Discrete element porosity calculation and interpolation optimization method and system based on graphic algorithm

Abstract

The present disclosure relates to the field of geotechnical numerical simulation technology, and proposes a discrete element porosity calculation and interpolation optimization method and system based on a graphic algorithm. First, the Delaunay triangulation meshing technology is used to perform triangular face / volume meshing with discrete particle point set coordinates as nodes, and then the Voronoi algorithm is used to construct Thiessen polygons. At the same time, a graphic algorithm is used to calculate the porosity of the current polygon, and it is determined whether further interpolation optimization processing is required, thereby achieving uniform continuous processing and smooth display of the entire discrete element calculation data. The present invention can overcome the problems of poor particle display effect in current discrete element calculations, automatically calculate local porosity based on the Voronoi polyhedron graphic algorithm, and quantitatively determine whether interpolation optimization processing is required, which can achieve uniform continuous optimization processing of non-uniform discrete element particle information, and the applicability and accuracy are greatly improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field related to geotechnical numerical simulation, and more specifically, to a discrete element porosity calculation and interpolation optimization method and system based on a graphics algorithm. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] With the vigorous development of modern transportation, water conservancy and hydropower and other infrastructure, a large number of complex geotechnical engineering problems such as tunnels, bridges, roadbeds, slopes, dams, etc. have also emerged. In the face of the design and analysis and evaluation of these complex problems, traditional theoretical analytical methods are often helpless, which has brought valuable opportunities for the development of numerical calculation methods. The outstanding advantage of numerical calculation methods is that they use advanced computer technology to quickly solve and analyze engineering problems. In the solution process, they can better consider the combination of one or more conditions such as the anisotropy, heterogeneity, discontinuity and nonlinear characteristics of geotechnical media and complex external force boundary conditions.

[0004] The particle discrete element method is a numerical simulation method proposed by PA Cundall. When using particle discrete elements to perform numerical simulations of geotechnical engineering problems, the rock and soil mass is first assumed to be a series of particle aggregates with interacting relationships, and then the force analysis and motion equations are solved for each particle unit to obtain the mechanical behavior characteristics of the entire rock and soil mass. At present, particle discrete elements have been widely used in rock mechanics, soil mechanics, fluid mechanics and other fields, and are one of the fastest-growing methods in the field of computational mechanics.

[0005] The inventors found in their research that since the discrete element method discretizes the computational domain into a finite number of particle units with contact interaction relationships, there are discontinuities in the processing and display of the computational results, which is not conducive to the comparative analysis of the computational results and the experimental results. For example, the patent "Data processing and analysis method suitable for continuous display of discrete element calculation information" discloses a processing method suitable for continuous display of discrete element calculation data, but it is only applicable to the discrete data processing of uniformly distributed particles. When processing discrete element particles with non-uniform random distribution, there are defects such as sharp corners and discontinuous surfaces on the boundaries, and the smoothing effect is poor, and even a continuous interface cannot be generated at all, which seriously affects the display effect of the numerical calculation results. Summary of the invention

[0006] In order to solve the above problems, the present disclosure proposes a discrete element porosity calculation and interpolation optimization method and system based on a graphics algorithm, which overcomes the problems of poor particle display effect in current discrete element calculations, and automatically calculates local porosity based on the Voronoi polyhedron graphics algorithm, and quantitatively determines whether interpolation optimization processing is required, which can realize uniform and continuous optimization processing of non-uniform discrete element particle information, and the applicability and accuracy are greatly improved.

[0007] In order to achieve the above objectives, the present disclosure adopts the following technical solutions:

[0008] One or more embodiments provide a discrete element porosity calculation and interpolation optimization method based on a graphical algorithm, comprising the following steps:

[0009] Numerical simulations are performed on geotechnical engineering problems to obtain a set of spatially discrete points with non-uniform random distribution in the computational domain;

[0010] Perform irregular meshing on the spatial discrete point set to obtain a tetrahedral mesh;

[0011] Based on the obtained tetrahedral mesh, a polyhedral space mesh corresponding to each discrete point is constructed;

[0012] The porosity at the current discrete point coordinates is calculated using a polyhedral graphics algorithm;

[0013] When the porosity is greater than the set value, a new particle unit is inserted at the current particle position to optimize the non-uniform discrete point set, and the optimized discrete particle point set is continuous.

[0014] One or more embodiments provide a discrete element porosity calculation and interpolation optimization system based on a graphical algorithm, including:

[0015] Spatial discrete point set acquisition module: configured to perform numerical simulation on geotechnical engineering problems and obtain a spatial discrete point set with non-uniform random distribution in the computational domain;

[0016] Tetrahedral mesh generation module: configured to perform irregular meshing on a set of discrete points in space to obtain a tetrahedral mesh;

[0017] A polyhedral space grid construction module: configured to construct a polyhedral space grid corresponding to each discrete point based on the obtained tetrahedral grid;

[0018] A calculation module: configured to calculate the porosity at the coordinates of the current discrete point using a polyhedral graphic algorithm for a polyhedral space grid;

[0019] Interpolation module: It is configured to insert a new particle unit at the current particle position to optimize the non-uniform discrete point set when the porosity is greater than the set value, and to perform continuous processing on the optimized discrete particle point set.

[0020] An electronic device comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps described in the above method are completed.

[0021] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the steps described in the above method are completed.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] In the present disclosure, based on the grid generation technology, the irregularly distributed discrete element particles in the calculation domain can be connected in sequence to form continuous grid units, thereby realizing the continuous display of the geotechnical medium; based on the polyhedron graphics algorithm, the local porosity size at each particle position can be automatically calculated, overcoming the shortcoming of low porosity calculation efficiency in the current discrete element; the interpolation optimization method provided by the present disclosure can realize the continuous smooth processing of non-uniform randomly distributed discrete element particle information, and compared with the traditional continuous processing technology, the smoothness and continuity at the numerical calculation boundary are greatly improved.

[0024] The advantages of the present disclosure and the advantages of additional aspects will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and the description thereof are used to explain the present disclosure but do not constitute a limitation of the present disclosure.

[0026] Figure 1 is a flow chart of the interpolation optimization method of Embodiment 1 of the present disclosure; DETAILED DESCRIPTION

[0027] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0028] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0029] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof. It should be noted that, in the absence of conflict, the various embodiments in the present disclosure and the features in the embodiments can be combined with each other. The embodiments will be described in detail below in conjunction with the accompanying drawings.

[0030] Example 1

[0031] In the technical solutions disclosed in one or more embodiments, Figure 1 As shown in FIG. 1 , the discrete element porosity calculation and interpolation optimization method based on the graphical algorithm includes the following steps:

[0032] Step 1: Perform numerical simulation on geotechnical engineering problems to obtain a set of spatial discrete points with non-uniform random distribution in the calculation domain;

[0033] Step 2, irregularly mesh the spatial discrete point set to obtain a tetrahedral mesh;

[0034] Step 3: Based on the obtained tetrahedral mesh, a polyhedral space mesh corresponding to each discrete point is constructed;

[0035] Step 4: Calculate the porosity at the current discrete point coordinates using a polyhedron graphics algorithm;

[0036] Step 5: When the porosity is greater than the set value, a new particle unit is inserted at the current particle position to optimize the non-uniform discrete point set, and the optimized discrete particle point set is processed continuously, thereby achieving uniform continuous processing and smooth display of the entire discrete element calculation data.

[0037] In this embodiment, based on the grid generation technology, the irregularly distributed discrete element particles in the calculation domain can be connected in sequence to form continuous grid units, thereby realizing the continuous display of the rock and soil medium; based on the polyhedron graphics algorithm, the local porosity size at each particle position can be automatically calculated, overcoming the shortcoming of low porosity calculation efficiency in the current discrete element; the interpolation optimization method provided in this embodiment can realize the continuous smooth processing of non-uniform randomly distributed discrete element particle information. Compared with the traditional continuous processing technology, the smoothness and continuity at the numerical calculation boundary are greatly improved.

[0038] In step 1, optionally, a particle discrete element method can be used to perform numerical simulation of geotechnical engineering problems to obtain a set of spatial discrete points with non-uniform random distribution in the computational domain.

[0039] Among them, the discrete point set carries physical information such as position coordinates, radius, velocity, stress, deformation, etc.

[0040] In step 2, the method of performing irregular meshing on the spatial discrete point set may optionally use the Delaunay tetrahedral meshing method to perform irregular meshing on the computational domain, that is, triangular meshing. Specifically, the method may include the following steps:

[0041] Step 21, obtaining the position coordinate information of the spatial discrete point set, mapping the discrete point set into a three-dimensional rectangular coordinate system, and recording them in sequence;

[0042] Step 22: Using fixed coordinate points in the three-dimensional space coordinate system as mesh nodes of a tetrahedron to form a tetrahedron irregular mesh; wherein the fixed coordinate points may be integer coordinate points in the coordinate system.

[0043] Step 23: According to the empty circumscribed circle criterion and the maximum and minimum angle criterion, the mesh of the spatial irregular tetrahedron is optimized to obtain a Delaunay tetrahedron mesh structure.

[0044] In this embodiment, based on the Delaunay tetrahedral meshing technology, the irregularly distributed discrete element particles in the calculation domain can be connected in sequence to form continuous tetrahedral mesh units, thereby realizing the continuous display of the geotechnical medium.

[0045] In step 3, the polyhedral space grid corresponding to each discrete point can be constructed by using the Voronoi algorithm to construct Thiessen polygons, and the Voronoi polyhedral space grid is constructed based on the above Delaunay tetrahedral grid. Specifically, for each discrete point A, the circumscribed sphere center of the tetrahedral unit adjacent to the discrete point A is obtained, and the circumscribed sphere centers are connected in sequence to obtain the Voronoi space polyhedron.

[0046] The porosity calculation method is: calculate the volume of each discrete point particle (or discrete element particle) in turn, use the geometric graphics algorithm to calculate the volume of the Voronoi polyhedron corresponding to the current particle coordinate, and calculate the porosity at the current particle coordinate based on the volume of the discrete point particle and the volume of the polyhedron; the calculation formula of the porosity is:

[0047]

[0048] Among them, P 0 is the porosity at the current particle coordinate, V 0 is the volume of the polyhedron, D p is the diameter of discrete particles.

[0049] Determine whether the porosity at each discrete point particle coordinate calculated exceeds the set maximum porosity critical value, and if it exceeds the critical value, perform particle interpolation optimization; if not, perform continuous processing of discrete point particles;

[0050] In this embodiment, based on the Voronoi polyhedron graphics algorithm, the local porosity size at each particle position can be automatically calculated, overcoming the low efficiency of porosity calculation in the current discrete element. Based on the Voronoi polyhedron graphics algorithm to obtain the local porosity, it is possible to quantitatively determine whether it is necessary to insert a new discrete element particle for optimization processing, and determine the coordinates and radius of the inserted particle.

[0051] In step 5, a new particle unit is inserted at the current particle position. The process of interpolating the new particle specifically includes the following: calculating the distance from the coordinates of the current particle centroid to each face of the Voronoi polyhedron, obtaining the face and the foot point of the perpendicular farthest from the current particle centroid, inserting a new discrete element particle with the foot point of the perpendicular farthest face as the center of the circle, and the radius of the new particle is calculated according to the porosity so that the filled new particle can fill the gap between the polyhedrons. The physical information of the new particle is obtained by linear interpolation of the physical information of two mutually symmetrical particles; the interpolation calculation method of the physical information of the new particle is:

[0052]

[0053] Among them, x, x 0 、x 1 are the coordinates of the new particle and the coordinates of the two symmetrical particles respectively; f(x) is the physical information of the new particle; f(x 0 )、f(x 1 ) is the physical information of two symmetrical particles.

[0054] The above process of interpolating new particles is repeated until the porosity at all discrete element particle coordinates meets the requirements, then the interpolation optimization process is completed, and then the discrete element particle continuity process is performed.

[0055] In some embodiments, the continuous processing can regenerate the Delaunay tetrahedral mesh with the interpolation optimized discrete particle point set as the standard data, so as to make the geotechnical computational domain equivalent to a series of interconnected tetrahedral mesh units. The physical information inside and on the surface of the tetrahedral mesh is obtained by linear interpolation of the discrete point physical information according to the position coordinates.

[0056] A further technical solution also includes a step of continuous display. Specifically, the regenerated Delaunay tetrahedral mesh can be read using the Paraview visualization tool for continuous display.

[0057] The interpolation optimization method provided in this embodiment can realize continuous smooth processing of non-uniform randomly distributed discrete element particle information. Compared with traditional continuous processing technology, the smoothness and continuity at the boundary of numerical calculation are greatly improved.

[0058] Example 2

[0059] Based on Example 1, this embodiment provides a discrete element porosity calculation and interpolation optimization system based on a graphics algorithm, including:

[0060] Spatial discrete point set acquisition module: configured to perform numerical simulation on geotechnical engineering problems and obtain a spatial discrete point set with non-uniform random distribution in the computational domain;

[0061] Tetrahedral mesh generation module: configured to perform irregular meshing on a set of discrete points in space to obtain a tetrahedral mesh;

[0062] A polyhedral space grid construction module: configured to construct a polyhedral space grid corresponding to each discrete point based on the obtained tetrahedral grid;

[0063] A calculation module: configured to calculate the porosity at the coordinates of the current discrete point using a polyhedral graphic algorithm for a polyhedral space grid;

[0064] Interpolation module: It is configured to insert a new particle unit at the current particle position to optimize the non-uniform discrete point set when the porosity is greater than the set value, and to perform continuous processing on the optimized discrete particle point set.

[0065] It should be noted here that the various modules in this embodiment correspond one-to-one to the various steps in Example 1, and the specific implementation process is the same, which will not be repeated here.

[0066] Example 3

[0067] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps described in the method of Embodiment 1 are completed.

[0068] Example 4

[0069] This embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps described in the method of Embodiment 1 are completed.

[0070] The electronic devices proposed in the present disclosure can be mobile terminals and non-mobile terminals. Non-mobile terminals include desktop computers, and mobile terminals include smart phones (such as Android phones, IOS phones, etc.), smart glasses, smart watches, smart bracelets, tablet computers, laptops, personal digital assistants, and other mobile Internet devices that can communicate wirelessly.

[0071] It should be understood that in the present disclosure, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0072] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor, and a portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0073] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software. The steps of the method disclosed in the present disclosure can be directly embodied as being executed by a hardware processor, or being executed by a combination of hardware and software modules in a processor. The software module can be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it is not described in detail here. A person of ordinary skill in the art can appreciate that the units of each example described in combination with the embodiments disclosed herein, i.e., the algorithm steps, can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present disclosure.

[0074] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0075] In the several embodiments provided in the present disclosure, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a division of logical functions. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, and the indirect coupling or communication connection of devices or units can be electrical, mechanical or other forms.

[0076] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present disclosure, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present disclosure. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0077] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

[0078] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. Discrete element porosity calculation and interpolation optimization method based on graphical algorithm, It is characterized in that The steps include: Numerical simulation is performed for geotechnical engineering problems. The geotechnical body is assumed to be a series of particle aggregates with interacting relationships. Then, the stress analysis is performed on each particle unit to obtain a set of spatial discrete points with non-uniform random distribution in the calculation domain. Perform irregular meshing on the spatial discrete point set to obtain a tetrahedral mesh; Based on the obtained tetrahedral mesh, a polyhedral space mesh corresponding to each discrete point is constructed; The porosity at the current discrete point coordinates is calculated using a polyhedral graphics algorithm; When the porosity is greater than the set value, a new particle unit is inserted at the current particle position to optimize the non-uniform discrete point set, and the optimized discrete particle point set is continuous. A new particle unit is inserted at the current particle position. The process of interpolating the new particle specifically includes the following: calculating the distance from the coordinates of the current particle centroid to each face of the Voronoi polyhedron, obtaining the face farthest from the current particle centroid and the foot point of the perpendicular, inserting a new discrete element particle with the foot point of the farthest face as the center of the circle, and the radius of the new particle is calculated based on the porosity so that the filled new particle can fill the gap between the polyhedrons. The physical information of the new particle is obtained by linear interpolation of the physical information of two mutually symmetrical particles.

2. The discrete element porosity calculation and interpolation optimization method based on a graphical algorithm as claimed in claim 1, Features: The particle discrete element method is used to carry out numerical simulation of geotechnical engineering problems and obtain a set of spatial discrete points with non-uniform random distribution in the computational domain.

3. The discrete element porosity calculation and interpolation optimization method based on a graphical algorithm as claimed in claim 1, Features: The Delaunay tetrahedral meshing method is used to perform irregular meshing of the computational domain.

4. The discrete element porosity calculation and interpolation optimization method based on a graphical algorithm as claimed in claim 3, It is characterized in that The method of using the Delaunay tetrahedral meshing method to perform irregular meshing on the computational domain includes the following steps: The position coordinate information of the discrete point set in space is obtained, and the discrete point set is mapped into a three-dimensional rectangular coordinate system; Using fixed coordinate points in the three-dimensional space coordinate system as mesh nodes of the tetrahedron to form a tetrahedron irregular mesh; According to the empty circumscribed circle criterion and the maximum and minimum angle criterion, the mesh of the irregular tetrahedron in space is optimized to obtain the Delaunay tetrahedron mesh structure.

5. The discrete element porosity calculation and interpolation optimization method based on a graphical algorithm as claimed in claim 1, It is characterized in that Construct a polyhedral space grid corresponding to each discrete point and use the Voronoi algorithm to construct Thiessen polygons: for each discrete point A, obtain the circumscribed sphere center of the tetrahedral unit adjacent to the discrete point A, connect the circumscribed sphere centers in sequence, and obtain the Voronoi space polyhedron.

6. The discrete element porosity calculation and interpolation optimization method based on a graphical algorithm as claimed in claim 1, It is characterized in that The porosity is calculated by calculating the volume of each discrete point particle or discrete element particle in turn, using a geometric graphics algorithm to calculate the volume of the Voronoi polyhedron corresponding to the current particle coordinate, and calculating the porosity at the current particle coordinate based on the volume of the discrete point particle and the volume of the polyhedron.

7. Discrete element porosity calculation and interpolation optimization system based on graphics algorithm, It is characterized in that include: Spatial discrete point set acquisition module: It is configured to perform numerical simulation on geotechnical engineering problems. The geotechnical body is assumed to be a series of particle aggregates with interacting relationships. Then, the force analysis is performed on each particle unit to obtain a spatial discrete point set with non-uniform random distribution in the calculation domain. Tetrahedral mesh generation module: configured to perform irregular meshing on a set of discrete points in space to obtain a tetrahedral mesh; A polyhedral space grid construction module: configured to construct a polyhedral space grid corresponding to each discrete point based on the obtained tetrahedral grid; A calculation module: configured to calculate the porosity at the coordinates of the current discrete point using a polyhedral graphic algorithm for a polyhedral space grid; Interpolation module: configured to insert a new particle unit at the current particle position to optimize the non-uniform discrete point set when the porosity is greater than the set value, and to perform continuous processing on the optimized discrete particle point set; A new particle unit is inserted at the current particle position. The process of interpolating the new particle specifically includes the following: calculating the distance from the coordinates of the current particle centroid to each face of the Voronoi polyhedron, obtaining the face farthest from the current particle centroid and the foot point of the perpendicular, inserting a new discrete element particle with the foot point of the farthest face as the center of the circle, and the radius of the new particle is calculated based on the porosity so that the filled new particle can fill the gap between the polyhedrons. The physical information of the new particle is obtained by linear interpolation of the physical information of two mutually symmetrical particles.

8. An electronic device, It is characterized in that The method comprises a memory and a processor and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the steps described in any one of the methods of claims 1 to 6 are completed.

9. A computer-readable storage medium, It is characterized in that Used to store computer instructions, which, when executed by a processor, complete the steps described in any one of claims 1 to 6.

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