Flange stiffness calculation method, device and medium based on finite element stiffness matrix

Abstract

This invention belongs to the field of finite element simulation and mechanical analysis technology, and particularly relates to a method, equipment, and medium for calculating flange stiffness based on the finite element stiffness matrix. The method includes: constructing a flange finite element model containing the flange, bolts, and sealing ring; applying bolt preload based on the flange finite element model, and extracting the flange stiffness matrix output by the substructure after the bolt preload is applied; and obtaining independent flange stiffness parameters by decoupling the flange stiffness matrix. This invention accurately obtains independent six-direction stiffness parameters of the flange through stiffness matrix extraction and decoupling, achieving efficient and accurate acquisition of flange stiffness.

Description

Technical Field

[0001] This invention belongs to the field of finite element simulation and mechanical analysis technology, and particularly relates to a method, equipment and medium for calculating flange stiffness based on the finite element stiffness matrix. Background Technology

[0002] Flange connections are widely used as a primary method of pipeline connection in launch vehicles. In finite element analysis of complex models, simplifying flanges into stiffened connection elements greatly improves computational efficiency. Therefore, accurately obtaining the stiffness parameters of flange connections is a prerequisite for accurate modeling and mechanical analysis. However, due to factors such as contact nonlinearity, preload, and geometric diversity involved in flange connections, accurately obtaining their stiffness parameters has always faced technical challenges, including high cost, cumbersome acquisition process, and insufficient accuracy.

[0003] Currently, the methods for obtaining flange stiffness parameters are mainly divided into the following two categories: 1. Based on experimental testing This is currently the most commonly used method in engineering. It typically involves setting up a test bench, applying static loading or dynamic excitation to the flange, measuring the force-displacement relationship, and then calculating the stiffness parameters. For example, patent CN102116990C proposes "a method for determining the foundation stiffness coefficient," which obtains the load-deflection curve through experiments and uses material mechanics formulas to calculate the foundation stiffness parameters. Although this method targets foundation stiffness, its "experiment-back-calculation" approach is widely used in stiffness determination.

[0004] 2. Inverse calculation or equivalent based on CAE simulation A detailed model is established using finite element software, and the load-displacement curve is obtained through post-processing to inversely calculate the equivalent stiffness. For example, CN106326502A proposes "a method for calculating the static stiffness of a support". The support is modeled, a load is applied, and the force-displacement relationship is calculated through post-processing to obtain the stiffness of the support.

[0005] These two methods are essentially the same: obtaining the force-displacement relationship through experiments / simulations, and then calculating the stiffness parameters in reverse.

[0006] However, the aforementioned prior art has the following technical defects: (1) The test measurement method has a long cycle and high cost. There are many flange specifications, and the test requires the manufacture of special tooling test equipment. Moreover, it can only obtain the equivalent stiffness under specific working conditions, which is difficult to keep up with the progress of digital and efficient simulation.

[0007] (2) Existing CAE inverse calculation methods rely on the calculation results after loading, and the calculation accuracy is affected by the loading method. For example, by loading in a single direction, the load-displacement curve in a single direction is obtained, and the stiffness is directly calculated. However, the coupling term is usually ignored, which leads to inaccurate stiffness. Summary of the Invention

[0008] The purpose of this invention is to provide a method, device, and medium for calculating flange stiffness based on a finite element stiffness matrix, so as to solve the above-mentioned defects in the acquisition of flange stiffness parameters in the prior art.

[0009] The first aspect of this invention provides a method for calculating flange stiffness based on a finite element stiffness matrix, comprising: Construct a finite element model of the flange, including the flange, bolts, and sealing ring; Based on the flange finite element model, a bolt preload is applied, and after the bolt preload is applied, the flange stiffness matrix output by the substructure is extracted. After decoupling the flange stiffness matrix, independent flange stiffness parameters are obtained.

[0010] In some embodiments, constructing a flange finite element model including the flange, bolts, and sealing ring includes: Create solid models of the connections between the flange face, bolts and flange, and sealing rings and flange, respectively; Based on the solid model, two reference points are generated at the center of the two welding surfaces of the flange, and the two reference points are used as control points of the coupling surfaces at both ends of the flange to obtain the finite element model of the flange. The coupling surface at one end of the flange is the first welding surface, and the coupling surface at the other end of the flange is the second welding surface.

[0011] In some embodiments, applying bolt preload based on the flange finite element model and extracting the stiffness matrix after the bolt preload is applied includes: The bolt preload is calculated based on the actual installation torque and torque coefficient. The bolt preload is then applied to each bolt, and the bolt position is fixed after the preload is applied. After generating substructures or super-elements from the flange finite element model, the stiffness matrix is ​​extracted, including retaining the control points of the coupling surfaces at both ends of the flange, and solving the corresponding stiffness matrix of the flange through the two control points.

[0012] In some embodiments, obtaining independent flange stiffness parameters after decoupling the flange stiffness matrix includes: The stiffness matrix of the two control points is obtained as a symmetric matrix of 12×12; The element stiffness matrix of size 6×6 in the upper left corner is extracted based on the 12×12 symmetric matrix. After removing the zero terms from the unit stiffness matrix, we obtain the unit stiffness matrix with the zero terms removed. Based on the decoupling of the element stiffness matrix after removing zero terms, six independent flange stiffness parameters are obtained.

[0013] In some embodiments, the unit stiffness matrix with zero terms removed is represented as follows: ; In the finite element method Represents the first in the stiffness matrix i Line number j The parameter of the column, its meaning is the first... j Each degree of freedom produces a unit displacement. d j =1 ， When all other displacements are zero, in the first... i Force required for each degree of freedom F i , .

[0014] In some embodiments, the decoupling based on the element stiffness matrix after removing zero terms yields six independent flange stiffness parameters, the calculation formula of which is expressed as follows: K1= ; K2= ; K3= ; K4= K5= ; K6= ; Where K1, K2, K3, K4, K5, and K6 are scalar linear stiffnesses along six degrees of freedom in the element's local coordinate system, representing the proportional relationship between force and displacement or torque and rotation in a single direction, i.e., K... i Indicates the first i Each degree of freedom produces a unit displacement. d i =1, in the... i Force required for each degree of freedom F i , i =1, 2, ..., 6 L The distance between the two control points is denoted as .

[0015] In some embodiments, the step of applying the bolt preload to each bolt and fixing the bolt position after the preload is applied further includes locking the bolt length.

[0016] A second aspect of the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the above embodiments.

[0017] A third aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in the above embodiments.

[0018] A fourth aspect of the present invention provides a computer product including a computer program that, when executed by a processor, implements the steps of the method described in the above embodiments.

[0019] This invention provides a method, device, and medium for calculating flange stiffness based on a finite element stiffness matrix. The method includes constructing a flange finite element model comprising a flange, bolts, and a sealing ring; applying bolt preload based on the flange finite element model; and extracting the flange stiffness matrix output by the substructure after the bolt preload is applied. The flange stiffness matrix is ​​then decoupled to obtain independent flange stiffness parameters. This invention accurately obtains independent six-direction stiffness parameters of the flange through stiffness matrix extraction and decoupling, achieving efficient and accurate acquisition of flange stiffness. Attached Figure Description

[0020] Figure 1 This is a flowchart of a flange stiffness calculation method based on the finite element stiffness matrix according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the solid model of each part of the flange in an embodiment of the present invention; Figure 3 This is a schematic diagram of the modeling of the flange finite element model according to an embodiment of the present invention. Detailed Implementation

[0021] Various embodiments and features of this application are described herein with reference to the accompanying drawings.

[0022] It should be understood that various modifications can be made to the embodiments described herein. Therefore, the above description should not be considered as limiting, but merely as an example of embodiments. Other modifications within the scope and spirit of this application will be apparent to those skilled in the art.

[0023] The accompanying drawings, which are included in and form part of this specification, illustrate embodiments of the present application and, together with the general description of the present application given above and the detailed description of the embodiments given below, serve to explain the principles of the present application.

[0024] These and other features of this application will become apparent from the following description of preferred forms of embodiments given as non-limiting examples, with reference to the accompanying drawings.

[0025] It should also be understood that although this application has been described with reference to some specific examples, those skilled in the art can certainly implement many other equivalent forms of this application.

[0026] Existing technologies are insufficient to meet the urgent need for efficient and accurate acquisition of flange connection stiffness parameters during the digital development of launch vehicles. The fundamental reason is that existing methods either rely on physical experiments (leading to long cycles and high costs) or utilize finite element loading-solution calculation results (adding loading and data back-calculation steps, potentially including coupling terms, resulting in inaccurate results). Therefore, there is an urgent need for a purely numerical method based on a finite element numerical model that directly derives the six-direction stiffness of the flange from the stiffness matrix generated by finite element software, without requiring physical experiments.

[0027] To address the challenges of high cost, long cycle time, and insufficient accuracy in obtaining flange stiffness parameters, this invention proposes a method for calculating flange stiffness parameters based on the finite element stiffness matrix. This method includes how to extract the stiffness matrix and how to decouple the stiffness matrix to obtain accurate six-direction stiffness parameters of the flange, achieving efficient and accurate acquisition of flange stiffness.

[0028] Figure 1 A flowchart of a flange stiffness calculation method based on a finite element stiffness matrix is ​​provided for an embodiment of the present invention, as shown below. Figure 1 As shown, a method for calculating flange stiffness based on the finite element stiffness matrix includes the following steps: S101, construct a finite element model of the flange including the flange, bolts and sealing ring; Specifically, finite element modeling of each component of the flange is used to establish a high-precision finite element model including the flange, bolts, and sealing rings, providing basic data for the subsequent stiffness matrix.

[0029] S102, apply bolt preload based on the flange finite element model, and extract the flange stiffness matrix output by the substructure after the bolt preload is applied; S103, after decoupling the flange stiffness matrix, independent flange stiffness parameters are obtained.

[0030] The present invention provides a method for calculating flange stiffness based on the finite element stiffness matrix. The stiffness matrix is ​​directly extracted by finite element software, and the flange stiffness parameters are obtained through decoupled calculation. Compared with the prior art, this method is simple to use, efficient, and accurate. It can realize parametric modeling and batch calculation of stiffness matrices of different specifications, which greatly saves experimental and time costs and improves simulation analysis efficiency.

[0031] Based on the above embodiments, the construction of a flange finite element model including flange, bolts, and sealing rings includes: Create solid models of the connections between the flange face, bolts and flange, and sealing rings and flange, respectively; Specifically, such as Figure 2As shown, solid models of each flange component are established, material properties are assigned to each component, meshes are generated, and contacts are defined (between flange faces, bolts and flange, and sealing rings and flange). It should be noted that the above finite element model can be further deformed: for example, sealing rings and bolts may not be modeled, and contacts may be replaced with other connection methods. These deformations affect the calculation accuracy but do not affect the stiffness calculation.

[0032] Based on the solid model, two reference points are generated at the center of the two welding surfaces of the flange, and the two reference points are used as control points of the coupling surfaces at both ends of the flange to obtain the finite element model of the flange. The coupling surface at one end of the flange is the first welding surface, and the coupling surface at the other end of the flange is the second welding surface.

[0033] Specifically, such as Figure 3 As shown, two reference points GA and GB are generated at the center of the two welding surfaces of the flange. Two coupling constraints are established for each, with GA as the control point and the coupling surface at one end of the flange as the welding surface; and GB as the control point and the coupling surface at the other end of the flange as the welding surface. Further modifications can be made based on this: for example, the coupling constraint can be replaced with other constraint methods, such as MPC.

[0034] Based on the above embodiments, the step of applying bolt preload based on the flange finite element model and extracting the stiffness matrix after the bolt preload is applied includes: The bolt preload is calculated based on the actual installation torque and torque coefficient. The bolt preload is then applied to each bolt, and the bolt position is fixed after the preload is applied.

[0035] Specifically, apply bolt preload: Calculate the bolt preload F based on the actual installation torque and torque coefficient. bolt The preload is applied to each bolt, fixing its position after the preload is applied. Further modifications are possible: for example, the bolt preload application method can be modified, which, while affecting calculation accuracy, does not affect the stiffness calculation.

[0036] It should be noted that during actual flange connection, a preload is applied to the bolts, and this preload has a significant impact on flange stiffness. Therefore, to ensure the accuracy of flange stiffness, the stiffness matrix extraction step should be performed after calculating the preload load step.

[0037] After generating substructures or super-elements from the flange finite element model, the stiffness matrix is ​​extracted, including retaining the control points of the coupling surfaces at both ends of the flange, and solving the corresponding stiffness matrix of the flange through the two control points.

[0038] Specifically, this invention proposes a method for extracting stiffness matrices by defining the generation of substructures / superelements in finite element software. For example, by retaining nodes GA and GB (the reference points defined above), the stiffness matrices of the two nodes GA and GB are solved and output.

[0039] Based on the above embodiments, obtaining independent flange stiffness parameters after decoupling the flange stiffness matrix includes: The stiffness matrix of the two control points is obtained as a symmetric matrix of 12×12; Specifically, the stiffness matrices of the two nodes GA and GB are obtained, which are 12×12 symmetric matrices (6 n ×6 n , n (Number of nodes), as shown below: .

[0040] The element stiffness matrix of size 6×6 in the upper left corner is extracted based on the 12×12 symmetric matrix. Specifically, since the element stiffness matrix describes the relationship between the relative displacement / rotation and the applied force / moment between two nodes, the 6×6 matrix in the upper left corner contains all the independent parameters required to describe the entire stiffness matrix, as shown below: .

[0041] After removing the zero terms from the unit stiffness matrix, we obtain the unit stiffness matrix with the zero terms removed. Specifically, by removing the "zero" terms from the element stiffness matrix, a stiffness matrix of the following form is obtained: .

[0042] Based on the decoupling of the element stiffness matrix after removing zero terms, six independent flange stiffness parameters are obtained.

[0043] Specifically, the stiffness matrix is ​​decoupled into six independent stiffness parameters. First, stiffness is defined as the force required to produce a unit displacement in the structure, i.e.: .

[0044] In the finite element method, Represents the first in the stiffness matrix i Line number j The parameter of the column, its meaning is the first... j Each degree of freedom produces a unit displacement. d j =1, while all other displacements are zero, in the first... i Force required for each degree of freedom F i .

[0045] For connected elements (such as BUSH elements), K1, K2, K3, K4, K5, and K6 (i.e., six independent stiffness parameters) are typically used to define the scalar linear stiffness along the six degrees of freedom in the element's local coordinate system. K1~K6 directly represent the proportional relationship between force and displacement (or moment and rotation) in a single direction, i.e., K... i ( i= 1, 2, ..., 6) represents the number of... i Each degree of freedom produces a unit displacement. d i =1, in the... i Force required for each degree of freedom F i The difference between this and the stiffness matrix is ​​that the displacements of other degrees of freedom may not be zero in this case.

[0046] From the stiffness K1~K6 of the connecting elements and the stiffness matrix From the definition, since degrees of freedom 1 and 4 are independent and not coupled with other degrees of freedom, when these two degrees of freedom produce a unit displacement, the displacement of other degrees of freedom is zero. Therefore, K1 = K4= .

[0047] When L≠0 (L is the distance between GA and GB), meaning the two nodes GA and GB do not coincide, coupling will occur between degrees of freedom 2 and 6, and between degrees of freedom 3 and 5. For example, applying a single load in the 6-degree-of-freedom direction at point GA... M With z=K6, point GA will experience a unit displacement in 6 degrees of freedom relative to point GB. d 6=1, and at the same time, it will also produce displacement in 2 degrees of freedom. d 2=- L / 2, at this time The meaning of K6 and They are different and cannot be directly correlated.

[0048] In this case, the present invention calculates K2, K6, and K6 according to the derivation process of the element stiffness matrix in the finite element method. , as well as The relationship.

[0049] The above explains the calculation principles for K2 and K6; the principles for K3 and K5 are the same.

[0050] The formulas for calculating the flange stiffness parameters K1~K6 can be derived as follows: K1= ; K2= ; K3= ; K4= K5= ; K6= ; Through the above decoupling process, the coupling parameters in the stiffness matrix are eliminated, and the six independent stiffness parameters of the flange can be obtained by calculation using the formula.

[0051] It's worth noting that this decoupling method can be further adapted: it can be used for all connections that can be simplified to two-node elements, not just flanges. By changing the finite element model to model other connections and extracting the stiffness matrix, this calculation can be performed.

[0052] Based on the above embodiments, the unit stiffness matrix after removing zero terms is expressed as follows: ; In the finite element method Represents the first in the stiffness matrix i Line number j The parameter of the column, its meaning is the first... j Each degree of freedom produces a unit displacement. d j =1 ， When all other displacements are zero, in the first... i Force required for each degree of freedom F i , .

[0053] Based on the above embodiments, the decoupling of the element stiffness matrix after removing zero terms yields six independent flange stiffness parameters, the calculation formula of which is as follows: K1= ; K2= ; K3= ; K4= K5= ; K6= ; Where K1, K2, K3, K4, K5, and K6 are scalar linear stiffnesses along six degrees of freedom in the element's local coordinate system, representing the proportional relationship between force and displacement or torque and rotation in a single direction, i.e., K... i Indicates the first i Each degree of freedom produces a unit displacement. d i =1, in the... iForce required for each degree of freedom F i , i =1, 2, ..., 6 L The distance between the two control points is denoted as .

[0054] Based on the above embodiments, the step of applying the bolt preload to each bolt and fixing the bolt position after the preload is applied also includes locking the bolt length.

[0055] In this embodiment of the invention, taking the oxygen pressurization pipeline of the first stage of a launch vehicle as an example, the pipeline uses flanges for connection in multiple locations. Accurate modeling of each flange would be extremely time-consuming and computationally expensive. Therefore, while ensuring the accuracy of the flange stiffness parameters, the flanges are simplified into connection units, allowing for accurate mechanical analysis.

[0056] The specific implementation method for calculating flange stiffness parameters is described below, with the following steps: (1) Establishing the flange finite element model In Abaqus software, a finite element model is constructed based on the actual model size, material, and contact location.

[0057] a) Create solid models of each flange component, assign material properties, mesh, and define contacts (between flange faces, bolts and flange, sealing rings and flange).

[0058] b) Generate two reference points GA and GB on the two welding surfaces of the flange, and establish the Coupling connection welding surfaces respectively.

[0059] (2) Apply preload c) Define load step 1: Apply bolt load. Calculate the bolt preload based on the actual installation torque and torque coefficient, and apply it to each bolt.

[0060] d) Define load step 2: pre-tightening locking step, after applying pre-tightening force, lock the bolt length.

[0061] (3) Substructure output flange stiffness e) Define load step 3: substructure generation, retain nodes GA and GB, define the output of the stiffness matrix, and solve to obtain the stiffness matrix .mtx.

[0062] (4) Decoupling calculations yield independent flange stiffness parameters f) Solving for the .mtx file yields a 12×12 stiffness matrix. k ij All data were used to calculate six independent stiffness parameters of the flange using formulas.

[0063] K1= K2= K3= K4= K5= K6= ; (5) Practical application of flange parameters (6 directions) g) When modeling the oxygen booster pipeline as a whole, Bush elements can be directly created at the flange location, and six independent stiffnesses K1~K6 can be input without building an actual flange model.

[0064] The technical innovations of this invention are as follows: 1) It solves the problems of numerous flange specifications, high cost, long cycle and insufficient precision in obtaining stiffness.

[0065] 2) The stiffness matrix obtained from the finite element method is calculated using formulas to obtain the independent stiffness of the flange in six directions, which can be directly used for subsequent overall modeling to improve calculation efficiency.

[0066] It should be noted that the present invention has the following advantages over the prior art: This invention proposes a method for rapidly and accurately calculating flange stiffness parameters. The stiffness matrix can be directly extracted using commercial finite element software, and the flange stiffness parameters can be obtained through decoupled calculation. It is simple to use, efficient, and highly accurate. It can realize parametric modeling and batch calculation of stiffness matrices of different specifications, which greatly saves experimental and time costs and improves simulation analysis efficiency.

[0067] Further improvements and modifications to the above technical solutions are also within the scope of protection of this invention, such as, but not limited to: 1) In actual use, the finite element model may be simplified to a certain extent, such as simplifying bolts and contact settings. This will lead to a certain degree of error in the accuracy of the stiffness matrix, but it can still be used.

[0068] 2) The stiffness matrix can be obtained directly in various ways without affecting the independent calculation of stiffness parameters from the stiffness matrix.

[0069] 3) The decoupling calculation method can be used for structures similar to flange connections that can be simplified to two-node units.

[0070] Based on the above embodiments, this embodiment of the invention provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the above embodiments.

[0071] In some embodiments of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method described in the above embodiments.

[0072] In some embodiments of the present invention, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of the method described in the above embodiments.

[0073] The processor may include, but is not limited to, one or more processors or microprocessors. Each processor may be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic component, for executing the methods in the above embodiments.

[0074] Computer-readable storage media can be implemented by any type of volatile or non-volatile storage device or a combination thereof. Computer-readable storage media may include, but are not limited to, random access memory (RAM), read-only memory (ROM), flash memory, EPROM memory, EEPROM memory, registers, and computer storage media (e.g., hard disks, floppy disks, solid-state drives, removable disks, CD-ROMs, DVD-ROMs, Blu-ray discs, etc.).

[0075] Computer-readable storage media may also store at least one computer-executable program / instruction, such as computer-readable instructions. Computer-readable storage media include, but are not limited to, volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and / or cache memory. Computer-readable storage media may include, for example, read-only memory (ROM), hard disk, flash memory, etc. For example, a non-transitory computer-readable storage medium may be connected to a computing device such as a computer, and then, when the computing device executes the computer-readable instructions stored on the computer-readable storage medium, the various methods described above can be performed.

[0076] In addition, the computer device may include (but is not limited to) a data bus, an input / output (I / O) bus, a display, and input / output devices (e.g., keyboard, mouse, speakers, etc.).

[0077] The processor can communicate with external devices via the I / O bus through wired or wireless networks.

[0078] In one embodiment, the at least one computer-executable instruction may also be compiled into or comprise a software product / computer program product, wherein one or more computer-executable instructions are executed by a processor to perform the steps of the various functions and / or methods in the embodiments described herein.

[0079] Those skilled in the art will understand that all or part of the steps of the methods described above can be implemented by a program instructing related hardware. The program can be stored in a readable storage medium, and when executed, the program includes one or a combination of the steps of the method implementation.

[0080] In the various embodiments of this application, the functional units can be integrated into a single processing module, or each unit can exist physically separately, or two or more units can be integrated into a single module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a readable storage medium. The storage medium can be a read-only memory, a disk, or an optical disk, etc.

[0081] In the description of this specification, the references to terms such as "one embodiment / mode," "some embodiments / modes," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment / mode or example is included in at least one embodiment / mode or example of this application. Furthermore, the described specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments / modes or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments / modes or examples described in this specification, as well as the features of different embodiments / modes or examples.

[0082] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0083] Those skilled in the art should understand that the above embodiments are merely for illustrative purposes and are not intended to limit the scope of this application. Those skilled in the art can make other changes or modifications based on the above disclosure, and these changes or modifications still fall within the scope of this application.

Claims

1. A method for calculating flange stiffness based on the finite element stiffness matrix, characterized in that, include: Construct a finite element model of the flange, including the flange, bolts, and sealing ring; Based on the flange finite element model, a bolt preload is applied, and after the bolt preload is applied, the flange stiffness matrix output by the substructure is extracted. After decoupling the flange stiffness matrix, independent flange stiffness parameters are obtained.

2. The method according to claim 1, characterized in that, The construction of the flange finite element model, which includes the flange, bolts, and sealing ring, includes: Create solid models of the connections between the flange face, bolts and flange, and sealing rings and flange, respectively; Based on the solid model, two reference points are generated at the center of the two welding surfaces of the flange, and the two reference points are used as control points of the coupling surfaces at both ends of the flange to obtain the finite element model of the flange. The coupling surface at one end of the flange is the first welding surface, and the coupling surface at the other end of the flange is the second welding surface.

3. The method according to claim 2, characterized in that, The process of applying bolt preload based on the flange finite element model and extracting the stiffness matrix after the bolt preload is applied includes: The bolt preload is calculated based on the actual installation torque and torque coefficient. The bolt preload is then applied to each bolt, and the bolt position is fixed after the preload is applied. After generating substructures or super-elements from the flange finite element model, the stiffness matrix is ​​extracted, including retaining the control points of the coupling surfaces at both ends of the flange, and solving for the corresponding stiffness matrix of the flange using the two control points.

4. The method according to claim 3, characterized in that, The process of decoupling the flange stiffness matrix to obtain independent flange stiffness parameters includes: The stiffness matrix of the two control points is obtained as a symmetric matrix of 12×12; The element stiffness matrix of size 6×6 in the upper left corner is extracted based on the 12×12 symmetric matrix. After removing the zero terms from the unit stiffness matrix, the unit stiffness matrix with zero terms removed is obtained. Based on the decoupling of the element stiffness matrix after removing zero terms, six independent flange stiffness parameters are obtained.

5. The method according to claim 4, characterized in that, The unit stiffness matrix with zero terms removed is expressed as follows: ； In the finite element method Represents the first in the stiffness matrix i Line number j The parameter of the column, its meaning is the first... j Each degree of freedom produces a unit displacement. d j =1, while all other displacements are zero, in the first... i Force required for each degree of freedom F i , .

6. The method according to claim 5, characterized in that, The decoupling based on the element stiffness matrix after removing zero terms yields six independent flange stiffness parameters, the calculation formula of which is as follows: K1= ； K2= ； K3= ； K4= K5= ； K6= ； Where K1, K2, K3, K4, K5, and K6 are scalar linear stiffnesses along six degrees of freedom in the element's local coordinate system, representing the proportional relationship between force and displacement or torque and rotation in a single direction, i.e., K... i Indicates the first i Each degree of freedom produces a unit displacement. d i =1, in the... i Force required for each degree of freedom F i , i =1, 2, ..., 6 L The distance between the two control points is denoted as .

7. The method according to claim 3, characterized in that, The process includes applying the bolt preload to each bolt, fixing the bolt position after the preload is applied, and then locking the bolt length.

8. A computer device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the flange stiffness calculation method based on the finite element stiffness matrix as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the flange stiffness calculation method based on the finite element stiffness matrix as described in any one of claims 1-7.

10. A computer product comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the flange stiffness calculation method based on the finite element stiffness matrix as described in any one of claims 1 to 7.

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