Multi-level encryption method for finite discrete element grid of contact interface of arbitrary shape object

Abstract

This invention provides a multi-level refinement method for finite discrete element meshes at contact interfaces of objects with arbitrary shapes, belonging to the field of finite discrete element mesh refinement. This invention develops a quadrangular prism refinement layer technique, combining it with contact error penetration determination to selectively adjust the mesh density of local interfaces at multiple levels. Simultaneously, the mesh on the contact interface maintains a quadrilateral shape, without increasing the overall model's additional degrees of freedom or distorted elements, thereby effectively controlling the error in contact numerical solutions. This method is applicable to contact interfaces of arbitrary shapes.

Description

Technical Field

[0001] This invention belongs to the field of finite discrete element mesh encryption, specifically involving a multi-level encryption method for finite discrete element meshes of contact interfaces of objects of arbitrary shapes. Background Technology

[0002] Finite Discrete Element Analysis (FEMI) for contact mechanics problems is widely used in defense, aerospace, and precision manufacturing. In numerical simulations of complex systems involving multi-body interactions, the simulation accuracy of the contact interface is crucial to the accuracy of load transfer paths and the reliability of structural failure analysis. To capture the contact state and local high-gradient stress fields of complex interface morphologies, the interface geometry is typically discretized into element meshes within the overall numerical model. Contact algorithms are integrated with FEMI, establishing constraints through master-slave surface contact relationships, and the deformation and stress under specific boundary value problems are solved using the FEMI method. The topology and discrete density of the interface mesh directly determine the accuracy of the numerical simulation and have received widespread attention.

[0003] Contact areas are often accompanied by drastic stress changes, especially in high-frequency fluctuations or impact dynamics problems. If the interface mesh is too coarse, the interpolation between nodes cannot capture the actual peak stress, thus underestimating the fatigue risk or yielding potential of the material. Most failures occur at the contact surface and its adjacent areas. Furthermore, geometric penetration or artificial gap errors caused by sparse contact points directly interfere with the determination of the contact state (adhesion, sliding, separation). Therefore, refining the interface mesh is fundamental to accurately reconstructing the overall stress and deformation state in multi-body contact problems.

[0004] With the improvement of computer performance, interface simulation methods based on contact mechanics calculations are gradually being applied to the dynamic analysis of large-scale engineering structures. Analyzing the structure-interface-foundation system as a whole is fundamental to accurately studying the dynamic interaction effects of soil and structure, and is also a challenging and popular area in engineering numerical simulation, such as the slippage of tunnel lining surfaces, the opening and closing of transverse joints in hydraulic arch dams, and the lift-off slippage of raft foundation surfaces. In wave finite element simulations involving contact, the discretization of the interface mesh is limited by the accuracy requirements of the contact solution, and is usually finer than that used in wave propagation simulations. The overall structure-foundation model is large-scale, and solving contact problems requires a large number of iterations. If a fine mesh is blindly used for the entire model, the computational cost will be unacceptable. Through effective local mesh refinement control, the efficiency of numerical computation can be significantly improved while ensuring the accuracy of key interface regions.

[0005] Existing contact mechanics calculations within the finite element framework are relatively mature, with classic solution algorithms including the Lagrange multiplier method and the penalty function method. However, interface mesh density and discretization mode remain sensitive conditions affecting the evolution of instantaneous contact relationships and the simulation of edge stresses, and are key factors in balancing efficiency and accuracy. For simplified structural geometric models, the interface mesh is relatively easy to control; however, for detailed modeling of the target structure with complex geometry, the scale, shape, and size of the mesh are difficult to plan, and the verification and adjustment of contact point pairs involve tedious local mesh re-distribution, resulting in a significant workload. Numerical simulations of engineering contact often lack verification of mesh discretization at the interface. For specific structural and site conditions, and for complex contacts of arbitrary shapes, a simple and practical method for local interface mesh refinement needs to be developed.

[0006] Currently, multi-level mesh refinement methods applicable to finite element interfaces of arbitrary shapes are rare. Researchers have conducted studies on local mesh refinement using the idea of ​​direct transition from polyhedral and octet tree meshes, constructing corresponding computational units such as multicellular elements, centroid-based elements, and scaled boundary finite element elements. However, these meshing methods are generally difficult to implement and limited to fixed mesh styles. Furthermore, when the model as a whole adopts a special meshing method, the increased proportion of special elements increases the computational load of finite element analysis. To address the irregularities in base geometry and partitioning caused by the refined construction of finite element models such as core island structures, it is necessary to formulate appropriate automatic mesh refinement rules for contact surfaces, develop flexible adjustment methods adapted to existing technologies, and further explore efficient and high-quality modeling methods for multi-body contact systems. There is a lack of an effective multi-level mechanism that can locally refine the mesh on top of a conventional coarse mesh, thereby facilitating mesh sensitivity analysis in the analysis of engineering contact problems.

[0007] As mentioned earlier, for contact interfaces of arbitrary shapes, excessively coarse meshes can affect local peak stress, contact state determination, and even lead to geometric penetration or artificial gaps. Conversely, blindly using fine meshes incurs unnecessary computational costs. To match the complex geometry of the target structure's contact interface, existing special element transition meshes are difficult to apply directly, and the verification and adjustment of contact point pairs involve tedious local mesh re-distribution, especially for large-scale engineering structure-foundation integrated models. The key issue here is how to flexibly adjust the mesh density of arbitrary contact interfaces at multiple levels based on the original matching mesh, discretizing the interface into sufficient contact point pairs; however, there is a lack of effective methods for this. Summary of the Invention

[0008] This invention aims to provide a multi-level refinement method for finite discrete element meshes at the contact interface of objects of arbitrary shapes. Its main principle is based on the principle of recursive transition meshes, proposing a quadrangular prism refinement layer model on the basis of the original irregular mesh at the target contact interface. Combined with the determination of contact pair error penetration, it selectively refines the local mesh at multiple levels, improving the density and shape of the interface mesh.

[0009] The technical solution of this invention is: A multi-level finite discrete element mesh refinement method for the contact interface of objects of arbitrary shapes, comprising the following steps: Step 1: Identification and information extraction of contact interface boundary layer units; Step 2: Solving the contact problem and determining the boundary layer elements to be refined based on the contact penetration amount; Step 3: Generate new nodes in the thickness direction of the boundary layer elements; Step 4: Update the density of nodes within the boundary layer element surface; Step 5: Generate encrypted boundary elements and non-conformal transition elements; Step 6: Multi-level encryption iteration based on contact penetration criterion.

[0010] Further, step 1 specifically involves: performing finite element modeling on all objects of arbitrary shape that are in contact with each other; the mesh element faces of the layer near the contact interface between the objects are quadrilaterals or triangles; based on the geometric dimensions of the contact interface between the objects, the mesh element in the layer near the contact interface between the objects is divided into boundary layer elements; and the node information and element information of the boundary layer elements are extracted; wherein, the node information includes the node number and coordinates, and the element information includes the element number and the node number associated with that element. Only the boundary layer cells are processed, without changing the mesh cells and node composition of other parts of the object. The boundary layer cells between objects that are in contact with each other need to be densified synchronously. The specific process is the same, which is steps 2 to 5.

[0011] Furthermore, step 2 specifically involves: Based on the partitioning results of step 1, establish the global equilibrium equations for the finite element system of the contact problem to be solved; The contact problem refers to the force analysis of contacting objects, and the numerical solution of the contact problem is performed using the penalty function method. In the numerical solution process, externally applied loads and boundary conditions are considered, and penalty stiffness is introduced at the contact interface. And allows for a small amount of penetration at the contact interface. This transforms geometric constraints into contact forces. The contact force will be incorporated as an additional internal force vector into the global equilibrium equation of the finite element system. The contact penetration amount in the equilibrium state can be obtained by iteratively solving the global equilibrium equation of the finite element system. In the numerical solution of contact problems, the contact penetration of the output contact pairs is judged. When the ratio of the contact penetration to the size of the boundary layer element exceeds the allowable penetration range, the corresponding contact pair is marked and the corresponding boundary layer element is defined as a set. .

[0012] Furthermore, step 3 specifically involves: Select boundary layer elements In a mesh element L, the set of nodes distributed on the contact interface in mesh element L is defined as follows: The set of nodes on the other side is , will node and the corresponding nodes The midpoint between them is used as the new node set. .

[0013] Furthermore, step 4 specifically involves: For each set of nodes and node set Take the midpoints of each edge of the face, and add the midpoints of each edge and the center points of the two faces to the corresponding node set. and node set In the context of node sets and node set Perform an update to obtain a new set of nodes. and .

[0014] Furthermore, step 5 specifically includes: by and The nodes in the diagram are used as vertices, and microhexahedral elements are used to divide the boundary layer elements of all objects. The microhexahedral elements in all mesh elements are integrated to obtain a new set of boundary elements. ,by and Using nodes as vertices, a non-conformal mesh element with dangling nodes is created. The non-conformal mesh element includes... All nodes; the suspended nodes are all nodes in the non-conformal mesh element except for the vertices; the boundary layer elements of all objects The non-conformal mesh cells in all mesh cells serve as a transition layer, completing the first-level encryption. For a given initial boundary layer cell, each refinement process generates a transition layer. All transition layers are collectively referred to as the transition region. The number of non-conformal mesh cells in the transition region is related to the number of refinement partitions. During this subdivision, the ratio of the size of the refined mesh cell to the size of the original mesh cell is... The number of cells in a non-conformal mesh for: (1) The scaled boundary finite element method further discretizes non-common mesh elements into multiple wedge-shaped regions, each wedge-shaped region being a sub-element; the governing equations of multiple sub-elements with the same similar center point and consistent radial boundaries of adjacent elements are assembled according to the degrees of freedom of the boundary discrete points, and defined as a super-element.

[0015] Furthermore, step 6 specifically includes: Based on the encryption results, a new finite element equation for the contact problem to be solved is established. When the contact penetration determination requires further encryption, the newly generated boundary element set is used. Repeat steps 2 through 5 until the mesh density at the contact interface meets the requirements.

[0016] The method is specifically designed for fine-grained mesh analysis of interfaces. The overall recursive generation algorithm flow is as follows: Figure 2 As shown, by using the strategy of quadrangular prism mesh refinement layer, an automatic multi-level refinement of interface mesh is achieved on the basis of the original corresponding node mesh. The unit layer connected to the contact interface becomes a finite element with a smaller mesh, and the mesh on the contact interface maintains a quadrilateral shape, without increasing the overall model's additional degrees of freedom and distorted elements, thus improving the accuracy of multibody contact mechanics simulation.

[0017] The method proposed in this invention can be used not only for finite element analysis but also integrated with the discrete element analysis framework. It performs local secondary refinement of the interface based on an existing mesh, while keeping the element-node information of other parts of the multi-body contact global model unchanged. Typically, mass points in the structure, as well as seismic forces and artificial boundaries in the foundation, are applied based on node numbers; therefore, updating the refinement layer does not affect these parameters, making it more efficient than re-meshing.

[0018] The beneficial effects of this invention are as follows: It develops a quadrangular prism densification layer technology, which, combined with the determination of contact error penetration, allows for targeted multi-level adjustment of the mesh density of the local interface. At the same time, the mesh on the contact interface remains quadrilateral, without increasing the overall model's additional degrees of freedom and distorted elements, thereby effectively controlling the error of contact numerical solution. It is applicable to contact interfaces of any shape. Attached Figure Description

[0019] Figure 1This is a schematic diagram of the topology of the re-divided mesh during first-level encryption, where (a) the initial interface mesh is a hexahedron and (b) the initial interface mesh is a triangular prism.

[0020] Figure 2 It is a recursive generation algorithm process for a multi-level encryption layer of the interface grid.

[0021] Figure 3 This is a schematic diagram of multi-level encryption of a hexahedral cell mesh.

[0022] Figure 4 This is a schematic diagram of multi-level encryption of triangular prism unit mesh.

[0023] Figure 5 This is a schematic diagram of the Hertzian contact problem of a cylinder.

[0024] Figure 6 This is a finite element model diagram of the Hertzian contact problem of a cylinder.

[0025] Figure 7 It is the result of local multi-level mesh refinement of the contact interface in the Hertzian contact problem of a cylinder.

[0026] Figure 8 This refers to the change in the calculated contact stress value under local multi-level mesh refinement at the contact interface in the Hertzian contact problem of a cylinder.

[0027] Figure 9 It is a curve showing the change in contact penetration as a function of the encryption level of the contact interface.

[0028] Figure 10 It is a curve showing the change of contact stress with the degree of densification of the contact interface.

[0029] Figure 11 This is an example of the application of the method in a multibody contact problem with complex geometry. Among them, (a) is the local refinement result of the mesh of the horseshoe-shaped lining cavern-foundation interface, (b) is the mesh refinement result of the irregular lining cavern-foundation interface, and (c) is the mesh refinement result of the nuclear island building structure-foundation interface. Detailed Implementation

[0030] The specific embodiments of the present invention will now be described in detail with reference to the technical solutions and accompanying drawings.

[0031] Hertzian contact is a classic problem in the field of multibody contact mechanics. The method proposed in this invention is used to perform contact simulation and multi-level mesh refinement analysis of the interface. The effectiveness and applicability of the method are verified by comparing the Hertzian theoretical solutions for contact stress and contact area.

[0032] In this embodiment, the contact problem is constructed as the compression of two cylinders, with pressure at both ends. The strength is 80kN, and the target contact interface is located between two cylinders, such as... Figure 5 As shown. The maximum contact stress calculated using Hertz's formula is: (10) The half-width of the contact surface is: (11) in, Indicates the width of the contact area. This represents the radius of cylinder 1. This represents the radius of cylinder 2. This represents the Poisson's ratio of cylinder 1. This represents the Poisson's ratio of cylinder 2. This represents the elastic modulus of cylinder 1. This represents the elastic modulus of cylinder 2; Due to the symmetry of the problem, we take half of the model for calculation, and use the following parameters at both ends of the model: Smooth loading was applied, and a face-to-face discretization method was used for the possible contact area, with cylinder 1 as the master surface and cylinder 2 as the slave surface. The initial mesh size of the contact interface was approximately 0.15 m. The material and geometric parameters of the cylinders are shown in Table 1. Under this contact problem, the Hertzian theoretical solutions for the maximum contact stress and the half-width of the contact surface are 123 MPa and 0.0825 m, respectively.

[0033] Table 1: Material and Geometric Parameters

[0034] The contact simulation of the above-mentioned problem is performed using the method proposed in this invention. The specific steps of the embodiment are as follows: Step 1. Perform finite element modeling on the two contacting cylinders (see...) Figure 6 The mesh cells in the layer near the contact interface between objects have quadrilateral faces. Based on the geometric dimensions of the contact interface between objects, the mesh cells in the layer near the contact interface between objects are divided into boundary layer cells, and the node information and cell information of the boundary layer cells are extracted. The node information includes the node number and coordinates, and the cell information includes the cell number and the node number associated with that cell. Step 2. Based on the partitioning results in Step 1, establish the global equilibrium equations for the finite element system of the contact problem to be solved; Step 3. Select boundary layer elements In a mesh element L, the set of nodes distributed on the contact interface in mesh element L is defined as follows: The set of nodes on the other side is , will node and the corresponding nodes The midpoint between them is used as the new node set. ; Step 4. For each node set and node set Take the midpoints of each edge of the face, and add the midpoints of each edge and the center points of the two faces to the corresponding node set. and node set In the context of node sets and node set Perform an update to obtain a new set of nodes. and ; Step 5. and The nodes in the diagram are used as vertices, and microhexahedral elements are used to divide the boundary layer elements of all objects. The microhexahedral elements in all mesh elements are integrated to obtain a new set of boundary elements. ,by and Using nodes as vertices, a non-conformal mesh element with dangling nodes is created. The non-conformal mesh element includes... All nodes; the suspended nodes are all nodes in the non-conformal mesh element except for the vertices; (the number of nodes in the non-conformal mesh element is 10 when the element face is triangular and 13 when the element face is quadrilateral), the boundary layer elements of all objects Non-conformal mesh elements in all mesh elements serve as a transition layer, completing the local refinement of the contact interface. The mesh after element re-division is as follows: Figure 7 As shown.

[0035] Step 6. Re-establish the finite element equations for the contact problem to be solved based on the encryption results. If further encryption is needed to determine the contact penetration amount, the newly generated boundary element set will be used. Repeat steps 2 through 5 until the mesh density at the contact interface meets the requirements. The calculated contact stress results under each mesh refinement level are as follows: Figure 8 As shown, the half-width of the contact surface also tends to 0.0825m, indicating that the calculation results gradually converge to the exact solution under multi-level encryption. Figure 9 , Figure 10 The changes in contact penetration and maximum contact stress with the number of mesh densification levels were compared. It can be seen that contact penetration is an important aspect of measuring the accuracy of contact calculation. The proposed method can adjust the mesh density of local and global interfaces in a targeted, flexible and effective manner at multiple levels, thereby improving the accuracy of contact calculation.

[0036] To further demonstrate the beneficial effects and applicability of the method proposed in this invention, which is suitable for the encryption of arbitrary triangular and quadrilateral unit surfaces, Figure 11The results show the local mesh refinement of the horseshoe-shaped lining cavern-foundation interface, the mesh refinement of the irregular-shaped lining cavern-foundation interface, and the mesh refinement of the nuclear island building structure-foundation interface.

Claims

1. A multi-level encryption method for finite discrete element grid of contact interface of arbitrary shaped objects, characterized in that, The steps are as follows: Step 1: Identification and information extraction of contact interface boundary layer units; Step 2: Solving the contact problem and determining the boundary layer elements to be refined based on the contact penetration amount; Step 3: Generate new nodes in the thickness direction of the boundary layer elements; Step 4: Update the density of nodes within the boundary layer element surface; Step 5: Generate encrypted boundary elements and non-conformal transition elements; Step 6: Multi-level encryption iteration based on contact penetration criterion.

2. The finite discrete element mesh multi-level refinement method for the contact interface of objects of arbitrary shapes according to claim 1, characterized in that, Step 1 specifically involves: performing finite element modeling on all objects of arbitrary shapes that are in contact with each other; the mesh element faces of the layer near the contact interface between objects are quadrilaterals or triangles; based on the geometric dimensions of the contact interface between objects, the mesh element in the layer near the contact interface between objects is divided into boundary layer elements; and the node information and element information of the boundary layer elements are extracted; wherein, the node information includes the node number and coordinates, and the element information includes the element number and the node number associated with that element. Only the boundary layer cells are processed, without changing the mesh cells and node composition of other parts of the object. The boundary layer cells between objects that are in contact with each other need to be densified synchronously. The specific process is the same, which is steps 2 to 5.

3. The finite discrete element mesh multi-level refinement method for the contact interface of objects of arbitrary shapes according to claim 2, characterized in that, Step 2 is as follows: Based on the partitioning results of step 1, establish the global equilibrium equations for the finite element system of the contact problem to be solved; The contact problem refers to the force analysis of contacting objects, and the numerical solution of the contact problem is performed using the penalty function method. In the numerical solution process, externally applied loads and boundary conditions are considered, and penalty stiffness is introduced at the contact interface. And allows for a small amount of penetration at the contact interface. This transforms geometric constraints into contact forces. The contact force will be incorporated as an additional internal force vector into the global equilibrium equation of the finite element system. The contact penetration amount in the equilibrium state can be obtained by iteratively solving the global equilibrium equation of the finite element system. In the numerical solution of contact problems, the contact penetration of the output contact pairs is judged. When the ratio of the contact penetration to the size of the boundary layer element exceeds the allowable penetration range, the corresponding contact pair is marked and the corresponding boundary layer element is defined as a set. .

4. The finite discrete element mesh multi-level refinement method for contact interfaces of objects of arbitrary shapes according to claim 3, characterized in that, Step 3 specifically involves: Select boundary layer elements In a mesh element L, the set of nodes distributed on the contact interface in mesh element L is defined as follows: The set of nodes on the other side is , will node and the corresponding nodes The midpoint between them is used as the new node set. .

5. The finite discrete element mesh multi-level refinement method for contact interfaces of objects of arbitrary shapes according to claim 4, characterized in that, Step 4 specifically involves: For each set of nodes and node set Take the midpoints of each edge of the face, and add the midpoints of each edge and the center points of the two faces to the corresponding node set. and node set In the context of node sets and node set Perform an update to obtain a new set of nodes. and .

6. The finite discrete element mesh multi-level refinement method for the contact interface of objects of arbitrary shapes according to claim 5, characterized in that, Step 5 specifically involves: by and The nodes in the diagram are used as vertices, and microhexahedral elements are used to divide the boundary layer elements of all objects. The microhexahedral elements in all mesh elements are integrated to obtain a new set of boundary elements. ,by and Using nodes as vertices, a non-conformal mesh element with dangling nodes is created. The non-conformal mesh element includes... All nodes; the suspended nodes are all nodes in the non-conformal mesh element except for the vertices; the boundary layer elements of all objects The non-conformal mesh cells in all mesh cells serve as a transition layer, completing the first-level encryption. For a given initial boundary layer cell, each refinement process generates a transition layer. All transition layers are collectively referred to as the transition region. The number of non-conformal mesh cells in the transition region is related to the number of refinement partitions. During this subdivision, the ratio of the size of the refined mesh cell to the size of the original mesh cell is... The number of cells in a non-conformal mesh for: (1) The scaled boundary finite element method further discretizes non-common mesh elements into multiple wedge-shaped regions, each wedge-shaped region being a sub-element; A super-element is defined by assembling the governing equations of multiple sub-elements with the same center point and consistent radial boundaries of adjacent elements according to the degrees of freedom of the boundary discrete points.

7. The finite discrete element mesh multi-level refinement method for contact interfaces of objects of arbitrary shapes according to claim 6, characterized in that, Step 6 specifically involves: Based on the encryption results, a new finite element equation for the contact problem to be solved is established. When the contact penetration determination requires further encryption, the newly generated boundary element set is used. Repeat steps 2 through 5 until the mesh density at the contact interface meets the requirements.

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