application discloses a bridge finite element real-time analysis method and system, which comprises the following steps: constructing a finite element model of a structure, dividing the model into a plurality of finite element units through discretization processing; calculating a total stiffness matrix K according to the established finite element model; re-calculating a processed total stiffness matrix K' in combination with the boundary conditions of the structure, and performing a serialization operation on the processed total stiffness matrix K'; selecting a position for storing a sparse matrix according to a specific calculation environment; converting load information obtained by a sensor into a corresponding load vector in the finite element model according to the load information; combining the cached total stiffness matrix K' and the load vector, solving node displacement and structure response, and delivering the results to a post-processing module. The application is based on the strategy of sparse matrix caching, efficiently accesses required data according to different calculation requirements, and only needs to re-calculate the load vector and solve when the load changes, without the need to re-calculate the total stiffness matrix, thereby improving the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of bridge structure simulation, and more particularly relates to a bridge finite element real-time analysis method and system. BACKGROUND

[0002] In finite element static analysis, the generation of the stiffness matrix is a key step in solving. The stiffness matrix is usually a sparse matrix, and such sparsity provides optimization space for matrix storage and calculation. Storage formats such as compressed sparse row (CSR) and compressed sparse column (CSC) are usually used to reduce memory requirements and improve calculation efficiency. However, the traditional finite element analysis method needs to repeatedly generate and assemble the stiffness matrix in each calculation, especially in dynamic working condition analysis, which leads to a large amount of redundant calculation and increases the difficulty of real-time analysis.

[0003] Finite element real-time analysis can quickly calculate the stress and deformation response of the structure according to the real-time working condition. The structure system and load distribution change at different stages. Through real-time analysis, the safety and stability of the construction working condition can be dynamically evaluated, and potential risks can be avoided. The design of the traditional solver usually targets one-time global calculation, and has limited support for matrix reuse. The stiffness matrix is cached in CSR format to support fast reading and reuse of the stiffness matrix in finite element real-time analysis. In dynamic working conditions, the sparse matrix cache needs to be partially updated to adapt to changes, rather than reassembling the entire matrix. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a bridge finite element real-time analysis method and system. By using sparse matrix caching technology, dynamic changes in finite element analysis can be efficiently handled, ensuring the real-time nature of structural analysis. Combined with the storage strategies of local cache and remote cache database, the system can flexibly select data storage locations according to different calculation needs. The multi-level cache mechanism not only improves data access speed, but also enhances the flexibility and response speed of the system. When the load changes, the system does not need to recalculate the overall stiffness matrix K, but only needs to recalculate the load vector and solve. This strategy significantly reduces the overhead of repeated calculations and significantly improves the calculation efficiency.

[0005] To achieve the above purpose, according to one aspect of the present application, the present application provides a bridge finite element real-time analysis method, comprising the following specific steps:

[0006] S100: Constructing a finite element model of the structure, the actual structure is discretized and divided into a plurality of finite element units;

[0007] S200: Calculating the overall stiffness matrix K according to the established finite element model;

[0008] S300: Recalculating the total stiffness matrix K according to the boundary conditions of the structure to obtain a processed total stiffness matrix K', and performing a serialization operation on it;

[0009] S400: Depending on the specific computing environment, the sparse matrix can be stored in a local storage device or a cache database;

[0010] S500: According to the load information obtained by the sensor, the load information is converted into the corresponding load vector in the finite element model;

[0011] S600: Combining the cached total stiffness matrix K' with the load vector, solving the node displacement, calculating the structural response, and structuring the calculation results or passing them to the post-processing module;

[0012] S700: Efficiently Web-service post-processing of the calculation results, generating RGB color data and deformation visualization data for cloud rendering, and then outputting, if the load information changes, returning to step S500, if the boundary conditions of the structure change, returning to step S300, if the entire structure changes, returning to step S100 to start the entire process again.

[0013] Further, the step S100 comprises:

[0014] S110: According to the material properties of the structure and the analysis requirements, selecting appropriate element types and defining the material properties of each element;

[0015] S120: Determine the node position of each element, number the nodes and elements according to certain rules, ensure the uniqueness and continuity of the numbering, define the coordinate information of the nodes, including x, y, z coordinates in three-dimensional space;

[0016] S130: Check the integrity and accuracy of the finite element model, ensure the correct connection relationship of all elements and nodes, and the correct material property allocation, avoid isolated nodes or unconnected elements.

[0017] Further, the step S200 comprises:

[0018] S210: For each finite element, according to its geometric shape, material properties and element type, calculate the element stiffness matrix ke in the local coordinate system, and then through the transformation matrix T, calculate the element stiffness matrix in the global coordinate system, the equation of the element stiffness matrix is:

[0019]

[0020] S220: Assemble the element stiffness matrix of all elements into a total stiffness matrix K according to the node number position of each element stiffness matrix Ke, and the total stiffness matrix equation is:

[0021]

[0022] Wherein: i, j are the indexes of global nodes, K ij is the element in the total stiffness matrix K, Ke ij is the contribution of the element stiffness matrix Ke at the total position i, j.

[0023] Further, 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 memory database and distributed cache.

[0024] Further, the step S500 includes the following contents:

[0025] By installing sensors at key positions of the structure, real-time collection of structural response data under load is realized, and the collected sensor data is preprocessed, and at the same time, the data is normalized to meet the input requirements of the finite element model. According to the sensor data and the stress characteristics of the structure, the load type acting on the structure is identified, and at the same time, the spatial distribution and time variation law of the load are analyzed. According to the load position and mode, the load is 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. a load vector.

[0026] Further, the data preprocessing in the step S500 includes removing noise, filling missing values, and performing 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.

[0027] Further, the step S600 includes:

[0028] S610: Load the corrected total stiffness matrix K' and the load vector P from the storage medium;

[0029] S620: Combine the processed total stiffness matrix K' and the load vector P into a structure equation K'U=P, wherein K' represents the corrected total stiffness matrix, U is the node displacement vector, and P is the load vector;

[0030] S630: Linearly solve the structure equation K'U=P to obtain the node displacement vector U of the structure, i.e. the displacement values of each node in different directions.

[0031] S640: Extract the displacement values of each node in different directions from the obtained node displacement vector U, calculate the internal force, stress, strain, deformation and support reaction of the structure according to the node displacement and the element information of the finite element model, and store or transfer these calculation results to the post-processing module.

[0032] Further, the step S700 further comprises: when post-processing the element stress or internal force, loading the calculated element result data corresponding to the model and working condition, defining the stress result value of the element e as σ and the internal force result value as F for the stress type of the specified type of element e; when the element e has multiple evaluation points, the following formula is used:

[0033]

[0034] Where |x| represents the absolute value of the stress or internal force of the element e, σ nodei and F nodei represent the result value of the stress or internal force of the element at the i endpoint, σ nodej and F nodej are the result values of the stress or internal force of the element at the j endpoint;

[0035] Obtain all similar elements and their corresponding result values under the current working condition, compare the result values, determine the maximum and minimum values, and slightly perturb the zero value to avoid division by zero error in subsequent calculation;

[0036]

[0037] Where σ max and σ min represent the maximum and minimum values of the stress result value, F max and F min represent the maximum and minimum values of the internal force result value;

[0038] Calculate the corresponding RGB color value of each element result value through a preset color mapping algorithm, and the color component value range is [0, 1], wherein the piecewise linear color mapping algorithm includes:

[0039]

[0040] Where (R e , G e , B e ) is the RGB color value of the element, τ e is the calculated element stress or internal force value;

[0041] Convert the floating-point RGB value to a hexadecimal color code:

[0042]

[0043] Wherein, H is the converted hexadecimal RGB, C e is the hexadecimal color code;

[0044] The post-processing data is returned in JSON format, including the unit ID, the unit stress σ or the unit internal force F, the hexadecimal color code C e , the unit, the maximum and minimum values of σ max and σ min stress result values or the maximum and minimum values of F max and F min internal force result values;

[0045] When post-processing the node deformation and displacement, the original coordinates (X, Y, Z) and displacement vector (u i,x , u i,y , u i,z ) of node i are loaded, and the displacement scalar value δ i of each node is calculated according to the specified displacement type:

[0046]

[0047] Wherein, δ xyz represents the total displacement of node i;

[0048] The three-dimensional coordinates of the deformed node i are calculated:

[0049]

[0050] Wherein, P i,def is the deformed three-dimensional coordinate, X i,d , Y i,d , Z i,d are the coordinate values of (X, Y, Z) multiplied by the magnification factor, and X i,o , Y i,o , Z i,o are the original coordinate values of (X, Y, Z);

[0051] The maximum and minimum values of the displacement scalar values of all nodes are calculated:

[0052]

[0053] The corresponding RGB color value of each node displacement scalar value is calculated by a pre-set color mapping algorithm, and each color component takes a value in the range [0, 1], wherein the piecewise linear color mapping algorithm includes:

[0054]

[0055] wherein is the RGB color value of node i, δ i corresponding to the calculated node i displacement scalar value;

[0056] Convert the floating-point RGB value to a hexadecimal color code:

[0057]

[0058] wherein is the converted hexadecimal RGB, and is the hexadecimal color code;

[0059] Return the post-processing data in JSON format, including the node ID, node displacement value, node coordinate after deformation, node color code, unit, and overall maximum / minimum displacement value.

[0060] Further, the color mapping algorithm includes mapping data values close to zero or a specific reference range to a first preset color, mapping data values of positive values or a stretched state to a first color system according to their sizes, and mapping data values of negative values or a compressed state to a second color system according to their sizes.

[0061] Post-process the unit stress or internal force and the node deformation or displacement, support receiving a post-processing request through an API interface, and return visual post-processing data in JSON format.

[0062] According to another aspect of the present application, a finite element real-time analysis system based on sparse matrix caching is provided, comprising:

[0063] A model establishing module: constructing a finite element model of a structure, and dividing an actual structure into a plurality of finite element units through discretization processing;

[0064] A stiffness matrix calculating module: calculating a total stiffness matrix K according to the established finite element model;

[0065] A boundary condition processing module: re-calculating the total stiffness matrix K to obtain a processed total stiffness matrix K' in combination with the boundary conditions of the structure, and performing a serialization operation on the total stiffness matrix K';

[0066] A storage module: storing the sparse matrix in a local storage device or a caching database according to a specific calculation environment;

[0067] A load vector generating module: converting load information obtained by a sensor into a corresponding load vector in the finite element model according to the load information;

[0068] A result calculating and delivering module: combining the cached total stiffness matrix K' and the load vector, solving node displacement, calculating structure response, and structurally storing or delivering these calculation results to a post-processing module;

[0069] Post-processing module: efficient Web service post-processing of the calculation results, generating RGB color data and deformation visualization data for cloud rendering, facilitating users to obtain and display the analysis results in real time through a network interface, returning to step S500 if the load information changes, returning to step S300 if the boundary conditions of the structure change, and returning to step S100 to start the entire process again if the entire structure changes.

[0070] Overall, compared with the prior art, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0071] 1. The finite element real-time analysis method of the present application 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 application avoids the overhead of repeated calculation of the overall stiffness matrix by caching the processed overall stiffness matrix K', only recalculating the load vector P when the load changes, and solving the structure equation KU=P, significantly reducing the calculation time and improving the real-time analysis.

[0072] 2. The finite element real-time analysis method of the present application adopts a multi-level caching strategy, combining local caching and remote caching databases to meet data access requirements in different computing environments. This flexible storage strategy not only improves the system's response speed, but also enhances the system's scalability, making it adaptable to a variety of scenarios from small local computing to large-scale distributed computing, thereby improving the overall system's running efficiency.

[0073] 3. The finite element real-time analysis method of the present application, through sparse matrix caching technology, only stores non-zero elements and their position information, greatly reducing the storage space occupation, and at the same time improving the calculation efficiency. Based on the strategy of sparse matrix caching, it can quickly process and analyze structural data to meet the needs of real-time analysis. For computing 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 reliable basis for engineering design and decision-making.

[0074] 4. The finite element real-time analysis method of the present application can provide detailed and accurate information for the mechanical analysis of bridge structures by accurately calculating unit stress, internal force, and node deformation and displacement data. It understands the stress and deformation state of the structure under different working conditions, and uses a pre-set color mapping algorithm to visually display the mechanical data through color, thereby quickly distinguishing different mechanical states in the structure and enhancing the intuitiveness of the analysis. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1A flowchart of a bridge finite element real-time analysis method according to an embodiment of the present application is shown in FIG. 1.

[0076] Figure 2 A flowchart of step S100 of a bridge finite element real-time analysis method according to an embodiment of the present application is shown in FIG. 2.

[0077] Figure 3 A flowchart of step S200 of a bridge finite element real-time analysis method according to an embodiment of the present application is shown in FIG. 3.

[0078] Figure 4 A flowchart of step S600 of a bridge finite element real-time analysis method according to an embodiment of the present application is shown in FIG. 6.

[0079] Figure 5 An analysis result visualization diagram of a bridge finite element real-time analysis method according to an embodiment of the present application is shown in FIG. 7.

[0080] Figure 6 A calculation time comparison diagram of a bridge finite element real-time analysis method according to an embodiment of the present application is shown in FIG. 8. DETAILED DESCRIPTION

[0081] In order to make the objectives, technical solutions, and advantages of the present application clearer, the present application 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 intended to explain the present application and should not be used to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other and can be realized by those of ordinary skill in the art.

[0082] It should be noted that the technical solutions of the various embodiments of the present application can be combined with each other, but must be based on the realization by those of ordinary skill in the art, and when the combination of technical solutions appears to be contradictory or unachievable, it should be considered that the combination of technical solutions does not exist and is not within the scope of protection required by the present application.

[0083] In the present application, the terms "comprise", "contain" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or device. Without more limitations, the elements defined by the statement "comprise" do not exclude the presence of additional identical elements in the process, method, article or device comprising the elements.

[0084] Embodiment 1

[0085] In the following, a bridge finite element real-time analysis system according to the present application is described by way of embodiment 1. In this embodiment, the system can comprise:

[0086] The model establishing module: a finite element model of the structure is constructed, and the actual structure is divided into a plurality of finite element units through discretization processing;

[0087] The stiffness matrix calculating module: the total stiffness matrix K is calculated according to the established finite element model;

[0088] The boundary condition processing module: the total stiffness matrix K is recalculated to obtain the processed total stiffness matrix K' in combination with the boundary conditions of the structure, and a serialization operation is performed on the total stiffness matrix K';

[0089] The storage module: the sparse matrix can be stored in a local storage device or a cache database according to a specific calculation environment;

[0090] The load vector generating module: the load information obtained by the sensor is converted into the corresponding load vector in the finite element model according to the load information;

[0091] The result calculating and transferring module: the cached total stiffness matrix K' and the load vector are combined to solve the node displacement, calculate the structural response, and the calculation results are stored in a structured manner or transferred to the post-processing module;

[0092] The post-processing module: the calculation results are efficiently Web-processed to generate RGB color data and deformation visualization data for cloud rendering, so that the user can obtain and display the analysis results in real time through a network interface, and if the load information changes, the step S500 is returned; if the boundary conditions of the structure change, the step S300 is returned, and if the entire structure changes, the step S100 is returned to start the entire process again.

[0093] Embodiment 2

[0094] In this embodiment, a bridge finite element real-time analysis method is realized by using the above system. In this embodiment, a bridge construction support is taken as an example. As shown in Figure 1 , the method comprises the following steps:

[0095] S100: a finite element model of the structure is constructed, and the actual structure is divided into a plurality of units through discretization processing; as shown in Figure 2 , the specific steps include the following steps:

[0096] S110: according to the material properties of the structure and the analysis requirements, a suitable unit type is selected, and the material properties of each unit are defined;

[0097] According to the structural material properties and analysis requirements, select the appropriate unit type. Different materials and analysis requirements require the use of different types of units. When defining the material properties of each unit, the corresponding attribute values need to be set according to the mechanical properties of the material, such as elastic modulus, Poisson's ratio, yield strength, etc.

[0098] Selecting the appropriate unit type and accurately defining the material properties is the key to ensuring the accuracy of the finite element analysis results. The appropriate unit type can better simulate the mechanical behavior of the material, and the accurate definition of the material properties can make the finite element model more realistically reflect the actual stress situation of the structure.

[0099] S120: Determine the node position of each unit, number the nodes and units according to certain rules, ensure the uniqueness and continuity of the numbering, and define the coordinate information of the nodes, including x, y, z coordinates in three-dimensional space;

[0100] Determining the node position of each unit is an important step in finite element modeling. The determination of the node position should be based on the geometric shape of the structure and the unit division, ensuring that the nodes can accurately reflect the geometric characteristics and stress situation of the structure. After determining the node position, the nodes and units need to be numbered according to certain rules, and the numbering rules should ensure the uniqueness and continuity of the numbering, avoiding repeated numbering or discontinuous numbering. At the same time, the numbering should have a certain regularity, which is convenient for quickly locating and processing nodes and units in subsequent analysis.

[0101] S130: Check the completeness and accuracy of the finite element model, ensure the correct connection relationship of all units and nodes, and the correct material property allocation, avoid isolated nodes or unconnected units.

[0102] After completing the construction of the finite element model, the completeness and accuracy of the model need to be checked comprehensively, which can be done by viewing the graphical display of the model, checking the connection list of nodes and units, verifying the setting of material properties and boundary conditions, etc.

[0103] Through the inspection of the completeness and accuracy of the finite element model, the total number of nodes of the bracket model is 116, the total number of beam elements is 198, the material is Q235 steel, the material parameters are elastic modulus 2×10 5 MPa, Poisson's ratio 0.3, bulk density 7.698×10 -5 N / mm3, the load is a concentrated load added to the top, the load is obtained through the sensor installed on the winch, and the boundary condition is fixed constraint at the bottom four points.

[0104] S200: According to the established finite element model, calculate the total stiffness matrix K; as shown in the following formula: Figure 3 The specific steps include:

[0105] S210: For each finite element, calculate the element stiffness matrix ke in the local coordinate system according to its geometry, material properties, and element type, and then calculate the element stiffness matrix in the global coordinate system through the transformation matrix T. The equation of the element stiffness matrix is:

[0106]

[0107] S220: Assemble the stiffness matrix Ke of each element into a total stiffness matrix K according to the node number position. The equation of the total stiffness matrix is:

[0108]

[0109] Where: i, j are the indices of global nodes, K ij is the element in the total stiffness matrix K, Ke ij is the contribution of the element stiffness matrix Ke to the total position i, j.

[0110] The total stiffness matrix K is global and reflects the stiffness characteristics of the entire structure. It is assembled from all element stiffness matrices Ke and contains the contribution of all elements in the structure. The total stiffness matrix K is usually a sparse matrix because each element is connected to a limited number of nodes. Sparsity makes storage and calculation more efficient. The assembly of the total stiffness matrix depends on the mapping relationship of the node number. The local node number needs to be correctly mapped to the global node number to ensure the correct assembly of the stiffness matrix.

[0111] S300: Combine the boundary conditions of the structure to recalculate the total stiffness matrix K and perform serialization operation on it to obtain the processed total stiffness matrix K';

[0112] According to the actual situation of the structure, determine the boundary conditions of the structure, including fixed support, hinged support, elastic support, etc. Consider the influence of boundary conditions on internal force and deformation of the structure, recalculate the total stiffness matrix K, and on the basis of modifying the total stiffness matrix K, recalculate the processed total stiffness matrix K'. For example, for fixed support, the stiffness matrix elements of some degrees of freedom of the corresponding node can be set to zero to represent that these degrees of freedom are completely constrained. For elastic support, the total stiffness matrix needs to be adjusted according to the stiffness coefficient of the support.

[0113] According to the actual demand and application scenario, select the appropriate serialization method. Common serialization methods include text serialization, binary serialization, etc. Text serialization is easy to read and debug, but the file size is larger; binary serialization has smaller file size, but poor readability. Use the selected serialization method to convert the processed total stiffness matrix K' into a serialized format, and save the serialized total stiffness matrix K' to a file or database, which can improve the storage and access efficiency of data, reduce the time and space cost of data storage and transmission.

[0114] S400: According to the specific computing environment, the sparse matrix can be stored in the local storage device or the cache database;

[0115] Further, the local storage device includes but is not limited to hard disk storage and database storage; the sparse matrix is stored in the form of a file on the local hard disk.

[0116] Specifically, the cache database includes but is not limited to memory database and distributed cache; memory database: use memory database to store sparse matrix, such as Redis, Memcached, etc. Memory database has the advantages of fast read-write speed and high performance, which is suitable for scenarios with high data access speed requirements. For large-scale structural engineering, distributed cache can be used to store sparse matrix, such as Redis Cluster, Memcached Cluster, etc. Distributed cache can provide higher storage capacity and access performance, which is suitable for distributed computing and large-scale data processing.

[0117] By storing the sparse matrix in the local storage device or the cache database, the computing efficiency can be improved. The local storage device can provide fast data read-write speed, and the cache database can provide faster data access speed, thereby reducing the computing time.

[0118] Sparse matrix usually has a large number of zero elements, and by using sparse matrix storage technology, a large amount of storage space can be saved. Local storage device and cache database can effectively store sparse matrix, thereby reducing storage cost.

[0119] S500: According to the load information obtained by the sensor, the load information is converted into the corresponding load vector in the finite element model;

[0120] By installing sensors at key parts of the structure, real-time collection of structural response data under load, such as strain, displacement, acceleration, etc. is realized, and the collected sensor data is preprocessed, including data cleaning, filtering, denoising, etc. to improve the accuracy and reliability of the data. At the same time, the data is normalized to meet the input requirements of the finite element model.

[0121] According to the sensor data and the force characteristics of the structure, the load type acting on the structure is identified, such as temperature load, concentrated load, distributed load, etc. At the same time, the spatial distribution and time variation of the load are analyzed to provide a basis for the construction of the load vector.

[0122] In finite element analysis, the load vector is usually represented by a column vector, and its elements correspond to the load size and direction of each node in the finite element model. For different load types and distribution forms, the construction method of the load vector is different. For example, for concentrated load, the load value can be directly applied to the corresponding node; for distributed load, it needs to be converted into equivalent node load through numerical integration and other methods.

[0123] The constructed load vector is applied to the finite element model. During the application process, the elements of the load vector need to be distributed to the corresponding node degrees of freedom according to the position and direction of the load. At the same time, considering the time history of the load, the load vector is applied to the model according to the time step to simulate the actual load application process.

[0124] When the load information changes, only the load vector needs to be recalculated, and the global stiffness matrix does not need to be recalculated, which improves the efficiency of the calculation and analysis and saves the calculation time;

[0125] S600: Combine the cached global stiffness matrix K' with the load vector to solve the node displacement, calculate the structure response, and structure the calculation results or pass them to the post-processing module; as shown in Figure 4 , specifically including the following steps:

[0126] S610: Load the modified global stiffness matrix K' and the load vector P from the storage medium;

[0127] S620: Combine the processed global stiffness matrix K' and the load vector P into the structure equation K'U=P, where K' represents the modified global stiffness matrix, U is the node displacement vector, and P is the load vector;

[0128] S630: Linearly solve the structure equation K'U=P to obtain the node displacement vector U of the structure, i.e. the displacement values of each node in different directions.

[0129] S640: Extract the displacement values of each node in different directions from the obtained node displacement vector U, calculate the internal force, stress, strain, deformation and reaction force of the structure according to the node displacement and the element information of the finite element model, and structure the calculation results or pass them to the post-processing module.

[0130] From the obtained node displacement vector U, the displacement values of each node in different directions are extracted. According to the displacement values and the element information of the finite element model, the internal force, stress, strain, deformation and support reaction of the structure can be calculated, and the calculation results are displayed in real time as shown in Figure 5 .

[0131] By extracting the displacement values from the node displacement vector U and calculating the internal force, stress, strain, deformation and support reaction of the structure according to the element information of the finite element model, the mechanical behavior and performance of the structure under external load can be comprehensively understood.

[0132] S700: Efficiently Web service post-processing of the calculation results, generating RGB color data and deformation visualization data for cloud rendering, and then outputting, if the load information changes, returning to step S500, if the boundary conditions of the structure change, returning to step S300, if the entire structure changes, returning to step S100 to start the entire process again.

[0133] Specifically, when post-processing the element stress or internal force, the calculated element result data under the corresponding model and working condition is loaded, and for the stress type of the specified type of element e, the stress result value of the element e is defined as σ, and the internal force result value is defined as F; when the element e has multiple evaluation points, it is expressed by the following formula:

[0134]

[0135] Where |x| represents the absolute value of the stress or internal force of the element e, σ nodei and F nodei represent the result values of the stress or internal force of the element at the i endpoint, σ nodej and F nodej are the result values of the stress or internal force of the element at the j endpoint;

[0136] All similar elements and their corresponding result values under the current working condition are obtained, and the result values are iteratively compared to determine the maximum and minimum values, and a small perturbation is applied to the zero value to avoid division by zero error in subsequent calculations;

[0137]

[0138] Where σ max and σ min represent the maximum and minimum values of the stress result value, F max and F min represent the maximum and minimum values of the internal force result value;

[0139] The result value of each unit is calculated by a preset color mapping algorithm to correspond to an RGB color value, and each color component takes a value range of [0, 1], wherein the piecewise linear color mapping algorithm comprises:

[0140]

[0141] wherein (R e ,G e ,B e ) is the RGB color value of the unit, τ e corresponds to the calculated unit stress or internal force value;

[0142] Convert the floating-point RGB value to a hexadecimal color code:

[0143]

[0144] wherein H is the converted hexadecimal RGB, C e is the hexadecimal color code;

[0145] Return the post-processing data in JSON format, which includes the unit ID, unit stress σ or unit internal force F, hexadecimal color code C e , unit, the maximum and minimum values of σ max and σ min stress result values or the maximum and minimum values of F max and F min internal force result values;

[0146] When post-processing the node deformation and displacement, load the original coordinates (X, Y, Z) and displacement vector (u i,x , u i,y , u i,z ) of node i, and calculate the displacement scalar value δ i of each node according to the specified displacement type:

[0147]

[0148] wherein δ xyz represents the total displacement of node i;

[0149] Calculate the three-dimensional coordinates of the deformed node i:

[0150]

[0151] wherein P i,def is the three-dimensional coordinates after deformation, X i,d , Y i,d , Z i,d are the coordinate values of (X, Y, Z) multiplied by the magnification factor after deformation, X i,o , Yi,o , Z i,o are the original coordinate values of (X, Y, Z);

[0152] Calculate the maximum and minimum values of all node displacement scalar values:

[0153]

[0154] The displacement scalar value of each node is calculated by a preset color mapping algorithm to obtain the corresponding RGB color value, and each color component takes a value in the range [0, 1], wherein the piecewise linear color mapping algorithm includes:

[0155]

[0156] wherein is the RGB color value of node i, and δ i corresponding to the calculated displacement scalar value of node i;

[0157] Convert the floating-point RGB value to a hexadecimal color code:

[0158]

[0159] wherein is the converted hexadecimal RGB, and is the hexadecimal color code;

[0160] Return the post-processing data including the node ID, node displacement value, node coordinate after deformation, node color code, unit, and overall maximum / minimum displacement value in JSON format;

[0161] Further, the color mapping algorithm includes mapping data values close to zero or a specific reference range to a first preset color, mapping positive or stretched state data values to a first color system according to their size, and mapping negative or compressed state data values to a second color system according to their size.

[0162] Post-process the unit stress or internal force and the node deformation or displacement, support receiving post-processing requests through an API interface, and return visual post-processing data in JSON format.

[0163] Further, if the load information changes, return to step S500 to regenerate the load vector and solve, if the boundary conditions of the structure change, return to step S300 to modify the overall stiffness matrix, and if the entire structure changes (such as changes in geometry or material properties), return to step S100 to re-establish the finite element model.

[0164] 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.

[0165] 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 6 As shown, the present invention significantly reduces the average computation time compared to methods that do not cache the matrix.

[0166] 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.

[0167] 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 bridge finite element real-time analysis method, characterized by, Comprise the following specific steps: S100: Construct the finite element model of the structure, and divide the actual structure into a plurality of finite element units through discretization processing; S200: Calculate the overall stiffness matrix K according to the established finite element model; S300: Recalculate the overall stiffness matrix K to obtain a processed overall stiffness matrix K', and perform a serialization operation thereon in combination with the boundary conditions of the structure; S400: According to the specific calculation environment, the sparse matrix can be stored in a local storage device or a cache database; S500: According to the load information obtained by the sensor, the load information is converted into a corresponding load vector in the finite element model; S600: Combine the cached overall stiffness matrix K' and the load vector to solve the node displacement, calculate the structure response, and structure the calculation results or pass them to the post-processing module; S700: Efficiently Web service the calculation results, generate RGB color data and deformation visualization data for cloud rendering, and then output, if the load information changes, return to step S500, if the boundary conditions of the structure change, return to step S300, and if the entire structure changes, return to step S100 to start the entire process again; When post-processing the unit stress or internal force, load the unit result data calculated under the corresponding model and working condition, define the stress result value of the unit e as σ and the internal force result value as F for the stress type of the specified type of unit e; when the unit e has multiple evaluation points, the following formula is used: where |x| denotes the absolute value of the stress or internal force of the element e, σ nodei and F nodei denotes the resulting value of the stress or internal force of the element at the i endpoint, σ nodej and F nodej is the resulting value of the stress or internal force of the element at the j endpoint; Obtain all units of the same type under the current working condition and their corresponding result values, traverse and compare the result values to determine the maximum and minimum values, and slightly perturb the zero value to avoid division by zero errors in subsequent calculations; where σ max and σ min denote the maximum and minimum values of the stress resultants, F max and F min denote the maximum and minimum values of the internal force resultants; Calculate the corresponding RGB color value of each unit result value through a preset color mapping algorithm, and the value range of each color component is [0, 1], wherein the piecewise linear color mapping algorithm includes: where (R e ,G e ,B e ) are the RGB color values of the cell, τ e corresponds to the computed cell stress or internal force value; Convert the floating-point RGB value to a hexadecimal color code: wherein H is the converted hexadecimal RGB, C e is a hexadecimal color code; In JSON format, return the unit ID, unit stress σ or internal force F, and hexadecimal color code C e , unit, σ max and σ min The maximum and minimum of the stress result value or F max and F min The maximum and minimum of the internal force result value of the post-processing data; When post-processing the node deformation and displacement, the original coordinates (X, Y, Z) and displacement vector (u i,x ,u i,y ,u i,z ) of the loading node i are loaded, and the displacement scalar value δ i of each node is calculated according to the specified displacement type. where δ xyz denotes the total displacement of node i; Calculate the three-dimensional coordinates of the deformed node i: wherein P i,def is the deformed three-dimensional coordinate, X i,d , Y i,d , and Z i,d are the coordinate values of (X, Y, Z) after being multiplied by the magnification factor, and X i,o , Y i,o , and Z i,o are the original coordinate values of (X, Y, Z). Calculate the maximum and minimum values of all node displacement scalars: Calculate the corresponding RGB color value of each node displacement scalar value through a preset color mapping algorithm, and the value range of each color component is [0, 1], wherein the piecewise linear color mapping algorithm includes: wherein is the RGB color value of node i, δ i corresponding to the calculated displacement scalar value of node i; Convert the floating-point RGB value to a hexadecimal color code: Wherein, is the converted hexadecimal RGB, and is the hexadecimal color code; Return the post-processing data including the node ID, node displacement value, deformed node coordinates, node color code, unit, and overall maximum / minimum displacement value in JSON format.

2. The method of claim 1, wherein, The step S100 comprises: S110: Select a suitable unit type according to the material properties of the structure and the analysis requirements, and define the material properties of each unit; S120: Determine the node positions of each unit, number the nodes and units 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 the three-dimensional space; S130: Check the integrity and accuracy of the finite element model, ensure that all the connection relationship of the unit and node is correct, the material property allocation is correct, avoid the isolated node or unconnected unit.

3. The method of claim 1, wherein the method is a real-time analysis method for a bridge finite element. The step S200 includes: S210: For each finite element unit, according to its geometry, material properties and unit type, calculate the unit stiffness matrix ke of the local coordinate system, and then calculate the unit stiffness matrix in the global coordinate system through the conversion matrix T, the unit stiffness matrix equation is: S220: Assemble the stiffness matrix Ke of each unit into a total stiffness matrix K according to the node number position, the total stiffness matrix equation is: where: i, j are indices of global nodes, K ij is an element in the global stiffness matrix K, K eij is the contribution of the element stiffness matrix Keat the global position i, j.

4. The method of claim 1, wherein, 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 memory database and distributed cache.

5. The method of claim 1, wherein the method is a real-time analysis method for a bridge finite element. The step S500 includes the following contents: By installing sensors at key positions of the structure, real-time collection of structural response data under load is realized, the collected sensor data is preprocessed, and at the same time, the data is normalized to meet the input requirements of the finite element model. According to the sensor data and the stress characteristics of the structure, the load type acting on the structure is identified, and at the same time, the spatial distribution and time variation law of the load are analyzed. According to the load position and mode, the load is distributed to the corresponding nodes of the finite element model, and the load values distributed to each node are arranged in a certain order to form a column vector, i.e. load vector.

6. The method of claim 5, wherein the bridge finite element real-time analysis method is characterized by, The data preprocessing in the step S500 includes removing noise, filling missing values 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 method of claim 1, wherein the method is a real-time analysis method for a bridge finite element. The step S600 includes: S610: Load the corrected total stiffness matrix K' and load vector P from the storage medium; S620: Combine the processed total stiffness matrix K' and load vector P into a structure equation K'U=P, where K' represents the corrected total stiffness matrix, U is the node displacement vector, and P is the load vector; S630: Linearly solve the structure equation K'U=P to obtain the node displacement vector U of the structure, i.e. the displacement values of each node in different directions; S640: Extract the displacement values of each node in different directions from the node displacement vector U obtained by solving, calculate the internal force, stress, strain, deformation and support reaction of the structure according to the node displacement and the unit information of the finite element model, and structure the calculation results or pass them to the post-processing module.

8. The method of claim 1, wherein, The color mapping algorithm includes mapping data values close to zero or a certain reference range to a first preset color, mapping positive or stretched state data values to a first color system according to their size, and mapping negative or compressed state data values to a second color system according to their size; The post-processing of unit stress or internal force and node deformation or displacement supports receiving post-processing requests through API interface and returning visual post-processing data in JSON format.

9. A bridge finite element real-time analysis system, characterized by, The application realizes a bridge finite element real-time analysis method as claimed in any one of claims 1-8, comprising: a model establishing module: constructing a finite element model of the structure, and dividing the actual structure into a plurality of finite element units through discretization processing; a stiffness matrix calculating module: calculating the overall stiffness matrix K according to the established finite element model; a boundary condition processing module: re-calculating the overall stiffness matrix K to obtain a processed overall stiffness matrix K' in combination with the boundary conditions of the structure, and performing a serialization operation on the processed overall stiffness matrix K'; a storage module: storing the sparse matrix in a local storage device or a cache database according to a specific calculation environment; a load vector generating module: converting the load information obtained by the sensor into a corresponding load vector in the finite element model according to the load information obtained by the sensor; a result calculating and transferring module: combining the cached overall stiffness matrix K' and the load vector, solving the node displacement, calculating the structural response, and structurally storing or transferring the calculation results to a post-processing module; a post-processing module: performing efficient Web service processing on the calculation results, generating RGB color data and deformation visualization data for cloud rendering, facilitating a user to obtain and display the analysis results in real time through a network interface, returning to step S500 if the load information changes, returning to step S300 if the boundary conditions of the structure change, and returning to step S100 to restart the entire process if the entire structure changes.

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