A method and device for automatic geometry reconstruction based on three-dimensional topology optimization results

Abstract

The present invention belongs to the technical field related to model geometry reconstruction, and discloses a method and device for automatic geometry reconstruction based on three-dimensional topology optimization results, and the steps are: S1, forming a skeleton line based on the skeleton position of the topology optimization result model; S2, automatic separation of the design domain and the non-design domain; S3, using the minimum rotation frame information at the sampling point to intersect the surface of the topology optimization result model with the ray, and then skinning the obtained cross-section fitting curve to obtain the branch surface; S4, determining the main curve and the main plane in turn, and then projecting the remaining extreme position points corresponding to the transition section to the main plane, and then filling the openings between the obtained side surface pieces to form a transition surface; S5, performing a surface stitching operation on the branch surface and the transition surface, and then obtaining the final CAD model of the topology optimization result expressed based on the NURBS surface. The present invention solves the problem that the topology optimization result is difficult to seamlessly connect with the existing CAD system.

Description

Technical Field

[0001] The present invention belongs to the technical field related to model geometry reconstruction, and more specifically, relates to a method and device for automatic geometry reconstruction based on three-dimensional topology optimization results. Background Art

[0002] With the advancement of computer science and technology, structural optimization design has become one of the important means to achieve lightweight and high performance of key components in the fields of aerospace, shipbuilding, automobile, biomedicine, etc. Different from size optimization and shape optimization, topology optimization technology autonomously searches for the optimal material distribution under a certain performance index under the premise of a given design domain, preset boundaries and loads. In the past few decades, topology optimization technology has received widespread attention from academia and industry, and a series of methods such as homogenization method, solid isotropic material penalty method, progressive structural optimization method and level set method have been developed; among them, solid isotropic material penalty method has been adopted by many commercial software (such as Altair OptiStruct, MSC Nastran, TOSCA, etc.) due to its significant advantages in computational efficiency and numerical stability.

[0003] In order to obtain the optimal topological form of the structure, the optimization results are usually presented in the form of triangular facets. However, these surface models are usually of poor quality, not smooth enough, and lack parameter control. In fact, no matter which topology optimization method is used, the original topology optimization results cannot be directly used for subsequent product structural analysis, parametric design, prototype manufacturing and other links. In order to meet the needs of various stages of subsequent product design and manufacturing, most of the current methods manually reconstruct the topology optimization results through manual intervention to generate a computer-aided design (CAD) model based on B-Rep expression, but this process is very time-consuming and cumbersome. Therefore, there is an urgent need for a method to quickly and effectively convert topology optimization results into CAD models automatically. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a method and device for automatic geometric reconstruction based on three-dimensional topology optimization results, which aims to solve the problem that topology optimization structures are difficult to seamlessly integrate with existing CAD systems.

[0005] To achieve the above object, according to one aspect of the present invention, a method for automatic geometry reconstruction based on three-dimensional topology optimization results is provided, the method comprising the following steps:

[0006] S1, forming a skeleton line representing the topology optimization result model based on the skeleton position of the topology optimization result model;

[0007] S2, Delaunay meshing is performed on the non-design domain information input in the form of B-Rep, and then the skeleton located in the non-design domain is deleted to realize the automatic separation of the design domain and the non-design domain;

[0008] S3, select an extreme position point near both ends of each skeleton line, and use an undirected graph to construct the topological adjacency relationship between the connection points and the extreme position points between adjacent skeleton lines; at the same time, establish a minimum rotation frame for the skeleton points between the two extreme position points of each skeleton line, and sequentially select several points on the skeleton line as sampling points, and use the minimum rotation frame information at the sampling points to perform ray intersection with the surface of the topology optimization result model to obtain a cross-section fitting curve, and then perform skinning and lofting on the cross-section fitting curve to obtain a branch surface;

[0009] S4, the skeleton line from the connection point to the extreme position point is the transition section, the tangent vector at the extreme position point corresponding to the transition section is calculated, and the difference between the angles between each tangent vector and its adjacent tangent vector is calculated, and the skeleton line where the tangent vector with the smallest difference is located is selected as the main curve, and the normal plane where the extreme position point of the main curve is located is selected as the main plane, and then the remaining extreme position points corresponding to the transition section are projected onto the main plane, and the side surface pieces are generated by skinning, and the openings between the side surface pieces are filled by surface filling to form a transition surface;

[0010] S5, all branch surfaces and transition surfaces are stitched to form a closed entity, and the non-design domain and the design domain are merged through Boolean operation to obtain the final CAD model of the topology optimization result expressed based on NURBS surface.

[0011] Further, step S4 includes the following sub-steps:

[0012] S41, obtaining the connection point and limit position point information corresponding to the transition segment according to the undirected graph information, including the index number, geometric information and corresponding RMF frame information of the point;

[0013] S42, according to the tangent vectors at the extreme position points corresponding to the transition section, by calculating the difference between the angles between each tangent vector and its adjacent tangent vector, the skeleton line where the tangent vector with the smallest difference is located is selected as the main curve, and the normal plane where the extreme position points of the main curve are located is selected as the main plane;

[0014] S43, projecting the remaining extreme position points corresponding to the transition segment toward the main plane direction, and obtaining the lofting range of the remaining extreme position points corresponding to each transition segment to the main curve by bisecting the projection direction on the main plane;

[0015] S44, repeat skinning and lofting to generate multiple side surface patches;

[0016] S45, filling the openings between the side surface pieces by means of surface filling, and forming a NURBS clipping surface by surface stitching.

[0017] Furthermore, the topology optimization result model input in the form of triangular facets is used to determine the skeleton position of the topology optimization result model using the mean curvature flow method, and the skeleton line of the topology optimization result model is formed according to the skeleton information.

[0018] Furthermore, the input topology optimization result model is firstly re-meshed isotropically, and the discrete Laplace operator is used to calculate the mean curvature flow, which is dynamically updated during the iterative contraction process to generate discrete skeleton segments; the skeleton line is generated by connecting the discrete segments end to end.

[0019] Furthermore, an axis-aligned bounding box is constructed for the triangular facets in the discrete non-design domain, and a hierarchical bounding tree N-BVH is constructed using a surface area heuristic algorithm. It is judged in turn whether the points on the skeleton line segments are in the non-design domain, the skeleton lines outside the non-design domain are retained, and the skeleton lines in the non-design domain are deleted.

[0020] Furthermore, a hierarchical bounding box T-BVH is first established for the input original topology optimization result model; secondly, the two endpoints of all skeleton lines are selected, and an undirected graph structure is established according to their node numbers; then, an extreme position point is selected near the two endpoints on each skeleton line, and finally the selected extreme position point is added to the undirected graph structure.

[0021] Furthermore, the distance between the limit position point and the connection point is proportional to the shortest distance from the connection point to the surface of the topology optimization result model, and the proportional coefficient is selected in the range of 2.0-3.0.

[0022] Furthermore, M sampling points are selected on each skeleton line to obtain the RMF frame field information U(u)=(r(u),s(u),t(u)) at the sampling point, and the r(u) direction is selected as the first projection direction And calculate N-1 projection vectors on the normal plane The specific calculation formula is:

[0023]

[0024] In the formula, is the i-th projection direction, θ is a constant, and the calculation formula is θ=2π / N, It is the direction of the tangent vector in the RMF frame of the current point.

[0025] The present invention also provides a system for automatically reconstructing geometry based on three-dimensional topology optimization results. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the method for automatically reconstructing geometry based on three-dimensional topology optimization results as described above.

[0026] 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 a processor, the machine-executable instructions prompt the processor to implement the method for automatic geometric reconstruction based on three-dimensional topology optimization results as described above.

[0027] In general, compared with the prior art, the method and device for automatic geometric reconstruction based on three-dimensional topology optimization results provided by the present invention mainly have the following beneficial effects:

[0028] 1. The present invention uses the topology optimization result model and non-design domain information as input, and automatically converts it into a CAD model of the topology optimization result based on parametric surface expression through a series of geometric processing. The topological relationship between geometric elements is completely established, and it has the characteristics of high degree of automation, stability and reliability, wide application range, strong feasibility and high calculation efficiency. It effectively solves the problem that the topology optimization results are difficult to be compatible with the existing CAD system. The reconstructed model can be directly converted into common file formats such as STEP and IGES, supporting subsequent finite element simulation verification and additive manufacturing process.

[0029] 2. The method of extracting the skeleton line of the model based on the mean curvature flow method uses the characteristic of area minimization to push the curvature flow to the limit to obtain the skeleton. It has the advantages of high efficiency and numerical stability. The result is smoother and closer to the central axis of the model.

[0030] 3. Since the minimum rotation frame field (RMF) is introduced in the skin lofting process, compared with the traditional Frenet frame, the RMF frame field does not have the problem of Frenet frame flipping at the point where the curve curvature is 0. At the same time, it has small calculation amount, high calculation accuracy and is easy to implement, so that the skin lofting surface torsion is smaller.

[0031] 4. The principal plane projection method adopted effectively solves the problem of difficulty in automatically constructing NURBS surfaces at the joints of branch surfaces with multi-connectivity features, and ensures a good transition between the branches.

[0032] 5. The surface area heuristic algorithm (SAH) is used to construct a hierarchical bounding tree, which improves the construction quality of the acceleration structure; the BVH-based model processing technology speeds up the calculation efficiency of ray intersection and nearest neighbor distance, indirectly ensuring the efficiency of the reconstruction method. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of a method for automatic geometric reconstruction based on three-dimensional topology optimization results provided by the present invention;

[0034] Figure 2 (a) and (b) are the topology optimization results based on triangular face expression and non-design domain information diagrams respectively;

[0035] Figure 3 It is a schematic diagram of skeleton extraction of topology optimization model;

[0036] Figure 4 This is a schematic diagram after the design domain and non-design domain are automatically separated;

[0037] Figure 5 It is a schematic diagram of the extreme position points selected from each skeleton line;

[0038] Figure 6 It is the branch surface graph generated by skinning and lofting each skeleton line;

[0039] Figure 7 It is a schematic diagram of the projection of other extreme position points to the key extreme point, in which a connection point is selected to enlarge the projection effect for illustration;

[0040] Figure 8 It is the intermediate section curve generated during the skinning lofting in the transition section, and the side surface piece generated based on the surface lofting operation;

[0041] Fig. 9 It is the final transition surface formed after the opening is filled with a curved surface;

[0042] Fig.10 It is the CAD model of the topology optimization result generated after surface stitching and Boolean operation. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended 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.

[0044] See also Figure 1 The present invention provides a method for automatic geometry reconstruction based on three-dimensional topology optimization results, the method mainly comprising the following steps:

[0045] S1, forming a skeleton line representing the topology optimization result model based on the skeleton position of the topology optimization result model.

[0046] Specifically, the topology optimization result model input in the form of triangular facets is used to determine the skeleton position of the topology optimization result model using the mean curvature flow (MCF) method (or the medial axis transformation method), and a skeleton line representing the topology optimization result model is formed based on the skeleton information.

[0047] In one embodiment, the input topology optimization result model is firstly re-meshed isotropically, and the discrete Laplace operator is used to calculate the mean curvature flow, which is dynamically updated during the iterative contraction process to generate discrete skeleton line segments; the skeleton line is generated by connecting the discrete line segments end to end.

[0048] See also Figure 2 and Figure 3 In this embodiment, the original topology optimization result model is re-divided into isotropic grids to generate a uniform grid. In this example, the non-design domain is a rectangular support. The skeleton line of the topology optimization result model is obtained by adopting a skeleton extraction method based on mean curvature flow.

[0049] S2, the non-design domain information input in the form of B-Rep is subjected to Delaunay segmentation, and then the skeleton located in the non-design domain is deleted to achieve automatic separation of the design domain and the non-design domain.

[0050] Specifically, the non-design domain information input in the form of B-Rep is subjected to Delaunay segmentation. By judging the positional relationship between the skeleton line and the non-design domain, the skeleton located in the non-design domain is deleted to achieve automatic separation of the design domain and the non-design domain.

[0051] The axis-aligned bounding box is constructed for the triangular facets in the discrete non-design domain. The hierarchical bounding tree N-BVH is constructed based on the surface area heuristic algorithm (SAH). The points on the skeleton line segments are judged in turn whether they are in the non-design domain. The skeleton lines outside the non-design domain are retained, and the skeleton lines in the non-design domain are deleted. The results are as follows: Figure 4 shown.

[0052] S3, select an extreme position point near the two ends of each skeleton line, and use an undirected graph to construct the topological adjacency relationship between the connection points between adjacent skeleton lines and the extreme position points; at the same time, establish a minimum rotation frame for the skeleton points between the two extreme position points of each skeleton line, and select several points on the skeleton line in sequence as sampling points. Use the minimum rotation frame information at the sampling points to perform ray intersection with the surface of the topology optimization result model to obtain a cross-section fitting curve, and then perform skinning and lofting on the cross-section fitting curve to obtain a branch surface.

[0053] Among them, firstly, a hierarchical bounding box T-BVH is established for the input original topology optimization result model; secondly, the two end points of all skeleton lines are selected, and an undirected graph structure is established according to their node numbers; then, an extreme position point is selected near the two end points on each skeleton line, where the distance between the extreme position point and the connection point is proportional to the shortest distance from the connection point to the surface of the topology optimization result model, and the scale factor is selected in the range of 2.0-3.0. The shortest distance here is also quickly achieved through T-BVH. It should be noted that if the degree of the endpoint is 1, the extreme position point coincides with the endpoint, that is, the scale factor is 0; finally, the selected extreme position point is added to the undirected graph structure.

[0054] In one embodiment, the connection point information is recorded by means of the connection relationship between the skeleton lines, and an extreme position point is selected near both ends of each skeleton line, and then a topological connection relationship between the connection point and the extreme position point information is established using an undirected graph.

[0055] Traverse each skeleton line in turn, record the node numbers at both ends of the skeleton line, establish an undirected graph structure, and extract and simplify the adjacency relationship of the skeleton line; then, select an extreme position point close to the two end points on each skeleton line, where the distance between the extreme position point is proportional to the shortest distance from the two end points of the skeleton line to the surface of the topology optimization result model. In this example, the proportional coefficient is selected as 2.5. The shortest distance here is also quickly achieved by T-BVH established based on the topology optimization result model; in this example, there are 12 nodes with a degree of 1 at the junction of the design domain and the non-design domain, so the extreme position points close to these nodes coincide with the endpoints, and then these extreme position point information is added to the undirected graph structure. The extreme position points selected on the skeleton line are as follows: Figure 5 shown.

[0056] Among them, a minimum rotation frame (RMF) is established for the skeleton points between the two extreme position points of each skeleton line, and several skeleton points on the skeleton line are selected in sequence. The RMF frame information at the selected points is used to perform ray intersection with the surface of the topology optimization result model, and the cross-section fitting curve is obtained, and then the cross-section fitting curve is skinned and lofted to obtain the branch surface.

[0057] Specifically, see Figure 6 , select M sampling points on each skeleton line, obtain the RMF frame field information U(u)=(r(u),s(u),t(u)) at the sampling point, and select the r(u) direction as the first projection direction And calculate N-1 projection vectors on the normal plane The specific calculation formula is:

[0058]

[0059] In the formula, is the i-th projection direction, θ is a constant, and the calculation formula is θ=2π / N, It is the direction of the tangent vector in the RMF frame of the current point.

[0060] Taking the sampling point as the center of the circle and the projection direction as the ray direction, T-BVH is used to quickly calculate the intersection with the surface of the topology optimization result model, and a cubic B-spline section curve is inversely obtained by interpolation. The above operation is performed on M sampling points to obtain a cluster of section surfaces {C k (u)}(k=1,2…M), and automatically construct branch surfaces by utilizing skinning.

[0061] For the skeleton line connecting the non-design domain and the design domain, it is necessary to calculate the nearest point from the boundary point to the non-design domain, and then perform skinning and lofting through the RMF frame field information to generate a branch surface to ensure a smooth connection between the design domain and the non-design domain.

[0062] S4, the skeleton line from the connection point to the extreme position point is the transition section, the tangent vector at the extreme position point corresponding to the transition section is calculated, and the difference in the angle between each tangent vector and its adjacent tangent vector is calculated. The skeleton line where the tangent vector with the smallest difference is located is selected as the main curve, and the normal plane where the extreme position point of the main curve is located is the main plane. Then the remaining extreme position points corresponding to the transition section are projected onto the main plane, and the side surface patches are generated by skinning. The openings between the side surface patches are filled by surface filling to form a transition surface.

[0063] See also Figure 7 , Figure 8 and Fig. 9 , step S4 includes the following sub-steps:

[0064] S41, obtaining the connection point and limit position point information corresponding to the transition segment according to the undirected graph information, including the index number, geometric information and corresponding RMF frame information of the point. The skeleton line from the connection point to the limit position point is the transition segment.

[0065] S42, according to the tangent vector at the extreme position point corresponding to the transition section, by calculating the difference in the angle between each tangent vector and its adjacent tangent vector, the skeleton line where the tangent vector with the smallest difference is located is selected as the main curve, and the normal plane where the extreme position point of the main curve is located is selected as the main plane.

[0066] S43, projecting the remaining extreme position points corresponding to the transition segment toward the main plane direction, and obtaining the lofting range of the remaining extreme position points corresponding to each transition segment to the main curve by bisecting the projection direction on the main plane.

[0067] S44, repeat skinning and lofting to generate multiple side surface patches.

[0068] S45, filling the openings between the side surface pieces by means of surface filling, and forming a NURBS clipping surface by surface stitching.

[0069] S5, all branch surfaces and transition surfaces are stitched to form a closed entity, and the non-design domain and the design domain are merged through Boolean operation to obtain the final CAD model of the topology optimization result expressed based on NURBS surface.

[0070] The cuboid support is used as a non-design domain, and Boolean operations are performed with the design domain stitched into a solid to generate a topology optimization model based on parametric surface expression, such as Fig.10 As shown, the model can be exported in IGES and STEP file formats for subsequent finite element simulation verification and additive manufacturing process.

[0071] The present invention also provides a system for automatically reconstructing geometry based on three-dimensional topology optimization results. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the method for automatically reconstructing geometry based on three-dimensional topology optimization results as described above.

[0072] 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 a processor, the machine-executable instructions prompt the processor to implement the method for automatic geometric reconstruction based on three-dimensional topology optimization results as described above.

[0073] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for automatic geometry reconstruction based on three-dimensional topology optimization results, characterized in that: The method comprises the following steps: S1, forming a skeleton line representing the topology optimization result model based on the skeleton position of the topology optimization result model; S2, Delaunay meshing is performed on the non-design domain information input in the form of B-Rep, and then the skeleton located in the non-design domain is deleted to realize the automatic separation of the design domain and the non-design domain; S3, select an extreme position point near both ends of each skeleton line, and use an undirected graph to construct the topological adjacency relationship between the connection points and the extreme position points between adjacent skeleton lines; at the same time, establish a minimum rotation frame for the skeleton points between the two extreme position points of each skeleton line, and sequentially select several points on the skeleton line as sampling points, and use the minimum rotation frame information at the sampling points to perform ray intersection with the surface of the topology optimization result model to obtain a cross-section fitting curve, and then perform skinning and lofting on the cross-section fitting curve to obtain a branch surface; S4, the skeleton line from the connection point to the extreme position point is the transition section, the tangent vector at the extreme position point corresponding to the transition section is calculated, and the difference between the angles between each tangent vector and its adjacent tangent vector is calculated, and the skeleton line where the tangent vector with the smallest difference is located is selected as the main curve, and the normal plane where the extreme position point of the main curve is located is selected as the main plane, and then the remaining extreme position points corresponding to the transition section are projected onto the main plane, and the side surface pieces are generated by skinning, and the openings between the side surface pieces are filled by surface filling to form a transition surface; S5, all branch surfaces and transition surfaces are stitched to form a closed entity, and the non-design domain and the design domain are merged through Boolean operation to obtain the final CAD model of the topology optimization result expressed based on NURBS surface.

2. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 1, characterized in that: Step S4 includes the following sub-steps: S41, obtaining the connection point and limit position point information corresponding to the transition segment according to the undirected graph information, including the index number, geometric information and corresponding RMF frame information of the point; S42, according to the tangent vectors at the extreme position points corresponding to the transition section, by calculating the difference between the angles between each tangent vector and its adjacent tangent vector, the skeleton line where the tangent vector with the smallest difference is located is selected as the main curve, and the normal plane where the extreme position points of the main curve are located is selected as the main plane; S43, projecting the remaining extreme position points corresponding to the transition segment toward the main plane direction, and obtaining the lofting range of the remaining extreme position points corresponding to each transition segment to the main curve by bisecting the projection direction on the main plane; S44, repeat skinning and lofting to generate multiple side surface patches; S45, filling the openings between the side surface pieces by means of surface filling, and forming a NURBS clipping surface by surface stitching.

3. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 1, characterized in that: The topology optimization result model input in the form of triangular facets is used to determine the skeleton position of the topology optimization result model using the mean curvature flow method, and a skeleton line representing the topology optimization result model is formed based on the skeleton information.

4. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 1, characterized in that: Firstly, the input topology optimization result model is isotropically meshed, and the discrete Laplace operator is used to calculate the mean curvature flow, which is dynamically updated during the iterative shrinkage process to generate discrete skeleton segments. The skeleton line is generated by connecting the discrete line segments end to end.

5. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 1, characterized in that: An axis-aligned bounding box is constructed for the triangular facets in the discrete non-design domain, and a hierarchical bounding tree N-BVH is constructed using a surface area heuristic algorithm. The points on the skeleton line segments are judged in turn whether they are in the non-design domain. The skeleton lines outside the non-design domain are retained, and the skeleton lines in the non-design domain are deleted.

6. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 1, characterized in that: First, a hierarchical bounding box T-BVH is established for the input original topology optimization result model; secondly, the two end points of all skeleton lines are selected, and an undirected graph structure is established according to their node numbers; then, an extreme position point is selected near the two end points on each skeleton line, and finally, the selected extreme position points are added to the undirected graph structure.

7. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 6, characterized in that: The distance between the limit position point and the connection point is proportional to the shortest distance from the connection point to the surface of the topology optimization result model, and the proportional coefficient is selected in the range of 2.0-3.

0.

8. The method for automatic geometric reconstruction based on three-dimensional topology optimization results according to claim 6, characterized in that: Select M sampling points on each skeleton line, obtain the RMF frame field information U(u)=(r(u),s(u),t(u)) at the sampling point, and select the r(u) direction as the first projection direction And calculate N-1 projection vectors on the normal plane The specific calculation formula is: In the formula, is the i-th projection direction, θ is a constant, and the calculation formula is θ=2π / N, It is the direction of the tangent vector in the RMF frame of the current point.

9. A system for automatic geometry reconstruction based on three-dimensional topology optimization results, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for automatic geometric reconstruction based on three-dimensional topology optimization results according to any one of claims 1 to 8 is executed.

10. A computer-readable storage medium, characterized in that: 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 prompt the processor to implement the method for automatic geometric reconstruction based on three-dimensional topology optimization results as described in any one of claims 1-8.

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