A rapid prediction method for failure probability of composite structures subjected to dense perforation damage

Abstract

The present invention discloses a method for rapidly predicting the failure probability of a composite material structure under dense perforation damage, and relates to the technical field of failure mechanism and failure probability prediction of composite material structures. The method comprises the following steps: determining the material and dimensional information and damage parameter range of the composite material structure; determining a residual strength finite element simulation model and solution method; establishing a residual strength distribution parameter data set; using the data set to train a proxy model for predicting the residual strength distribution parameters; testing the prediction accuracy of the proxy model; determining the critical residual strength for structural failure; calculating the failure probability of the structure under given damage parameters; predicting the failure probability of the structure considering the uncertainty of the damage parameters; establishing a failure probability surface, etc. The method realizes the rapid prediction of the failure probability of a composite material structure under dense perforation damage mode through a proxy model method, and solves the problems of high failure data acquisition cost and difficulty in failure probability prediction in the prediction process of the failure probability of composite materials.

Description

Technical Field

[0001] The present invention belongs to the technical field of failure mechanism and failure probability prediction of composite material structures, and particularly relates to a method for quickly predicting the failure probability of a composite material structure under dense perforation damage. Background Art

[0002] Compared to conventional metals, composite materials offer advantages such as high specific strength, high specific stiffness, and enhanced design capabilities, and are currently being widely used in various fields. Composite materials, such as carbon fiber reinforced composite laminates, are extensively used in aircraft fuselages, wings, and control surfaces. However, research has shown that composite materials are more sensitive to impact damage than metals, making high-speed impact sources generated by explosives a significant threat to aircraft composite structures. Furthermore, the resulting structural damage and failure from violent processes such as explosions and impacts is often uncertain, necessitating the use of failure probabilities to assess these outcomes.

[0003] Regarding impact damage in composite materials, researchers worldwide have conducted extensive research on damage mechanisms such as energy absorption, delamination, and joint failure in composite laminates under impact loading. However, this research has primarily focused on the material scale and low-velocity impacts from a single or small number of impact sources. Failure of composite structures after high-velocity impacts from multiple impact sources is relatively rare. Furthermore, some researchers have chosen to equate impact damage to laminates with circular hole damage and use cohesive elements to predict the residual strength of impact-damaged laminates. Experimental research on the high-velocity impact and post-damage load-bearing capacity of composite structures is challenging and currently relies primarily on simulations. However, existing simulation methods are computationally inefficient and lack the computational efficiency required for large-scale and rapid computations. To balance computational efficiency and accuracy, some researchers have used surrogate models for high-precision simulations and prototype testing. Surrogate models are data-driven, resulting in results very close to the original model but at a lower cost. While research and engineering applications of surrogate models are relatively mature, there is no research on their application to predicting the failure probability of aerospace composite structures under dense perforation damage patterns. On the other hand, current research on probabilistically evaluating structural failure outcomes primarily focuses on low-cost testing, large data sets, and intuitively measurable test results. However, the failure mechanisms of composite aircraft structures subjected to dense impact sources are complex, and the cost of acquiring failure data is high, making it difficult to establish a failure probability model through extensive testing.

[0004] Based on this, the present invention proposes a rapid prediction method for the failure probability of composite material structures under dense perforation damage to solve the problems of high failure data acquisition cost and difficulty in failure probability prediction in the process of predicting the failure probability of aircraft composite material structures under dense perforation damage mode. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a method for rapidly predicting the failure probability of composite materials under dense perforation damage, which is used to solve the problems of high failure data acquisition cost and difficulty in predicting failure probability in the process of predicting the failure probability of aircraft composite materials under dense perforation damage.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A rapid prediction method for the failure probability of composite structures under dense perforation damage includes:

[0008] Step 1: Determine the composite material structure information and the range of dense perforation damage parameters;

[0009] Step 2: Based on the composite material structure information and dense perforation damage parameters determined in step 1, a composite structure residual strength simulation model and its solution method are established;

[0010] Step 3: Perform working condition simulation on the simulation model established in step 2 to obtain a data set of residual strength distribution parameters of the composite structure;

[0011] Step 4: Use the dataset of residual strength distribution parameters of the composite structure obtained in step 3 to train the surrogate model, and quickly predict the expected and standard deviation of the residual strength of the damaged structure based on the dense perforation damage parameters;

[0012] Step 5: Test the prediction accuracy of the proxy model trained in step 4. Once the prediction accuracy meets the usage requirements, the training of the proxy model is completed.

[0013] Step 6: Determine the critical residual strength of the composite structure for failure;

[0014] Step 7: Based on the critical residual strength, the proxy model obtained in step 5 is used to calculate the failure probability of the structure under given damage parameters;

[0015] Step 8: Based on the failure probability calculation method in step 7, the Monte Carlo method is used to predict the structural failure probability taking into account the uncertainty of damage parameters;

[0016] Step 9: Based on the results of the failure probability prediction in step 8, establish a failure probability surface.

[0017] In a preferred embodiment of the present invention, the composite material structure information in step 1 includes the structural form, material information and loading conditions of the composite material structure; the dense perforation damage parameters include at least the perforation diameter D and number of perforations N .

[0018] In a preferred embodiment of the present invention, the process of step 2 of establishing a composite structure residual strength simulation model and its solution method includes:

[0019] Step 2.1: Establish a simulation model of the residual strength of the composite structure;

[0020] Draw the structural geometry model of the composite material and import it into the simulation software. Complete the composite mesh division and layup settings based on the composite material type and layup method information of the structure. Finally, insert zero-thickness cohesive elements between each layer to simulate the interlayer connection of the composite material to obtain a lossless structural mesh model.

[0021] Step 2.2: Preset damage according to damage parameters;

[0022] According to the expected damage parameters, randomly placed perforation damage is preset on the mesh model of the damage-free structure established in step 2.1;

[0023] Step 2.3: Determine the material constitutive structure;

[0024] Step 2.4: Set up the residual strength simulation model solution;

[0025] Set the boundary constraints and loading conditions of the grid model, output the support reaction forces of the constraint boundaries of the grid model; and simulate and solve the grid model of the residual strength of the damaged composite structure.

[0026] In a preferred embodiment of the present invention, the process of performing working condition simulation on the simulation model in step 3 to obtain a data set of structural residual strength distribution parameters includes:

[0027] Step 3.1: Determine the simulation sampling conditions;

[0028] Determine n groups of simulation sampling conditions within the damage parameter value range U i ;

[0029] Where i=0, 1, 2, 3,…, n, i =0 represents the damage-free state of the structure;

[0030] Step 3.2: Fitting the residual intensity distribution parameters;

[0031] For each simulation sampling condition except non-destructive U i Perform residual strength simulation with random perforation positions m times to obtain the residual strength simulation results of the damaged composite structure S 1 i , S 2 i ,…, S mi , and fitting the expectation of the residual intensity distribution S μ i and standard deviation :

[0032] ;

[0033] ;

[0034] in, S μ i and They are respectively the simulation sampling conditions U i The mean and standard deviation of the residual intensity distribution under S j i Sampling conditions for simulation U i Simulation results of residual strength at random perforation positions for the jth time;

[0035] Step 3.3: Form a data set of structural residual strength distribution parameters;

[0036] Considering the uncertainty of the perforation position, the residual strength distribution parameters of the composite material structure after damage under each simulation sampling condition are obtained through step 3.2. , forming a data set of structural residual strength distribution parameters for training the proxy model.

[0037] In a preferred embodiment of the present invention, in step 4, in the process of training the proxy model using the data set of the structural residual strength distribution parameters, a radial basis function neural network model is used as the proxy model for training. In the radial basis function neural network model, the mapping relationship from input to output of the neural network is determined by the Gaussian formula, as shown in the following formula: ;

[0038] in, X= [ D, N ,…] T is the perforation damage parameter, which is the input of the model; Y =[ y 1, y 2] T =[ S μ , σ] T is the residual intensity distribution parameter, which is the output of the model; o is the number of hidden nodes; w ik is the weight coefficient; is the basis function; Ck For the k The center of the node; d k For the k The base width parameter of each node; is the Euclidean distance between the input vector and the node center.

[0039] In a preferred embodiment of the present invention, the process of step 5 of testing the prediction accuracy of the proxy model includes:

[0040] Take test sample points outside the training data set to test the prediction accuracy of the proxy model. When the prediction accuracy meets the usage requirements, the training of the proxy model is completed. Otherwise, increase the training sampling conditions and further train the model.

[0041] In a preferred embodiment of the present invention, in the process of determining the critical residual strength of the structure failure in step 6, the structural non-destructive strength S 2 / 3 of 0 is used as the critical strength for failure after structural damage S limit .

[0042] In a preferred embodiment of the present invention, when calculating the failure probability of the structure under given damage parameters using the proxy model in step 7, the distribution parameters of the residual strength are quickly predicted according to the given damage parameters. Then, according to the normal probability distribution, the residual strength of the damaged structure is lower than the critical strength. S limit The probability of failure of the structure under given damage parameters is calculated. P k / h for: in, P k / h is the failure probability of the structure under given damage parameters, S limit is the critical strength of the structure after failure due to damage, S μ and are the expected value and standard deviation of the residual strength distribution of the structure under given damage parameters.

[0043] In a preferred embodiment of the present invention, step 8, based on the failure probability calculation method of step 7, combines the Monte Carlo method to predict the structural failure probability considering the uncertainty of the damage parameters, including:

[0044] Step 8.1: Determine the distribution of perforation damage parameters;

[0045] Step 8.2: Determine the expected perforation injury parameters;

[0046] Estimate the expected damage parameters of the structure based on the explosive information and intersection conditions ( D e , N e ,…); and combined with the distribution form of damage parameters, determine the probability distribution F of the actual damage parameters ( D e , N e ,…);

[0047] Step 8.3: Extract actual perforation damage parameters;

[0048] The Monte Carlo method is used to perform the i-th sampling in the probability distribution of the actual damage parameters to obtain the i-th group of actual damage parameters ( D i , N i ,…);

[0049] Step 8.4: Predict the residual strength distribution parameters of the structure under actual damage parameters;

[0050] The actual damage parameters of group i ( D i , N i ,…) Input the proxy model to obtain the corresponding structural residual strength distribution parameter prediction results ;

[0051] Step 8.5: Calculate the failure probability of the structure under actual damage parameters;

[0052] The prediction results of the residual strength distribution parameters of the structure under the actual damage parameters of the i-th group are Substituting into the formula: The failure probability prediction value of the structure under the actual damage parameters of group i is calculated P k / h i ;

[0053] in, P k / h i is the failure probability of the structure under the actual damage parameters of the i-th group, S limit is the critical strength of the structure after failure due to damage, S μ i and are the expected value and standard deviation of the residual strength distribution of the structure under the actual damage parameters of group i;

[0054] Step 8.6: Calculate the failure probability of the structure under the expected perforation damage parameters;

[0055] Repeat steps 8.3 to 8.5 w times, and then w Failure probability prediction value of the structure under the actual damage parameters P k / h i Average value As the expected damage parameter, the structural failure probability prediction result considering the uncertainty of the damage parameter is obtained.

[0056] In a preferred embodiment of the present invention, the process of establishing the failure probability surface in step 9 includes:

[0057] Step 9.1: Sampling of expected damage parameters;

[0058] Within the range of damage parameter values, sampling points are set densely and evenly;

[0059] Step 9.2: Failure probability prediction;

[0060] According to step 8, the failure probability prediction of each sampling point is completed;

[0061] Step 9.3: Interpolate to establish the failure probability surface;

[0062] According to the failure probability prediction results of each sampling point, the failure probability surface is finally established by interpolation.

[0063] Compared with the existing technology, the present invention provides a rapid prediction method for the failure probability of composite materials under dense perforation damage, which has the following beneficial effects:

[0064] The present invention uses a proxy model method to achieve rapid prediction of the failure probability of aircraft composite structures under dense perforation damage patterns, which can provide a reference for weapon equipment design and mission decision-making, and save engineering simulation analysis and testing costs.

[0065] The present invention takes into account both the uncertainty of the distribution of perforation positions on the structure caused by dense impact sources and the uncertainty of the perforation damage parameters themselves, thus refining the study of the structural failure probability and reasonably characterizing the impact of the uncertainty of the damage process on the structural failure probability.

[0066] The composite material progressive damage finite element simulation method and failure probability calculation method used in the present invention can be applied to damage and failure problems of various composite material structures. Compared with failure prediction engineering algorithms that are only applicable to specific structural forms, the scope of application of the present invention is wider.

[0067] The present invention establishes component function failure criteria by using a proxy model method, which can greatly reduce costs and provide basic data for failure assessment of complex equipment systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a diagram showing the architecture of a method for rapidly predicting failure probability of composite material structures under dense perforation damage mode of the present invention;

[0069] Figure 2 A schematic diagram of the geometric shape and dimensions of a typical carbon fiber reinforced composite (CFRP) stiffened panel test piece in an embodiment of the present invention;

[0070] Figure 3 Schematic diagram of a finite element simulation model of the residual strength of a stiffened plate established in an embodiment of the present invention;

[0071] Figure 4 A comparison chart of the shear residual strength simulation and verification test of a damaged composite reinforced plate in an embodiment of the present invention;

[0072] Figure 5 Schematic diagram of the structure of the radial basis function (RBF) neural network model of the present invention;

[0073] Figure 6 The response surface of the rapid prediction proxy model for residual strength distribution of composite material stiffened plates finally established in the embodiment of the present invention;

[0074] Figure 7 This is a flowchart of the structural failure probability prediction process considering the uncertainty of perforation damage parameters in the present invention;

[0075] Figure 8 This is a schematic diagram of a failure probability surface established by interpolation in an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0077] See also Figures 1-8 As shown in FIG, a method for rapidly predicting the failure probability of a composite structure under dense perforation damage is described. This embodiment is verified using a carbon fiber reinforced composite (CFRP) stiffened wall panel as a test piece. The specific process includes:

[0078] Step 1: Determine the composite material structure information and the range of dense perforation damage parameters;

[0079] According to the structural characteristics of typical composite material stiffened panels on aircraft wings, this embodiment designs carbon fiber reinforced composite (CFRP) stiffened panels as test pieces. The test piece structure is as follows: Figure 2 The test piece is mainly composed of three parts: face plate, ribs and clamping section. The material of the reinforced wall panel is T300 / QY8911. Each part of the wall panel is made of overlapping unidirectional tape. The face plate and ribs are laid at an angle of [45 / 0 / -45 / 90]. 7s, the thickness of single layer molding is 0.125mm. This example selects the in-plane four-side shear as the load form of the reinforced plate to study the change of shear residual strength of the composite reinforced plate under the dense perforation damage mode. This example focuses on the number of perforations N and perforation diameter D Two perforation damage parameters, among which the number of perforations N The research range is 5 to 100, and the perforation diameter D The research range is 10 to 30 mm. The information of composite material structure includes its structural form, material information and loading conditions and other parameters.

[0080] It should be noted that the structural form, material information and loading conditions of the composite material structure in this step, as well as the type and value range of the expected damage parameter, can all be adjusted according to actual engineering needs.

[0081] Step 2: Based on the composite material structure information and dense perforation damage parameters determined in step 1, a composite structure residual strength simulation model and its solution method are established;

[0082] Step 2.1: Establish a simulation model of the residual strength of the composite structure;

[0083] Step 2.1.1: Draw a geometric model of the structure in CATIA 3D modeling software according to its shape and geometric dimensions. In this embodiment, specifically: draw a geometric model of the structure in CATIA 3D modeling software according to the shape and geometric dimensions of the stiffened plate of the test piece;

[0084] Step 2.1.2: Then import the structural geometry model into ABAQUS simulation software, and complete the composite material mesh division and layup setting based on the structure's composite material type and layup method;

[0085] Step 2.1.3: Finally, insert zero-thickness interlayer cohesive elements between each layer to simulate the interlayer connection of the composite material and obtain a lossless structural mesh model;

[0086] Step 2.2: Preset damage according to damage parameters;

[0087] Number of perforations according to expected damage parameters N and perforation diameter D , through Python secondary development, preset random perforation damage on the mesh model of the lossless structure established in step 2.1;

[0088] Among them, the layer diameter of the interlayer cohesive unit is 1.5 times the perforation diameter;

[0089] Step 2.3: Determine the material constitutive structure;

[0090] The three-dimensional Hashin criterion and asymptotic damage constitutive method were used to simulate the initiation and evolution of damage within composite materials. For interlaminar damage, a traction-separation cohesive model was employed, with a quadratic nominal stress criterion used as the damage initiation criterion. Under a mixed stress model, the energy-based Benzeggagh-Kenane fracture criterion was applied to describe the damage evolution of cohesive elements. The material constitutive model was implemented in ABAQUS using the VUMAT subroutine. The corresponding material parameters are shown in Table 1.

[0091] Table 1: CFRP and interlaminar cohesion material parameters

[0092] Step 2.4: Set up the residual strength simulation model solution;

[0093] The model boundary constraints and loading conditions are set according to the structural bearing characteristics; the support reaction forces of the model constraint boundaries are output; and the Dynamic-Explicit analysis step is used to simulate and solve the mesh model of the residual strength of the damaged composite structure.

[0094] In this embodiment, the following steps are performed: loading reference points are set on the four sides of the wall panel to couple with the nodes around the mounting holes of the clamping section, and then a smooth displacement load is applied at the reference points to simulate shear loading on the four sides; the support reaction curve of the loading reference point is output; the residual strength simulation model is solved using the Dynamic-Explicit analysis step, the simulation duration is set to 1s, and the minimum time step is controlled to 2e by setting automatic mass scaling. -5 s; The final established finite element simulation model of the residual strength of the stiffened plate is as follows Figure 3 shown.

[0095] Step 2.5: Test and verify the accuracy of the simulation;

[0096] The test piece was processed and carried out a ground static explosion test. Then, the shear residual strength simulation and loading test were carried out on the stiffened plate test piece after the impact of the dense impact source. The consistency between the simulation and the test was verified by comparison. The results are as follows: Figure 4 As shown, from Figure 4 It can be seen that the relative error between the residual strength obtained by simulation and the experimental results is 7.7%.

[0097] Step 3: Perform finite element simulation on the simulation model established in step 2 to obtain a data set of structural residual strength distribution parameters;

[0098] Step 3.1: Determine the simulation sampling conditions;

[0099] According to the computational cost requirements, select the appropriate DOE (experimental design) method to determine n groups of simulation sampling conditions within the damage parameter value range. Ui ( D i , N i ,…)(i=0, 1, 2, 3,…, n), where i=0 represents the lossless state of the structure.

[0100] In this embodiment, 23 groups of simulation sampling conditions are determined within the range of damage parameter values according to the full factorial design (FFD) method. U i ( D i , N i )(i=0, 1, 2, 3,…, 22), where i=0 represents the lossless state of the structure;

[0101] Step 3.2: Fitting the residual intensity distribution parameters;

[0102] For each simulation sampling condition U i ( D i , N i ,…) to perform residual strength simulation with random perforation positions for m times and obtain the residual strength results of the damaged composite structure ( S 1 i , S 2 i ,…, S m i ), and fit the expectation of the residual intensity distribution according to the following formula S μ i and standard deviation :

[0103] ;

[0104] ;

[0105] in, S μ i and They are respectively the simulation sampling conditions U i The mean and standard deviation of the residual intensity distribution under S j i Sampling conditions for simulation U i Simulation results of residual strength at random perforation locations for the jth time.

[0106] In this embodiment, specifically: for each simulation sampling condition except non-destructive U i ( D i , N i ) to conduct 5 random residual strength simulations of the perforation positions and obtain the shear residual strength simulation results of the damaged composite reinforced plate ( S 1 i , S 2 i , S 3 i , S 4 i , S 5 i ), and fit the expectation of the residual intensity distribution according to the following formula S μ i and standard deviation :

[0107] ;

[0108] ;

[0109] in, S μ i and They are respectively the simulation sampling conditions U i The mean and standard deviation of the residual intensity distribution under S j i Sampling conditions for simulation U i Simulation results of residual strength at random perforation locations for the jth time.

[0110] Step 3.3: Form a data set of structural residual strength distribution parameters;

[0111] Considering the uncertainty of the perforation position, the residual strength distribution parameters of the composite material structure after damage under each simulation sampling condition are obtained in step 3.2. (i=0, 1, 2, 3,…, n), forming a data set of structural residual strength distribution parameters for training the proxy model.

[0112] In this embodiment, the uncertainty of the perforation position is taken into consideration, and the residual strength distribution parameters of the composite stiffened plate after damage under each simulation sampling condition are obtained. (i=0, 1, 2, 3,…, 22), forming the residual intensity distribution parameter dataset used to train the proxy model as shown in Table 2;

[0113] Table 2: Dataset of shear residual strength distribution of damaged composite stiffened panels

[0114] Step 4: Use the dataset of residual strength distribution parameters of the composite structure obtained in step 3 to train the surrogate model, and quickly predict the expected and standard deviation of the residual strength of the damaged structure based on the dense perforation damage parameters;

[0115] The radial basis function (RBF) neural network model is selected as the proxy model. The structure of the RBF neural network model is as follows: Figure 5 As shown in Figure 3, the residual strength distribution parameter data set generated by simulation in step 3 is used to train the RBF neural network model to achieve rapid prediction of the residual strength distribution of composite reinforced panels under dense perforation damage mode. In the RBF neural network model, the mapping relationship from input to output of the neural network can be determined by the Gaussian formula, as shown in the following formula: ;

[0116] in, X= [ D, N ,…] T is the perforation damage parameter, which is the input of the model; Y =[ y 1, y 2] T =[ S μ , σ] T is the residual intensity distribution parameter, which is the output of the model; o is the number of hidden nodes; w ik is the weight coefficient; is the basis function; C k For the k The center of the node; d k For the k The base width parameter of each node; is the Euclidean distance between the input vector and the node center.

[0117] Step 5: Test the prediction accuracy of the proxy model trained in step 4. Once the prediction accuracy meets the usage requirements, the training of the proxy model is completed.

[0118] Take test sample points outside the training data set to test the prediction accuracy of the proxy model. When the prediction accuracy meets the usage requirements, the training of the proxy model is completed. Otherwise, increase the training sampling conditions and further train the model to improve the prediction accuracy.

[0119] Among them, the training data set and test sample points are both taken from the data set of structural residual strength distribution parameters, and the test sample points do not participate in the training of the proxy model.

[0120] Specifically in this embodiment: in addition to the training data set, a test sample point is selected ( D =25mm, N =25), the shear residual strength of the stiffened plate under 5 different perforation position distributions was obtained by simulation and the distribution parameters N (793.6, 72.0 2 ), compared with the proxy model's prediction results of the residual intensity distribution parameters of the test sample points N (728.7, 67.5 2 ) and the distribution parameters obtained based on finite element simulation, the relative errors of the proxy model in predicting the expected and standard deviation of the residual strength are 8.2% and 6.3% respectively. The prediction accuracy meets the use requirements, and the training of the proxy model is completed.

[0121] Step 6: Determine the critical residual strength of the composite structure for failure;

[0122] According to aircraft structure design theory, the design safety factor of aircraft structural parts is usually 1.5, so the structural non-destructive strength S 2 / 3 of 0 is used as the critical strength for failure after structural damage S limit , where lossless strength S 0 is obtained through the residual strength simulation of the lossless structure.

[0123] In this embodiment, according to the aircraft structure design theory, the design safety factor of aircraft structural parts is usually 1.5, so the stiffened plate is non-destructive shear strength S 0 = 2 / 3 of 1401.1KN is taken as the critical residual strength of the damaged stiffened plate S limit =934.1KN. The final established proxy model response surface for rapid prediction of residual strength distribution of composite stiffened panels is shown in the attached figure. Figure 6 shown. Figure 6 The response surface of three typical values for residual strength prediction of damaged stiffened panels is shown in the figure. S μ 、 S μ + 2× σ and S μ - 2× σ ,in S μ and σare the expected value and standard deviation of the residual strength distribution respectively. The critical failure section of the response surface contains three response surfaces and the critical failure strength S limit =934.1KN plane, the plane is divided into four areas, from bottom to top are the extremely low probability failure areas (blue, P k / h <2.275%), low probability failure area (green, 2.275%< P k / h <50%), high probability failure area (light red, 50%< P k / h <97.725%) and the high probability failure area (dark red, 97.725%< P k / h The critical damage parameters corresponding to the four types of failure regions can be determined based on the critical failure cross-section. For example, when the number of perforations is 30, the perforation diameter must be at least 18.7 mm to cause a high probability of shear failure in the stiffened plate.

[0124] Step 7: Based on the critical residual strength, the proxy model obtained in step 5 is used to calculate the failure probability of the structure under given damage parameters;

[0125] Using the proxy model trained in step 5, the distribution parameters of the residual strength can be quickly predicted based on the given damage parameters. Then, according to the normal probability distribution, the residual strength of the damaged structure is lower than the critical strength. S limit The probability of failure of the structure under given damage parameters is calculated. P k / h for: ;

[0126] in, P k / h is the failure probability of the structure under given damage parameters, S limit is the critical strength of the structure after failure due to damage, S μ and s are the expected value and standard deviation of the residual strength distribution of the structure under given damage parameters, respectively.

[0127] In this embodiment, the trained proxy model can be used to quickly predict the distribution parameters of the residual strength according to the given damage parameters. Then, according to the normal probability distribution, the residual strength of the damaged structure is lower than the critical strength. S limit =934.1KN probability is calculated. For example, the damage parameter ( D =15mm,N =30), the prediction results of the proxy model for the residual intensity distribution parameters are ( S μ =949.9, =74.7), and then calculate the failure probability of the stiffened plate under this damage parameter P k / h =41.6%, the calculation process is as follows: .

[0128] Step 8: Based on the failure probability calculation method in step 7, the Monte Carlo method is used to predict the structural failure probability taking into account the uncertainty of damage parameters;

[0129] Based on the proxy model established in step 5, the Monte Carlo random sampling method is used to predict the structural failure probability considering the uncertainty of damage parameters. Figure 7 As shown, the specific process is as follows:

[0130] Step 8.1: Determine the distribution of perforation damage parameters;

[0131] According to the explosive information and intersection conditions, the appropriate distribution form F of the perforation damage parameters of the dense impact source is selected ( D , N ,…), which is used to characterize the uncertainty in the explosion, shock source propagation and structural response to the shock.

[0132] In this embodiment, the following truncated normal distribution is selected to describe the uncertainty of the damage parameters: perforation diameter D Obeying normal distribution N ( D e, σ D 2 , D min , D max ),in: D e is the expected value of the perforation diameter, the standard deviation of the perforation diameter σ D = 0.05 D e , the lower limit of the distribution D min = 0.85 D e , the upper limit of the distribution D max = 1.15 D e ; Number of perforations N Obeying normal distribution N (N e, σ N 2 , N min , N max ), N e is the expected value of the number of perforations, the standard deviation of the number of perforations σ N = 0.05 N e , the lower limit of the distribution N min =0.85 N e , the upper limit of the distribution N max = 1.15 N e .

[0133] Step 8.2: Determine the expected perforation injury parameters;

[0134] Estimate expected perforation damage parameters based on explosive information and explosion conditions ( D e , N e ,…), and combined with the distribution form of perforation damage parameters, determine the probability distribution F of the actual perforation damage parameters ( D e , N e ,…).

[0135] In this embodiment, the specific method is: using the expected damage parameter ( D e =15mm, N e =30) as an example, considering the uncertainty of damage parameters, the failure probability prediction process based on the surrogate model and Monte Carlo method is demonstrated.

[0136] Step 8.3: Extract actual perforation damage parameters;

[0137] The Monte Carlo method is used to perform the i-th sampling in the probability distribution of the actual damage parameters to obtain the i-th group of actual damage parameters ( D i , N i );

[0138] Step 8.4: Predict the residual strength distribution parameters of the structure under actual perforation damage parameters;

[0139] The actual damage parameters of group i ( D i , N i ) Input the proxy model to obtain the corresponding structural residual strength distribution parameter prediction results ;

[0140] Step 8.5: Calculate the failure probability of the structure under the actual perforation damage parameters;

[0141] The prediction results of the residual strength distribution parameters of the structure under the actual damage parameters of the i-th group are Substituting into the formula: The failure probability prediction value of the structure under the actual damage parameters of group i is calculated P k / h i ;

[0142] in, P k / h i is the failure probability of the structure under the actual damage parameters of the i-th group, S limit is the critical strength of the structure after failure due to damage, S μ i and are the expected value and standard deviation of the residual strength distribution of the structure under the actual damage parameters of group i;

[0143] Step 8.6: Calculate the failure probability of the structure under the expected perforation damage parameters;

[0144] Repeat steps 8.3 to 8.5 w times, and then w Failure probability prediction value of the structure under the actual damage parameters P k / h i (i=1,2,…, w ) As the expected damage parameter ( D e , N e ,…), the structural failure probability prediction results considering the uncertainty of damage parameters are obtained.

[0145] In this embodiment, the specific steps are as follows: Steps 8.3 to 8.5 are repeated 10 times (for the sake of demonstration, the number of repeated samplings can be increased in actual applications), and then the failure probability prediction values of the structures under the 10 sets of actual damage parameters are calculated. P k / h i Average value of (i=1,2,…,10) As the expected damage parameter ( D e =15mm, N e =30), the structural failure probability prediction results considering the uncertainty of damage parameters are shown in Table 3.

[0146] Table 3: Failure probability calculation process considering damage parameter uncertainty (example)

[0147] Step 9: Based on the failure probability prediction method in step 8, establish the failure probability surface;

[0148] In order to facilitate the analysis of the changing trend of the structural failure probability, this step further establishes a failure probability surface. The specific process is as follows:

[0149] Step 9.1: Sampling of expected damage parameters;

[0150] Within the range of damage parameter values, 10,000 sampling points were densely and evenly set;

[0151] Step 9.2: Failure probability prediction;

[0152] According to step 8, the failure probability prediction of each sampling point is completed;

[0153] Step 9.3: Interpolate to establish the failure probability surface;

[0154] According to the failure probability prediction results of each sampling point, the failure probability surface is finally established through interpolation. Figure 8 As shown, from Figure 8 It can be seen from the figure that with the increase of perforation diameter and number of perforations, the failure probability of the composite stiffened plate increases monotonically from 0 to 1, and the failure probability increases faster with the number of perforations when the perforation diameter is large.

[0155] Therefore, combined with the above results, it can be seen that the rapid prediction method for failure probability of composite material structures under dense perforation damage proposed in this embodiment has the following advantages:

[0156] 1. The composite structure failure probability prediction method based on residual strength finite element analysis and surrogate model methods proposed in this embodiment can realize failure assessment and failure probability prediction of aircraft composite structures under dense perforation damage patterns, taking into account the uncertainty in the damage process. It can provide a reference for weapon equipment design and mission decision-making, and save engineering simulation analysis and testing costs.

[0157] 2. The prediction method proposed in this example considers both the uncertainty of the perforation location distribution on the impact source structure and the uncertainty of the dense perforation damage parameters themselves. This refines the study of the structural failure probability and reasonably characterizes the impact of the uncertainty of the damage process on the structural failure probability.

[0158] 3. The composite material progressive damage finite element simulation method and failure probability calculation method used in this method can be applied to damage and failure problems of various composite materials structures. Compared with failure assessment engineering algorithms that are only applicable to specific structural forms, this embodiment has a wider range of applications.

[0159] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A rapid prediction method for the failure probability of composite structures under dense perforation damage, characterized by: include: Step 1: Determine the composite material structure information and the range of dense perforation damage parameters; Step 2: Based on the composite material structure information and dense perforation damage parameters determined in step 1, a composite structure residual strength simulation model and its solution method are established; Step 3: Perform working condition simulation on the simulation model established in step 2 to obtain a data set of residual strength distribution parameters of the composite structure; Step 4: Use the dataset of residual strength distribution parameters of the composite structure obtained in step 3 to train the surrogate model, and quickly predict the expected and standard deviation of the residual strength of the damaged structure based on the dense perforation damage parameters; Step 5: Test the prediction accuracy of the proxy model trained in step 4. Once the prediction accuracy meets the usage requirements, the training of the proxy model is completed. Step 6: Determine the critical residual strength of the composite structure for failure; Step 7: Based on the critical residual strength, the proxy model obtained in step 5 is used to calculate the failure probability of the structure under given damage parameters; Step 8: Based on the failure probability calculation method in step 7, the Monte Carlo method is used to predict the structural failure probability considering the uncertainty of damage parameters; Step 8: Based on the failure probability calculation method in step 7, the process of predicting the structural failure probability considering the uncertainty of damage parameters by combining the Monte Carlo method includes: Step 8.1: Determine the distribution of perforation damage parameters; Step 8.2: Determine the expected perforation injury parameters; Estimate the expected damage parameters (D) of the structure based on the explosive information and intersection conditions e ,N e ,…); and combined with the distribution form of damage parameters, determine the probability distribution F(D e ,N e ,…); Step 8.3: Extract actual perforation damage parameters; The Monte Carlo method is used to perform the i-th sampling in the probability distribution of the actual damage parameters to obtain the i-th group of actual damage parameters (D i ,N i ,…); Step 8.4: Predict the residual strength distribution parameters of the structure under actual damage parameters; The actual damage parameter of group i (D i ,N i ,…) input the proxy model and obtain the corresponding structural residual strength distribution parameter prediction results (S μ i ,σ i ); Step 8.5: Calculate the failure probability of the structure under actual damage parameters; The predicted results of the residual strength distribution parameters of the structure under the actual damage parameters of group i (S μ i ,σ i ) into the formula: The predicted failure probability value P of the structure under the actual damage parameters of the i-th group is calculated. k / h i ; Among them, P k / h i is the failure probability of the structure under the actual damage parameters of the i-th group, S limit is the critical strength of the structure after failure, S μ i and σ i are the expected value and standard deviation of the residual strength distribution of the structure under the actual damage parameters of group i; Step 8.6: Calculate the failure probability of the structure under the expected perforation damage parameters; Repeat steps 8.3 to 8.5 w times, and then calculate the predicted failure probability P of the structure under w sets of actual damage parameters. k / h i Average value As the expected damage parameter, the structural failure probability prediction result considering the uncertainty of the damage parameter is obtained. Step 9: Based on the results of the failure probability prediction in step 8, establish a failure probability surface.

2. The method for rapidly predicting the failure probability of a composite material structure under dense perforation damage according to claim 1, characterized in that: The composite material structure information in step 1 includes the structural form, material information and loading conditions of the composite material structure; the dense perforation damage parameters include at least the perforation diameter D and the number of perforations N.

3. The method for rapidly predicting the failure probability of a composite material structure under dense perforation damage according to claim 1, characterized in that: Step 2: The process of establishing the composite structure residual strength simulation model and its solution method includes: Step 2.1: Establish a simulation model of the residual strength of the composite structure; Draw the structural geometry model of the composite material and import it into the simulation software. Complete the composite mesh division and layup settings based on the composite material type and layup method information of the structure. Finally, insert zero-thickness cohesive elements between each layer to simulate the interlayer connection of the composite material to obtain a lossless structural mesh model. Step 2.2: Preset damage according to damage parameters; According to the expected damage parameters, randomly set perforation damage on the mesh model of the damage-free structure established in step 2.1; Step 2.3: Determine the material constitutive structure; Step 2.4: Set up the residual strength simulation model solution; Set the boundary constraints and loading conditions of the grid model, output the support reaction forces of the constraint boundaries of the grid model; and simulate and solve the grid model of the residual strength of the damaged composite structure.

4. The method for rapidly predicting the failure probability of a composite material structure under dense perforation damage according to claim 2, characterized in that: Step 3: The process of performing working condition simulation on the simulation model to obtain a data set of structural residual strength distribution parameters includes: Step 3.1: Determine the simulation sampling conditions; Determine n groups of simulation sampling conditions U within the range of damage parameter values i ; Where i = 0, 1, 2, 3, ..., n, i = 0 represents the lossless state of the structure; Step 3.2: Fitting the residual intensity distribution parameters; For each simulation sampling condition U except non-destructive i Perform residual strength simulation with random perforation positions m times to obtain the residual strength simulation result S1 of the damaged composite structure i ,S2 i ,…,S m i , and fitting the expected S of the residual intensity distribution μ i and standard deviation σ i : Among them, S μ i and σ i They are respectively the simulation sampling conditions U i The mean and standard deviation of the residual intensity distribution under j i The simulation sampling condition U i Simulation results of residual strength at random perforation positions for the jth time; Step 3.3: Form a data set of structural residual strength distribution parameters; Considering the uncertainty of the perforation position, the residual strength distribution parameters (S μ i ,σ i ), forming a data set of structural residual strength distribution parameters for training the proxy model.

5. The method for rapidly predicting the failure probability of a composite material structure under dense perforation damage according to claim 4, characterized in that: In step 4, in the process of training the proxy model using the data set of the structural residual strength distribution parameters, the radial basis neural network model is used as the proxy model for training. In the radial basis neural network model, the mapping relationship from input to output of the neural network is determined by the Gaussian formula, as shown in the following formula: Where X = [D, N, …] T is the perforation damage parameter, which is the input of the model; Y = [y1, y2] T =[S μ ,σ] T is the residual intensity distribution parameter, which is the output of the model; o is the number of hidden nodes; w ik is the weight coefficient; is the basis function; C k is the center of the kth node; d k is the base width parameter of the kth node; ||XC k || is the Euclidean distance between the input vector and the node center.

6. The method for rapidly predicting failure probability of composite material structures under dense perforation damage according to claim 1, characterized in that: Step 5: The process of testing the prediction accuracy of the surrogate model includes: Take test sample points outside the training data set to test the prediction accuracy of the proxy model. When the prediction accuracy meets the usage requirements, the training of the proxy model is completed. Otherwise, increase the training sampling conditions and further train the model.

7. The method for rapidly predicting failure probability of composite material structures under dense perforation damage according to claim 5, characterized in that: In the process of determining the critical residual strength of the structure failure in step 6, 2 / 3 of the intact strength S0 of the structure is used as the critical strength S0 of the structure after damage. limit .

8. The method for rapidly predicting the failure probability of a composite material structure under dense perforation damage according to claim 7, characterized in that: Step 7: When using the surrogate model to calculate the failure probability of the structure under given damage parameters, the distribution parameter (S μ ,σ), and then the residual strength of the damaged structure is lower than the critical strength S according to the normal probability distribution. limit The probability of failure of the structure under given damage parameters is calculated. k / h for: Among them, P k / h is the failure probability of the structure under given damage parameters, S limit is the critical strength of the structure after failure, S μ and σ are the expected value and standard deviation of the residual strength distribution of the structure under given damage parameters, respectively.

9. The method for rapidly predicting the failure probability of a composite material structure under dense perforation damage according to claim 1, characterized in that: Step 9: The process of establishing the failure probability surface includes: Step 9.1: Sampling of expected damage parameters; Within the range of damage parameter values, sampling points are set densely and evenly; Step 9.2: Failure probability prediction; According to step 8, the failure probability prediction of each sampling point is completed; Step 9.3: Interpolate to establish the failure probability surface; According to the failure probability prediction results of each sampling point, the failure probability surface is finally established by interpolation.

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