A method for constructing a proxy model for predicting uncertainty failure of a composite bolted connection

Abstract

The application discloses a kind of composite bolt connection uncertainty failure prediction proxy model construction methods, belong to composite structure uncertainty analysis field, this method includes: the material constitutive relation with damage evolution characteristics is constructed, and parameterized finite element model of composite material bolt connection is established;The factor leading to strength dispersion is classified into two scales of micro and macro, and is further classified into random and interval uncertainty variable;Sampling points are generated by optimal Latin hypercube sampling, and equivalent material properties in original design space are obtained by inverse transformation method and homogenization method;Strength observation values at sampling points are obtained by batch simulation, and sample set is obtained;Model training is carried out based on Kriging principle, and a high-precision composite material bolt connection uncertainty failure prediction proxy model is established.The application can lay a foundation for reliability analysis of composite material bolt connection under multi-source multi-scale uncertainty.

Description

Technical Field

[0001] This invention belongs to the field of uncertainty analysis of composite structures, and specifically relates to a method for constructing a proxy model for predicting uncertainty failure of composite bolted connections. Background Technology

[0002] Fiber-reinforced polymer (FRP) composites, especially carbon fiber reinforced polymer (CFRP), have become an important alternative to traditional metallic materials due to their excellent specific strength, specific modulus, high temperature resistance, fatigue resistance, thermal stability, and designability. They are widely used in aerospace, shipbuilding, and automotive fields, effectively achieving structural weight reduction and lifespan extension. In FRP structures, the connection between components is crucial, and bolted connections, as the primary connection method and force transmission hub, offer significant advantages such as high load-bearing capacity, ease of disassembly, and insensitivity to surface treatment. However, bolted connections also present significant challenges. Holes disrupt the continuity of the material, leading to significant stress concentration at the hole edges, making them a weak point in the composite structure. Furthermore, the drilling process easily induces initial damage such as delamination, tearing, and burrs at the hole openings in the laminate, resulting in large dispersion in connection strength and making accurate prediction difficult.

[0003] Currently, significant progress has been made in the research of surrogate models for predicting uncertain failures in composite bolted connections. However, existing research remains limited to single uncertainties, either stochastic or cognitive, and only considers structural or material parameters of a single-layer plate at a single scale. This dual limitation leads to significant errors in strength distribution characteristics, and uncertainty analysis often requires extensive and complex structural analysis. Therefore, to fully leverage the performance advantages of advanced composite materials, it is urgent to establish surrogate models that can fully consider multi-source and multi-scale uncertainties to efficiently and accurately quantify the failure uncertainty of composite bolted connections, thereby ensuring the safety of the overall structure. Addressing this practical engineering problem, this invention proposes a Kriging model construction method for predicting uncertain failures in composite bolted connections. Summary of the Invention

[0004] Purpose of the invention: This invention proposes a proxy model construction method for predicting uncertain failures in composite bolted connections, which addresses the technical problems of low efficiency and large errors in existing uncertainty analysis methods that only consider a single scale or a single source in quantifying the strength dispersion of composite bolted connection structures.

[0005] The technical solution adopted in this invention is a surrogate model construction method for predicting uncertain failures in composite bolted connections, comprising the following steps:

[0006] S1: Constructing material constitutive relations with damage evolution characteristics;

[0007] S2: Based on the material constitutive relation described in step S1, develop a user-defined material subroutine VUMAT using the Fortran language;

[0008] S3: Write a highly parameterized finite element model script for composite material bolted connections based on Python language, and embed the subroutine VUMAT described in step S2 into the Python model script;

[0009] S4: Select uncertainty parameters from different scales and sources, and use them as design variables;

[0010] S5: For the uncertainties described in step S4, design variables and determine their number of samples, sampling dimensions, and the original physical space of the samples;

[0011] S6: Use the optimal Latin hypercube sampling and inverse transformation method to generate actual sampling points of design variables in the original physical space;

[0012] S7: Using a homogenization method, the component-level material properties in the sampling points described in step S6 are equivalent to the single-layer plate level, and together with the macroscopic geometric parameters, they constitute the input parameters of the Python model script described in step S3;

[0013] S8: Run the Python model script described in step S3 by calling the Abaqus kernel program through MATLAB, thereby obtaining the failure load observation values ​​in batches;

[0014] S9: Using the sampling points described in step S6 and the observations described in step S8 as a sample set, a Kriging surrogate model for predicting uncertain failures in composite bolted connections is established through parameter estimation and model training.

[0015] Furthermore, in step S1, the material constitutive relation with damage evolution characteristics is constructed collaboratively by the three-dimensional constitutive model in the undamaged state, the 3D Hashin failure criterion, and the material property degradation model, as follows:

[0016] The three-dimensional constitutive relation of the composite material in the undamaged state is as follows:

[0017]

[0018] in, The stress field of the composite laminate structure; For the corresponding strain field; The material stiffness matrix can be expressed in the following form:

[0019]

[0020]

[0021]

[0022] in, These are the elements of the material stiffness matrix; Normalization factor; Young's modulus; Shear modulus; Poisson's ratio; , The values ​​can be 1, 2, or 3. 1 represents the fiber direction, 2 represents the in-plane transverse direction perpendicular to the fiber direction, and 3 represents the out-of-plane normal direction perpendicular to the plane.

[0023] Under incremental loading, the stress and strain in the composite laminate continuously increase. When one or more layers satisfy the 3D Hashin failure criterion, the corresponding engineering constants are multiplied by a degradation factor according to the material property degradation model to reduce the material stiffness. The effective engineering constants after damage can then be expressed as follows:

[0024]

[0025] in, As a degradation factor, the function , , Calculation methods related to material property degradation models; , , These represent the engineering constants after damage occurs; and the material stiffness matrix after damage occurs. This can be expressed as:

[0026]

[0027] Therefore, for composite materials, the constitutive relation of materials with damage evolution characteristics can be expressed as:

[0028]

[0029] in, This is the material stiffness matrix after damage occurs; and These represent the stress field and strain field after damage occurs.

[0030] Furthermore, the 3D Hashin failure criterion is as follows:

[0031] 1) Fiber tensile failure ( ):

[0032]

[0033] 2) Fiber compression failure ( ):

[0034]

[0035] 3) Matrix tensile failure ( ):

[0036]

[0037] 4) Matrix compression failure ( ):

[0038]

[0039] 5) Fiber-matrix shear failure ( ):

[0040]

[0041] 6) Interlaminar tensile failure ( ):

[0042]

[0043] 7) Interlayer compression failure ( ):

[0044]

[0045] in, ( () represents the normal stress component of the unidirectional composite material in the principal coordinate system of the material; ( () represents the shear stress component of the unidirectional composite material in the principal coordinate system of the material; and These represent the longitudinal tensile and compressive strengths of a single-layer plate, respectively. and These are the transverse tensile and compressive strengths of a single-layer plate, respectively. and These represent the tensile and compressive strengths of a single-layer plate along its thickness direction, respectively. , and These represent the in-plane and out-of-plane shear strengths of a single-layer plate, respectively.

[0046] Furthermore, the material property degradation model is as follows:

[0047] 1) Fiber tensile failure:

[0048]

[0049] 2) Fiber compression failure:

[0050]

[0051] 3) Matrix tensile failure:

[0052] , , , ,

[0053] 4) Matrix compression failure ( ):

[0054] , , , ,

[0055] 5) Fiber-matrix shear failure ( ):

[0056] , , , , ,

[0057] 6) Interlaminar tensile failure ( ):

[0058] , , , ,

[0059] 7) Interlayer compression failure ( ):

[0060] , , , ,

[0061] Among them, the parameter marked with "d" is the engineering constant after damage, and its value is determined by the degradation factor. ( The results are obtained from calculations using non-destructive engineering constants, as follows:

[0062]

[0063]

[0064]

[0065] in, and These are the volume fractions of the fiber and the matrix, respectively. and These are Young's modulus and shear modulus of the matrix, respectively. , , , All of these are engineering constants for single-layer plates.

[0066] Furthermore, the specific implementation process of step S3 is as follows:

[0067] S3.1: Using the Abaqus scripting interface, based on the geometric dimensions and positional relationships of each component in the composite material bolted connection, write a Python script to create each part and complete the assembly, and at the same time complete the following model creation steps;

[0068] S3.2: Assign material properties to laminates, bolts, and test fixtures, including stiffness and strength parameters;

[0069] S3.3: Assign element properties and use selection functions to divide the overlapping area into a fine radial mesh, while using a coarser mesh for the non-overlapping area.

[0070] S3.4: Define contact pairs, set boundary conditions, and apply tensile displacement load steps;

[0071] S3.5: Pass the address of the subroutine VUMAT described in step S2 on the local computer to the Python script, and use the ABAQUS / Explicit explicit solver to complete the parametric modeling.

[0072] Furthermore, the specific implementation process of step S6 is as follows:

[0073] S6.1: Generating a Normalized Space Based on Optimal Latin Hypercube Sampling Sampling points within ;

[0074] in, The dimension of the sample; Design variables The One sampling point; Design variables for random uncertainty; Design variables for interval uncertainty;

[0075] S6.2: Perform the following inverse transformation on the design variables of random uncertainty:

[0076]

[0077] in, Design variables for random uncertainty after inverse transformation; Design the cumulative probability distribution function of variables for random uncertainty;

[0078] S6.3: Perform the following inverse transformation on the design variables for interval uncertainty:

[0079]

[0080] in, Design variables for the interval uncertainty after inverse transformation; For interval variables The upper bound of the value; interval variable The lower bound of the value;

[0081] S6.4: After the above inverse transformation, the actual sampling points of the design variables in the original physical space are obtained. .

[0082] Furthermore, the specific implementation process of step S7 is as follows:

[0083] S7.1: The actual sampling points of the uncertain design variables described in step S6. According to the structural hierarchy, the parameters are divided into component-level micro-parameters and single-layer plate-level macro-parameters, as detailed below:

[0084]

[0085] in, These are the component-level micromaterial parameters, including fiber stiffness, fiber strength, fiber volume fraction, matrix stiffness, matrix strength, and matrix volume fraction. and These are the component-level micro-geometric parameters and the single-layer plate-level macro-geometric parameters, respectively.

[0086] S7.2: Using the Mori-Tanaka model based on the homogenization method, the equivalent stiffness (engineering constant) of the single-layer plate (unidirectional composite material) is obtained from the fiber stiffness, fiber volume fraction, matrix stiffness, and matrix volume fraction described in step S7.1. The specific formula is as follows:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] in, , , , , This is the equivalent stiffness of a single-layer plate; For Mori-Tanaka-Eshelby bridge matrix elements, and The possible values ​​are 1, 2, 3, 4, 5, and 6. This represents the fiber volume fraction. This represents the volume fraction of the matrix. For fiber flexibility matrix elements, For matrix compliance matrix elements, and Options 1, 2, and 3 are acceptable. , , , and All are constants;

[0098] S7.3: Using the formula proposed by Chamis, the equivalent strength of the single-layer plate (unidirectional composite material) is obtained from the fiber stiffness, fiber strength, fiber volume fraction, matrix stiffness, matrix strength, and matrix volume fraction described in step S7.1. The specific formula is as follows:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] in, , , , , These are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength, and in-plane shear strength of a single-layer plate, respectively. , , , , These are the axial elastic modulus, transverse elastic modulus, shear modulus, and Poisson's ratio of the fiber, respectively. , These are the tensile and compressive strengths of the fiber, respectively. , These are the elastic modulus and shear modulus of the matrix, respectively. , , These are the tensile, compressive, and shear strengths of the matrix, respectively. This represents the fiber volume fraction. This represents the volume fraction of the matrix.

[0105] S7.4: Combine the equivalent stiffness and strength parameters of the single-layer plate obtained in steps S7.2 and S7.3 with the macroscopic geometric parameters of the single-layer plate level, and use them as input parameters for the Python model script described in step S3.

[0106] Beneficial effects:

[0107] This invention proposes a comprehensive solution for predicting uncertain failures in composite bolted connections by integrating three major modules: progressive damage analysis, experimental design, and the Kriging model. It systematically addresses the technical challenges in existing research on connection structure failure analysis, such as insufficient accuracy, lack of uncertainty consideration, and inefficient sampling calculations. Compared to traditional uncertainty analysis methods that only consider a single scale or single source, this invention, based on deterministic progressive damage analysis, considers multi-scale and multi-source uncertainty parameters as design variables. Combining optimal Latin hypercube sampling, inverse transformation, homogenization methods, and the fundamental principles of Kriging, it constructs a surrogate model for predicting uncertain failures in composite bolted connections. This lays the foundation for accurately and efficiently quantifying the probabilistic strength of composite bolted connections under multi-scale and multi-source uncertainties. Attached Figure Description

[0108] Figure 1 The flowchart below shows a method for constructing a proxy model for predicting uncertain failures in composite bolted connections according to the present invention.

[0109] Figure 2 This is a schematic diagram of a single-nail double-shear bolt connection structure of T700 carbon fiber / bismaleimide (BMI) resin composite material in a specific embodiment of the present invention.

[0110] Figure 3This is a three-dimensional progressive damage finite element model of composite material bolted connections established in a specific embodiment of the present invention;

[0111] Figure 4 This is a projection distribution diagram of the sample points based on the optimal Latin hypercube sampling in the first two dimensions in a specific embodiment of the present invention;

[0112] Figure 5 This is a comparison chart of the failure load prediction results and finite element calculation results of composite bolt connection structures based on the Kriging model in a specific embodiment of the present invention. Detailed Implementation

[0113] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0114] like Figure 1 As shown, a surrogate model construction method for predicting uncertain failures in composite bolted connections is presented. This method specifically includes the following steps:

[0115] S1: Construct material constitutive relations with damage evolution characteristics.

[0116] In a preferred embodiment of the present invention, in step S1, the material constitutive relation with damage evolution characteristics is constructed collaboratively by a three-dimensional constitutive model in the undamaged state, a 3D Hashin failure criterion, and a material property degradation model, as detailed below:

[0117] The three-dimensional constitutive relation of the composite material in the undamaged state is as follows:

[0118]

[0119] in, The stress field of the composite laminate structure; For the corresponding strain field; The material stiffness matrix can be expressed in the following form:

[0120]

[0121]

[0122]

[0123] in, These are the elements of the material stiffness matrix; Normalization factor; Young's modulus; Shear modulus; Poisson's ratio; , The values ​​can be 1, 2, or 3. 1 represents the fiber direction, 2 represents the in-plane transverse direction perpendicular to the fiber direction, and 3 represents the out-of-plane normal direction perpendicular to the plane.

[0124] Under incremental loading, the stress and strain in the composite laminate continuously increase. When one or more layers satisfy the 3D Hashin failure criterion, the corresponding engineering constants are multiplied by a degradation factor according to the material property degradation model to reduce the material stiffness. The effective engineering constants after damage can then be expressed as follows:

[0125]

[0126] in, As a degradation factor, the function , , Calculation methods related to material property degradation models; , , These represent the engineering constants after damage occurs; and the material stiffness matrix after damage occurs. This can be expressed as:

[0127]

[0128] Therefore, for composite materials, the constitutive relation of materials with damage evolution characteristics can be expressed as:

[0129]

[0130] in, This is the material stiffness matrix after damage occurs; and These represent the stress field and strain field after damage occurs.

[0131] As a preferred embodiment of the present invention, the 3D Hashin failure criterion is as follows:

[0132] 1) Fiber tensile failure ( ):

[0133]

[0134] 2) Fiber compression failure ( ):

[0135]

[0136] 3) Matrix tensile failure ( ):

[0137]

[0138] 4) Matrix compression failure ( ):

[0139]

[0140] 5) Fiber-matrix shear failure ( ):

[0141]

[0142] 6) Interlaminar tensile failure ( ):

[0143]

[0144] 7) Interlayer compression failure ( ):

[0145]

[0146] in, ( () represents the normal stress component of the unidirectional composite material in the principal coordinate system of the material; ( () represents the shear stress component of the unidirectional composite material in the principal coordinate system of the material; and These represent the longitudinal tensile and compressive strengths of a single-layer plate, respectively. and These are the transverse tensile and compressive strengths of a single-layer plate, respectively. and These represent the tensile and compressive strengths of a single-layer plate along its thickness direction, respectively. , and These represent the in-plane and out-of-plane shear strengths of a single-layer plate, respectively.

[0147] As a preferred embodiment of the present invention, the material property degradation model is as follows:

[0148] 1) Fiber tensile failure:

[0149]

[0150] 2) Fiber compression failure:

[0151]

[0152] 3) Matrix tensile failure:

[0153] , , , ,

[0154] 4) Matrix compression failure ( ):

[0155] , , , ,

[0156] 5) Fiber-matrix shear failure ( ):

[0157] , , , , ,

[0158] 6) Interlaminar tensile failure ( ):

[0159] , , , ,

[0160] 7) Interlayer compression failure ( ):

[0161] , , , ,

[0162] Among them, the parameter marked with "d" is the engineering constant after damage, and its value is determined by the degradation factor. ( The results are obtained from calculations using non-destructive engineering constants, as follows:

[0163]

[0164]

[0165]

[0166] in, and These are the volume fractions of the fiber and the matrix, respectively. and These are Young's modulus and shear modulus of the matrix, respectively. , , , All of these are engineering constants for single-layer plates.

[0167] S2: Based on the material constitutive relation described in step S1, develop a user-defined material subroutine VUMAT using the Fortran language.

[0168] S3: Write a highly parameterized finite element model script for composite material bolted connections based on the Python language, and embed the subroutine VUMAT described in step S2 into the Python model script.

[0169] As a preferred embodiment of the present invention, the specific implementation process of step S3 is as follows:

[0170] S3.1: Using the Abaqus scripting interface, based on the geometric dimensions and positional relationships of each component in the composite material bolted connection, write a Python script to create each part and complete the assembly, and at the same time complete the following model creation steps;

[0171] S3.2: Assign material properties to laminates, bolts, and test fixtures, including stiffness and strength parameters;

[0172] S3.3: Assign element properties and use selection functions to divide the overlapping area into a fine radial mesh, while using a coarser mesh for the non-overlapping area.

[0173] S3.4: Define contact pairs, set boundary conditions, and apply tensile displacement load steps;

[0174] S3.5: Pass the address of the subroutine VUMAT described in step S2 on the local computer to the Python script, and use the ABAQUS / Explicit explicit solver to complete the parametric modeling.

[0175] S4: Select uncertainty parameters from different scales and sources, and use them as design variables.

[0176] S5: Design variables for the uncertainties described in step S4, and determine their number of samples, sampling dimensions, and the original physical space of the samples.

[0177] S6: Use the optimal Latin hypercube sampling and inverse transformation method to generate the actual sampling points of the design variables in the original physical space.

[0178] As a preferred embodiment of the present invention, the specific implementation process of step S6 is as follows:

[0179] S6.1: Generating a Normalized Space Based on Optimal Latin Hypercube Sampling Sampling points within ;

[0180] in, The dimension of the sample; Design variables The One sampling point; Design variables for random uncertainty; Design variables for interval uncertainty;

[0181] S6.2: Perform the following inverse transformation on the design variables of random uncertainty:

[0182]

[0183] in, Design variables for random uncertainty after inverse transformation; Design the cumulative probability distribution function of variables for random uncertainty;

[0184] S6.3: Perform the following inverse transformation on the design variables for interval uncertainty:

[0185]

[0186] in, Design variables for the interval uncertainty after inverse transformation; For interval variables The upper bound of the value; interval variable The lower bound of the value;

[0187] S6.4: After the above inverse transformation, the actual sampling points of the design variables in the original physical space are obtained. .

[0188] S7: Using a homogenization method, the component-level material properties in the sampling points described in step S6 are equivalent to the single-layer plate level, and together with the macroscopic geometric parameters, they constitute the input parameters of the Python model script described in step S3.

[0189] As a preferred embodiment of the present invention, the specific implementation process of step S7 is as follows:

[0190] S7.1: The actual sampling points of the uncertain design variables described in step S6. According to the structural hierarchy, the parameters are divided into component-level micro-parameters and single-layer plate-level macro-parameters, as detailed below:

[0191]

[0192] in, These are the component-level micromaterial parameters, including fiber stiffness, fiber strength, fiber volume fraction, matrix stiffness, matrix strength, and matrix volume fraction. and These are the component-level micro-geometric parameters and the single-layer plate-level macro-geometric parameters, respectively.

[0193] S7.2: Using the Mori-Tanaka model based on the homogenization method, the equivalent stiffness (engineering constant) of the single-layer plate (unidirectional composite material) is obtained from the fiber stiffness, fiber volume fraction, matrix stiffness, and matrix volume fraction described in step S7.1. The specific formula is as follows:

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204] in, , , , , This is the equivalent stiffness of a single-layer plate; For Mori-Tanaka-Eshelby bridge matrix elements, and The possible values ​​are 1, 2, 3, 4, 5, and 6. This represents the fiber volume fraction. This represents the volume fraction of the matrix. For fiber flexibility matrix elements, For matrix compliance matrix elements, and Options 1, 2, and 3 are acceptable. , , , and All are constants;

[0205] S7.3: Using the formula proposed by Chamis, the equivalent strength of the single-layer plate (unidirectional composite material) is obtained from the fiber stiffness, fiber strength, fiber volume fraction, matrix stiffness, matrix strength, and matrix volume fraction described in step S7.1. The specific formula is as follows:

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] in, , , , , These are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength, and in-plane shear strength of a single-layer plate, respectively. , , , , These are the axial elastic modulus, transverse elastic modulus, shear modulus, and Poisson's ratio of the fiber, respectively. , These are the tensile and compressive strengths of the fiber, respectively. , These are the elastic modulus and shear modulus of the matrix, respectively. , , These are the tensile, compressive, and shear strengths of the matrix, respectively. This represents the fiber volume fraction. This represents the volume fraction of the matrix.

[0212] S7.4: Combine the equivalent stiffness and strength parameters of the single-layer plate obtained in steps S7.2 and S7.3 with the macroscopic geometric parameters of the single-layer plate level, and use them as input parameters for the Python model script described in step S3.

[0213] S8: Run the Python model script described in step S3 by calling the Abaqus kernel program through MATLAB, thereby obtaining the failure load observation values ​​in batches.

[0214] S9: Using the sampling points described in step S6 and the observations described in step S8 as a sample set, a Kriging surrogate model for predicting uncertain failures in composite bolted connections is established through parameter estimation and model training.

[0215] Example

[0216] The composite material bolted connection structure specimen is a single-nail double-shear laminate specimen, and its connection structure schematic diagram is shown below. Figure 2As shown, the laminate is constructed from 32 layers of uniformly and symmetrically laid-up T700 carbon fiber / BMI unidirectional prepreg, with each layer having the same thickness. The lay-up sequence is [45 / 0 / -45 / 90]. 4S The fiber volume fraction is 63%. The detailed geometry and nominal values ​​of the layup angles of the laminate are shown in Table 1.

[0217] Table 1 Nominal values ​​of laminate geometry and ply angles

[0218]

[0219] A three-dimensional finite element model of the connection structure was built using the Python language, such as Figure 3 As shown, the model includes three types of components: laminated plates, bolts, and test fixtures. A user-defined material subroutine, VUMAT, was developed based on the Fortran language to embed the failure criteria and material property degradation model into the finite element model. Numerical calculations were then performed using the ABAQUS / Explicit explicit solver.

[0220] Uncertainty parameters from different scales and sources were fully considered. The laminate width was... Aperture Hole end distance Single layer thickness The macroscopic scale parameters are assumed to be normally distributed random variables, and their distribution parameters are determined. Simultaneously, the fiber orientation angle is... , , , Fiber volume fraction Microscopic parameters such as the mechanical properties of fibers and the matrix are assumed to be interval variables, and the range or limits of these parameters are determined based on limited statistical information. Table 2 lists the distribution types or interval boundaries of all uncertain parameters considered in composite bolted connections.

[0221] Table 2 Distribution types or interval boundaries of all uncertainty parameters considered for composite material bolted connections

[0222]

[0223] Based on optimal Latin hypercube sampling, 150 uniformly distributed sampling points are generated in the normalized space. Figure 4The projection distribution of sample points in the first two dimensions is shown. A training sample set containing 150 data points was then constructed using a batch processing workflow. Using the same method, an additional 50 data points were extracted as the test set for the Kriging model. Based on the established Kriging surrogate model, to ensure the model's prediction accuracy, the model's error was tested using the additional 50 data points. The observed values, predicted values, and relative errors of the failure load at the test sampling points were calculated using both the finite element model and the Kriging surrogate model. The observed values ​​were then sorted in ascending order. Figure 5 The comparison results are presented in the figure. The results show that the Kriging model has a maximum prediction error of no more than 3.0%, and its prediction accuracy is high.

[0224] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for constructing a surrogate model for predicting uncertain failures in composite bolted connections, characterized in that, Includes the following steps: S1: Constructing material constitutive relations with damage evolution characteristics; S2: Based on the material constitutive relation described in step S1, develop a user-defined material subroutine VUMAT using the Fortran language; S3: Write a highly parameterized finite element model script for composite material bolted connections based on Python language, and embed the subroutine VUMAT described in step S2 into the Python model script; S4: Select uncertainty parameters from different scales and sources, and use them as uncertainty design variables; S5: For the uncertainties described in step S4, design variables and determine their number of samples, sampling dimensions, and the original physical space of the samples; S6: Use the optimal Latin hypercube sampling and inverse transformation method to generate actual sampling points of design variables in the original physical space; S7: Using a homogenization method, the component-level material properties in the sampling points described in step S6 are equivalent to the single-layer plate level, and together with the macroscopic geometric parameters, they constitute the input parameters of the Python model script described in step S3; S8: Run the Python model script described in step S3 by calling the Abaqus kernel program through MATLAB, thereby obtaining the failure load observation values ​​in batches; S9: Using the sampling points described in step S6 and the observations described in step S8 as a sample set, a Kriging surrogate model for predicting uncertain failures in composite bolted connections is established through parameter estimation and model training.

2. The method for constructing a surrogate model for predicting uncertain failures in composite bolted connections according to claim 1, characterized in that, In step S1, the material constitutive relation with damage evolution characteristics is constructed collaboratively by the three-dimensional constitutive model under the undamaged state, the 3D Hashin failure criterion, and the material property degradation model, as detailed below: The three-dimensional constitutive relation of the composite material in the undamaged state is as follows: ， in, The stress field of the composite laminate structure; For the corresponding strain field; The material stiffness matrix is ​​expressed in the following form: ， ， ， in, These are the elements of the material stiffness matrix; Normalization factor; Young's modulus; Shear modulus; Poisson's ratio; , Let 1, 2, and 3 be used. 1 represents the fiber direction, 2 represents the in-plane transverse direction perpendicular to the fiber direction, and 3 represents the out-of-plane normal direction perpendicular to the plane. Under incremental loading, the stress and strain in the composite laminate continuously increase. When one or more layers satisfy the 3D Hashin failure criterion, the corresponding engineering constants are multiplied by a degradation factor according to the material property degradation model to reduce the material stiffness. The effective engineering constants after damage occur are expressed as follows: ， in, As a degradation factor, the function , , Calculation methods related to material property degradation models; , , These represent the engineering constants after damage occurs; and the material stiffness matrix after damage occurs. Expressed as: ， Therefore, for composite materials, the constitutive relation of materials with damage evolution characteristics is expressed as: ， in, This is the material stiffness matrix after damage occurs; and These represent the stress field and strain field after damage occurs.

3. The method for constructing a surrogate model for predicting uncertain failures in composite bolted connections according to claim 2, characterized in that, The 3D Hashin failure criteria are as follows: 1) Fiber tensile failure, : ， 2) Fiber compression failure, : ， 3) Matrix tensile failure, : ， 4) Matrix compression failure, : ， 5) Fiber-matrix shear failure, : ， 6) Interlaminar tensile failure, : ， 7) Interlayer compression failure, : ， in, ,in : represents the normal stress component of a unidirectional composite material in the material's principal coordinate system; ,in : represents the shear stress component of a unidirectional composite material in the material's principal coordinate system; and These represent the longitudinal tensile and compressive strengths of a single-layer plate, respectively. and These are the transverse tensile and compressive strengths of a single-layer plate, respectively. and These represent the tensile and compressive strengths of a single-layer plate along its thickness direction, respectively. , and These represent the in-plane and out-of-plane shear strengths of a single-layer plate, respectively.

4. The method for constructing a surrogate model for predicting uncertain failures in composite bolted connections according to claim 2, characterized in that, The specific material property degradation model is as follows: 1) Fiber tensile failure: ， 2) Fiber compression failure: ， 3) Matrix tensile failure: ， ， ， ， ， 4) Matrix compression failure, : ， ， ， ， ， 5) Fiber-matrix shear failure, : ， ， ， ， ， ， 6) Interlaminar tensile failure, : ， ， ， ， ， 7) Interlayer compression failure, : ， ， ， ， ， Among them, the parameter marked with "d" is the engineering constant after damage, and its value is determined by the degradation factor. ,in The results are obtained from calculations using non-destructive engineering constants, as follows: ， ， ， in, and These are the volume fractions of the fiber and the matrix, respectively. and These are Young's modulus and shear modulus of the matrix, respectively. , , , All of these are engineering constants for single-layer plates.

5. The method for constructing a surrogate model for predicting uncertain failures in composite bolted connections according to claim 1, characterized in that, The specific implementation process of step S3 is as follows: S3.1: Using the Abaqus scripting interface, based on the geometric dimensions and positional relationships of each component in the composite material bolted connection, write a Python script to create each part and complete the assembly, and at the same time complete the following model creation steps; S3.2: Assign material properties to laminates, bolts, and test fixtures, including stiffness and strength parameters; S3.3: Assign element properties and use selection functions to divide the overlapping area into a fine radial mesh, while using a coarser mesh for the non-overlapping area. S3.4: Define contact pairs, set boundary conditions, and apply tensile displacement load steps; S3.5: Pass the address of the subroutine VUMAT described in step S2 on the local computer to the Python script, and use the ABAQUS / Explicit explicit solver to complete the parametric modeling.

6. The method for constructing a surrogate model for predicting uncertain failures in composite bolted connections according to claim 1, characterized in that, The specific implementation process of step S6 is as follows: S6.1: Generating a Normalized Space Based on Optimal Latin Hypercube Sampling Sampling points within ; in, The dimension of the sample; Design variables The One sampling point; Design variables for random uncertainty; Design variables for interval uncertainty; S6.2: Perform the following inverse transformation on the design variables of random uncertainty: ， in, Design variables for random uncertainty after inverse transformation; Design the cumulative probability distribution function of variables for random uncertainty; S6.3: Perform the following inverse transformation on the design variables for interval uncertainty: ， in, Design variables for the interval uncertainty after inverse transformation; For interval variables The upper bound of the value; interval variable The lower bound of the value; S6.4: After the above inverse transformation, the actual sampling points of the design variables in the original physical space are obtained. .

7. The method for constructing a surrogate model for predicting uncertain failures in composite bolted connections according to claim 1, characterized in that, The specific implementation process of step S7 is as follows: S7.1: The actual sampling points of the uncertain design variables described in step S6. According to the structural hierarchy, the parameters are divided into component-level micro-parameters and single-layer plate-level macro-parameters, as detailed below: ， in, These are the component-level micromaterial parameters, including fiber stiffness, fiber strength, fiber volume fraction, matrix stiffness, matrix strength, and matrix volume fraction. and These are the component-level micro-geometric parameters and the single-layer plate-level macro-geometric parameters, respectively. S7.2: Using the Mori-Tanaka model based on the homogenization method, the equivalent stiffness of the single-layer plate is obtained from the fiber stiffness, fiber volume fraction, matrix stiffness, and matrix volume fraction described in step S7.

1. The specific formula is as follows: ， ， ， ， ， ， ， ， ， ， in, , , , , This is the equivalent stiffness of a single-layer plate; For Mori-Tanaka-Eshelby bridge matrix elements, and Choose 1, 2, 3, 4, 5, 6; This represents the fiber volume fraction. This represents the volume fraction of the matrix. For fiber flexibility matrix elements, For matrix compliance matrix elements, and Options 1, 2, and 3 are acceptable. , , , and All are constants; S7.3: Using the formula proposed by Chamis, the equivalent strength of the single-layer board is obtained from the fiber stiffness, fiber strength, fiber volume fraction, matrix stiffness, matrix strength, and matrix volume fraction mentioned in step S7.

1. The specific formula is as follows: ， ， ， ， ， in, , , , , These are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength, and in-plane shear strength of a single-layer plate, respectively. , , , , These are the axial elastic modulus, transverse elastic modulus, shear modulus, and Poisson's ratio of the fiber, respectively. , These are the tensile and compressive strengths of the fiber, respectively. , These are the elastic modulus and shear modulus of the matrix, respectively. , , These are the tensile, compressive, and shear strengths of the matrix, respectively. This represents the fiber volume fraction. This represents the volume fraction of the matrix. S7.4: Combine the equivalent stiffness and strength parameters of the single-layer plate obtained in steps S7.2 and S7.3 with the macroscopic geometric parameters of the single-layer plate level, and use them as input parameters for the Python model script described in step S3.

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