A Modeling Method and Device for Random Dot Array Structure Based on F-Rep
Through the F-Rep-based modeling method, the mesh topological data structures of Delaunay triangulation and half-face encoding are used to model complex random lattice structures, solving the problems of low modeling efficiency and large storage overhead in the existing technology, and achieving efficient and accurate structural modeling.
Patent Information
- Application Number
- CN202411304582.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-19
- Publication Date
- 2025-05-30
- Estimated Expiration
- 2044-09-19
AI Technical Summary
When designing complex random lattice structures, the prior art has low modeling efficiency and large storage overhead, making it difficult to effectively express the multi-scale complex features of the structure.
Using the F-Rep-based modeling method, the vertex data and unit information of tetrahedral mesh cells are obtained through Delaunay triangulation, combined with the half-face coded mesh topological data structure, the connection relationship between tetrahedral mesh cells is topologically reconstructed, and the truss-like primitives are transformed into hidden function expressions to realize the functional expression of random lattice structures.
It improves modeling efficiency and calculation accuracy, reduces memory overhead, supports information transmission and exchange between two scales, and realizes efficient modeling of complex random lattice structures.
Smart Images
Figure CN119312610B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field related to CAD model representation, and more specifically, relates to a method and device for modeling a random lattice structure based on F-Rep. Background Art
[0002] The lattice structure with both functional and structural dual characteristics is widely used in the design of major equipment such as aerospace due to its mechanical properties such as light weight, high specific strength / stiffness, and its unique multi-functional characteristics such as load-bearing, stealth, and drag reduction. The random lattice structure relying on Delaunay triangulation often exhibits enhanced mechanical properties, and thus is used in energy absorption or impact resistance and other scenarios. As a kind of heterogeneous multi-scale structure, the random lattice structure has the largest design space and degrees of freedom, and theoretically is a kind of structure with the most fully exploited potential for multi-scale structure performance optimization.
[0003] Such structures usually have complex features at multiple scales geometrically, and the non-periodicity of the structure is strong. Existing CAD systems based on B-Rep expression are very difficult to complete the design of such complex structures in terms of shape and scale only by geometric description. Using standard CAD software to design lattice structures is very inefficient, time-consuming, and the obtained models are error-prone. On the other hand, although voxel modeling is easy to implement and has high robustness, the memory overhead of its models and the discreteness defects of the modeling method itself cannot be ignored. Similar to voxel modeling, directly modeling using triangular patches will also cause inaccurate geometric representation and excessive memory overhead, and these two indicators are often contradictory. Summary of the Invention
[0004] In view of the above defects or improvement requirements of the prior art, the present invention provides a method and device for modeling a random lattice structure based on F-Rep, aiming to solve the problems of low modeling efficiency and high storage overhead when establishing a lattice structure model by existing modeling methods.
[0005] To achieve the above object, according to one aspect of the present invention, there is provided a method for modeling a random lattice structure based on F-Rep, the modeling method comprising the following steps:
[0006] S1, performing Delaunay triangulation on the macroscopic design domain of the random lattice structure, and then obtaining the vertex data and cell information of the tetrahedral mesh cells;
[0007] S2, explicitly storing and implicitly expressing the body-half-edge-vertex three-layer topological elements of the tetrahedral mesh cells according to the cell information, and performing topological reconstruction on the connection relationship between the tetrahedral mesh cells by using a semi-face encoded mesh topological data structure based on the local topological relationship inside the tetrahedral mesh cells;
[0008] S3. Transform the truss - type primitive elements into the geometric control parameters of the radius of the node circle and the conic curve tangent to the corresponding circle in the modeling coordinate system, and then obtain the expression of the truss - type primitive elements, so as to realize the implicit function unified representation of the truss - type primitive elements of the tetrahedral mesh elements in the local coordinate system. Among them, the truss - type primitive elements include cylindrical truss primitive elements, conical truss primitive elements and quadratic - surface - type primitive elements; the geometric control parameters include \(t\), \(r\) 1 and \(r\) 2 , \(r\) 1 and \(r\) 2 which are the radii of two node circles respectively, and \(t\) represents the shape parameter of the truss between the two node circles;
[0009] S4. Directly construct the implicit expression function of the truss primitive elements in the global coordinate system based on the geometric control parameters of the truss primitive elements, and then obtain the implicit expression function of each truss primitive element in the global coordinate system according to the mesh topology data structure, so as to realize the function expression of the random dot - matrix structure model.
[0010] Furthermore, in the half - face - encoded mesh topology data structure, every two tetrahedral mesh elements share a face. Referring to the definition of the half - edge data structure: divide this face into two half - faces, and each half - face is defined by a binary tuple composed of the serial number of the corresponding tetrahedral element and the local index on the element where the half - face is located. Encode the binary tuple of the half - face as a 32 - bit unsigned integer. The last three bits store the local index of the half - face, and the remaining bits store the index of the tetrahedral mesh element.
[0011] Furthermore, perform Delaunay triangulation on the macroscopic design domain of the random dot - matrix structure to obtain the vertex data \(P\) and element information \(C\) as follows:
[0012]
[0013] In the formula, \(m\) is the number of vertices, \(n\) represents the number of tetrahedral elements, represents the four - vertex indices of the \(u\) - th element; \(i = 1,2,3,4\).
[0014] Furthermore, step S2 includes the following sub - steps:
[0015] S21: Define and store the three - layer topological elements of body - half - face - vertex on the tetrahedral mesh elements;
[0016] S22. Every two tetrahedral mesh elements share a face. Referring to the definition of the half - edge data structure: divide this face into two half - faces, and each half - face is defined by a binary tuple composed of the serial number of the corresponding tetrahedral element and the local index on the element where the half - face is located. Encode the binary tuple of the half - face as a 32 - bit unsigned integer. The last three bits store the local index of the half - face, and the remaining bits store the index of the tetrahedral mesh element;
[0017] S23: Construct topological relationships between tetrahedral mesh elements.
[0018] Furthermore, in S23, two intermediate mappings are first established by traversing all half-faces: v2hfs and v2adj. v2hfs records the mapping between the maximum index vertex and the half-face on each half-face; v2adj records the corresponding mapping between the remaining vertices and the half-face. Secondly, each half-face is traversed again to obtain the maximum vertex index as the key, and the remaining vertex indices are used as additional information of the key. Furthermore, the matching partner half-face is searched in the set of half-faces with the same key value, thereby constructing a mapping relationship between the half-faces.
[0019] Furthermore, step S3 includes the following sub-steps:
[0020] S31: The local modeling coordinate system is defined on the xOy plane. The two node circles and the truss primitives correspond to three basic functions in the local modeling coordinate system: the conic section equations of the circles at (-1, 0) and (1, 0) and the truss primitives tangent to the circles are:
[0021]
[0022] where r 1 and r 2 are the radii of the two node circles respectively. According to the tangency condition, equations (2) and (3) are combined with (1) to calculate the two parameters c and d of equation (1);
[0023] S32: Define the third circle with its center at (0, 0) and radius The third control parameter t is introduced to make the third circle tangent to the truss, and the third parameter a is calculated by using equation (1);
[0024] S33: By r 1 、r 2 The conic curve equations corresponding to the three geometric control parameters, t and t, define the outer contour of the truss primitive. The three-dimensional truss primitive in the local modeling coordinate system is generated by rotating around the X-axis. 1 、r 2 The conic section equations corresponding to the three geometric control parameters t and t are the function expressions of the truss primitives.
[0025] Furthermore, when the truss primitive corresponds to an ellipsoidal surface, assuming that the center point of the ellipsoidal surface is o, the three symmetry axes are u, v, and w, where u represents the rotation axis of the quadratic curve, and the semi-axis lengths are m, n, and n, respectively, then the surface equation is expressed as:
[0026]
[0027] Furthermore, when the truss element corresponds to a hyperboloid of one sheet, the surface equation is constructed as follows:
[0028]
[0029] When the conic degenerates into a straight line, the truss elements correspond to a cylindrical surface and a conical surface respectively; assuming the radius of the cylindrical surface is r, a point on the axis is o, and the axis direction is n, according to the fact that the distance from any point x on the cylindrical surface to the axis is r, the equation of the cylindrical surface is expressed as:
[0030] (x - o) T (I - nn T )(x - o) = r 2
[0031] Let the vertex of the cone be o, the semi-vertical angle be θ, the axis direction be n, the generatrix direction be l, and the cosine value of the angle between the generatrix and the axis be cosθ = l T n. From the geometric relationship, the equation of the conical surface is:
[0032]
[0033] The present invention also provides an F-Rep based random lattice structure modeling system, which includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the above-mentioned F-Rep based random lattice structure modeling method.
[0034] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the above-mentioned F-Rep based random lattice structure modeling method.
[0035] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the F-Rep based random lattice structure modeling method and device provided by the present invention mainly have the following beneficial effects:
[0036] 1. Expressing the truss element by an implicit function, compared with the cumbersome and complex topological transformation, especially the rotation transformation based on the Euler matrix, the proposed method simplifies the calculation process, improves the calculation accuracy and efficiency. At the same time, a half-plane encoded grid topology data structure is used to reconstruct the connection relationship between tetrahedral mesh elements. This encoding method can accommodate about 500 million elements, while maintaining the data volume, improving the compactness of the data structure and greatly reducing the memory overhead.
[0037] 2. The grid topology data structure based on half-plane encoding constructs the adjacency relationship between adjacent tetrahedral grid cells. As the connection between the macroscopic design domain and the mesoscopic truss elements, it can effectively support the information transfer and exchange between the two scales.
[0038] 3. While accurately defining the geometric shape of the lattice object, the topological relationship between the truss elements is also constructed, which has the characteristics of high automation, stability and reliability, wide application range, strong realizability, and high computational efficiency. Brief Description of the Drawings
[0039] Figure 1 is the flowchart of a method for modeling a stochastic lattice structure based on F-Rep provided by the present invention;
[0040] Figure 2 is the schematic diagram of the GE engine bracket for representing the macroscopic design domain of the stochastic lattice structure;
[0041] Figure 3 is the schematic diagram of the macroscopic design domain expressed by discrete tetrahedral grid cells after Delaunay triangulation;
[0042] Figure 4 In (a), (b), and (c) of are respectively the schematic diagrams of the definitions of the topological elements of the grid topology data structure of half-plane encoding;
[0043] Figure 5 is the schematic diagram of the result showing the mapping relationship between half-planes after topological reconstruction;
[0044] Figure 6 is the schematic diagram of the truss-like element in the local two-dimensional modeling coordinate system;
[0045] Figure 7 In (a), (b), (c), (d), and (e) of are respectively the schematic diagrams of the models of the truss-like elements formed in the three-dimensional space after rotation around the axis;
[0046] Figure 8 is the design drawing of the complex stochastic lattice structure expressed based on the F-Rep model. Detailed Embodiments
[0047] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
[0048] Please refer to Figure 1, a method for modeling a random dot matrix structure based on F-Rep provided by the present invention mainly includes the following steps:
[0049] S1. By performing Delaunay triangulation on the macroscopic design domain of the random dot matrix structure, the vertex data and cell information of the tetrahedral mesh cells are obtained.
[0050] The macroscopic design domain of the random dot matrix structure can be any shape with a complex geometric shape. Generally, it is stored in a general CAD format such as IGES and STEP. The three-dimensional complex design domain is subjected to Delaunay triangulation to obtain the vertex data P and cell information C as follows:
[0051]
[0052] In the formula, m is the number of vertices, n represents the number of tetrahedral elements, represents the indices of the four vertices of the u-th element.
[0053] In one embodiment, please refer to Figure 2 and Figure 3 , in this example, the macroscopic design domain of the random dot matrix structure is selected as the GE engine bracket model, and the Delaunay triangulation process is completed. After statistics, a total of 28,077 vertices and 18,075 tetrahedral mesh cells are generated.
[0054] S2. According to the cell information, the volume-half face-vertex three-layer topological elements of the tetrahedral mesh cells are explicitly stored and implicitly expressed respectively, and the connection relationship between the tetrahedral mesh cells is topologically reconstructed by using a half-face encoded mesh topological data structure based on the local topological relationship inside the tetrahedral mesh cells.
[0055] In order to establish the adjacency relationship between adjacent tetrahedral mesh cells, a half-face encoded mesh topological data structure will be introduced to organize the discrete mesh data. The specific steps are as follows:
[0056] S21: Define and store the volume-half face-vertex three-layer topological elements on the tetrahedral mesh cells: The index of the vertex starts from 0, and the index of the cell starts from 1. For each cell, it is agreed that the storage relationship of the four vertices on the tetrahedral mesh cell follows the CGNS rule.
[0057] S22: Every two tetrahedral mesh cells share a face. Referring to the definition of the half-edge data structure: this face is divided into two half-faces, each half-face is defined by a binary tuple consisting of the serial number of the corresponding tetrahedral cell and the local index on the cell where this half-face is located. The binary tuple of the half-face is encoded as a 32-bit unsigned integer. The last three bits store the local index of this half-face, and the remaining bits store the index of the tetrahedral mesh cell. This encoding method can accommodate approximately 500 million cells, while maintaining the data volume, improving the compactness of the data structure and significantly reducing the memory overhead.
[0058] S23: Construct the topological relationship between tetrahedral mesh cells. The key lies in constructing the mapping relationship between half-faces. First, two intermediate mappings, v2hfs and v2adj, are established by traversing all half-faces. v2hfs records the mapping between the maximum-index vertex on each half-face and the half-face; v2adj records the mapping between the corresponding remaining vertices and the half-face. Secondly, traverse each half-face again to obtain the maximum vertex index as the key and the additional information with the remaining vertex indices as the key. Secondly, find the matching partner half-face in the set of half-faces with the same key value, thereby constructing the mapping relationship between half-faces.
[0059] In one embodiment, please refer to Figure 4 and Figure 5 , taking a group of adjacent tetrahedral cells as an example, Figure 4 details the definition of underlying topological elements, including the explicit storage of vertices and cells and the rules of half-face encoding, etc. Figure 5 Taking a set of finitely many adjacent tetrahedral mesh cells as an example, it shows the mapping relationship between adjacent half-faces established based on the mesh topology data encoded by half-faces.
[0060] S3. Under the modeling coordinate system, transform the truss-like primitive into the radius of the node circle and the geometric control parameters of the conic curve tangent to the corresponding circle, and then obtain the expression of the truss-like primitive, so as to realize the implicit function unified representation of the truss-like primitive of the tetrahedral mesh cell in the local coordinate system; wherein, the truss-like primitive includes cylindrical truss primitives, conical truss primitives and quadratic surface primitives; the geometric control parameters include t, r 1 and r 2 , r 1 and r 2 are the radii of two node circles respectively, and t represents the shape parameter of the truss between the two node circles.
[0061] The truss primitive expressed based on F-Rep includes two node circles located at the vertices and the truss primitive composed of the conic curve as the contour. The specific steps are as follows:
[0062] S31: The local modeling coordinate system is defined on the xOy plane. The two node circles and the truss primitives correspond to three basic functions in the local modeling coordinate system: the circles at (-1, 0) and (1, 0) and the conic section equations of the truss primitives tangent to the circles, as shown below:
[0063]
[0064] where r 1 and r 2 are the radii of the two node circles respectively. According to the tangency condition, equations (2) and (3) are combined with equation (1) to calculate the two parameters c and d of equation (1).
[0065] S32: Define the third circle with its center at (0, 0) and radius The third control parameter t is introduced to make the third circle tangent to the truss, and the third parameter a is calculated by solving equation (1).
[0066] S33: By r 1 、r 2 The conic curve equations corresponding to the three geometric control parameters, t and t, define the outer contour of the truss primitive. By rotating around the X-axis, a three-dimensional truss primitive in the local modeling coordinate system can be generated. 1 、r 2 The conic section equations corresponding to the three geometric control parameters t and t are the function expressions of the truss primitives.
[0067] In one embodiment, see Figure 6 and Figure 7 , step S3 includes the following sub-steps:
[0068] S31: The local modeling coordinate system is defined on the xOy plane. The three primitives correspond to the three basic functions in the local modeling coordinate system: the conic section equations of the circles at (-1, 0) and (1, 0) and the truss primitives tangent to the circles, Figure 6 Shows the geometric shape definition of the primitive in the local modeling coordinate system.
[0069] S32: Define the third circle with its center at (0, 0) and radius The third control parameter t is introduced to make the third circle tangent to the truss element, and the third parameter a is calculated by solving equation (1).
[0070] S33: By r 1 、r 2 The conic section equations controlled by the three parameters of and t define the outer contour of the truss primitive. By rotating around the X-axis, the three-dimensional truss primitive contour in the local modeling coordinate system can be generated. Figure 7Shows the three-dimensional primitive shape after rotation around the X-axis, including four types of truss primitive shapes.
[0071] S4. Based on the geometric control parameters of the truss primitive, directly construct the implicit expression function of the truss primitive in the global coordinate system, and then obtain the implicit expression function of each truss primitive in the global coordinate system according to the mesh topology data structure, so as to realize the function expression of the random lattice structure model.
[0072] According to different types of truss primitives, the truss primitive can be expressed as an elliptical primitive, a hyperboloid of one sheet primitive, and traditional cylindrical and conical primitives. The position of the truss primitive in space depends on the coordinates of the two end points of the edge in the mesh. According to the geometric control parameters of the truss primitive in S3, calculate the coordinates of the center point and the semi-major axis length of the truss primitive in the global coordinate system. In order to transform the implicit function of the truss primitive in the local modeling coordinate system to the global coordinate system, the specific steps are as follows:
[0073] S41: The implicit functions of the two spherical primitives located at the vertex of the grid line are directly calculated through the coordinates and radii of the vertex.
[0074] S42: When the truss primitive corresponds to an ellipsoidal surface, assume that the center point of the ellipsoidal surface is o, and the three symmetry axes are u, v, and w respectively, where u represents the rotation axis of the conic section, and the semi-axis lengths are denoted as m, n, and n respectively. Then the surface equation is expressed as:
[0075]
[0076] Similarly, when the truss primitive corresponds to a hyperboloid of one sheet, the surface equation is constructed as:
[0077]
[0078] When the conic section degenerates into a straight line, the truss primitive corresponds to a cylindrical surface and a conical surface respectively.
[0079] Assume that the radius of the cylindrical surface is r, a point on the axis is o, and the axis direction is n. According to the fact that the distance from any point x on the cylindrical surface to the axis is r, the cylindrical surface equation is expressed as:
[0080] (x - o) T (I - nn T )(x - o) = r 2
[0081] Let the vertex of the cone be o, the semi-vertical angle be θ, the axis direction be n, the generatrix direction be l, and the cosine value of the angle between the generatrix and the axis be cosθ = l T n. From the geometric relationship, the equation of the conical surface can be obtained as:
[0082]
[0083] In one embodiment, the implicit expression of the truss primitive in the global coordinate system includes the following steps:
[0084] S41: The implicit functions of two spherical primitives located at the vertices of the grid lines are directly calculated through the coordinates and radii of the vertices. In this example, the coordinates of the primitive nodes are specified by the grid vertices, and 1 / 8 of the shortest distance of the 1-neighborhood of each vertex is selected as the radius.
[0085] S42: Designate all truss primitives as conical primitives, then the implicit function equation of the truss primitive in the global coordinate system is expressed as:
[0086]
[0087] S5: According to the grid topology data structure, perform implicit modeling on each truss primitive in the global coordinate system to realize the functional expression of the random lattice structure CAD model.
[0088] Please refer to Figure 8 For the modeling result of the final random lattice structure, after testing, the construction time of the F-Rep model is only 59.07 s.
[0089] The present invention also provides a random lattice structure modeling system based on F-Rep. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the above-mentioned random lattice structure modeling method based on F-Rep.
[0090] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the above-mentioned random lattice structure modeling method based on F-Rep.
[0091] It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.
Claims
1. A random lattice structure modeling method based on F-Rep, characterized in that: The modeling method comprises the following steps: S1, by performing Delaunay triangulation on the macroscopic design domain of the random lattice structure, the vertex data and unit information of the tetrahedral mesh unit are obtained; S2, based on the unit information, the three-layer topological elements of the tetrahedral mesh unit, namely, body, half-edge, and vertex, are explicitly stored and implicitly expressed, and the connection relationship between the tetrahedral mesh units is topologically reconstructed using a half-face-encoded mesh topological data structure based on the local topological relationship inside the tetrahedral mesh unit; S3, in the modeling coordinate system, the truss-like primitives are transformed into the radius of the node circle and the geometric control parameters of the conic curve tangent to the corresponding circle, and then the expressions of the truss-like primitives are obtained to realize the unified implicit function representation of the truss-like primitives of the tetrahedral grid unit in the local coordinate system; wherein the truss-like primitives include cylindrical truss primitives, cone truss primitives and quadratic surface primitives; the geometric control parameters include t, r1 and r2, r1 and r2 are the radii of the two node circles respectively, and t represents the shape parameters of the truss between the two node circles; S4, based on the geometric control parameters of the truss primitive, directly construct the implicit expression function of the truss primitive in the global coordinate system, and then obtain the implicit expression function of each truss primitive in the global coordinate system according to the grid topology data structure, realizing the functional expression of the random lattice structure model.
2. The random lattice structure modeling method based on F-Rep according to claim 1, characterized in that: In the half-face encoded grid topology data structure, every two tetrahedral grid units share one face. Refer to the definition of the half-edge data structure: this face is divided into two half-faces. Each half-face is defined by a tuple consisting of the serial number of the corresponding tetrahedral unit and the local index of the unit where the half-face is located. The tuple of the half-face is encoded as a 32-bit unsigned integer, the last three bits store the local index of the half-face, and the remaining bits store the index of the tetrahedral grid unit.
3. The random lattice structure modeling method based on F-Rep according to claim 1, characterized in that: Perform Delaunay triangulation on the macroscopic design domain of the random lattice structure, and obtain vertex data P and unit information C respectively: Where m is the number of vertices, n is the number of tetrahedral units, {N i (u) } represents the four vertex indices of the u-th unit; i = 1, 2, 3, 4.
4. The random lattice structure modeling method based on F-Rep according to claim 1, characterized in that: Step S2 includes the following sub-steps: S21: Define and store the volume-half-face-vertex three-layer topological elements on the tetrahedral mesh unit; S22, every two tetrahedral mesh units share a face, refer to the definition of the half-edge data structure: divide this face into two half-faces, each half-face is defined by a tuple consisting of the serial number of the corresponding tetrahedral unit and the local index of the unit where the half-face is located, and encode the half-face tuple as a 32-bit unsigned integer, the last three bits store the local index of the half-face, and the remaining bits store the index of the tetrahedral mesh unit; S23: Construct topological relationships between tetrahedral mesh elements.
5. The random lattice structure modeling method based on F-Rep according to claim 4, characterized in that: In S23, two intermediate mappings are first established by traversing all half-faces: v2hfs and v2adj. v2hfs records the mapping between the maximum index vertex and the half-face on each half-face; v2adj records the mapping between the corresponding remaining vertices and half-faces. Secondly, each half-face is traversed again to obtain the maximum vertex index as the key, and the remaining vertex indices are used as additional information of the key. Furthermore, the matching partner half-face is searched in the set of half-faces with the same key value, thereby constructing a mapping relationship between the half-faces.
6. The random lattice structure modeling method based on F-Rep according to claim 1, characterized in that: Step S3 includes the following sub-steps: S31: The local modeling coordinate system is defined on the xOy plane. The two node circles and the truss primitives correspond to three basic functions in the local modeling coordinate system: the conic section equations of the circles at (-1, 0) and (1, 0) and the truss primitives tangent to the circles are: Where r1 and r2 are the radii of the two node circles respectively. According to the tangency condition, equations (2) and (3) are combined with equation (1) to calculate the two parameters c and d of equation (1). S32: Define the third circle with its center at (0, 0) and radius The third control parameter t is introduced to make the third circle tangent to the truss, and the third parameter a is calculated by using equation (1); S33: The conic section equations corresponding to the three geometric control parameters r1, r2 and t define the outer contour of the truss element, and a three-dimensional truss element located in the local modeling coordinate system is generated by rotating around the X-axis; among them, the conic section equations corresponding to the three geometric control parameters r1, r2 and t are the function expressions of the truss element.
7. The random lattice structure modeling method based on F-Rep according to any one of claims 1 to 6, characterized in that: When the truss primitive corresponds to an ellipsoid, assuming that the center point of the ellipsoid is o, the three symmetry axes are u, v, and w, where u represents the rotation axis of the quadratic curve, and the semi-axis lengths are m, n, and n, respectively. The surface equation is expressed as:
8. The random lattice structure modeling method based on F-Rep according to claim 7, characterized in that: When the truss primitive corresponds to a single-leaf hyperboloid, the surface equation is constructed as: When the quadratic curve degenerates into a straight line, the truss primitives correspond to the cylindrical surface and the conical surface respectively; assuming that the radius of the cylindrical surface is r, a point on the axis is o, and the axis direction is n, the distance from any point x on the cylindrical surface to the axis is r, and the cylindrical surface equation is expressed as: (xo) T (I-nn T )(xo)=r 2 Assume that the vertex of the cone is o, the semi-vertex angle is θ, the axis direction is n, the generatrix direction is l, and the cosine value of the angle between the generatrix and the axis is cosθ=l T n, the equation of the cone surface is obtained from the geometric relationship:
9. A random lattice structure modeling system based on F-Rep, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the F-Rep-based random lattice structure modeling method according to any one of claims 1 to 8 when executing the computer program.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, and when the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the F-Rep-based random lattice structure modeling method described in any one of claims 1-8.
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