A node-discrete strain field analysis method

Abstract

The application discloses a node discrete type strain field analysis method, and steps of the method comprise the following steps: (1) carrying out configuration decomposition on a structure solving domain to obtain extreme values and residual parameters with space coordinates as variables; (2) constructing a virtual definition domain, and realizing smooth analytic continuation based on the extreme values and the residual parameters to obtain an analytic continuation overall smooth virtual configuration; (3) constructing a weight function and a shape function based on the analytic continuation overall smooth virtual configuration and the virtual definition domain to obtain a moving least square approximation of a displacement field; and (4) solving a node discrete type strain field of an original solving domain based on the analytic continuation smooth virtual configuration and the shape function. The application has the beneficial effects that the condition number of the shape function and its derivative is significantly reduced, and the numerical solving stability is effectively improved; and the strain solution of the original problem domain is extracted in combination with the definition domain truncation strategy, and the strain estimation precision of the node discrete type method at the boundary is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of strain field analysis, and particularly relates to a node discrete type strain field analysis method. BACKGROUND

[0002] Strain estimation based on full-field displacement is a core technology in solid mechanics, material science and experimental mechanics, which is used to inversely deduce the strain distribution of an object through displacement field data. Accurate analysis of strain field is crucial for structural health monitoring, material performance evaluation, engineering failure prediction, etc., and how to accurately reconstruct the continuous strain field from discrete displacement measurement data (such as digital image correlation technology, optical fiber sensing or numerical simulation results) is very important. The methods of converting displacement field to strain field mainly include the following:

[0003] (1) Directly differentiating the displacement field or solving the strain field through difference;

[0004] (2) Solving the strain field by fitting the displacement field based on finite element smoothing denoising;

[0005] (3) Solving the strain by using least square fitting method on displacement field.

[0006] Among them, the direct difference method for solving the strain field is unstable, poor in reliability, and easy to expand the influence of the external environment; the strain field solving method based on finite element smoothing denoising involves mathematical operations of multiple processes, and the calculation process is complex and not easy to program; the least square fitting method for solving the strain field by fitting the displacement field through a quadratic surface and then differentiating the strain field, but due to the inability to grasp the deformation of the full field, it is impossible to select the fitting coefficients, and there is a certain limitation.

[0007] In view of the existing problems, a node discrete type strain field analysis method is proposed.

[0008] The above information disclosed in the background section of this specification is only used to understand the background of the present inventive concept, and therefore, it can include information which does not constitute prior art. SUMMARY

[0009] The present application aims to provide a node discrete type strain field analysis method to solve the problems raised in the background technology.

[0010] The steps of a node discrete type strain field analysis method include:

[0011] (1) Decompose the structure solution domain to obtain extreme values and residual parameters with spatial coordinates as variables;

[0012] (2) Construct a virtual domain, and realize smooth analytic continuation based on extreme value and residue parameter to obtain an overall smooth virtual configuration of analytic continuation;

[0013] (3) Based on the overall smooth virtual configuration of analytic continuation and the virtual domain, construct a weight function and a shape function to obtain a moving least square approximation of displacement field;

[0014] (4) Based on the smooth virtual configuration of analytic continuation and the shape function, solve the node discrete strain field of the original solving domain.

[0015] Preferably, the method for obtaining the extreme value and residue parameter comprises:

[0016] 1) For , the number of discrete points is , and the discrete interval is . The Hankel matrix is constructed by formula (1-3), and formula (1-3) is , =0,1,…, , and are the selected rows and columns of the Hankel matrix, respectively.

[0017] 2) The eigenvalues of the state matrix are extracted from the Hankel matrix in step 1) by singular value decomposition , there are n of them.

[0018] 3) The extreme value parameter with spatial coordinates as variables is obtained by formula (1-5) , and the residue parameter with spatial coordinates as variables is obtained by solving the linear equation system of formula (1-6) by least square method , and formula (1-6) is .

[0019] Preferably, the method for obtaining the state matrix is to construct the Hankel matrix in step 1), let , and singular value decomposition is performed on in the Hankel matrix to obtain the transformation matrix S1, the left singular vector matrix U and the right singular vector matrix V1, and the state matrix is represented by formula (1-4) .

[0020] Preferably, the method for obtaining the overall smooth virtual configuration comprises:

[0021] 1) The virtual domain is obtained by extension by formula (1-9), and formula (1-9) is ,

[0022] , wherein ​Indicates the first at the starting end One virtual definition point; Indicates the first term at the termination end One virtual definition point;

[0023] 2) Reconstruct the configuration of the extended interval domain obtained in step 1) using formula (1-10) to obtain the extended configuration of the virtual solution domain. Formula (1-10) is: In the formula and To decompose the extreme values ​​and residue parameters obtained from the discrete spatial domain configuration;

[0024] 3) Based on the extended configuration of the virtual solution domain obtained in step 2), the global smooth virtual form of the analytical extension is obtained by assembling it using formula (1-11). Overall smooth fictional Use formula (1-11) It means that, among them Formula (1-2) can be used. It means that in the formula This is the domain corresponding to the discrete spatial domain configuration.

[0025] Preferred methods for obtaining the weight function, shape function, and displacement field using moving least squares approximation include:

[0026] 1) For weighted residuals The norm is obtained by taking the minimum value using formula (1-18). coefficients, weighted residuals The norm is given by formula (1-14). It means that in the formula It is the weighting function; formula (1-18) is ;

[0027] 2) Combining formula (1-18) and equation (1-14), we obtain

[0028] (1-19);

[0029] In the formula This represents the vector of displacement values ​​of each node within the support domain; and All are weight functions, where

[0030] (1-20)

[0031] (1-21)

[0032] The coefficient is expressed by formula (1-22) as follows:

[0033] (1-22);

[0034] 3) Using formulas (1-22) and (1-12), the least squares approximation of the displacement field is obtained. Formula (1-12) is: In the formula For point Approximate displacement at; Point Supports the number of nodes in the domain; This represents the displacement component of the i-th node in the support domain; Let represent the shape function of the i-th node. The displacement field translation least squares approximation is obtained from formula (1-23). It means that in the formula These are basis functions, and the shape function matrix is ​​given by formula (1-24). express;

[0035] 4) The least squares approximation of the displacement field is derived from formulas (1-23) and (1-24) and formula (1-25). express.

[0036] Preferred methods for obtaining the discrete strain field at the solution domain nodes include:

[0037] 1) Calculate the first derivative of the shape function obtained in step (3) using formula (1-26), where formula (1-26) is: The second derivative of the shape function obtained in step (3) is obtained using formula (1-27), where formula (1-27) is... ;

[0038] 2) Using formula (1-31), the strain values ​​of the global virtual domain are obtained by applying the first derivative, second derivative, and global smooth virtual domain obtained in step (2) to the global virtual domain. Formula (1-31) is In the formula For axial strain, For bending strain;

[0039] 3) Apply formula (1-32) to the strain value of the overall virtual domain obtained in step 2) above. According to the domain corresponding to the discrete space domain configuration After truncation, the discrete strain field at the solution domain nodes is obtained. The discrete strain field at the solution domain nodes can be expressed by formula (1-32). Formula (1-32) is... .

[0040] Preferably, the weight function is a cubic spline function, and the formula of the cubic spline function is (1-15), wherein , is the support domain size of the weight function, and is 4 times or more of .

[0041] Preferably, the weight function is a Gaussian function, and the formula of the Gaussian function is (1-16), wherein is a shape parameter of the Gaussian function.

[0042] Preferably, the weight function is an exponential function, and the formula of the exponential function is (1-17), wherein is a shape parameter of the exponential function.

[0043] Compared with the prior art, the present application has the beneficial effects that the condition number of the shape function and its derivative is significantly reduced, and the numerical solution stability is effectively improved; and the strain solution of the original problem domain is extracted by combining the domain truncation strategy, and the strain estimation accuracy of the node discrete method at the boundary is effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a cantilever beam model;

[0045] Figure 2 is a function of the first three vibration modes;

[0046] Figure 3 is a comparison diagram of a complex exponential reconstruction displacement field based on a spatial configuration;

[0047] Figure 4 is a schematic diagram of the node discretization and the domain after bidirectional extension;

[0048] Figure 5 is a relative error diagram of the reconstructed displacement and the analytical value;

[0049] Figure 6 is a diagram of the node discretization and the compactly supported function construction based on the virtual domain;

[0050] Figure 7 is a comparison diagram of the condition number of the shape function and its derivative matrix constructed by different methods;

[0051] Figure 8 is a comparison diagram of the estimated displacement and strain field based on the direct MLS meshless method and the present application. DETAILED DESCRIPTION

[0052] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0053] An embodiment of the present application provides a method for analyzing a node discrete strain field.

[0054] A step of a node discrete strain field analysis method is as follows:

[0055] 1. A configuration decomposition is performed on a structure solution domain to obtain extreme value and residual parameters with spatial coordinates as variables, wherein the extreme value and residual parameters are obtained by the following method:

[0056] 1) When n is an integer, the discrete point number is n, the discrete interval is 1 / n, and the discrete space domain configuration is as shown in the following formula (1-1): The Hankel matrix is constructed by formula (1-3), and the formula (1-3) is as follows:

[0057] , wherein =0, 1, …, , and are selected rows and columns of the Hankel matrix;

[0058] 2) The eigenvalues of the state matrix are extracted from the Hankel matrix in step 1) by singular value decomposition. There are n.

[0059] Specifically, the state matrix is obtained by the Hankel matrix constructed in the previous step, and the state matrix is expressed by formula (1-4): and singular value decomposition is performed on the Hankel matrix to obtain a transformation matrix S1, a left singular vector matrix U, and a right singular vector matrix V1.

[0060] 3) The extreme value parameters with spatial coordinates as variables are obtained by formula (1-5): The linear equation group of formula (1-6) is solved by a least square method, and the residual parameters with spatial coordinates as variables are obtained: .

[0061] ​​​​​​​​2. Constructing a virtual definition domain, realizing smooth analytic continuation based on the extreme value and the residual parameter, and obtaining an analytically continued overall smooth virtual configuration, and the method for obtaining the overall smooth virtual configuration is:

[0062] 1) using formula (1-9) to obtain the virtual definition domain, and the formula (1-9) is

[0063]

[0064] wherein represents the first virtual definition point at the starting end; represents the first virtual definition point at the ending end;

[0065] 2) using formula (1-10) to reconstruct the definition domain of the extended interval obtained in the above step 1), and obtaining the extended configuration of the virtual solution domain, and the formula (1-10) is

[0066] wherein and are the extreme value and the residual parameter obtained by decomposing the discrete spatial domain configuration;

[0067] 3) based on the extended configuration of the virtual solution domain obtained in the above step 2), assembling the analytically continued overall smooth virtual configuration by formula (1-11) , wherein the overall smooth virtual configuration is represented by formula (1-11) , wherein can be represented by formula (1-2) , wherein is the definition domain corresponding to the discrete spatial domain configuration.

[0068] 3. Based on the analytically continued overall smooth virtual configuration and the virtual definition domain, constructing a weight function and a shape function, and obtaining a moving least squares approximation of a displacement field, and the method for obtaining the weight function, the shape function and the moving least squares approximation of the displacement field is:

[0069] 1) taking the minimum value of the weighted residual norm by formula (1-18) to obtain the coefficient, and the weighted residual norm is represented by formula (1-14) , wherein is a weight function; and the formula (1-18) is

[0070] ​​​​​​Specifically, the weighting function can be a cubic spline function, and the formula for the cubic spline function is: (1-15), where , The size of the support domain is the weight function. Four times or more.

[0071] Specifically, the weighting function can also be a Gaussian function, and the formula for the Gaussian function is: (1-16), where, The shape parameters of the Gaussian function

[0072] Specifically, the weighting function is an exponential function, and the formula for the exponential function is: (1-17), where, is the shape parameter of the exponential function.

[0073] 2) Combining formula (1-18) and equation (1-14), we obtain

[0074] (1-19);

[0075] In the formula This represents the vector of displacement values ​​of each node within the support domain; and All are weight functions, where

[0076] (1-20)

[0077] (1-21)

[0078] The coefficient is expressed by formula (1-22) as follows:

[0079] (1-22);

[0080] 3) Using formulas (1-22) and (1-12), the least squares approximation of the displacement field is obtained. Formula (1-12) is: In the formula For point Approximate displacement at; Point Supports the number of nodes in the domain; This represents the displacement component of the i-th node in the support domain; Let represent the shape function of the i-th node. The displacement field translation least squares approximation is obtained from formula (1-23). It means that in the formula These are basis functions, and the shape function matrix is ​​given by formula (1-24). express;

[0081] 4) The least squares approximation of the displacement field is derived from formulas (1-23) and (1-24) and formula (1-25). express.

[0082] 4. Based on the smooth fictitious form of the analytical continuation and the shape function, solve for the discrete strain field at the nodes of the original solution domain. The method for obtaining the discrete strain field at the nodes of the original solution domain is as follows:

[0083] 1) Calculate the first derivative of the shape function obtained in step (3) using formula (1-26), where formula (1-26) is: The second derivative of the shape function obtained in step (3) is obtained using formula (1-27), where formula (1-27) is... ;

[0084] 2) Using formula (1-31), the strain values ​​of the global virtual domain are obtained by applying the first derivative, second derivative, and global smooth virtual domain obtained in step (2) to the global virtual domain. Formula (1-31) is In the formula For axial strain, For bending strain;

[0085] 3) Apply formula (1-32) to the strain value of the overall virtual domain obtained in step 2) above. According to the domain corresponding to the discrete space domain configuration After truncation, the discrete strain field at the solution domain nodes is obtained. The discrete strain field at the solution domain nodes can be expressed by formula (1-32). Formula (1-32) is... .

[0086] This invention provides an embodiment:

[0087] A schematic diagram of the cantilever beam model is attached. Figure 1 As shown, the length of the cantilever beam For 1 m, the elastic modulus 2.1×10 11 Pa, material density is 7850 kg / m³ 3 The cross-sectional dimensions are 0.025 m × 0.02 m, and the cross-sectional area is 5 × 10⁻⁶ m. -4 m 2 Moment of inertia of cross section It is 1.67 × 10 -8 m 4 The mode shape function of a cantilever beam can describe the most representative configuration of the entire structure in space, as shown in the attached figure.Figure 2 As shown. Circular frequency in structural dynamics. and the corresponding mode shape function The equations for the undamped free vibration of a cantilever beam (where p represents the mode order) can be derived from formulas (a)-(b), and are expressed as follows:

[0088] (a)

[0089] (b)

[0090] (c)

[0091] In the formula, Indicates the bending displacement of the structure; Represents the roots of the frequency equation; Represents unit mass; defines amplitude parameters. .

[0092] Correspondingly, the second derivative of the mode shape function The bending strain corresponding to the spatial configuration of the structure is expressed as: (d)

[0093] (1) Perform configuration decomposition on the structural solution domain

[0094] In interval Under the given discreteness, the domain is first discretized along the length of the cantilever beam. Then, a displacement segment at the left and right boundaries of the cantilever beam described by formula (c) is selected to perform configurational decomposition on the structural solution domain, obtaining the extrema and residue parameters with spatial coordinates as variables. The decomposition and reconstruction results are attached. Figure 3 As shown, this application can accurately decompose the extreme parameter values ​​corresponding to the mode shape function, which also highly match the amplitude of the displacement configuration. It can also be seen that the extreme imaginary part and the analytical frequency value obtained by decomposition are both 7.855, indicating that this application can accurately decompose the extreme parameters.

[0095] (2) Constructing a global smooth virtual type of virtual domain and analytic extension

[0096] Similarly in the interval Given a certain degree of discreteness, a virtual domain extension is performed along the length direction of the cantilever beam, as shown in the attached figure. Figure 4 As shown, the extension length is determined based on the condition number of the truncated shape function and its matrix after extension, with the condition number of the second derivative of the shape function not exceeding 10. 3 For optimal performance, this embodiment selects 1 / 10 of the beam length for boundary extension, using formula (1-9). ( Indicates the first at the starting end One virtual definition point; Indicates the first term at the termination end The virtual domain [-0.2, 1.2] is obtained by extending the domain from the virtual definition points, and then further extended using formula (1-10). ( and To decompose the extreme values ​​and residue parameters of the discrete spatial domain, the configuration is reconstructed based on the extreme values, residue parameters, and virtual domain obtained from the decomposition, resulting in the extended configuration of the virtual solution domain. Then, the configuration is obtained through formula (1-11). ( Formula (1-2) can be used. express, Assemble the obtained extended configurations (where the domain corresponds to the discrete spatial domain configuration) to obtain the globally smooth fictitious form of the analytic extension, as shown in the appendix. Figure 5 As shown, the global smooth fictitious form of the analytic continuation and the analytic value described by formula (c) also maintain a high degree of agreement within the continuation domain.

[0097] The above results show that this application can accurately realize the global smooth virtual reconstruction based on analytical continuation and ensure the high-order continuity characteristics at the boundary, which can be further used to solve the nodal discrete strain field.

[0098] (3) Constructing the shape function and the least squares approximation of the displacement field

[0099] From formula (1-24) The shape functions were calculated, as shown in the appendix. Figure 6 As shown, within the virtual domain [-0.2, 1.2], the shape function and its second derivative exhibit asymmetry and divergence at the boundary. Thanks to the extended virtual domain, the asymmetric shape function and its derivative are confined to the virtual domains [-0.2, 0] and [1, 1.2], while the shape function at each node within the domain [0, 1] displays good symmetry. Comparisons of the condition numbers of the shape function and its derivative matrix constructed using different methods are attached. Figure 7 As shown, the condition number of the shape function matrix constructed by the direct moving least squares (MLS) meshless method is less than 10, while the first and second derivative matrices of the shape functions increase sharply to 10. 11 The order of magnitude is significantly larger, exhibiting severe pathological behavior. In contrast, this application extends the virtual domain and truncates it within the [0,1] domain; the condition numbers of its shape functions and their derivative matrices are all below 10. 2 In numerical calculations, this can be defined as a well-state matrix. Furthermore, using formula (1-23)... ( (These are basis functions) and formula (1-24) The least squares approximation of the analytical displacement field is obtained, as shown in the appendix. Figure 8 As shown.

[0100] The above results show that the application can construct a lower condition number shape function, which can accurately approximate the existing displacement field, thereby ensuring the stability of the strain solution at the boundary from the numerical calculation principle.

[0101] (4) solving the original solving domain node discrete strain field

[0102] Using formula (1-26) The first-order derivative of the shape function obtained in step (3) is calculated, and formula (1-27) is used The second-order derivative of the shape function obtained in step (3) is calculated, and formula (1-31) is used is the axial strain, is the bending strain) to obtain the strain value of the overall smooth virtual domain And through formula (1-32) The strain value of the overall virtual domain obtained According to the definition domain corresponding to the discrete spatial domain configuration The truncation processing is performed, and the strain estimation results of the original definition domain corresponding interval are retained, based on the direct MLS meshless method and the application to estimate the displacement and strain field, and the comparison with the analytical value described in formula (d) is shown in the attached Figure 8 .

[0103] As shown in the attached Figure 8 , the application can significantly improve the numerical oscillation problem of the direct MLS meshless method at the boundary, especially for the estimation of the strain field, and the estimation error at the boundary of the strain field is controlled within 0.5%.

[0104] Working principle and use process of the application:

[0105] First, the analytical continuation is performed by introducing the complex exponential function decomposition and reconstruction method based on the spatial configuration, to construct a smooth transition boundary between the virtual definition domain and the structure solving domain with continuous; then based on the method, the shape function space distribution in the structure solving domain in the virtual definition domain presents a symmetric characteristic, which significantly reduces the condition number of the shape function and its derivative, effectively improving the numerical solution stability; at the same time, the strain solution of the structure solving domain is extracted by combining the definition domain truncation strategy, which effectively improves the strain estimation accuracy of the node discrete method at the boundary.

[0106] The application constructs a virtual definition domain to improve the ill-conditioned problem of the shape function and its derivative matrix in the structure solving domain, aiming at the numerical oscillation effect caused by the singularity of the shape function and the weight function at the boundary of the traditional moving least square meshless method. Based on the smooth analytical continuation of the discrete spatial domain configuration, high-order continuous transition at the boundary of the virtual definition domain and the structure solving domain is realized, and the boundary singularity problem of the node discrete strain estimation method is solved.​

[0107] While embodiments of the application have been shown and described herein, it will be obvious to those skilled in the art that many changes, modifications, substitutions and variations can be made thereto without departing from the principles and spirit of the application, the scope of which is defined by the claims and their equivalents.

Claims

1. A method of nodal discrete strain field analysis, characterized by, The steps of the analysis method comprise: (1) performing configuration decomposition on a structural solution domain to obtain extreme value and residual parameter with spatial coordinates as variables; (2) constructing a virtual definition domain, and realizing smooth analytical continuation based on the extreme value and the residual parameter to obtain an analytically continued overall smooth virtual configuration; (3) constructing a weight function and a shape function based on the analytically continued overall smooth virtual configuration and the virtual definition domain to obtain a moving least square approximation of a displacement field; (4) solving a node-discrete strain field of an original solution domain based on the analytically continued smooth virtual configuration and the shape function; The method for obtaining the extreme value and the residual parameter comprises: 1) on the condition that the number of discrete points is and the discrete interval is a discrete space domain configuration The Hankel matrix is constructed by formula (1-3), and formula (1-3) is where = 0,1,..., , and are selected rows and columns of the Hankel matrix, respectively. 2) extracting eigenvalues of a state matrix from the Hankel matrix using singular value decomposition , the number of which is n; 3) using formula (1-5) to obtain the extreme parameter with spatial coordinates as variables , using the least square method to solve the linear equation group of formula (1-6), and obtaining the residual parameter with spatial coordinates as variables , the formula (1-6) is ; The method for obtaining the overall smooth virtual configuration comprises: 1) using formula (1-9) to obtain a virtual definition domain, wherein formula (1-9) is ， wherein represents the first virtual definition point at the start end; represents the first virtual definition point at the start end; represents the first virtual definition point at the end end; represents the first virtual definition point at the end end; 2) using formula (1-10) to reconstruct a configuration of the virtual definition domain to obtain a continued configuration of a virtual solution domain, wherein formula (1-10) is where and are the extremum and residual parameters resulting from the decomposition of the discrete spatial domain configuration; 3) Based on the extended configuration of the virtual solution domain, the overall smooth virtual form of the analytical extension is obtained by assembling it using formula (1-11). The overall smooth virtual type Use formula (1-11) It means that, among them Formula (1-2) can be used. It means that in the formula The domain is the domain corresponding to the discrete spatial domain configuration.

2. The method of claim 1, wherein, The state matrix is obtained by singular value decomposition of and in the Hankel matrix to obtain a transformation matrix S1, a left singular vector matrix U and a right singular vector matrix V1, and the state matrix is represented by formula (1-4) .

3. The method of claim 1, wherein, The method for obtaining the weight function, the shape function and the moving least square approximation of the displacement field comprises: 1) minimizing the norm of the weighted residual using equation (1-18) The coefficients of the weighted residual norm are obtained by minimizing the norm of the weighted residual using equation (1-14) where the weight function is given by and the equation (1-18) is ; 2) combining the formula (1-18) and the formula (1-14) to obtain （1-19）； wherein represents a support of the displacement value vector of each node in the domain; and are weight functions, wherein （1-20） （1-21） The coefficient is expressed by formula (1-22) as follows: （1-22） 3) Using formulas (1-22) and (1-12), the least squares approximation of the displacement field is obtained. Formula (1-12) is: In the formula For point Approximate displacement at; Point Supports the number of nodes in the domain; This represents the displacement component of the i-th node in the support domain; Let represent the shape function of the i-th node. The displacement field translation least squares approximation is obtained from formula (1-23). It means that in the formula These are basis functions, and the shape function matrix is ​​given by formula (1-24). express; 4) The moving least squares approximation of the displacement field is given by Equations (1-23) and (1-24) as Equation (1-25) 4. The method of claim 1, wherein, The method for obtaining the node-discrete strain field of the original solution domain comprises: 1) first derivative of the shape function with respect to x by equation (1-26), where equation (1-26) is second derivative of the shape function with respect to x by equation (1-27), where equation (1-27) is are weight functions, and the​​​ 2) solving the strain value of the whole virtual domain by using formula (1-31) on the first derivative, the second derivative and the whole smooth imaginary type , wherein formula (1-31) is ; wherein is the axial strain, is the bending strain; 3) the strain value of the whole virtual domain is calculated by using formula (1-32) the definition domain corresponding to the discrete spatial domain configuration The truncated processing is performed to obtain the discrete strain field of the solution domain node, which can be expressed by formula (1-32) .

5. The method of claim 3, wherein, The weight function is a cubic spline function, and the cubic spline function formula is (1-15), wherein , is a weight function support domain size, and is 4 times or more of .

6. The method of claim 3, wherein, The weight function is a Gaussian function, and the Gaussian function formula is (1-16), wherein, is a Gaussian function shape parameter.

7. The method of claim 3, wherein, The weight function is an exponential function, and the exponential function formula is (1-17), wherein, is an exponential function shape parameter.

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