An adaptive coupling calculation method based on stable node integration and smooth particle method

Abstract

The present invention discloses an adaptive coupling calculation method based on stable node integration and smooth particle method. The method comprises: generating a particle model on an unstructured background grid in the simulation of the impact collision process; marking nodes for the stable node integration method and particles for the smooth particle method in the particle model; identifying composite units at the interface between nodes and particles in the particle model; constructing a grid particle interface tracking mechanism based on adjacent unit search and a composite unit physical quantity solving method to realize automatic coupling calculation of grid-based methods and particle-based methods; the present invention can adapt to complex geometric boundaries while greatly improving the calculation accuracy based on unstructured grids, reducing the numerical errors caused by frequent mapping of nodes and integration points, improving the efficiency of the existing finite element smooth particle adaptive coupling calculation, and making full use of the respective advantages of stable node integration and smooth particle methods.

Description

Technical Field

[0001] The present invention relates to the technical field of high-performance numerical simulation analysis in engineering, and in particular to an adaptive coupling calculation method based on stable node integration and a smooth particle method. Background Art

[0002] Impact and collision phenomena are ubiquitous. In the actual engineering mechanics simulation process, complex impact and collision situations are often involved. The finite element algorithm has obvious advantages in dealing with medium and low-speed collision situations due to its high calculation accuracy and high calculation efficiency. The particle method has a meshless characteristic that the finite element method cannot match in calculating ultra-high-speed collisions, that is, there is no mesh distortion, but the use of the particle method in the entire domain will have the problem of low calculation efficiency. If an algorithm model that can realize finite element-smooth particle coupling calculation can be established, the advantages of the finite element method and the smooth particle dynamics method in their respective fields can be combined, and the finite element algorithm can be used in the stable small deformation area, and the smooth particle algorithm can be used in the large deformation area, then the calculation effect that cannot be achieved when the two algorithms are used alone can be achieved.

[0003] However, there are significant differences between the finite element method and the smooth particle dynamics method in terms of algorithmic theoretical basis and computational process. The difference in theoretical basis between the two methods leads to different discrete equations and forms of the two algorithms. In terms of unit geometry, the finite element unit is generally a multi-node sub-region with a certain geometric shape, while the smooth particle algorithm is a single particle point with a certain range of action. These have increased the difficulty of combining the finite element algorithm with the smooth particle algorithm. It is worth noting that the control equations of both the finite element and smooth particle dynamics contain mass conservation, momentum conservation, energy conservation, and constitutive equations describing material properties. After spatial discretization of the control equation based on the finite element, it can be found that it is consistent with the control equation of the smooth particle algorithm in form. Both are ordinary differential equations based on time variables, and can be explicitly solved using the central difference method in the time domain, which provides a natural gene for the coupled calculation of the finite element and the smooth particle.

[0004] Coupling algorithms can be roughly divided into two categories: one is the fixed coupling algorithm, which determines the area to be calculated by the finite element method and the smooth particle method at the initial moment of the calculation, and remains unchanged in the subsequent process; the other is the adaptive coupling algorithm, which uses the finite element method for all calculations at the initial moment, and automatically converts the units in the large deformation area into particles during the calculation process, and uses the smooth particle method for calculation. The introduction of the adaptive coupling algorithm can convert the finite element into smooth particles for continued calculation after the distortion reaches a certain degree, reducing manual intervention in the meshing process and improving the adaptability of the finite element-smooth particle coupling algorithm to actual engineering cases. At the same time, the finite element only needs to focus on the calculation of the continuous medium stage, avoiding the special processing algorithms such as mesh re-division and viscous unit layer that need to be added to the finite element unit when large deformation and fracture occur, simplifying the complexity of the finite element algorithm. The introduction of the smooth particle algorithm in the large deformation and continuous-discontinuous transformation stage will also give full play to the advantages of the smooth particle algorithm.

[0005] In order to ensure the calculation accuracy, the calculation scheme based on the finite element method often uses structured grids such as quadrilaterals and hexahedrons for discretization in the actual analysis process. However, the finite element method based on structured grids generally has the following problems to be solved: (1) High pre-processing cost. Since the structured grid is highly dependent on geometry, complex models often need to be subjected to geometric cutting and other operations to meet the meshing requirements. Therefore, too much manual intervention is required in the pre-processing stage, resulting in a long pre-processing cycle and increased labor costs. (2) Low calculation efficiency. Since the number of integral points of the structured grid in solving the system equations is too large, the calculation amount is too large, the calculation time is too long, and self-locking phenomenon is prone to occur in explicit calculations. (3) Poor anti-grid distortion ability. In the process of solving large deformation problems such as metal magnetic pulse forming, the grid often undergoes severe distortion as the workpiece deforms. At this time, due to the coordinate mapping and isoparametric transformation in the quadrilateral and hexahedron structure, the determinant of the unit Jacobian matrix may be negative, resulting in calculation termination. In addition, the finite element method based on unstructured grids such as triangles and tetrahedrons has the inherent defect of "hard" overall stiffness, which makes it not very accurate in numerical calculations and difficult to meet the accuracy requirements of actual engineering problems. In addition, the finite element method uses Gaussian integrals for calculations. Gaussian integral points carry physical information such as stress and strain. When converting finite elements to smooth particles, it is often necessary to inversely interpolate the Gaussian integral point information to the nodes, and then map the nodes to smooth particles, or introduce an interpolation method based on Gaussian integral points to convert the physical information to smooth particles. This brings the problem of difficult physical information conversion to the finite element-smooth particle adaptive coupling calculation, greatly reducing the coupling efficiency. Therefore, it is urgent to introduce new and efficient conversion methods or new algorithms to improve the calculation efficiency and accuracy of the finite element-smooth particle adaptive coupling. Summary of the invention

[0006] The present invention provides an adaptive coupling calculation method based on stable node integration and smooth particle method to solve the problems of how to alleviate the contradiction between the accuracy and efficiency of the finite element method, how to construct finite element-particle conversion rules, how to achieve efficient data mapping from finite elements to smooth particles, and how to couple the finite element algorithm with the smooth particle method to effectively predict components under high-speed and ultra-high-speed impact loads.

[0007] The present invention provides an adaptive coupling calculation method based on stable node integration and smooth particle method, comprising:

[0008] Generate particle models on unstructured background grids in impact collision process simulations;

[0009] Mark the nodes for the stable nodal integration method and the particles for the smooth particle method in the particle model;

[0010] Identify the composite elements at the interface between nodes and particles in the particle model;

[0011] A grid-particle interface tracking mechanism based on adjacent unit search and a composite unit physical quantity solution method are constructed to realize automatic coupling calculation of grid-based methods and particle-based methods.

[0012] Furthermore, the method further comprises:

[0013] In the stable node integration method, the integration domain is constructed based on the nodes, and the nodes in the grid are used as the integration points used for calculation. The nodes carry information on field variables including displacement, velocity, acceleration and their derived variables, as well as information on field variable gradients including strain and stress and their derived variables.

[0014] In the smooth particle method, particles are used as the smallest unit of calculation, and the particles carry all the physical information in the simulation of the impact collision process;

[0015] Data transmission is carried out based on nodes and particles to realize the analysis of impact collision process simulation.

[0016] Furthermore, the method further comprises:

[0017] Establish a multi-level domain contact system, introduce contact points, contact edges, contact blocks, contact surfaces, contact bodies and contact systems;

[0018] Set nodes and particles as points for contact search and integrate them into the contact search system of finite elements;

[0019] The point-to-point contact setting points are set as spheres, and the radius of the particle determines the size of the corresponding sphere; the contact search process is used to find all particle pairs that meet the contact conditions.

[0020] Furthermore, the method further comprises:

[0021] Based on the geometric parameters of the units around the node, the node-particle conversion rules are constructed. When the mesh is distorted to a preset degree, the node is converted to a particle and data is transferred.

[0022] The grid area and the particle area realize data exchange through the nodes or particles at the coupling interface to achieve adaptive coupling solution.

[0023] The present invention has the following beneficial effects: the present invention is based on a stable node integral and smooth particle method adaptive coupling calculation method, integrates the grid and particle coupling calculation, node particle conversion rules, develops a stable node integral and smooth particle method adaptive coupling method, establishes solutions to key problems such as high-speed and ultra-high-speed impact collisions, and realizes accurate prediction of mechanical response. Traditional linear units based on unstructured grids such as triangles and tetrahedrons are difficult to guarantee calculation accuracy, and structured grids based on quadrilaterals and hexahedrons do not have good discrete adaptability. The present invention constructs a stable node integral unit based on an unstructured grid, greatly improves the calculation accuracy on the premise of being able to adapt to complex geometric boundaries, solves the problem of the contradiction between calculation accuracy and calculation efficiency to a certain extent, and provides a new idea for solving practical engineering problems with complex boundaries. Based on the basic characteristics of nodes and particles carrying physical information, the present invention integrates node particle conversion criteria and coupling calculation rules, and develops a node particle adaptive coupling method, which reduces the numerical error caused by frequent mapping of nodes and integral points and improves mapping efficiency, and avoids the calculation termination problem caused by extreme grid distortion. The present invention makes full use of the advantages of grid-based methods and particle-based methods, quickly predicts the mechanical response of impact penetration, and provides a new method for solving high-speed and ultra-high-speed collision problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0025] Figure 1 This is a schematic diagram of the calculation of the stable node integral-smooth particle coupling;

[0026] Figure 2 Schematic diagram of nodes converted into smooth particles for stabilizing the node integration method;

[0027] Figure 3 Schematic diagram of unit-particle complex contact, where (a) is a schematic diagram of particle-particle contact, (b) is a schematic diagram of particle-unit contact, and (c) is a schematic diagram of unit-unit contact;

[0028] Figure 4 Schematic diagram for searching for particle-particle contact;

[0029] Figure 5 Schematic diagram of the adaptive coupling between stable nodal integration and smooth particles. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The technical solutions provided by the embodiments of the present invention are described in detail below in conjunction with the drawings.

[0031] When numerical simulation is used to explore high-speed and ultra-high-speed impact collisions such as erosion problems, the erosion finite element method is usually used. This method has the advantage of high computational efficiency, but deleting the distorted unit from the model can easily cause the total energy loss of the computational model, making the accuracy of the calculation results unguaranteed. The smooth particle method can effectively avoid mesh distortion and can naturally simulate material destruction, splashing and other phenomena, but its relatively low computational efficiency has become a bottleneck in its application in three-dimensional modeling and analysis. In the finite element algorithm, the smooth particle method with meshless properties is introduced to replace the extremely distorted mesh. In order to automatically convert the finite element into a smooth particle, an effective criterion is needed to judge the degree of distortion of the unit, so as to determine the distorted finite element that needs to be converted into a smooth particle. Under normal circumstances, the degree of distortion of the finite element can be judged based on physical criteria or geometric criteria, such as when the physical quantities such as equivalent plastic strain and equivalent stress exceed a certain threshold; for example, when the distortion, collapse, Jacobian, aspect ratio and other geometric criteria of the finite element determine the degree of distortion of the unit. Thus, the over-distorted finite element is converted into a smooth particle. It will not cause the finite element in the non-large deformation area to be converted into a smooth particle, resulting in the generation of too many smooth particles. There are also many ways to convert finite elements into particles, such as converting finite element nodes into smooth particles, converting finite element integration points into smooth particles, converting internal generation points of finite elements into smooth particles, etc. In addition, the conversion of finite elements into smooth particles mainly includes the following steps: deleting finite elements, generating smooth particles, updating the surface of finite element regions, and updating the coupling relationship between finite element regions and smooth particle regions. To delete a finite element, you only need to remove the finite element from the list of valid finite elements. In each deleted finite element, one or more smooth particles will be generated to replace the corresponding finite element, and the generated smooth particles will be added to the original list of smooth particles. The generated smooth particles inherit all the physical information of the original finite element, such as position, velocity, acceleration, etc. The physical information of the smooth particles can be obtained by interpolation of the nodes of the finite element. If there is physical information carried by the integration points such as strain / stress, it can be first reversed to the finite element nodes, and then interpolated based on the finite element nodes.

[0032] Therefore, how to alleviate the contradiction between the accuracy and efficiency of the finite element method, how to construct the finite element-particle conversion rules, how to achieve efficient data mapping from finite elements to smooth particles, and how to couple the finite element algorithm with the smooth particle method to effectively predict components under high-speed and ultra-high-speed impact loads are key scientific issues that need to be solved urgently. The present invention is based on stable node integration and smooth particle method, integrates grid and particle coupling calculation, node / particle conversion rules, develops a stable node integration and smooth particle method adaptive coupling method, establishes solutions to key problems such as high-speed and ultra-high-speed impact collisions, and achieves accurate prediction of mechanical response.

[0033] See also Figures 1 to 5, which is an adaptive coupling calculation method based on stable node integration and smooth particle method provided by the present invention, comprising:

[0034] Step 1: Generate a particle model on the unstructured background grid in the impact collision process simulation.

[0035] Step 2: Mark the nodes for the stable node integration method and the particles for the smooth particle method in the particle model.

[0036] Step 3: Identify the composite units at the interface between nodes and particles in the particle model.

[0037] Step 4: Construct a grid-particle interface tracking mechanism based on adjacent unit search and a composite unit physical quantity solution method to achieve automatic coupling calculation of grid-based methods and particle-based methods.

[0038] Figure 1 In, Ω FEM Indicates the calculation area of ​​the grid class method, Ω SPH Indicates the example class method to calculate the area, Ω C Indicates the transformation area. Figure 2 In the figure, A represents the node integration domain, B represents the particle support domain, and the arrow between A and B represents the inheritance of physical quantities. Figure 3 In the figure, (a) is a schematic diagram of particle-particle contact, (b) is a schematic diagram of particle-unit contact, and (c) is a schematic diagram of unit-unit contact. Figure 4 In, R i and R j represent the radius of the first particle i and the second particle j respectively, δ represents the penetration distance of the first particle i and the second particle j, d ij represents the distance between the first particle i and the second particle j.

[0039] In the simulation of high-speed and ultra-high-speed impact collision processes, the particle and grid coupling calculation method is introduced, and a grid-particle interface fast tracking and composite unit physical quantity solution method based on adjacent unit search is constructed to realize automatic coupling calculation of grid and particle methods, avoid calculation termination problems caused by grid distortion, and save a lot of calculation time.

[0040] In this embodiment, the method further includes:

[0041] In the stable node integration method, the integration domain is constructed based on the nodes, and the nodes in the grid are used as the integration points used for calculation. The nodes carry information on field variables including displacement, velocity, acceleration and their derived variables, as well as information on field variable gradients including strain and stress and their derived variables. In the smooth particle method, particles are used as the smallest unit of calculation, and the particles carry all physical information in the simulation of the impact collision process. Data is transferred based on nodes and particles to realize the analysis of the simulation process of the impact collision process. Efficient data transfer based on nodes and particles greatly avoids time loss and calculation errors caused by repeated mapping between nodes and integration points.

[0042] In the high-speed and ultra-high-speed impact collision simulation calculation process, the model initially uses a grid-based stable node integration method for calculation. As the collision penetration fails and damage occurs, the nodes in the stable node integration method are converted into smooth particles. The entire calculation process involves mutual contact between units, units and particles, and particles and particles. A large number of complex contact surface fine features are generated for the large deformation and crushing of the impact collision process. The contact search has missed detections and false detections, and it is difficult to construct accurate contact pairs, which leads to low calculation accuracy and even causes calculation termination. The present invention proposes a multi-level domain search strategy, establishes multi-level contact modes such as point-to-block, point-to-line, and point-to-point, sets a contact extension domain to expand the search range, and forms specific search processes such as test pairs and contact pairs.

[0043] In this embodiment, the method also includes: establishing a multi-level domain contact system, introducing contact points, contact edges, contact blocks, contact surfaces, contact bodies and contact systems; setting nodes and particles as points for contact search, and integrating them into the contact search system of finite elements; setting point-to-point contact points as spheres, and the radius of the particle determines the size of the corresponding sphere; the contact search process is used to find all particle pairs that meet the contact conditions.

[0044] For example, given two objects, with M and N particles respectively, if a direct search method is used, that is, each particle of one object is judged to be in contact with each particle of the other object, the complexity of the contact search is o(M×N), and the search efficiency is very low. Considering that the adjacent particle search is necessary for the smooth particle method calculation, the results of the adjacent particle search are used to perform the contact search to improve the search efficiency.

[0045] In this embodiment, the method also includes: constructing node-particle conversion rules based on the geometric parameters of the units around the node, and when the grid is distorted to a preset degree, the nodes are converted into particles, and data is transmitted; the grid area and the particle area realize data interaction through the nodes or particles at the coupling interface to achieve adaptive coupling solution.

[0046] High-speed and ultra-high-speed collisions will form mesh distortion areas in local areas. The present invention constructs node-particle conversion rules based on the geometric parameters of the units around the nodes, such as the minimum internal angle <20°, that is, nodes are converted into particles. When the mesh is distorted to a certain extent, it is converted from nodes to particles and data is transferred. The coupled calculation of stable node integration and smooth particle method is shown in Figure 4. The mesh area and the particle area pass through the nodes at the coupling interface. Particles realize data interaction and adaptive coupling solution.

[0047] In summary, the present invention constructs a stable node integration method based on unstructured grids, which can adapt to complex geometric boundaries and greatly improve the calculation accuracy based on unstructured grids; the node particle data automatic mapping scheme proposed in the present invention reduces the numerical errors caused by frequent mapping of nodes and integration points, and greatly improves the calculation efficiency of the existing finite element smooth particle adaptive coupling; the stable node integration smooth particle adaptive coupling method of the present invention fully utilizes the respective advantages of stable node integration and smooth particle methods, and is a type of calculation method that is very effective in processing high-speed and ultra-high-speed impact collisions.

[0048] The above-described embodiments of the present invention do not limit the protection scope of the present invention.

Claims

1. A method for adaptive coupling calculation based on stable node integration and smooth particle method, characterized in that: include: Generate particle models on unstructured background grids in impact collision process simulations; Mark the nodes for the stable nodal integration method and the particles for the smooth particle method in the particle model; Identify the composite elements at the interface between nodes and particles in the particle model; Construct a mesh particle interface tracking mechanism based on adjacent unit search and a composite unit physical quantity solution method to achieve automatic coupling calculation of mesh and particle methods; The method further comprises: In the stable node integration method, the integration domain is constructed based on the nodes, and the nodes in the grid are used as the integration points used for calculation. The nodes carry information on field variables including displacement, velocity, acceleration and their derived variables, as well as information on field variable gradients including strain and stress and their derived variables. In the smooth particle method, particles are used as the smallest unit of calculation, and the particles carry all the physical information in the simulation of the impact collision process; Data transmission based on nodes and particles is used to realize the analysis of impact and collision simulation process; The method further comprises: Establish a multi-level domain contact system, introduce contact points, contact edges, contact blocks, contact surfaces, contact bodies and contact systems; Set nodes and particles as points for contact search and integrate them into the contact search system of finite elements; The contact points between points are set as spheres, and the radius of the particle determines the size of the corresponding sphere; the contact search process is used to find all particle pairs that meet the contact conditions; The method further comprises: Based on the geometric parameters of the units around the node, the node-particle conversion rules are constructed. When the mesh is distorted to a preset degree, the node is converted to a particle and data is transferred. The grid area and the particle area realize data exchange through the nodes or particles at the coupling interface to achieve adaptive coupling solution.

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