A method for solving V-notch stress intensity factor based on neural network

Abstract

The present invention provides a method for solving the stress intensity factor of a V-notch based on a neural network, comprising the following steps: step 1, performing adaptive grid division according to the geometric features of a V-notch specimen; step 2, obtaining Gaussian integral sample points of a V-notch structure according to the adaptive grid; step 3, performing parameter scaling on Gaussian sample points in the domain, boundary Gaussian sample points, material parameters and external loads; step 4, constructing a neural network for predicting displacement components in two directions; step 5, transforming the neural network according to the displacement boundary so that the neural network satisfies the hard boundary condition; step 6, calculating the loss function of the neural network; step 7, using the adjusted neural network to predict the displacement field and stress field at the crack tip. The present invention overcomes the problem that the neural network model in the notch stress concentration area is difficult to accurately solve, and can directly predict the notch tip stress intensity factor under different notch angles.

Description

Technical Field

[0001] The invention relates to the technical field of material fatigue strength, and mainly relates to a method for solving a V-notch stress intensity factor based on a neural network. Background Art

[0002] V-notch is a common structural defect that has a significant impact on the strength and durability of materials. By studying the behavior of V-notch structures under stress, engineers can better understand the performance of materials in stress concentration areas, thereby guiding the design and improvement of engineering structures.

[0003] In the field of computational solid mechanics, many scholars use a large amount of experimental data or simulation data to build data-driven models to describe complex physical processes. Although data-driven methods have achieved some initial success, most machine learning methods are currently unable to extract interpretable information and knowledge from data. Purely data-driven models can adapt to observed data, but due to extrapolation and observation bias, the predictions of pure data-driven models may be physically inconsistent or unreliable, which leads to defects in the generalization ability of trained neural networks. In fact, there is a lot of prior knowledge in the modeling of many physical systems, such as basic physical laws, proven rules, and domain expertise. Encoding this structured information into the learning algorithm can enhance the algorithm's understanding of the data and guide the algorithm to automatically develop towards the correct solution. By embedding physical knowledge into neural networks, neural networks can show good generalization performance even when only a small amount of training data is available. Representative research work in this area is the series of physics-induced neural network work. Recently, physics-induced neural networks (PINN) have also achieved a series of research results in computational solid mechanics problems.

[0004] Although PINN has made many advances in the field of computational solid mechanics, most of the work has focused on solving linear elastic mechanics problems without defects, and has not yet involved the solution of the V-notch structure type. The V-notch is a common structural defect that has an important impact on the strength and durability of the material. By studying the behavior of the V-notch structure under stress, engineers can better understand the performance of the material in the stress concentration area, thereby guiding the design and improvement of engineering structures. Compared with conventional linear elastic problems, the V-shaped structure has a stress concentration area at the tip of the notch, and its stress gradient shows a strong nonlinear change. This particularity makes it difficult for the existing PINN to adapt to the solution of this problem. Therefore, it is very necessary to develop a suitable stress intensity factor rapid evaluation method for the V-notch structure using physical information neural network technology. Summary of the invention

[0005] The purpose of the invention is to construct a V-notch stress intensity factor solving method based on a neural network for a linear elastic V-notch structure.

[0006] Specifically, the present invention proposes a method for solving a V-notch stress intensity factor based on a neural network, and the method for solving a V-notch stress intensity factor based on a neural network comprises the following steps:

[0007] Step 1, adaptive meshing is performed according to the geometric characteristics of the V-notch specimen;

[0008] Step 2, obtaining Gaussian integral sample points of the V-notch structure according to the adaptive grid;

[0009] Gaussian integral sample points include Gaussian sample points within the domain and Gaussian sample points at the boundary;

[0010] Step 3, parameter scaling of Gaussian sample points within the domain, boundary Gaussian sample points, material parameters and external loads;

[0011] Step 4, construct a neural network to predict the displacement components in two directions;

[0012] Step 5, transforming the neural network according to the displacement boundary so that the neural network meets the hard boundary condition;

[0013] Step 6, calculate the loss function of the neural network;

[0014] Step 7: Use the adjusted neural network to predict the displacement field and stress field at the crack tip.

[0015] Furthermore, in step 2, for a V-notch structure with a fixed opening angle;

[0016] In step 3, the parameter scaling includes:

[0017]

[0018] Among them, X represents the coordinates of the sample point, u represents the displacement field, λ is the first Lame constant, which represents the compressibility of the material, μ is the second Lame constant, which represents the shear modulus of the material, and t is the external load. Indicates the parameters after scaling; c This is usually the maximum value of this parameter within the V-notch domain; the scaled energy is shown below:

[0019]

[0020] Among them, n1 is the number of sample points in the domain, i is the number of Gaussian sample points in the domain, j is the number of Gaussian sample points at the boundary, ω i and ω j is the Gaussian weight, εxx is the lateral normal strain, ε yy is the longitudinal normal strain, ε xy is the shear strain, σ xx is the transverse normal stress, σ yy is the longitudinal normal stress, σ xy is the shear stress, and It is the lateral traction and longitudinal traction.

[0021] Furthermore, in step 5, the boundary condition of the V-notch structure is:

[0022]

[0023] Where u(X) represents the displacement field, represents the prescribed displacement, t(X) is the traction force, Indicates the specified traction force; is the Dirichlet boundary, is the Neumann boundary;

[0024] The boundary conditions are implemented in the neural network and can be expressed as follows:

[0025]

[0026] Among them, G1(X) and G2(X) represent the boundary displacement data respectively. Smooth expansion in x and y directions, and represents two independent artificial neural networks without boundary condition constraints, f1(X) and f2(XX) are distance functions considering displacement boundary characteristics in two directions respectively;

[0027] When X is on the displacement boundary When , f1(X)=f2(X)=0, which satisfies the displacement boundary condition; when X is within the inner area Ω of the V-notch, f1(X) and f2(X) are polynomial functions about the sample point X.

[0028] Furthermore, in step 7, the NSIF is solved based on the neural network to predict the displacement and stress fields at the crack tip:

[0029]

[0030] Among them, α(Ψ) is a constant related to the notch angle Ψ, (r,θ) is the polar coordinate system with the V-notch tip as the origin, and σ θ | θ＝0 is the normal stress of the notch bisector of the V-notch structure in the polar coordinate system at θ = 0. When θ = 0, σ θ =σyy ; After taking the logarithm, the normal stress σ yy And the distance r to the origin is fitted:

[0031] lnσ yy =-αlnr+lnK I -αln(2π)

[0032] The stress intensity factor K of the V-notch structure can be obtained by the intercept in the above formula: I .

[0033] Furthermore, in step 2, the method for obtaining Gaussian integral sample points for V-shaped notches with various opening angles is as follows:

[0034] When the V-notch opening angle is Ψ i When the Gaussian sample point data set is the corresponding spatial geometric coordinates (x k ,y k ) represents the coordinates of the kth sample point;

[0035] The Gaussian sample point data set of the V-notch structure with various opening angles contains not only the spatial geometric coordinates (x, y) but also the angle information Ψ. The data set consisting of the spatial geometric coordinates and angles of the V-notch structure is as follows:

[0036] Dataset={{Ψ1,X1},…,{Ψ n ,X n}}

[0037] n is the number of samples in the Gaussian sample point data set.

[0038] Furthermore, in step 3, the total potential energy of a series of angle V-notch structures is integrated as the loss function of the neural network:

[0039]

[0040] Among them, ∫ Ω is the integral in the V-notch domain, is the integral on the displacement boundary, ε is the strain, σ is the stress, Ω is the inner area of ​​the V-notch, Γ t is the displacement boundary, is the specified traction force and u is the displacement.

[0041] The beneficial effects achieved by the present invention are:

[0042] The physical law used in the algorithm of the present invention comes from the potential energy variational energy method derived from the virtual displacement principle of elastic mechanics. For the V-notch structure, a neural network with hard constraint boundary conditions is constructed, the displacement field is output according to the input spatial coordinates, and the stress intensity factor is calculated using the neural network prediction results. During the training process, the Gaussian integral sample points are obtained by the adaptive sampling method, and the scaling loss technology is used to help the neural network model find the optimal parameters.

[0043] The technical solution of the present invention provides a method for solving the stress intensity factor of a V-notch based on a neural network. The method uses a physical induction neural network to predict the SIF of a V-notch. In the absence of data, a neural network model that accurately predicts the response can be established by integrating physical laws. The present invention provides an adaptive local sampling strategy and a loss scaling method to overcome the problem that the neural network model in the notch stress concentration area is difficult to accurately solve. The present invention also proposes a physical induction neural network that can predict the stress intensity factor of a V-notch with any notch angle, and can directly predict the notch tip stress intensity factor under different notch angles.

[0044] The test method includes: adaptive sampling method, V-notch structure data set, loss scaling method, PINNs prediction module, V-notch stress intensity factor calculation module. The features are:

[0045] The adaptive sampling method automatically identifies the geometric features of the V-notch and generates Gaussian sample points that meet the needs of the V-notch structure.

[0046] The V-notch structure data set includes Gaussian integration sample points in the domain and Gaussian integration points on the force boundary. The elastic potential energy is calculated through the Gaussian sample points in the domain, and the external force potential energy is calculated through the Gaussian sample points on the force boundary.

[0047] The loss scaling method scales the parameters so that they are closer in magnitude, which can help the optimization algorithm learn and adjust the network parameters more effectively, thereby obtaining more accurate prediction results.

[0048] The PINNs prediction module defines the network structure, selects the activation function, initializes the network parameters, and builds a feedforward neural network. The neural network is modified according to the displacement boundary conditions, and the total potential energy integral of the V-notch structure is used as the loss function of the neural network for training. The trained neural network is used to predict the displacement field and stress field at the tip of the V-notch.

[0049] The V-notch stress intensity factor calculation module calculates the notch stress intensity factor through the predicted displacement field combined with the V-notch structural stress intensity factor definition. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1It is a flow chart of a method for solving V-notch stress intensity factor based on neural network provided by the present invention;

[0051] Figure 2 It is a PINN framework with two independent network outputs in the present invention;

[0052] Figure 3 It is a two-dimensional V-shaped notch structure in the present invention;

[0053] Figure 4 Solve the PINN-V-notch framework for the sequences in the present invention with V-notches of arbitrary angles;

[0054] Figure 5 It is a V-notch structure specimen under plane stress conditions in the present invention;

[0055] Figure 6 It is a training sample point of the 60° V-notch structure in the present invention;

[0056] Figure 7 is the training loss of the neural network with V-shaped notch structures at different angles in the present invention;

[0057] Figure 8 Comparison of FEM and PINN solution results of V-notch structures with different opening angles in the present invention;

[0058] Fig. 9 The NSIF of the V-notch structure with different opening angles is solved for the PINN-V-notch in the present invention. DETAILED DESCRIPTION

[0059] The technical solution of the present invention is described in more detail below in conjunction with the accompanying drawings. The present invention includes but is not limited to the following embodiments.

[0060] Embodiment 1

[0061] like Figure 1 As shown, a method for solving the V-notch stress intensity factor based on a neural network provided by the present invention comprises the following steps:

[0062] Step 1, adaptive meshing is performed according to the geometric characteristics of the V-notch specimen;

[0063] Gaussian integral points are adaptively generated within the V-notch domain and on the boundary to solve the problem of inaccurate total potential energy calculation due to the strong nonlinear stress field of the V-notch specimen. The adaptive sampling strategy automatically identifies the geometric features of the V-notch and generates Gaussian sample points that meet the needs of the V-notch structure. The Gaussian sample points are densely distributed near the tip of the V-notch and sparsely distributed in the area far away from the tip.

[0064] Firstly, the adjacent features are automatically identified by checking the distances between all geometric elements of the V-notch structure. Secondly, the boundaries of the V-notch structure are adaptively discretized based on the identified features. Thirdly, the adaptive meshing of the V-notch structure is realized by constructing an adaptive mesh unit size information field. Finally, the Gaussian sample points of the adaptive V-notch structure are generated based on the adaptively divided mesh.

[0065] Step 2, obtaining Gaussian integral sample points of the V-notch structure with a fixed opening angle according to the adaptive grid;

[0066] The adaptive Gaussian integration points of the V-notch structure are generated according to the adaptive grid to form n1 Gaussian sample points in the domain; n2 boundary Gaussian sample points are generated on the force boundary according to the boundary conditions. This sampling method can adaptively generate dense Gaussian integration nodes near the stress singularity points according to the characteristics of the V-notch structure.

[0067] Step 3: Parameter scaling is performed on the Gaussian sample points within the domain, the boundary Gaussian sample points, the material parameters, and the external loads.

[0068] By scaling parameters, the parameters are made closer in magnitude, which can help the optimization algorithm learn and adjust network parameters more effectively, thereby obtaining more accurate prediction results. This scaling operation helps to balance the influence of various parameters, improve the stability and convergence speed of optimization, make the model better adapt to the differences between parameters of different magnitudes, and obtain accurate prediction results. The parameters after scaling are as follows:

[0069]

[0070] Among them, X represents the coordinates of the sample point, u represents the displacement field, λ is the first Lame constant, which represents the compressibility of the material, μ is the second Lame constant, which represents the shear modulus of the material, and the total potential energy of the V-notch structure is as follows:

[0071]

[0072] Among them, n1 is the number of Gaussian sample points in the domain, i is the number of Gaussian sample points in the domain, j is the number of Gaussian sample points at the boundary, ω i and ω j are the Gaussian weights of the sample points in the domain and at the boundary, ε xx is the lateral normal strain, ε yy is the longitudinal normal strain, ε xy is the shear strain, σ xx is the transverse normal stress, σ yy is the longitudinal normal stress, σ xy is the shear stress, and are the two components of traction along the coordinate axis, namely, lateral traction and longitudinal traction.

[0073] Step 4, construct a neural network;

[0074] Define the network structure, select the activation function, initialize the network parameters, and build a feedforward neural network. Select a fully connected layer network to build a neural network. Each network has 8 hidden layers, each hidden layer has 20 neurons, and the hyperbolic tangent function (Tanh) is used as the activation function. Initialize the network parameters through Xaiver. Figure 2 As shown in the figure, two independent neural network structures are established to predict the displacement components in two directions respectively. In the network, tanh is selected as the activation function, and the network parameters are initialized using the Xavier initialization method.

[0075] Step 5: According to the displacement boundary, the neural network is transformed so that the neural network meets the hard boundary condition.

[0076] Consider the V-notch structure to satisfy the following boundary conditions:

[0077]

[0078] Where u(X) represents the displacement field, represents the prescribed displacement, t(X) is the traction force, Indicates the specified pulling force. is the Dirichlet boundary, is the Neumann boundary. Formula (5) is implemented in the neural network through hard boundary conditions and can be expressed as follows:

[0079]

[0080] Where G1(X) and G2(X) represent the boundary displacement data respectively. Smooth expansion in x and y directions, and represents two independent artificial neural networks without boundary conditions, f1(X) and f2(XX) are distance functions considering the displacement boundary characteristics in two directions. When , f1(X) = f2(X) = 0, and formula (6) satisfies the displacement boundary condition; when X is within the inner region Ω of the V-notch, f1(X) and f2(X) are polynomial functions about the sample point X.

[0081] Step 6, calculate the loss function;

[0082] Through the automatic differentiation technology of neural network, the stress and strain at the sample points in the domain are calculated to obtain the elastic strain energy of the V-notch structure; the displacement at the boundary sample points is predicted by the neural network to obtain the external force potential energy. As shown in formula (4), the total potential energy of the V-notch structure is obtained through the elastic strain energy and the external force potential energy, which is used as the loss function of the neural network:

[0083]

[0084] ε represents the strain field, σ represents the stress field, represents the traction force, and u represents the displacement field.

[0085] Step 7, displacement field prediction and stress intensity factor solution.

[0086] The above trained neural network is used to predict the displacement field and stress field at the crack tip. Figure 3 As shown in the figure, for an infinitely sharp V-notch with an opening angle of Ψ, the tip stress intensity factor NSIF (notch stress intensity factor) is defined as follows:

[0087]

[0088] where α(Ψ) is a constant related to the notch angle Ψ, (r,θ) is the polar coordinate system with the V-notch tip as the origin, and σ θ | θ＝0 is the normal stress of the notch bisector of the V-notch structure in the polar coordinate system at θ = 0. When θ = 0, σ θ =σ yy After taking the logarithm of formula (7), the normal stress σ yy Fitting with the distance r to the origin gives the following form:

[0089] lnσ yy =-αln r+ln K I -αln(2π) (8)

[0090] The stress intensity factor K of the V-notch structure can be obtained by the intercept in the above formula: I .

[0091] Embodiment 2

[0092] The above method can realize the rapid evaluation of the stress intensity factor of the V-notch structure with a specific opening angle. On this basis, the present invention proposes a physical information neural network (PINN-V-notch) model that can solve any opening angle. The PINN-V-notch model of the NSIF of a series of angle V-notch structures needs to contain the physical information of V-notches with multiple angles.

[0093] In this embodiment, the adaptive grid division scheme in step 1 is the same as that in the first embodiment.

[0094] In step 2, the method for obtaining Gaussian integral sample points of the V-shaped notch structure containing different opening angle information is as follows:

[0095] When the V-notch opening angle is Ψ i When the training data set is the corresponding spatial geometric coordinates (x k ,y k ) represents the coordinates of the kth sample point.

[0096] like Figure 4 As shown in the figure, the training data set of a series of angle V-notch structures contains not only the spatial geometric coordinates (x, y), but also the angle information Ψ. n The data set consisting of the spatial geometric coordinates and angles of the V-notch structure is shown below:

[0097] Dataset={{Ψ1,X1},…,{Ψ n ,X n}} (9)

[0098] In step 3, the solution is obtained by finding the network parameters that minimize the total potential energy integral of a series of angular V-notch structures, that is, the total potential energy integral of a series of angular V-notch structures is used as the loss function of the neural network:

[0099]

[0100] Gaussian node integration is used to approximate the total potential energy integral of the above formula. Gaussian integration sampling is performed on the opening angle of the V-notch structure, and n Gaussian integration node angles Ψ1, Ψ2, …Ψ are selected. n , by taking the weighted sum of the total potential energies of the V-notch structures at these n angles, the total potential energy integral is approximately calculated.

[0101] Substituting formula (9) into formula (10), the loss function can be expressed as follows:

[0102]

[0103] Among them, ∫ Ω is the integral in the V-notch domain, is the integral on the displacement boundary, ε is the strain, σ is the stress, Ω is the inner area of ​​the V-notch, Γ t is the displacement boundary, is the specified traction force and u is the displacement.

[0104] Steps 4-7 are solved using the same technical solution as in Example 1. Compared with Example 1, the input parameters of the sequence solving neural network in this embodiment also include angle information. Therefore, the neural network can predict the displacement field of any coordinate point (x, y) at any opening angle Ψ of the V-notch structure, thereby realizing NSIF calculation of a series of opening angles.

[0105] like Figure 5 As shown, in one embodiment, the present invention is described for a V-notch structure specimen under plane stress conditions. The elastic modulus of the specimen is E = 70 MPa, and the Poisson's ratio ν = 0.3. The side lengths are W = 20 mm, L = 20 mm, the notch size a = 4 mm, and the notch opening angle Ψ is analyzed at five typical angles of 30°, 60°, 90°, 120°, and 150°. Figure 5 As shown, the displacement boundary condition is that there is no lateral displacement on the right side of the specimen, no longitudinal displacement on the lower boundary of the specimen, and the force boundary condition is that a uniform load of q = 100 MPa is applied to the upper boundary, which is vertically stretched upward. The remaining edges are free boundaries and are not subject to external loads. The Cartesian coordinate origin is located at the vertex of the V-notch. The displacement boundary conditions of the model in the coordinate system are as follows:

[0106] u| x＝16 =0

[0107] v| y＝-10 =0 (12)

[0108] like Figure 4 The physical information neural network of the V-notch structure specimen is shown in the figure. The input of the network is the spatial coordinate (x, y). Through two independent densely connected networks (Densely connected NN), the lateral displacement u and longitudinal displacement v are predicted respectively. Each network has 8 hidden layers, each with 20 neurons. According to the displacement boundary condition of formula (12), a neural network with hard constraint boundary condition is constructed to solve the displacement:

[0109] u=(x-16)×u NN

[0110] v=(y+10)×v NN (13)

[0111] During the training process, the first-order partial derivative of the displacement component with respect to the spatial coordinates is obtained through the automatic differentiation technology of the neural network. The total potential energy of the V-notch structure specimen is calculated by formula (4) as the loss function of the network.

[0112] Take the 60° V-notch as an example for sampling. The training sample points are divided into in-domain sample points and boundary sample points. The internal energy is calculated through the in-domain sample points, and the external force potential energy is calculated through the boundary sample points. This example generates the training data set through uniform sampling and adaptive sampling, such as Figure 6 As shown in Figure 2, uniform sampling generates a total of 28,220 sample points, and adaptive sampling generates a total of 26,880 Gaussian integral points. It is worth noting that Figure 6 The Gaussian integral points in (b) are obviously densely distributed near the tip, which is conducive to the accurate calculation of the total potential energy of the V-shaped structure. In order to calculate the external work, it is also necessary to sample the boundary sample points. Since the neural network uses hard constraints, the neural network automatically satisfies the displacement boundary conditions and only needs to sample on the force boundary. The external load in this example is a uniformly distributed load applied to the upper boundary, so sampling is performed at the upper boundary y = 10mm. Figure 6 In (a), uniform sampling is performed on the upper boundary to generate 2000 sample points uniformly; Figure 6 (b) Gaussian sampling is performed on the upper boundary, and the upper boundary is divided into 1000 intervals. Two Gaussian integral points are taken in each interval, so there are a total of 2000 Gaussian sampling points. In summary, the uniform sampling training data set includes 28220 uniform sampling points in the domain and 2000 uniform sampling points at the boundary. The training data set obtained by the adaptive sampling method includes 26880 Gaussian integral points in the domain and 2000 Gaussian integral points at the boundary. Figure 6 As shown in the figure, the sample points in the domain are represented by red points, and the sample points at the upper boundary are represented by black points. The loss function curves of the neural network training process of the V-notch structure with different angles are shown in the figure. Figure 7 shown.

[0113] This embodiment conducts research on the case where the opening angles of the V-notch structure are five typical angles of 30°, 60°, 90°, 120°, and 150°, and the upper boundary uniformly distributed load is 100 MPa. A physical information neural network is established, and the stress intensity factor is solved by predicting the displacement field and stress field. Figure 8 The displacement field and stress field solved by finite element (FEM) at different typical angles are shown, as well as the prediction results of PINN-V-notch based on the adaptive sampling training data set. The results show that the results of PINN-V-notch are consistent with the FEM results.

[0114] According to the stress intensity factor, formula (8) is solved. Based on the trained network, 100 sample points are collected near the apex of the V-notch on the x-axis, and the longitudinal stress component σ is predicted. yy .like Fig. 9 The fitting is performed as shown in the figure, where the horizontal axis is the logarithm of the distance from the sample point to the V-notch vertex, and the vertical axis is the stress component σ yyThe stress intensity factor is calculated based on the logarithm of the fitted curve. Fig. 9 The stress fields predicted by the PINN-V-notch method at five different typical angles of the V-notch structure are shown respectively, and the NSIF is obtained by fitting. Table 1 lists the NSIFs solved by FEM, PINN based on uniform sampling sample points, and PINN based on adaptive sampling method. Taking FEM NSIF as the benchmark, the results show that the accuracy based on the adaptive sampling method is higher than that based on the uniform sampling method, and its error does not exceed 1%. The effectiveness of the physical information neural network based on the adaptive sampling method proposed in this paper to calculate NSIF is verified.

[0115] Table 1 Comparison of NSIF results of two-dimensional V-Notch specimens

[0116]

[0117] *NSIF Unit:

[0118] In the above embodiment, five PINNs are trained for five V-notch structures with different angles to calculate their respective NSIFs. However, when the notch opening angle of the V-notch structure changes, the network needs to be retrained. This embodiment considers training a universal network of a V-notch structure, without the need for retraining when the notch angle changes, and can achieve sequential solution of NSIFs at different angles. When the notch angle is 0, the V-notch becomes a crack, and when the notch angle is 180°, the V-shaped structure becomes a rectangular elastic plate, and there is no stress concentration phenomenon. In this embodiment, the side length, notch size, external load and boundary conditions of the V-notch structure are consistent with the above embodiment, wherein the notch opening angle Ψ∈(0°, 180°).

[0119] Construct a sequence to solve the PINN of V-notch with arbitrary angle, such as Figure 4 As shown, the spatial coordinate data sets at different angles plus the corresponding angles together constitute the data set of the neural network for solving the V-notch structure at any angle. Five Gaussian integration nodes are selected within (0°, 180°), and the total potential energy integral is approximately calculated by weighted summing the total potential energy of the V-notch structure at these five angles.

[0120] After training, the physical information neural network can learn the mapping relationship between the V-notch structure angle and spatial coordinates and the displacement field. At this time, the neural network can sequentially solve the displacement field and stress field of the V-notch structure with different opening angles, and then solve its stress intensity factor. At the same time, using the finite element NSIF corresponding to the above-mentioned Gaussian integral node angle as label data, the training data-driven neural network learns the mapping relationship between the V-notch angle and spatial coordinates and NSIF, which is used to predict the NSIF of the V-notch structure at different angles. Take any 4 angles between (0°, 180°), and Table 2 shows the NSIF obtained by FEM solution of the V-notch structure at 4 different angles. Based on this, the NSIF predicted by the sequential solution neural network and the traditional pure data-driven neural network are compared. It can be observed from the table that both the PINN-V-notch method and the finite element method show a common trend: as the opening angle of the V-notch structure decreases, the stress concentration phenomenon at the tip becomes more obvious, and the corresponding stress intensity factor also increases. Taking the results of FEM as a benchmark, it can be seen that the NSIF prediction error of the PINN-V-notch method does not exceed 1%, while the NSIF prediction error obtained by the traditional pure data-driven neural network is very large and cannot effectively predict the NSIF. This verifies the advantage of the PINN-V-notch method proposed in the present invention in terms of prediction accuracy, which comes from the fused physical information.

[0121] Table 2 NSIF of V-notch structure at different angles

[0122]

[0123] *NSIF Unit:

[0124] The present invention is not limited to the above-mentioned specific implementation modes. A person skilled in the art may implement the present invention in various other specific implementation modes according to the embodiments and the disclosure of the drawings. Therefore, any design that adopts the design structure and concept of the present invention and makes some simple transformations or changes shall fall within the scope of protection of the present invention.

Claims

1. A method for solving V-notch stress intensity factor based on neural network, characterized in that: The neural network-based V-notch stress intensity factor solution method comprises the following steps: Step 1, adaptive meshing is performed according to the geometric characteristics of the V-notch specimen; Step 2, obtaining Gaussian integral sample points of the V-notch structure according to the adaptive grid; Gaussian integral sample points include Gaussian sample points within the domain and Gaussian sample points at the boundary; Step 3, parameter scaling of Gaussian sample points within the domain, boundary Gaussian sample points, material parameters and external loads; Step 4, construct a neural network to predict the displacement components in two directions; Step 5, transforming the neural network according to the displacement boundary so that the neural network meets the hard boundary condition; Step 6, calculate the loss function of the neural network; Step 7, using the adjusted neural network to predict the displacement field and stress field at the crack tip; In step 5, the boundary conditions of the V-notch structure are: Where u(X) represents the displacement field, represents the prescribed displacement, t(X) is the traction force, Indicates the specified traction force; is the Dirichlet boundary, is the Neumann boundary; The boundary conditions are implemented in the neural network and can be expressed as follows: Among them, G1(X) and G2(X) represent the boundary displacement data respectively. Smooth expansion in x and y directions, and represents two independent artificial neural networks without boundary condition constraints, f1(X) and f2(X) are distance functions considering displacement boundary characteristics in two directions respectively; When X is on the displacement boundary When , f1(X) = f2(X) = 0, which satisfies the displacement boundary condition; when X is within the inner region Ω of the V-notch, f1(X) and f2(X) are polynomial functions about the sample point X.

2. The method for solving the V-notch stress intensity factor based on a neural network according to claim 1, characterized in that: In step 2, for a V-notch structure with a fixed opening angle; In step 3, the parameter scaling includes: Where X represents the coordinates of the sample point, u represents the displacement field, λ is the first Lame constant, which represents the compressibility of the material, μ is the second Lame constant, which represents the shear modulus of the material, and t is the external load. Indicates the parameters after scaling; c is the maximum value of this parameter within the V-notch domain; the scaled energy is shown below: Among them, n1 is the number of sample points in the domain, i is the number of Gaussian sample points in the domain, j is the number of Gaussian sample points at the boundary, ω i and ω j is the Gaussian weight, ε xx is the lateral normal strain, ε yy is the longitudinal normal strain, ε xy is the shear strain, σ xx is the transverse normal stress, σ yy is the longitudinal normal stress, σ xy is the shear stress, and It is the lateral traction and longitudinal traction.

3. The method for solving the V-notch stress intensity factor based on a neural network according to claim 1, characterized in that: In step 7, the displacement field and stress field at the crack tip are predicted based on the neural network to solve the tip stress intensity factor NSIF: Among them, α(Ψ) is a constant related to the notch angle Ψ, (r,θ) is the polar coordinate system with the V-notch tip as the origin, and σ θ | θ＝0 is the normal stress of the notch bisector of the V-notch structure in the polar coordinate system at θ = 0. When θ = 0, σ θ =σ yy ; After taking the logarithm, the normal stress σ yy And the distance r to the origin is fitted: lnσ yy =-αlnr+lnK I -αln(2π) The stress intensity factor K of the V-notch structure can be obtained by the intercept in the above formula: I .

4. The method for solving the V-notch stress intensity factor based on a neural network according to claim 1, characterized in that: In step 2, the method for obtaining Gaussian integral sample points for V-notches with various opening angles is as follows: When the V-notch opening angle is Ψ i When the Gaussian sample point data set is the corresponding spatial geometric coordinates (x k ,y k ) represents the coordinates of the kth sample point; The Gaussian sample point data set of the V-notch structure with various opening angles contains not only the spatial geometric coordinates (x, y) but also the angle information Ψ. The data set consisting of the spatial geometric coordinates and angles of the V-notch structure is as follows: Dataset={{Ψ1,X1},…,{Ψ n ,X n }} n is the number of samples in the Gaussian sample point data set.

5. The method for solving the V-notch stress intensity factor based on a neural network according to claim 4, characterized in that: In step 3, the total potential energy of a series of angle V-notch structures is integrated as the loss function of the neural network: Among them, ∫ Ω is the integral in the V-notch domain, is the integral on the displacement boundary, ε is the strain, σ is the stress, θ is the inner area of ​​the V-notch, Γ t is the displacement boundary, is the specified traction force and u is the displacement.

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