CN117454706A - Hexahedral grid generation method based on hybrid model decomposition - Google Patents
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Abstract
The invention discloses a hexahedral mesh generation method based on hybrid model decomposition. Firstly, obtaining a B-Rep model of an actual product; generating a swept surface set of the B-Rep model based on surface classification aggregation, generating swept blocks after optimizing and dividing the swept surface set, thereby obtaining a swept block set and realizing the optimized and divided swept body without grafting; then the remaining area in the B-Rep model is marked as a total non-scanned area; then, constructing a dual-face set of the total non-swept area according to the types of each characteristic edge in the total non-swept area, and generating a six-face block set of the total non-swept area based on the dual-face set; and finally, generating a hexahedral mesh of the product according to the hexahedral block set divided by the swept block set and the total non-swept area. The method for generating the hexahedral mesh based on model decomposition can effectively improve the capacity and efficiency of processing complex models by using the method for generating the hexahedral mesh based on model decomposition.
Description
Technical Field
The invention relates to a hexahedral mesh generation method in finite element calculation, in particular to a hexahedral mesh generation method based on mixed model decomposition.
Background
With the rapid development of computer technology, finite element analysis is widely used in simulation and design processing of manufacturing industry with the advantages of low cost and short period. The finite element analysis is a numerical method for solving partial differential equation approximation solution, and the method firstly requires that the whole entity model is discretized into finite element grids, and an effective grid structure plays a decisive role in the accuracy and efficiency of subsequent finite element calculation.
Common three-dimensional grid structures include tetrahedral grids and hexahedral grids, and the generation technology of the tetrahedral grids is mature at present and has been widely used in the industry. The hexahedral mesh is considered as an ideal mesh structure because of the advantages of less unit number, higher calculation precision, higher convergence speed and the like, and even in some fields, effective simulation results can be obtained only by using the hexahedral mesh for simulation, so that the research of the high-quality hexahedral mesh automatic generation method has been highly focused by industry and academia.
However, due to the strong topological constraints of hexahedral meshes and the high complexity of industrial models, the automatic generation of high quality hexahedral meshes remains a difficult problem. At present, in industrial software, for generating a hexahedral mesh by a complex model, an engineer needs to manually divide the model into sub-blocks capable of automatically generating the hexahedral mesh, which can generate a great amount of manual interaction and seriously affect the efficiency. Although several hexahedral mesh generation methods based on automatic model decomposition have been proposed, the existing methods have a great gap from the actual needs of industry, and there are many problems to be solved, among which the most critical problems include how to automatically and efficiently decompose a complex model into sub-blocks suitable for high-quality hexahedral mesh generation, and how to automatically generate high-quality hexahedral mesh consistent at the joint surfaces between the sub-blocks based on the decomposition result.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a hexahedral mesh generation method based on hybrid model decomposition.
The technical scheme adopted by the invention is as follows:
1) Acquiring a B-Rep model of an actual product;
2) Generating a scanned surface set of the B-Rep model based on surface classification aggregation, and generating scanned blocks after optimizing and dividing the scanned surface set so as to obtain a scanned block set; then the remaining area in the B-Rep model is marked as a total non-scanned area;
3) Constructing a dual-surface set of the total non-swept area according to the types of each characteristic edge in the total non-swept area, and generating a six-surface block set of the total non-swept area based on the dual-surface set;
4) And generating a hexahedral mesh of the product according to the hexahedral block set divided by the swept block set and the total non-swept area.
The 2) is specifically:
2.1 According to the characteristics of the surfaces, dividing the characteristic surfaces in the B-Rep model into a source surface, a side surface, an invalid surface and a full-energy surface;
2.2 Selecting a source surface which is not added with the scanned surface set as a seed surface, and adding the seed surface into the corresponding potential scanned surface set; the surface type in the B-Rep model is a source surface or a full-energy surface, a second-order adjacent-order surface which is a current seed surface is marked as a surface to be matched, and when the normal direction of the surface to be matched is opposite to the normal direction of the current seed surface and the projection of the surface to be matched and the current seed surface has a superposition area, the surface to be matched is added into the current potential scanning surface set of the current seed surface;
2.3 A side surface type surface adjacent to the current potential scanning surface concentrated source surface type surface and a full-energy surface type surface are used as surfaces to be matched, and if the normal direction of the surfaces to be matched is perpendicular to the normal direction of the corresponding source surface, the surfaces to be matched are added into the potential scanning surface concentrated of the current seed surface; when the potential scanned surface set is effective, the potential scanned surface set is used as an effective scanned surface set, and then the potential scanned surface set is added into the scanned surface set;
2.4 Repeating 2.2) -2.3), selecting source surfaces which are not traversed as seed surfaces, matching to obtain effective swept surface sets of all seed surfaces, and adding the effective swept surface sets into the swept surface set;
2.5 When the full-function surface which is not traversed exists in the B-Rep model, marking the full-function surface as a seed surface, repeating the steps of 2.2) -2.3), and matching to obtain effective scanned surface sets corresponding to all the full-function surfaces, so as to obtain an updated scanned surface set;
2.6 Taking each scanned surface set in the current scanned surface set as a node, and constructing a scanned surface set relation graph according to the connection relation between the scanned surface sets;
2.7 Adding the scanned face set corresponding to the node with the least degree in the scanned face set relation graph into the set to be segmented;
2.8 Selecting one of the scanned surface sets, generating a segmented surface by taking the normal direction of a potential segmented surface of the scanned surface set as the normal direction of the segmented surface and taking the potential segmented position of the scanned surface set as the insertion position of the segmented surface, separating all non-scanned directional characteristics on the scanned surface set by utilizing the generated segmented surface to obtain scanned blocks and the scanned surface set after the scanned blocks are separated, and adding the generated scanned blocks into the scanned blocks to be scanned; determining the surface type of the dividing surface according to the dividing surface normal direction of each dividing surface, updating the scanned surface set and the scanned surface set after separating and scanning into blocks, and further updating the scanned surface set relation diagram;
2.9 Classifying the set of to-be-scanned blocks into a set of scanned blocks or a set of non-scanned areas according to the type of the surface of the partition surface in 2.8), and updating the set to be partitioned;
2.10 Traversing the swept area set in the current set to be segmented, repeating 2.8) -2.9) to obtain a swept block set and a non-swept area set until the set to be segmented is empty;
2.11 Repeating 2.7) -2.10) to obtain a scanned block set and a non-scanned area set corresponding to each scanned surface set until the scanned surface set is empty, and forming a total non-scanned area by an undivided area in the B-Rep model and a final non-scanned area set.
In the step 2.3), when the number of the surfaces in the potential scanned surface set corresponding to the current seed surface is greater than 3, the potential scanned surface set is valid.
In the step 2.8), when the normal direction of the dividing surface of each dividing surface is the scanning direction of the scanning surface set, the dividing surface is marked as a source surface, and then 2.2-2.3) is repeated according to the source surface), the updated scanning surface set and the updated scanning surface set after separating and scanning the blocks are updated, and then the scanning surface set relation diagram is updated; when the normal direction of the dividing surface of each dividing surface is the fork multiplication direction of the source surface characteristic edge direction of the scanned surface set and the scanning direction of the scanned surface set or the fork multiplication direction of the normal direction of the scanned surface set and the normal direction of the adjacent scanned surface set, the dividing surface is marked as a side surface;
the 2.9) is specifically:
if the side type dividing surface does not exist in the step 2.8), adding all the scanned blocks in the to-be-scanned block set into the scanned block set; if the generated side type of the divided surface of 2.8) is not classified as any scanned surface set in the current scanned surface set, marking the surface type corresponding to the surface still positioned in the current scanned surface set in the to-be-scanned block set as a source surface, and classifying all scanned blocks in the to-be-scanned block set into a non-scanned area set; if the generated side face belongs to a certain scanned face set in the current scanned face set, adding the scanned face set into the set to be segmented.
The 3) is specifically as follows:
3.1 Selecting an unprocessed non-scanned area in the total non-scanned area, calculating according to the dihedral angles of the characteristic edges in the non-scanned area to obtain the initial types of all the characteristic edges in the non-scanned area, optimizing the initial types of the characteristic edges through the effective edge type sequences corresponding to the characteristic points in the non-scanned area, and determining the final types of the characteristic edges;
3.2 Generating a pair face corresponding to each characteristic edge according to the final type of the characteristic edge, constructing six-sided block nodes on each area divided by the pair face based on the pair face, thereby directly generating a six-sided topological structure, optimizing the nodes based on the six-sided topological structure to obtain an optimized six-sided block, thereby obtaining a six-sided block set of the non-scanned area, and projecting a quadrilateral structure of an interface with the scanned area to other non-scanned areas along the scanning direction of the scanned area if the non-scanned area is adjacent to other scanned areas to serve as additional characteristic edges of other non-scanned areas;
3.3 Traversing the total non-swept area, repeating 3.1) -3.2) until the non-swept area is empty, and obtaining a six-sided block set of the total non-swept area.
3.2), specifically including the following steps for the dual surface of each characteristic edge:
firstly, determining the positions and the number of the dual rings according to the optimized type of each characteristic edge, then searching the corresponding number of the dual rings at the corresponding positions on the surface of the model where the non-scanned block area is located, and generating the dual faces corresponding to the current characteristic edges by using a graph cut algorithm based on the dual rings.
The 4) is specifically as follows:
and performing edge discretization on all the hexahedral blocks in the scanning block and the non-scanning area according to constraint conditions, and then generating hexahedral grids of the product model.
The constraint condition comprises the following three points:
projecting the cross four sides of all the six blocks of the non-scanned area connected with the source surface of the same scanned block onto the source surface of the current scanned block along the scanning direction and taking the cross four sides as a quadrilateral grid of the source surface of the current scanned block;
the number of edge discrete segments of the public four sides of the adjacent six-sided blocks is the same, and the number of opposite edge discrete segments of the public four sides is the same;
the number of discrete segments on opposite sides of the side faces of the scanned block is equal, and the number of discrete segments of a common side on the dividing face of the adjacent scanned block is equal.
The beneficial effects of the invention are as follows:
according to the invention, after classification is carried out on the model surface on the B-Rep model, the set of scanned surfaces is formed by aggregation according to the adjacent relation, and then the segmentation surface is generated on the characteristic edges or the characteristic surfaces intersected by different sets of scanned surfaces, so that separation of scanned surfaces is completed, and the processing of a large-scale triangular patch grid can be effectively avoided. Meanwhile, the invention introduces optimization of the segmentation priority and the segmentation plane direction in the segmentation process, so that the grafting problem between different scanned adults after separation can be avoided to the greatest extent, the difficulty of generating the subsequent hexahedral mesh is simplified, and a better hexahedral mesh structure can be generated.
The invention simplifies the model by identifying and separating the swept body, greatly reduces the area needing six-sided block decomposition, and then constructs the template type of the effective dual surface by starting with the characteristic points and the characteristic edges, thereby generating and optimizing the dual surface structure, fully utilizing the geometric information of the model and completing six-sided block decomposition more robustly.
According to the method, after the position of the dual surface to be inserted is determined, the final six-face number and quality are used as targets to generate the dual ring in an optimized mode, the dual surface is generated through the dual ring optimization, the corresponding six-face structure is generated according to the dual space divided by the dual surface, the condition that the hexahedral mesh is used as input to perform multi-layer deletion to generate the final six-face structure is avoided, and therefore algorithm performance is optimized.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a swept surface set result.
FIG. 3 is a swept block generated after model decomposition.
FIG. 4 is a non-swept area after model decomposition.
Fig. 5 shows the structure of the valid edge types corresponding to the feature points with different degrees.
Fig. 6 shows four types of feature edges and their corresponding dual-face structures.
FIG. 7 is a graph of a swept block optimization segmentation to avoid grafting situations.
Fig. 8 is a hexahedral mesh of the model.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples. It should be understood that the detailed description and specific examples, while indicating and illustrating the invention, are not intended to limit the invention.
As shown in fig. 1, the present invention includes the steps of:
1) After modeling an actual product model by SolidWorks or other industrial software, a user obtains a B-Rep model; in the specific implementation, directly importing a B-Rep model of an actual product;
2) Generating a scanned surface set of the B-Rep model based on surface classification aggregation, and generating scanned blocks after optimizing and dividing the scanned surface set so as to obtain a scanned block set; then the total residual area (namely the area except the swept block set) in the B-Rep model is recorded as a total non-swept area;
2) The method comprises the following steps:
2.1 According to the characteristics of the surfaces, dividing the characteristic surfaces in the B-Rep model into a source surface (source), a side surface (side), an invalid surface (invalid) and a full-energy surface (almighty); specifically: when the type of feature plane is a plane, then it contains the source plane attributes. The type of feature surface is plane or cylindrical, and when all feature edges on the surface meet the parallel or perpendicular relationship, the feature surface contains side attributes. When the feature plane only contains the source plane attribute, dividing the feature plane into source planes; when the feature surface only contains the attribute with the side surface, the feature surface is divided into the side surfaces; when one feature plane contains both source plane attributes and side plane attributes, dividing the feature plane into all-purpose planes; when a feature plane contains neither source plane attributes nor side plane attributes, it is classified as an invalid plane.
2.2 Selecting a source surface which is not added with the scanned surface set as a seed surface, and adding the seed surface into the corresponding potential scanned surface set; the surface type in the B-Rep model is a source surface or a full-energy surface, a second-order adjacent-order surface which is a current seed surface is marked as a surface to be matched, and when the normal direction of the surface to be matched is opposite to the normal direction of the current seed surface and the projection of the surface to be matched and the current seed surface has a superposition area, the surface to be matched is added into the current potential scanning surface set of the current seed surface;
2.3 A side surface type surface adjacent to the current potential scanning surface concentrated source surface type surface and a full-energy surface type surface are used as surfaces to be matched, and if the normal direction of the surfaces to be matched is perpendicular to the normal direction of the corresponding source surface, the surfaces to be matched are added into the potential scanning surface concentrated of the current seed surface; when the potential scanned surface set is effective, the potential scanned surface set is used as an effective scanned surface set, and then the potential scanned surface set is added into the scanned surface set;
2.3 If the number of faces in the potential swept face set corresponding to the current seed face is greater than 3, then the potential swept face set is valid.
2.4 Repeating 2.2) -2.3), selecting source surfaces which are not traversed as seed surfaces, matching to obtain effective swept surface sets of all seed surfaces, and adding the effective swept surface sets into the swept surface set;
2.5 When the full-function surface which is not traversed exists in the B-Rep model, marking the full-function surface as a seed surface, repeating the steps of 2.2) -2.3), and matching to obtain effective scanned surface sets corresponding to all the full-function surfaces, so as to obtain an updated scanned surface set; as shown in fig. 2, (a) of fig. 2-fig. 2 (c) are identified swept surface sets a, b, c, respectively;
2.6 Taking each scanned surface set in the current scanned surface set as a node, and constructing a scanned surface set relation graph according to the connection relation between the scanned surface sets; specifically: if the two swept surfaces have common characteristic edges in a concentrated mode, edge connection exists between the two nodes.
2.7 Adding the scanned face set corresponding to the node with the least degree in the scanned face set relation graph into the set to be segmented;
2.8 Selecting one of the to-be-segmented sets, generating a segmented surface by taking the normal direction of a potential segmented surface of the to-be-segmented set as the normal direction of the segmented surface and taking the potential segmented position of the to-be-segmented set as the insertion position of the segmented surface, separating all non-scanned directional features on the to-be-segmented set by utilizing the generated segmented surface to obtain scanned blocks and the scanned surface set after the scanned blocks are separated, adding the generated scanned blocks into the to-be-segmented set, wherein the generated scanned blocks do not contain the non-scanned directional features; wherein the non-swept direction of each swept surface set is characterized by a surface that is not in the swept surface set but is adjacent to the swept surface set, and wherein all sides of the surface that are neither parallel nor perpendicular to the swept surface set are swept in the direction. In constructing the segmented facets, it is necessary to exclude these features from the swept blocks generated by the swept facet set, and a swept facet set that needs to be segmented must have non-swept direction features that would otherwise constitute a finished swept block, and no segmentation is required. The normal direction of the potential dividing surface is the cross-multiplication direction of the scanning direction of each scanning surface set, the source surface characteristic edge direction of each scanning surface set and the scanning direction of the scanning surface set or the cross-multiplication direction of the normal direction of the scanning surface set and the normal direction of the adjacent scanning surface set. The potential segmentation locations are feature edges, feature point locations on each swept surface set, or non-swept direction feature locations of the swept surface set. Determining the surface type of the dividing surface according to the dividing surface normal direction of each dividing surface, updating the scanned surface set and the scanned surface set after separating and scanning into blocks, and further updating the scanned surface set relation diagram;
2.8 If the normal direction of the dividing plane of each dividing plane is the scanning direction of the scanning plane set, the dividing plane is marked as a source plane, and then 2.2-2.3) is repeated according to the source plane), the scanning plane set after the dividing and scanning into blocks and the scanning plane set are updated, and then the scanning plane set relation diagram is updated, as shown in fig. 2 (d) -fig. 2 (g), and fig. 2 (d) -fig. 2 (g) are respectively the scanning plane sets d, e, f, g updated after the dividing; when the normal direction of the dividing surface of each dividing surface is the fork multiplication direction of the source surface characteristic edge direction of the scanned surface set and the scanning direction of the scanned surface set or the fork multiplication direction of the normal direction of the scanned surface set and the normal direction of the adjacent scanned surface set, the dividing surface is marked as a side surface;
2.9 Classifying the set of to-be-scanned blocks into a set of scanned blocks or a set of non-scanned areas according to the type of the surface of the partition surface in 2.8), and updating the set to be partitioned;
2.9 Specifically:
if the side type segmentation surface does not exist in the step 2.8), indicating that grafting conditions do not exist in the set of to-be-scanned blocks, and adding all the scanned blocks in the set of to-be-scanned blocks into the set of scanned blocks; if the generated side type segmentation surface of 2.8) is not attributed to any scanned surface set in the current scanned surface set, explaining that the segmentation mode can lead to the grafting condition of scanned blocks, marking the surface type corresponding to the surface still positioned in the current scanned surface set in the to-be-scanned block set as a source surface, and classifying all scanned blocks in the to-be-scanned block set into a non-scanned area set; if the side generated in 2.8) belongs to a certain scanned surface set in the current scanned surface set, adding the scanned surface set into a set to be segmented, as shown in fig. 7, marking the segmented surface as a side as shown in fig. 7 (b) after the separation of the scanned surface set is completed once by the model in fig. 7 (a), and further decomposing the scanned surface set to which the measured surface belongs to obtain fig. 7 (c), wherein if the marked scanned surface set is not used, the segmentation mode in fig. 7 (d) appears, so that grafting condition appears, and finally the whole model can only be treated as a non-scanned area;
2.10 Traversing the swept area set in the current set to be segmented, repeating 2.8) -2.9) to obtain a swept block set and a non-swept area set until the set to be segmented is empty;
2.11 Repeating 2.7) -2.10) to obtain a swept block set and a non-swept area set corresponding to each swept surface set, wherein all swept blocks obtained by recursively decomposing the corresponding model in fig. 2 are shown in fig. 3, all non-swept areas obtained by decomposing the corresponding model in fig. 2 are shown in fig. 4 until the swept surface set is empty, and the total non-swept area is formed by the non-segmented area in the B-Rep model and the final non-swept area set.
3) Constructing a high-quality dual-surface set of the total non-swept area according to the types of each characteristic edge in the total non-swept area, and directly generating a six-sided block set of the total non-swept area based on the dual-surface set;
3) The method comprises the following steps:
3.1 Selecting an unprocessed non-scanned area in the total non-scanned area, calculating according to the dihedral angles of the characteristic edges in the non-scanned area to obtain the initial types of all the characteristic edges in the non-scanned area, optimizing the initial types of the characteristic edges through the effective edge type sequences (shown in figure 5) corresponding to the characteristic points in the non-scanned area, and determining the final types of the characteristic edges;
wherein the edge Type is divided to determine the position and number of the dual-planes to be inserted, and in ideal case, the Type of the feature edge is Type ori Only by its dihedral angle α:
in this embodiment, in order to ensure that the inserted dual surface can generate an effective six-sided block structure, the types of feature edges need to satisfy certain conditions: according to the invention, only common characteristic points with degrees of 3 and 4 are considered, namely 3 or 4 characteristic edges corresponding to the characteristic points, when a plurality of characteristic edges are intersected at one characteristic point, a type sequence formed by all types of the characteristic edges adjacent to the characteristic point is required to meet one of the following 10 effective patterns, namely 1-1,1-1-2,1-1-3,1-3, 2-2-2,2-3, 3-3,1-2-1-2,2-2-2-2,2-3-2-3. In this embodiment, the type sequence starts with the smallest type feature edge adjacent to the feature point (i.e., the feature edge with the smallest edge type of the feature edges around the feature point), and the types of all adjacent feature edges are given in a clockwise order. Therefore, after generating the edge types according to the dihedral angles, the feature edge types which do not conform to the 10 groups of patterns also need to be optimized, and the least optimized conditions are adjusted by the feature edge types:
argmin∑abs(Type new -Type ori )
wherein, type ori Type for feature edge Type before adjustment new For the adjusted feature edge type, abs (·) is an absolute function.
3.2 Generating a pair face corresponding to each characteristic edge according to the final type of the characteristic edge, generating six-sided block nodes on a pair space based on the pair face, directly generating a six-sided topological structure, optimizing the node positions based on the six-sided topological structure, obtaining an optimized six-sided block, and obtaining a high-quality six-sided block set of the non-scanned area, and projecting a quadrilateral structure of an interface with the scanned block to other non-scanned areas along the scanning direction of the scanned block if the non-scanned area is adjacent to other scanned blocks, and taking the quadrilateral structure as an additional characteristic edge of other non-scanned areas;
and determining the number of the dual faces to be inserted in the position of the characteristic edge according to the type of the characteristic edge after division. In specific implementation, for a feature edge with the type 1, two pairs of faces respectively tracking adjacent feature faces of the feature edge are needed to be inserted to capture the feature edge; for a feature edge of type 2, it requires the insertion of 1 pair of faces that track the adjacent feature faces of the feature edge and 2 pairs of faces that isolate the feature edge to capture the feature edge; for a type 3 feature edge, it is necessary to insert 2 pairs of faces that track the adjacent feature faces of the feature edge and two pairs of faces that isolate the feature edge to capture the feature edge.
3.2 For the dual face of each feature edge, specifically comprising the steps of:
after the number and the positions of the dual rings to be inserted in each position are determined, the direct generation of the dual surfaces is difficult, so that firstly, the positions and the number of the dual rings are determined according to the optimized type of each characteristic edge, then, the corresponding positions on the model surface where the non-scanned block area is located are searched for the corresponding number of the dual rings, the dual rings are paths of the model surface, the boundary positions of the dual surfaces can be guided when the dual surfaces are generated, the dual rings are generated at the positions where the dual surfaces are required to be generated, and the dual surfaces corresponding to the current characteristic edges are generated based on the dual rings by using a graph cut algorithm.
The generation of the dual ring is an optimization process, the position of the dual ring is required to be generated, the dual ring is perpendicular to the characteristic edge and the dual ring is smooth, the shortest path is searched through Dijkstra algorithm, and meanwhile, in order to ensure that the generated dual ring can generate an effective dual surface structure, the path of the dual ring is required to be met, and the path of the dual ring can only pass through one characteristic surface once. Meanwhile, in order to ensure that the final dual-plane can be mapped into an effective hexahedral grid structure, the dual-ring cannot overlap and selfe.
After the dual ring is built, generating a dual surface through a graph cut algorithm, wherein graph nodes in the graph cut are defined as tetrahedron grids, connecting edges of the graph nodes are defined as adjacent triangular patch grids of two adjacent tetrahedron grids, and a corresponding objective function is designed in consideration of enabling the dual surface to be as consistent as possible with the dual ring and enabling the generated dual surface to be as smooth as possible, dividing a non-scanned area into two areas of the same type after the dual surface is divided, namely k=0, 1, wherein the formula is as follows:
E＝argmin(∑E L (i，k)+λ∑E s (i，j))
wherein E is the overall cost, E L (i, k) region cost classified as k for tetrahedral mesh i, E S (i, j) represents the segmentation costs of adjacent tetrahedral meshes i, j belonging to different regions, lambda represents the region cost and the weighting factor of the segmentation cost.
The label item in the graph cut is given according to the distance and the position relation between the tetrahedral mesh and the dual surface:
wherein E is L (i) k Representing the region cost of tetrahedral mesh i classified as k, SIGN (·) represents the extracted SIGN function, norm loop Represents the loop normal determined by the right hand rule,a vector representing the points in the ring to the tetrahedral mesh i, dist i Representing the distance from the points in the ring to the tetrahedral mesh i.
The smooth term is obtained according to the point multiplication of the normal direction of the triangular patch grid and the normal direction of the dual ring:
wherein E is S (i, j) represents the segmentation cost of adjacent tetrahedral meshes i, j belonging to different regions, norm loop Representing the normal direction of the dual ring,representing the vector from the center of the dual ring to the center of the adjacent triangular patch mesh of the tetrahedral mesh.
3.3 Traversing the total non-swept area, repeating 3.1) -3.2) until the non-swept area is empty, and obtaining a six-sided block set of the total non-swept area.
4) And generating a hexahedral mesh of the product according to the hexahedral block set divided by the swept block set and the total non-swept area.
4) The method comprises the following steps:
and performing edge discretization on all the hexahedral blocks in the scanning block and the non-scanning area according to constraint conditions, and then generating a hexahedral grid of the product.
The constraint includes the following three points:
in order to ensure the grid consistency of the scanned block and the six-sided block, the cross four sides of all the six-sided blocks in the non-scanned area connected with the source surface of the same scanned block are projected onto the source surface of the current scanned block along the scanning direction and used as the quadrilateral grid of the source surface of the current scanned block;
in order to ensure the grid consistency among six blocks in a non-scanned area, the number of edge discrete segments of a public four-sided surface of the adjacent six blocks is restrained to be the same, and the number of opposite edge discrete segments of the public four-sided surface is restrained to be the same;
to generate a grid of swept blocks, the number of discrete segments on opposite sides of the sides of a constrained swept block is equal, and the number of discrete segments on a common side on the dividing plane of an adjacent swept block is the same.
According to the invention, the identification and the optimized segmentation of the scanned area are carried out on the model, so that grafting conditions are not existed among the separated scanned blocks, and the interface between the scanned blocks and the non-scanned blocks only exists on the source surface of the scanned blocks, thus the generation of the final full hexahedral mesh can be ensured.
Firstly, the number of the hexahedral discretization grid segments of all non-scanned blocks is the same, the discretization condition on the joint surface of the adjacent hexahedral blocks is guaranteed to be the same, hexahedral grids are formed on all hexahedral blocks, the grid consistency problem exists in the hexahedral block joint area of the non-scanned blocks and the scanned blocks, as no grafting condition exists in the scanned blocks separated in 2.6, namely, the side surface of the scanned block is adjacent to the source surface of another scanned block or the non-scanned block, therefore, the joint surface of the non-scanned block and the scanned block only exists on the source surface of the scanned block, the surface grid restraint belt generated on the non-scanned block is tied on the source surface of the scanned block, the number of the grid layers is discretized by the scanned block along the scanning direction, the quadrilateral surface grid is stretched into the hexahedral grid, and the hexahedral grid of the product is obtained, and finally the hexahedral grid of the non-scanned area is shown in a front view and a side view as shown in fig. 8 (a) and fig. 8 (d).
The invention provides a hexahedral mesh generation method based on hybrid model decomposition, by which a hexahedral mesh with high quality can be provided for finite element simulation. In the scanned body recognition part, the same as the existing scanned body recognition technology, the scanned bodies are required to be matched in the normal direction of the surface, but the scanned bodies which are seriously intersected can be recognized by generating a scanned surface set, so that the scanned block separation is completed; the non-swept bulk processing portion requires directly generating a corresponding six-sided block structure from the dual structure after insertion of the dual face.
The invention provides a method for constructing a swept surface set based on B-Rep surface classification, completing an algorithm for identifying and separating swept volumes in a model, avoiding grafting conditions by dividing priority and optimizing dividing direction, and enabling a finally formed swept block to complete hexahedral grid generation through a swept method.
The invention provides a dual-face generating algorithm based on a characteristic edge structure, which is characterized in that the characteristic edge is subjected to type division, then a dual-ring structure is optimally constructed, a dual ring is extended to be a dual face, a dual face is added to a non-scanned area of a model, six-face block nodes are constructed on each area divided by the dual face, and a six-face block structure is generated, so that the method can process a complex model with non-scanned body characteristics.
Fig. 6 (a) is a dual-face structure corresponding to a feature edge type 1, the feature edge of type 1 needs to generate two dual faces corresponding to adjacent feature faces to capture the feature edge and feature face features, and fig. 6 (e) is a hexahedral mesh structure diagram corresponding to the dual-face structure.
Fig. 6 (b) is a dual surface structure corresponding to a feature edge type 2, 3 dual surfaces are required to be generated by the feature edge of the type 2, and the dual surfaces of the adjacent feature surfaces of 1 tracking feature edge and the dual surfaces of 2 isolation feature edges are inserted to capture the hexahedral mesh structure corresponding to the feature edge structure in fig. 6 (f).
Fig. 6 (c) is a dual surface structure corresponding to a feature edge type 3, and the feature edge of the type 3 needs to generate 4 dual surfaces, which need to insert 2 dual surfaces respectively tracking the adjacent feature surfaces of the feature edge and 2 dual surfaces isolating the feature edge to capture the hexahedral mesh structure corresponding to the feature edge structure shown in fig. 6 (g).
Fig. 6 (d) is a dual surface structure corresponding to a feature edge type of 4, and the feature edge of type 4 needs to generate 4 dual surfaces, which need to insert 2 dual surfaces respectively tracking the adjacent feature surfaces of the feature edge and 2 dual surfaces isolating the feature edge to capture the hexahedral mesh structure corresponding to the feature edge structure in fig. 6 (h).
Finally, it should be noted that the above-mentioned embodiments and descriptions are only illustrative of the technical solution of the present invention and are not limiting. It will be understood by those skilled in the art that various modifications and equivalent substitutions may be made to the present invention without departing from the spirit and scope of the present invention as defined in the appended claims.
Claims (9)
1. The hexahedral mesh generation method based on the mixed model decomposition is characterized by comprising the following steps of:
1) Acquiring a B-Rep model of an actual product;
2) Generating a scanned surface set of the B-Rep model based on surface classification aggregation, and generating scanned blocks after optimizing and dividing the scanned surface set so as to obtain a scanned block set; then the remaining area in the B-Rep model is marked as a total non-scanned area;
3) Constructing a dual-surface set of the total non-swept area according to the types of each characteristic edge in the total non-swept area, and generating a six-surface block set of the total non-swept area based on the dual-surface set;
4) And generating a hexahedral mesh of the product according to the hexahedral block set divided by the swept block set and the total non-swept area.
2. The hexahedral mesh generating method based on hybrid model decomposition according to claim 1, wherein the 2) specifically is:
2.1 According to the characteristics of the surfaces, dividing the characteristic surfaces in the B-Rep model into a source surface, a side surface, an invalid surface and a full-energy surface;
2.2 Selecting a source surface which is not added with the scanned surface set as a seed surface, and adding the seed surface into the corresponding potential scanned surface set; the surface type in the B-Rep model is a source surface or a full-energy surface, a second-order adjacent-order surface which is a current seed surface is marked as a surface to be matched, and when the normal direction of the surface to be matched is opposite to the normal direction of the current seed surface and the projection of the surface to be matched and the current seed surface has a superposition area, the surface to be matched is added into the current potential scanning surface set of the current seed surface;
2.3 A side surface type surface adjacent to the current potential scanning surface concentrated source surface type surface and a full-energy surface type surface are used as surfaces to be matched, and if the normal direction of the surfaces to be matched is perpendicular to the normal direction of the corresponding source surface, the surfaces to be matched are added into the potential scanning surface concentrated of the current seed surface; when the potential scanned surface set is effective, the potential scanned surface set is used as an effective scanned surface set, and then the potential scanned surface set is added into the scanned surface set;
2.4 Repeating 2.2) -2.3), selecting source surfaces which are not traversed as seed surfaces, matching to obtain effective swept surface sets of all seed surfaces, and adding the effective swept surface sets into the swept surface set;
2.5 When the full-function surface which is not traversed exists in the B-Rep model, marking the full-function surface as a seed surface, repeating the steps of 2.2) -2.3), and matching to obtain effective scanned surface sets corresponding to all the full-function surfaces, so as to obtain an updated scanned surface set;
2.6 Taking each scanned surface set in the current scanned surface set as a node, and constructing a scanned surface set relation graph according to the connection relation between the scanned surface sets;
2.7 Adding the scanned face set corresponding to the node with the least degree in the scanned face set relation graph into the set to be segmented;
2.8 Selecting one of the scanned surface sets, generating a segmented surface by taking the normal direction of a potential segmented surface of the scanned surface set as the normal direction of the segmented surface and taking the potential segmented position of the scanned surface set as the insertion position of the segmented surface, separating all non-scanned directional characteristics on the scanned surface set by utilizing the generated segmented surface to obtain scanned blocks and the scanned surface set after the scanned blocks are separated, and adding the generated scanned blocks into the scanned blocks to be scanned; determining the surface type of the dividing surface according to the dividing surface normal direction of each dividing surface, updating the scanned surface set and the scanned surface set after separating and scanning into blocks, and further updating the scanned surface set relation diagram;
2.9 Classifying the set of to-be-scanned blocks into a set of scanned blocks or a set of non-scanned areas according to the type of the surface of the partition surface in 2.8), and updating the set to be partitioned;
2.10 Traversing the swept area set in the current set to be segmented, repeating 2.8) -2.9) to obtain a swept block set and a non-swept area set until the set to be segmented is empty;
2.11 Repeating 2.7) -2.10) to obtain a scanned block set and a non-scanned area set corresponding to each scanned surface set until the scanned surface set is empty, and forming a total non-scanned area by an undivided area in the B-Rep model and a final non-scanned area set.
3. The method for generating a hexahedral mesh based on hybrid model decomposition according to claim 2, wherein in 2.3), when the number of faces in the potential swept face set corresponding to the current seed face is greater than 3, the potential swept face set is valid.
4. The hexahedral mesh generating method based on hybrid model decomposition according to claim 2, wherein in 2.8), when the normal direction of the dividing plane of each dividing plane is the sweeping direction of the sweeping surface set, the dividing plane is marked as a source plane, and then 2.2) -2.3 are repeated according to the source plane), the updated sweeping surface set and the sweeping surface set after separating and sweeping the blocks are updated, and then the sweeping surface set relation diagram is updated; and when the normal direction of the dividing surface of each dividing surface is the cross-multiplication direction of the source surface characteristic edge direction of the scanned surface set and the scanning direction of the scanned surface set or the cross-multiplication direction of the normal direction of the scanned surface set and the normal direction of the adjacent scanned surface set, marking the dividing surface as a side surface.
5. The hexahedral mesh generating method based on hybrid model decomposition according to claim 2, wherein the 2.9) specifically is:
if the side type dividing surface does not exist in the step 2.8), adding all the scanned blocks in the to-be-scanned block set into the scanned block set; if the generated side type of the divided surface of 2.8) is not classified as any scanned surface set in the current scanned surface set, marking the surface type corresponding to the surface still positioned in the current scanned surface set in the to-be-scanned block set as a source surface, and classifying all scanned blocks in the to-be-scanned block set into a non-scanned area set; if the generated side face belongs to a certain scanned face set in the current scanned face set, adding the scanned face set into the set to be segmented.
6. The hexahedral mesh generating method based on hybrid model decomposition according to claim 1, wherein the 3) specifically comprises:
3.1 Selecting an unprocessed non-scanned area in the total non-scanned area, calculating according to the dihedral angles of the characteristic edges in the non-scanned area to obtain the initial types of all the characteristic edges in the non-scanned area, optimizing the initial types of the characteristic edges through the effective edge type sequences corresponding to the characteristic points in the non-scanned area, and determining the final types of the characteristic edges;
3.2 Generating a pair face corresponding to each characteristic edge according to the final type of the characteristic edge, constructing six-sided block nodes on each area divided by the pair face based on the pair face, thereby directly generating a six-sided topological structure, optimizing the nodes based on the six-sided topological structure to obtain an optimized six-sided block, thereby obtaining a six-sided block set of the non-scanned area, and projecting a quadrilateral structure of an interface with the scanned area to other non-scanned areas along the scanning direction of the scanned area if the non-scanned area is adjacent to other scanned areas to serve as additional characteristic edges of other non-scanned areas;
3.3 Traversing the total non-swept area, repeating 3.1) -3.2) until the non-swept area is empty, and obtaining a six-sided block set of the total non-swept area.
7. The method for generating a hexahedral mesh based on hybrid model decomposition according to claim 6, wherein 3.2) specifically comprises the following steps for each of the dual faces of the feature sides:
firstly, determining the positions and the number of the dual rings according to the optimized type of each characteristic edge, then searching the corresponding number of the dual rings at the corresponding positions on the surface of the model where the non-scanned block area is located, and generating the dual faces corresponding to the current characteristic edges by using a graph cut algorithm based on the dual rings.
8. The hexahedral mesh generating method based on hybrid model decomposition according to claim 1, wherein the 4) specifically is:
and performing edge discretization on all the hexahedral blocks in the scanning block and the non-scanning area according to constraint conditions, and then generating hexahedral grids of the product model.
9. The hexahedral mesh generating method based on the hybrid model decomposition according to claim 8, wherein the constraint condition comprises the following three points:
projecting the cross four sides of all the six blocks of the non-scanned area connected with the source surface of the same scanned block onto the source surface of the current scanned block along the scanning direction and taking the cross four sides as a quadrilateral grid of the source surface of the current scanned block;
the number of edge discrete segments of the public four sides of the adjacent six-sided blocks is the same, and the number of opposite edge discrete segments of the public four sides is the same;
the number of discrete segments on opposite sides of the side faces of the scanned block is equal, and the number of discrete segments of a common side on the dividing face of the adjacent scanned block is equal.
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