A near-field dynamics-finite element coupling method and system

Abstract

The application discloses a near-field dynamics-finite element coupling method and system, relates to the technical field of quasi-brittle material failure prediction and mechanical numerical simulation, and comprises the following steps: the method is simple to calculate, a finite element method is completely used in a structure solving process, a near-field dynamics-finite element coupling region is used as a "submodel" and does not directly participate in calculation; displacement calculated by the finite element method is applied as a boundary condition on the boundary of the coupling region, and near-field dynamics model calculation is carried out; when a crack appears in the near-field dynamics model, element deletion is carried out on the finite element unit according to the length of the crack, so that the structural stiffness decline caused by crack propagation is realized. The coupling model can predict the damage of brittle materials, simulate spontaneous initiation and propagation of cracks, and compared with a pure near-field dynamics model, the coupling model can greatly improve the calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of failure prediction and mechanical numerical simulation technology for quasi-brittle materials, specifically to a near-field dynamics-finite element coupling method and system. Background Technology

[0002] Currently, classical continuum mechanics theory has limitations in solving displacement discontinuity problems. Finite element methods (FEM) or extended FEM based on continuum mechanics theory exhibit numerical singularities and mesh dependence when dealing with problems such as crack propagation. Perifield dynamics, as a nonlocal theory, has significant advantages in handling discontinuity problems such as crack propagation and has made considerable progress. However, perifield dynamics theory is based on integral equations, and the model contains numerous interactions, requiring substantial computational resources and resulting in low computational efficiency. To address this issue, coupling perifield dynamics with the finite element method can be considered, ensuring that the analysis of discontinuity problems is performed while reducing computation time.

[0003] Chinese patent applications CN116913439A, CN116895352A, and CN116895351A employ a shared-node method to couple near-field dynamics and the finite element method, overcoming the fixed Poisson's ratio problem of traditional bond-based near-field dynamics theory. This method can simulate and predict the spontaneous initiation and propagation of cracks in quasi-brittle materials. Because the shared-node method requires near-field dynamic particles and finite element nodes to have the same scale near the coupling boundary, the finite element mesh density and the near-field dynamic particle density are very close in scale. While excessively fine meshing in the finite element method can improve accuracy, it consumes excessive time. Summary of the Invention

[0004] The purpose of this invention is to propose a near-field dynamics-finite element coupling method and system that can simulate crack initiation and propagation, predict the failure of brittle materials, and improve computational efficiency.

[0005] According to a first aspect of the present disclosure, a near-field dynamics-finite element coupling method is provided, comprising the following steps:

[0006] Step 1: Establish a finite element model to determine the coupling region, and establish a near-field dynamic model based on the shape of the coupling region;

[0007] Step 2, based on the element stiffness matrix [k] of the finite element model. e Obtain the overall structural stiffness matrix [K], and then obtain the relationship between the nodal forces and nodal displacements of the overall structure {F}=[K]{u}. Based on the nodal displacements {u}, extract all finite element nodal displacements {u} at the boundary of the coupling region. couple ;

[0008] Step 3: To ensure consistent deformation between the finite element model and the near-field dynamics model in the coupled region, the displacements {u} of all finite element nodes at the boundary of the coupled region are adjusted. couple As boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes.

[0009] Step 4: Calculate the peri-field dynamic model based on continuous displacement boundary conditions; if the peri-field dynamic model is damaged, proceed to Step 5; if the peri-field dynamic model is not damaged, proceed to Step 2.

[0010] Step 5: Based on the damage observed in the near-field dynamics model, reduce the stiffness of the finite element elements at the same location. If the crack formed by the damage penetrates the finite element element, delete the finite element element and update the stiffness matrix of the finite element element.

[0011] Furthermore, based on the finite element equations, the relationship between the nodal forces and nodal displacements of the overall structure is obtained as follows:

[0012] To obtain the relationship between the displacement of any point within a finite element and the nodal displacements:

[0013]

[0014] Where u and v represent horizontal and vertical displacements, u i u j Let represent the horizontal and vertical displacements of the four nodes of the quadrilateral element; [N] is the shape function matrix, represented as:

[0015]

[0016] The relationship between nodal displacement and strain is expressed as:

[0017] {ε}=[B]{δ} e

[0018] Where {ε} represents the element strain, [B] represents the element strain matrix, and {δ} e For nodal displacement, i.e., {u i v i u j v j u m v m u p v p} T ;

[0019] The relationship between element stress and nodal displacement is expressed as:

[0020] {σ}=[D]{ε}=[D][B]{δ} e =[S]{δ} e

[0021] Where {σ} is the element stress, [D] is the elastic modulus matrix, and [S] is the element stress matrix;

[0022] The relationship between nodal forces and nodal displacements of an element is expressed as follows:

[0023] {F} e =∫∫ A [B] T [D][B]dxdy·t·{δ} e =[k] e {δ} e

[0024] Among them, {F} e For element nodal forces, [k] e Let A be the element stiffness matrix, and let A be the area integration domain of the element.

[0025] Therefore, the relationship between the nodal forces and nodal displacements of the overall structure is expressed as:

[0026] {F}=[K]{u}

[0027] Where {F} represents the nodal forces of the entire structure, [K] represents the overall stiffness matrix, and {u} represents the nodal displacements of the entire structure.

[0028] Furthermore, the continuous displacement boundary conditions are obtained as follows: finite element node A and finite element node B generate nodal displacement u1 and nodal displacement u2 respectively. Linear interpolation is performed between u1 and u2 to obtain the displacement boundary conditions of each near-field dynamic element.

[0029] Furthermore, the calculation of the peridynamic model is based on the peridynamic equations of motion, specifically:

[0030]

[0031] In the formula, ρ is the density of the near-field dynamic element. Let H(x) be the acceleration of the near-field dynamic element, and H(x) be the near-field integration domain. T dV represents the force state between near-field dynamic elements, dV represents the volume of the near-field dynamic element, and b represents the volume force.

[0032] Furthermore, the force state in the near-field dynamics equations can be expressed as:

[0033]

[0034] Where K and G represent the bulk modulus and shear modulus in classical mechanics, respectively, and ν is Poisson's ratio; ω For the influence function, x Let m be the initial distance between near-field dynamical elements, and m be the weighted volume in near-field dynamics, m = ( ωx )· x θ represents the volume expansion term. e d This refers to the skewed portion of the elongation.

[0035] Furthermore, in near-field dynamics, damage is defined as follows:

[0036]

[0037] Where φ(x) represents the degree of damage to the near-field dynamics unit. d (ξ) represents the breaking of the "bond" between two near-field dynamic units. When d When (ξ) = 0, it indicates that the "bond" is complete; when d When (ξ) = 1, it indicates that the "bond" is broken.

[0038] Furthermore, the bond breaking criterion adopts the energy density criterion; when the energy density of the bond is greater than the critical energy density, the bond breaks, i.e. d (ξ)=1, and the critical energy density is expressed as:

[0039]

[0040] Among them, G c Let h be the critical energy release rate, and h be the plate thickness in the two-dimensional problem.

[0041] Furthermore, the element deletion method was introduced to realize the reaction of damage cracks on the structure. The appearance of cracks reduces the load-bearing area of ​​the structure, resulting in insufficient load-bearing capacity. Further loading accelerates the propagation of cracks. This will increase the displacement increment in the region near the crack. Excessive displacement increment may cause the loading boundary to be destroyed in the near-field dynamics region during calculation. Therefore, after the crack appears, the displacement boundary conditions calculated by the finite element model need to be applied to the near-field dynamics model multiple times.

[0042] According to a second aspect of the present disclosure, a near-field dynamics-finite element coupled system is provided, comprising:

[0043] The near-field dynamics model acquisition module establishes a finite element model to determine the coupling region, and establishes a near-field dynamics model based on the shape of the coupling region. The near-field dynamics model does not directly participate in structural calculations, but serves as a "sub-model" of the finite element unit.

[0044] The nodal displacement extraction module extracts displacements based on the finite element stiffness matrix [k]. e Obtain the overall structural stiffness matrix [K]. Based on the finite element equations, derive the relationship between nodal forces and nodal displacements of the overall structure: {F} = [K]{u}. Based on the nodal displacements {u}, extract all nodal displacements {u} at the boundary of the coupled region. couple ;

[0045] The displacement boundary condition acquisition module, based on deformation compatibility conditions, acquires the displacements {u} of all nodes at the boundary of the coupled region. couple As boundary conditions are applied to the near-field dynamics unit, continuous displacement boundary conditions are obtained by linear interpolation between adjacent nodes.

[0046] The judgment module calculates the near-field dynamic model based on continuous displacement boundary conditions; if the near-field dynamic model is damaged, it is handled by the deletion and update module.

[0047] The deletion and update module reduces the stiffness of finite element units at the same location based on the damage observed in the near-field dynamics model. If the crack formed by the damage penetrates the finite element unit, the finite element unit is deleted and the overall stiffness matrix is ​​updated.

[0048] According to a third aspect of the present disclosure, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the memory, wherein the processor executes the program to implement the aforementioned near-field dynamics-finite element coupling method.

[0049] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the aforementioned near-field dynamics-finite element coupling method.

[0050] Compared with the prior art, the above technical solutions adopted in this invention have the following advantages: the near-field dynamic model is used as a "sub-model" and the main structure is calculated entirely by finite element method, thus achieving a unified solution mode; information is transferred from the finite element model to the near-field dynamic model through displacement boundary condition loading; and finite element elements are deleted according to the damage degree calculated by the near-field dynamic model, thus achieving information transfer from the near-field dynamic model to the finite element model.

[0051] Compared to using peri-field dynamics alone, this invention significantly improves computational efficiency. It also solves the numerical singularity and mesh dependency problems inherent in the finite element method when dealing with discontinuous problems. Attached Figure Description

[0052] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0053] Figure 1 This is a flowchart of a near-field dynamics-finite element coupling method.

[0054] Figure 2 This is a schematic diagram of the finite element-near field dynamics coupled displacement boundary.

[0055] Figure 3 This is a schematic diagram of the coupling model of an embodiment.

[0056] Figure 4 This is a simulation result diagram of the unit deletion method introduced in the embodiment.

[0057] Figure 5 This is a simulation result diagram of the embodiment without introducing the unit deletion method.

[0058] Figure 6 This is a comparison chart of load-displacement curves for the implementation method with and without the element deletion method. Specific implementation methods

[0059] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0060] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0061] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0062] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and systems according to various embodiments of this disclosure. It should be noted that each block in a flowchart or block diagram may represent a module, segment, or portion of code, which may include one or more executable instructions for implementing the logical functions specified in the various embodiments. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutively represented blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, may be implemented using a dedicated hardware-based system that performs the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0063] Example 1:

[0064] like Figure 1 As shown, this embodiment provides a near-field dynamics-finite element coupling method, including the following steps:

[0065] Step 1: Establish a finite element model to determine the coupling region, and establish a peri-field dynamic model based on the shape of the coupling region. The peri-field dynamic model does not directly participate in the structural calculation, but serves as a "sub-model" of the finite element element.

[0066] Specifically, this embodiment uses a planar model of a beam, such as... Figure 3 As shown, neglecting gravity, the beam is 16m long, 4m high, and has an elastic modulus of 10000N / m. 2 The Poisson's ratio is 0.2. A rectangular element is 1m long and 0.5m high, divided into 16×8 finite element elements. A downward displacement is applied at the top center of the beam. The near-field dynamics-finite element coupling region is set at the bottom center of the beam, with a length of 4m and a height of 2m, divided into 80×40 near-field dynamic elements and 4×4 finite element elements.

[0067] Step 2, based on the element stiffness matrix [k] of the finite element model. e Obtain the overall structural stiffness matrix [K], and then obtain the relationship between the nodal forces and nodal displacements of the overall structure {F}=[K]{u}. Based on the nodal displacements {u}, extract all finite element nodal displacements {u} at the boundary of the coupling region. couple ;

[0068] Step 3: To ensure consistent deformation between the finite element model and the near-field dynamics model in the coupled region, the displacements {u} of all finite element nodes at the boundary of the coupled region are adjusted. coupleAs boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes.

[0069] like Figure 2 As shown, the large border represents the finite element element, and the small squares represent the near-field dynamic element. Nodal displacements u1 and u2 are generated at finite element nodes A and B, respectively, which are represented by solid lines in the figure. Linear interpolation is performed between u1 and u2 to obtain the displacement boundary conditions of each near-field dynamic element, which are represented by dashed lines in the figure.

[0070] Step 4: Calculate the peri-field dynamic model based on the displacement boundary conditions; if the peri-field dynamic model is damaged, proceed to Step 5; if the peri-field dynamic model is not damaged, proceed to Step 2.

[0071] Specifically, the calculation of the peridynamic model is based on the peridynamic equations of motion, as follows:

[0072]

[0073] In the formula, ρ is the density of the near-field dynamic element. Let H(x) be the acceleration of the near-field dynamic element, and H(x) be the near-field integration domain. T dV represents the force state between near-field dynamic elements, dV represents the volume of the near-field dynamic element, and b represents the volume force.

[0074] Using the plane strain form of normal ground-based near-field dynamics, the force state can be expressed as:

[0075]

[0076] In this table, K and G represent the bulk modulus and shear modulus in classical mechanics, respectively, and ν is Poisson's ratio. ω For the influence function, x Let m be the initial distance between near-field dynamical elements, and m be the weighted volume in near-field dynamics, m = ( ωx )· x θ represents the volume expansion term. e d This refers to the skewed portion of the elongation.

[0077] The critical energy density of a "bond" is expressed as:

[0078]

[0079] Among them, G c Let h be the critical energy release rate, and h be the plate thickness in the two-dimensional problem.

[0080] Step 5: Based on the damage observed in the near-field dynamics model, reduce the stiffness of the finite element elements at the same location. If the crack formed by the damage penetrates the finite element element, delete the finite element element and update the stiffness matrix of the finite element element.

[0081] Specifically, in order to avoid excessive displacement increments leading to loading boundary failure in the near-field dynamics region, the displacement boundary conditions calculated by the finite element model need to be applied to the near-field dynamics model multiple times after the crack appears.

[0082] Figure 4 and Figure 5 The simulation results obtained with and without the element removal method are shown respectively. It can be seen that the crack extends upwards from the center of the beam bottom, which is consistent with actual conditions. Without the element removal method, the crack has no effect on the model; the load-bearing area of ​​the structure remains unchanged. Even though the near-field dynamic model shows damage, it does not affect the original structure in any way. The model is always calculated using finite element methods, resulting in a discrepancy with reality. The element removal method, on the other hand, realizes the reaction of the damage crack on the structure. The appearance of the crack reduces the load-bearing area of ​​the structure, leading to insufficient load-bearing capacity. Further loading accelerates the structural failure and crack propagation. Figure 4 This also indicates that the result of introducing element deletion is a larger crack width and a deeper crack length, which is consistent with the actual situation. Figure 6 The comparison of load-displacement curves with and without the element deletion method shows that the coupled model can reflect the decrease in bearing capacity after structural damage.

[0083] This invention provides a near-field dynamics-finite element coupling method. This method is computationally simple, and the structural solution process is entirely based on the finite element method. The near-field dynamics-finite element coupling region is treated as a "sub-model" and does not directly participate in the calculation. The displacement calculated by the finite element method is applied as a boundary condition on the boundary of the coupling region, and the near-field dynamic model is calculated. When a crack appears in the near-field dynamic model, finite element elements are deleted according to the crack length to realize the decrease in structural stiffness caused by crack propagation. This coupling model can predict the failure of brittle materials, simulate the spontaneous initiation and propagation of cracks, and improve computational efficiency compared to a pure near-field dynamics model.

[0084] Example 2:

[0085] This embodiment provides a near-field dynamics-finite element coupled system, including:

[0086] The near-field dynamics model acquisition module establishes a finite element model to determine the coupling region, and establishes a near-field dynamics model based on the shape of the coupling region;

[0087] The nodal displacement extraction module extracts displacements based on the element stiffness matrix [k] of the finite element model. e Obtain the overall structural stiffness matrix [K], and then obtain the relationship between the nodal forces and nodal displacements of the overall structure {F}=[K]{u}. Based on the nodal displacements {u}, extract all finite element nodal displacements {u} at the boundary of the coupling region. couple ;

[0088] The displacement boundary condition acquisition module, to ensure consistent deformation between the finite element model and the near-field dynamics model in the coupled region, acquires the displacements {u} of all finite element nodes at the boundary of the coupled region. couple As boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes.

[0089] The judgment module calculates the near-field dynamic model based on continuous displacement boundary conditions; if the near-field dynamic model is damaged, it is handled by the deletion and update module.

[0090] The deletion and update module reduces the stiffness of finite element elements at the same location based on the damage observed in the near-field dynamics model. If the crack formed by the damage penetrates the finite element element, the finite element element is deleted and the stiffness matrix of the finite element element is updated.

[0091] Example 3:

[0092] An electronic device includes a memory, a processor, and a computer program stored in the memory and running thereon, wherein the processor, when executing the program, implements the aforementioned near-field dynamics-finite element coupling method, comprising:

[0093] Step 1: Establish a finite element model to determine the coupling region, and establish a near-field dynamic model based on the shape of the coupling region;

[0094] Step 2, based on the element stiffness matrix [k] of the finite element model. e Obtain the overall structural stiffness matrix [K], and then obtain the relationship between the nodal forces and nodal displacements of the overall structure {F}=[K]{u}. Based on the nodal displacements {u}, extract all finite element nodal displacements {u} at the boundary of the coupling region. couple ;

[0095] Step 3: To ensure consistent deformation between the finite element model and the near-field dynamics model in the coupled region, the displacements {u} of all finite element nodes at the boundary of the coupled region are adjusted. couple As boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes.

[0096] Step 4: Calculate the peri-field dynamic model based on continuous displacement boundary conditions; if the peri-field dynamic model is damaged, proceed to Step 5; if the peri-field dynamic model is not damaged, proceed to Step 2.

[0097] Step 5: Based on the damage observed in the near-field dynamics model, reduce the stiffness of the finite element elements at the same location. If the crack formed by the damage penetrates the finite element element, delete the finite element element and update the stiffness matrix of the finite element element.

[0098] Example 4:

[0099] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned near-field dynamics-finite element coupling method, comprising:

[0100] Step 1: Establish a finite element model to determine the coupling region, and establish a near-field dynamic model based on the shape of the coupling region;

[0101] Step 2, based on the element stiffness matrix [k] of the finite element model. e Obtain the overall structural stiffness matrix [K], and then obtain the relationship between the nodal forces and nodal displacements of the overall structure {F}=[K]{u}. Based on the nodal displacements {u}, extract all finite element nodal displacements {u} at the boundary of the coupling region. couple ;

[0102] Step 3: To ensure consistent deformation between the finite element model and the near-field dynamics model in the coupled region, the displacements {u} of all finite element nodes at the boundary of the coupled region are adjusted. couple As boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes.

[0103] Step 4: Calculate the peri-field dynamic model based on continuous displacement boundary conditions; if the peri-field dynamic model is damaged, proceed to Step 5; if the peri-field dynamic model is not damaged, proceed to Step 2.

[0104] Step 5: Based on the damage observed in the near-field dynamics model, reduce the stiffness of the finite element elements at the same location. If the crack formed by the damage penetrates the finite element element, delete the finite element element and update the stiffness matrix of the finite element element.

[0105] Those skilled in the art will understand that the modules or steps described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, which can then be stored in a storage device for execution by a computer device. Alternatively, they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. This disclosure is not limited to any particular combination of hardware and software.

[0106] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0107] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A near-field dynamics-finite element coupling method, characterized in that, For a planar model of the beam, a downward displacement is applied at the top center of the beam. A near-field dynamics-finite element coupling region is set at the bottom center of the beam, and this coupling region is divided into near-field dynamics elements and finite element elements. The coupling method includes the following steps: Step 1: Establish a finite element model to determine the coupling region, and establish a near-field dynamic model based on the shape of the coupling region; Step 2, based on the element stiffness matrix of the finite element model. Obtain the overall stiffness matrix of the structure This leads to the relationship between the nodal forces and nodal displacements of the overall structure. Based on nodal displacement Extract all finite element nodal displacements of the coupled region boundary ; Step 3: To ensure consistent deformation between the finite element model and the near-field dynamics model in the coupled region, the displacements of all finite element nodes at the boundary of the coupled region are adjusted. As boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes. Step 4: Calculate the peri-field dynamic model based on continuous displacement boundary conditions; if the peri-field dynamic model is damaged, proceed to Step 5; if the peri-field dynamic model is not damaged, proceed to Step 2. Step 5: Based on the damage observed in the near-field dynamics model, reduce the stiffness of the finite element elements at the same location. If the crack formed by the damage penetrates the finite element element, delete the finite element element and update the stiffness matrix of the finite element element.

2. The near-field dynamics-finite element coupling method according to claim 1, characterized in that, The relationship between nodal forces and nodal displacements of the overall structure is obtained based on the finite element equations, specifically: To obtain the relationship between the displacement of any point within a finite element and the nodal displacements: in, and Indicates horizontal and vertical displacement. , , , , , , , This represents the horizontal and vertical displacements of the four nodes of the quadrilateral element; The shape function matrix is ​​represented as: The relationship between nodal displacement and strain is expressed as: in, For unit strain, The strain matrix of the element. For nodal displacement, i.e. ; The relationship between element stress and nodal displacement is expressed as: in, For element stress, The elastic modulus matrix, The stress matrix of the element; The relationship between nodal forces and nodal displacements of an element is expressed as follows: in, For element nodal forces, The element stiffness matrix, For the area integration domain of the element; Therefore, the relationship between the nodal forces and nodal displacements of the overall structure is expressed as: in, For the nodal forces of the entire structure, The overall stiffness matrix, This represents the nodal displacement of the entire structure.

3. The near-field dynamics-finite element coupling method according to claim 1, characterized in that, The method to obtain continuous displacement boundary conditions is as follows: finite element node A and finite element node B generate nodal displacements respectively. and nodal displacement ,exist and Linear interpolation is performed between them to obtain the displacement boundary conditions for each near-field dynamic element.

4. The near-field dynamics-finite element coupling method according to claim 1, characterized in that, The calculation of the peri-field dynamics model is based on the peri-field dynamics equations of motion, specifically: In the formula, For near-field dynamic unit density, For the acceleration of the near-field dynamics unit, For the near-field integration domain, For the force state between near-field dynamic units, For the volume of the near-field dynamics unit, It is a volume force.

5. The near-field dynamics-finite element coupling method according to claim 4, characterized in that, The force state in the near-field dynamics equations of motion is expressed as: in, and The separate tables represent the bulk modulus and shear modulus in classical mechanics. Poisson's ratio; For the influence function, The initial distance between near-field dynamic units. For the weighted volume in peri-field dynamics, ; This is the volume expansion term. ; This refers to the skewed portion of the elongation. .

6. The near-field dynamics-finite element coupling method according to claim 1, characterized in that, In peridynamics, damage is defined as follows: in, This indicates the degree of damage to the near-field dynamic unit. This indicates the breaking of the "bond" between two near-field dynamic units; when When, it indicates that the "key" is complete; when When the "key" breaks, it indicates that the "bond" is broken.

7. The near-field dynamics-finite element coupling method according to claim 6, characterized in that, The bond breaking criterion uses the energy density criterion; when the energy density of a bond is greater than the critical energy density, the bond breaks. The critical energy density is expressed as: in, The critical energy release rate. Let's consider the plate thickness in a two-dimensional problem.

8. The near-field dynamics-finite element coupling method according to claim 1, characterized in that, After the crack appears, the displacement boundary conditions calculated by the finite element model need to be applied to the near-field dynamic model multiple times.

9. A near-field dynamics-finite element coupled system, characterized in that, For the planar model of the beam, a downward displacement is applied at the top center of the beam. The near-field dynamics-finite element coupling region is set at the bottom center of the beam, and the coupling region is divided into near-field dynamics elements and finite element elements. The coupling system includes: The near-field dynamics model acquisition module establishes a finite element model to determine the coupling region, and establishes a near-field dynamics model based on the shape of the coupling region; The nodal displacement extraction module extracts displacements based on the element stiffness matrix of the finite element model. Obtain the overall stiffness matrix of the structure This leads to the relationship between the nodal forces and nodal displacements of the overall structure. Based on nodal displacement Extract all finite element nodal displacements of the coupled region boundary ; The displacement boundary condition acquisition module, to ensure consistent deformation between the finite element model and the near-field dynamic model in the coupled region, acquires the displacements of all finite element nodes at the boundary of the coupled region. As boundary conditions applied to the near-field dynamics elements, continuous displacement boundary conditions are obtained by linear interpolation between adjacent finite element nodes. The judgment module calculates the near-field dynamic model based on continuous displacement boundary conditions; if the near-field dynamic model is damaged, it is handled by the deletion and update module. The deletion and update module reduces the stiffness of finite element elements at the same location based on the damage observed in the near-field dynamics model. If the crack formed by the damage penetrates the finite element element, the finite element element is deleted and the stiffness matrix of the finite element element is updated.

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