CN105787226B - The parameterized model of four side finite element mesh models is rebuild - Google Patents

Abstract

The invention provides a parametric reconstruction algorithm for a four-sided finite element grid model, based on the quadrilateral grid model obtained by finite element analysis software, and using the unit number and node coordinates of the quadrilateral grid model as input information to reconstruct the quadrilateral grid unit According to the topological information obtained, merging operations such as unit grid specification merging and block domain self-adaptive merging are performed to reduce the number of block domains and obtain merged subdomains. The feature points are connected to the feature points to obtain a certain number of quadrilateral final sub-domains, and the volume parameter model is constructed, adjusted and optimized according to the boundaries of the obtained final sub-domains, and finally the volume parameterized model is obtained. The algorithm can parametrically reconstruct the quadrilateral mesh model of structures such as perforated plates, and the obtained volume parameterized model is suitable for isogeometric analysis, and has the advantages of concise expression and global smoothness.

Description

Parametric Model Reconstruction of Four-sided Finite Element Mesh Model

technical field

The invention relates to a parametric reconstruction algorithm of a finite element model, in particular to a parametric reconstruction algorithm of a four-sided finite element grid model.

Background technique

In the current product design process, since the development of CAE (computer-aided engineering) technology is ahead of CAD (computer-aided design), the seamless integration of the two is a bottleneck problem, and about 70% of the running time of CAE software is used for data exchange , while the workload of discrete mesh generation accounts for about 80% of the entire CAD/CAE process.

In order to solve the problem of seamless integration of CAE and CAD, a variety of analysis methods are available, among which the medium geometry analysis method has the advantages of strong flexibility, high accuracy, convergence, and simple setting of boundary conditions. The isogeometric analysis method of the simplified model has the potential to solve the seamless integration of CAE and CAD. There is not much research on applying volume parametric models to isogeometric analysis, but it has received more and more attention from scholars.

Constructing a volume parametric model is the first step in the above-mentioned isogeometric analysis method. For zero-genus entities, create bivariate (corresponding to planar models) or trivariate (corresponding to 3D models) tensor volumes that map one-to-one to planar squares or cubes, and in both cases the resulting parameterization The models are collectively called volume parameterized models; for genus entities, they are decomposed into multiple zero-genus lattice domains for processing, and volume parameterized models can also be obtained.

If the NUBRS spline is used as the mapping function in the process of creating the above volume parameterized model, the created model is a spline volume parameterized model. Using NUBRS spline as the mapping function can make the obtained volume parameterized model have the advantages of concise expression, global smoothness, and easy integration with CAD, which can play a great role in the fields of isogeometric analysis and volume modeling.

At present, the finite element analysis method is the mainstream method for the simulation analysis of CAD products in the field of CAE, and the mesh model obtained by using this method can be used for the construction of the above-mentioned volume parameterized model. When using this method to create a mesh model, it is necessary to model the porous plate structure. Due to the existence of a large number of dense holes in these porous plate structures, the mesh obtained by the finite element analysis often exceeds the The calculation capacity of the computer is not conducive to the subsequent calculation.

Contents of the invention

In order to solve the above problems, the present invention adopts the following technical solutions:

A parametric model reconstruction algorithm for a quadrilateral finite element mesh model, which is used to reconstruct a volume parametric model suitable for isogeometric analysis on a quadrilateral mesh model, where the quadrilateral mesh model is reconstructed from the created model by finite element software Obtained by quadrilateral grid division, the numbers and node coordinates of all quadrilateral grid units in the quadrilateral grid model are used as input information for the implementation of the parametric model reconstruction algorithm. The algorithm is characterized in that it includes the following steps:

Step S1, according to the input information, reconstruct the topological relationship between the quadrilateral grid units, including the unit adjacency relationship and the unit arrangement relationship;

In step S2, according to the topological relationship obtained in step S1, grid unit normative merging and block domain adaptive merging are performed to obtain the final sub-domain and the final sub-domain boundary;

In step S3, the two-dimensional parameter domain model is obtained by performing boundary control point inversion and intra-domain control point interpolation on the final subdomain obtained in step S2, and adjusting and optimizing the control points in the two-dimensional parameter domain model to obtain a suitable Volume parametric model for isogeometric analysis;

Wherein, step S2 specifically includes the following steps:

Step S2.1, grid unit canonical merging, combined with UV growth algorithm and relative edge growth algorithm, canonical merging of quadrilateral grid units to obtain a certain number of basic block domains;

Step S2.2, performing block domain self-adaptive merging on the basic block domains obtained in step S2.1, including merging fully shared edge domains, most shared edge domains and island domains, to obtain a certain number of subdomains;

Step S2.3, take all the corner points on the boundary of the sub-domain obtained in step S2.2 as feature points, retain the feature points, keep the outer boundary feature points unchanged, and adjust the inner boundary feature points to the limit position of the boundary rule Adjust the feature points; connect the adjusted feature points with a straight line to generate a new quadrilateral domain, and obtain the final subdomain and the corresponding final subdomain boundary.

Further, in the parametric model reconstruction algorithm of the quadrilateral finite element mesh model provided by the present invention, step S1 includes the following steps:

Step S1.1, extracting basic information by analyzing the unit number and node coordinates of the quadrilateral grid unit;

Step S1.2, traversing all the quadrilateral grid units, analyzing the shared information of nodes and edges of the quadrilateral grid units, obtaining all common edge information and identifying the adjacency relationship between the quadrilateral grid units;

Step S1.3, select a quadrilateral grid unit as the starting point, and search for the arrangement relationship of the quadrilateral grid units from two mutually perpendicular directions respectively according to the adjacency information, and the two directions are respectively defined as the U direction and the V direction;

Step S1.4, classify all quadrilateral grid units, set the quadrilateral grid units located on the boundary line as boundary quadrilaterals, and the rest as internal quadrilaterals; the boundary quadrilaterals containing boundary corner points are set as boundary corner point quadrilaterals , and the rest are bounding general quadrilaterals;

The quadrilaterals whose number of adjacent quadrilaterals in the midpoint of the inner quadrilateral is not equal to the number of side adjacent quadrilaterals, and the quadrilaterals whose number of adjacent quadrilaterals in the boundary quadrilateral is not less than the number of side adjacent quadrilaterals are defined as characteristic quadrilaterals, and the surrounding quadrilaterals are all The nodes of a characteristic quadrilateral are defined as characteristic nodes, and the characteristic quadrilaterals and characteristic nodes are marked; among them, the point adjacent is defined as two quadrilaterals have and only one common node, and the edge adjacent is defined as two quadrilaterals have and only Two quadrilaterals with two common nodes, adjacent points or adjacent sides are called adjacent quadrilaterals.

Further, in the step S1 of the parametric model reconstruction algorithm of the quadrilateral finite element mesh model provided by the present invention, the UV growth algorithm includes the following steps:

According to the unit arrangement relationship in step S1, select the starting quadrilateral, and merge along the U and V directions of the starting quadrilateral, until both directions touch the characteristic quadrilateral, and the merging ends.

Further, in the step S1 of the parametric model reconstruction algorithm of the four-sided finite element mesh model provided by the present invention, the relative edge growth algorithm includes the following steps:

In the process of unit grid specification merging, when the U direction and V direction of the quadrilateral cannot be judged, the quadrilateral is used as the initial quadrilateral, and the two adjacent sides of the initial quadrilateral are selected as From the starting side, grow the side adjacent to the starting side to the quadrilateral until the two sides in the growth direction belong to the characteristic quadrilateral, and the merge ends.

Further, in the step S2.3 of the parametric model reconstruction algorithm of the quadrilateral finite element mesh model provided by the present invention, the connection steps of the feature points are:

Step S2.3.1, traversing all the inner boundary feature points and outer boundary feature points, connecting the nearest inner boundary feature points and outer boundary feature points with a straight line;

Step S2.3.2, traversing all the inner boundary feature points, connecting the nearest inner boundary feature points with a straight line to obtain a certain number of N polygons, and the value of N is 4 to 20;

In step S2.3.3, a straight line is generated inside the N-gon according to the method of dividing the polygon into quadrilaterals, and a new sub-domain is generated, so that the sub-domains are all quadrilateral domains.

Further, the parametric model reconstruction algorithm of the quadrilateral finite element mesh model provided by the present invention also has the following technical features:

In step S3, the method of inverse calculation of the boundary control points is: perform B-spline curve fitting on the boundary points on the boundary of the final subdomain obtained in step S2 to obtain the initial control points, and then perform node insertion and upgrade on the curve , stitching, so that it is unified and of the same order as the node vectors of the adjacent subdomain boundary curves, so as to obtain the final boundary control points;

The method of interpolation of control points in the domain is: according to the Coons surface theory, set four spline curves P(u,0), P(u,1), P(0,v), P(1, v), u, v∈[0,1], the corresponding control vertices are The four corner points are P(0,0), P(0,1), P(1,0), P(1,1), as shown below. The control points in the four-sided surface domain are obtained as follows:

Invention function and effect

According to the parametric model reconstruction algorithm of the four-sided finite element grid model provided by the present invention, the quadrilateral grid model obtained by the finite element analysis software is used as the basis, and the grid model is combined with unit grid specification and block domain adaptive combination The number of block domains is reduced by merging operations such as merging, and a certain number of subdomains are obtained; by retaining the feature points on the subdomain boundaries and connecting the feature points, a certain number of final subdomains are obtained, and the final subdomain is obtained according to the boundary of the final subdomain. The construction, adjustment and optimization of the parametric model finally obtains a volume parametric model suitable for isogeometric analysis. This model has the advantages of simple expression, global smoothness, and easy integration with CAD. It can be used in the fields of isogeometric analysis and volume modeling. great effect.

Description of drawings

Fig. 1 is the general flow chart of the parametric model reconstruction algorithm of the quadrilateral finite element mesh model provided by the present invention;

Fig. 2 is a schematic diagram of the common side structure of the grid unit;

Fig. 3 is a schematic diagram of UV direction division;

Fig. 4 is the schematic diagram of unit grid specification merging;

Fig. 5 is the schematic diagram of the quadrilateral priority growth model of UV growth algorithm;

Fig. 6 is the flowchart of UV growth algorithm;

Figure 7 is a schematic diagram of the UV direction reverse adjustment error;

Fig. 8 is a schematic diagram of merging of fully shared edge domains;

Fig. 9 is a flow chart of fully sharing edge block domain merging;

Fig. 10 is a schematic diagram of merging most shared edge domains;

Figure 11(A) and Figure 11(B) are schematic diagrams of merging island block domains;

Fig. 12 is a schematic diagram of feature point adjustment;

Figure 13 is a schematic diagram of U and V direction ruled surface;

Fig. 14 is a schematic diagram of quadrilateral domain control points;

Fig. 15 is a flow chart of volume parameterized mesh model quality optimization;

Figure 16 is an example diagram of a nine-hole plate grid model divided in ANSYS;

Figure 17 is the unit information table ELIST of the nine-hole plate grid model exported by ANSYS;

Fig. 18 is the node information table NLIST of the nine-hole plate grid model exported by ANSYS;

Fig. 19 is a schematic diagram of the results of the nine-hole plate grid model after the grid unit specification is merged;

Fig. 20 is the schematic diagram of the merged final result of the nine-hole plate grid model;

Fig. 21 is the schematic diagram of the adjusted feature points of the nine-hole plate grid model;

Fig. 22 is the final subdomain boundary schematic diagram of the nine-hole plate grid model;

Fig. 23 is the running instance diagram of the L-shaped plate with holes;

Fig. 24 is the running example figure of foot type belt hole plate model;

Fig. 25 is an example diagram of the operation of the random nine-hole plate model.

Detailed ways

The specific implementation manner of the present invention will be described below in conjunction with the accompanying drawings and embodiments.

[Example 1]

Figure 16 is an example diagram of a nine-hole plate grid model divided in ANSYS. The model selected in Example 1 is a regularly distributed nine-hole plate model, which is a square plate with nine through holes regularly distributed on it, as shown in Figure 16, using the finite element analysis software ANSYS to analyze the model, The resulting model is a mesh model, where the mesh elements are all quadrilaterals.

Figure 17 is the unit information table ELIST of the nine-hole plate grid model exported by ANSYS, and Figure 18 is the node information table NLIST of the nine-hole plate grid model exported by ANSYS. After using the finite element software to obtain the quadrilateral mesh model, the element number and node coordinates of the mesh model obtained by the finite element analysis software are used as input information, as shown in Figure 17. In NLIST, the first column is the node number, and the following The x, y, and z coordinates of the nodes in turn; as shown in Figure 18, in ELSIT, the first column is the unit number, and the last four columns are the node numbers.

Fig. 1 is a general flow chart of the parametric model reconstruction algorithm of the quadrilateral finite element mesh model provided by the present invention.

As shown in Figure 1, after the input information is obtained, the following steps are performed to reconstruct the volume parameterized model.

Step S1, grid model preprocessing. According to the above input information, the topological relationship of the model is reconstructed, and the relevant topological information is obtained. The specific steps are as described in steps S1.1-1.4.

Step S1.1, basic information extraction, analyzing the unit number ELSIT and node coordinates NLIST of the quadrilateral grid unit, and extracting basic information;

Step S1.2, adjacency extraction, identifies the adjacency between units through the shared information of nodes and edges. Two adjacencies between cells are defined here:

The edges are adjacent, and the two units have and only two common nodes;

The points are adjacent, and the two elements have one and only one common node.

Fig. 2 is a schematic diagram of the common edge structure of grid units. As shown in Figure 2, there must be a common edge between any two adjacent units. Firstquad and secondquad are used to represent unit 1 and unit 2 respectively, and Node[0] and Node[1] are the common nodes of the two units. Traverse all grid cells, finally get all common edge information, and store them for later use.

Step S1.3, extracting the arrangement relationship, selecting a certain quadrilateral grid unit as the starting unit, and using the unit adjacency relationship to search from two directions according to the adjacency relationship to obtain the arrangement relationship of the unit.

Fig. 3 is a schematic diagram of UV direction division. As shown in Figure 3, in the extraction of the arrangement relationship, the UV direction storage rule is introduced. There are at most four adjacent quadrilaterals around any quadrilateral. Define 0 as the u+ direction, 2 as the u- direction, 1 as the v+ direction, and 3 as In the v-direction, using the relationship between the centroids of the adjacent units and the centroids of the central unit, the adjacent units can be regularly sorted around the central unit, and the relevant information can be stored for future use.

Step S1.4, labeling feature information.

First classify all quadrilaterals. Among all units, those located on the boundary line are boundary quadrilaterals, and the rest are internal quadrilaterals; among all boundary quadrilaterals, those with boundary corners among the four vertices are boundary corner quadrilaterals, and the rest are boundary general quadrilaterals.

Then, define the special units and nodes existing in the quadrilateral mesh model as characteristic units and characteristic nodes, and mark them. The definition of feature unit and feature node is as follows:

For internal quadrilaterals, if the number of point-adjacent quadrilaterals is not equal to the number of side-adjacent quadrilaterals, the quadrilateral is a characteristic quadrilateral; for boundary quadrilaterals, if the number of adjacent quadrilaterals is not less than the number of side-adjacent quadrilaterals, then the quadrilateral Boundary quadrilaterals are also characteristic quadrilaterals. Among all nodes, if the quadrilaterals around a certain node are characteristic quadrilaterals, then the node is a characteristic node.

Step S2, volume parameterized domain boundary generation, according to the topological information obtained in step S1, perform a series of merging operations, the specific steps are as described in steps S2.1-S2.3.

Step S2.1, grid unit specification merging.

Fig. 4 is a schematic diagram of grid cell specification merging. As shown in Figure 4, select a border corner quadrilateral as the merged starting quadrilateral, and use the UV growth algorithm and the opposite side growth algorithm to merge.

Fig. 5 is a schematic diagram of a quadrilateral priority growth model of the UV growth algorithm. The UV growth algorithm takes the diagonal model as the priority growth model, so that the initial quadrilaterals are merged along the two directions of UV respectively. The diagonal growth model requires that the result of each merger is still a quadrilateral domain, as shown in Figure 5, the U direction If one step is added, each unit in the V direction needs to be increased by one step in the V direction; similarly, every time the V direction is increased by one step, all units in the U direction also need to be increased by one step in the U direction, so as to ensure that the graph obtained by the growth is still a quadrilateral.

Fig. 6 is a flowchart of the UV growth algorithm. As shown in Figure 6, define index[0][0] as the growth starting quadrilateral, uAddFlag as the U-direction growth flag, vAddFlag as the V-direction growth flag, the initial value is true, and if set to false, the growth will stop. First, increase one step in the U direction, and at the same time judge whether the current quadrilateral is a characteristic quadrilateral; if so, set uAddFlag to false and stop growing in the U direction, otherwise continue to grow; then increase one step in the V direction, and judge whether the current quadrilateral is a characteristic quadrilateral; if so, set vAddFlag to false and the V direction stops growing, otherwise it continues to grow. If the growth flags in both directions of the UV are set to false, the merge is terminated, and the merged result is stored for future use.

Fig. 7 is a schematic diagram of UV direction reversal error. In some cases, at the arc boundary as shown in Figure 7, the UV direction of the quadrilateral will change with the arc until the direction is completely exchanged. At this time, the UV direction cannot be accurately judged. If you continue to use the UV merging algorithm, Will result in a merge error, so choose the opposite edge merge algorithm to continue merging at this time. According to the unit number of the starting quadrilateral, according to the relative side storage rules, any two adjacent sides of the starting quadrilateral are taken as the starting side, and the side adjacent to the quadrilateral on these two adjacent sides is increased, and the quadrilateral in the growth direction is judged Whether it is a characteristic quadrilateral, if so, stop growing, otherwise continue to grow, the algorithm flow is the same as the UV growth algorithm, and will not be repeated here.

Figure 19 is a schematic diagram of the results of the nine-hole plate grid model after the grid unit specification is merged. As shown in Figure 19, the original grid model is merged into several basic block domains after grid unit specification merging.

Step S2.2, block domain adaptive merging. After merging unit grid specifications, the number of units is reduced to 1/10 to 1/30 of the original, and a certain number of basic block domains are obtained. However, the number of these basic block domains is still large and needs to be merged. Since the obtained basic block fields are all quadrilateral fields, four pieces of boundary information of each basic block field can be obtained, and the faster than adaptive merging is performed according to these boundary information, and the steps are as follows.

A fully shared edge domain merge is performed first. The merging rule is that if any two basic block domains have a boundary completely coincident, then the two basic block domains will be merged.

Fig. 8 is a schematic diagram of fully shared edge block domain merging. As shown in Fig. 8, domains 1 to 4 of the basic blocks are obtained after unit grid specification merging in step S2.1. According to the rules for domain merging of completely shared edge blocks, domain 1 and domain 3 are merged, and domain 2 and domain 4 are merged. The block domains obtained by the first merger are merged again, and finally the four block domains are merged into one.

Fig. 9 is a flow chart of domain merging of fully shared edge blocks. As shown in Figure 9, the process of merging fully shared edge block domains is to traverse all basic block domains to find whether there is a completely overlapping boundary between the two block domains, and if so, merge the two domains and continue to search for the next block domains until none of the block domains have exactly coincident boundaries.

Most of the shared edge domain merges are then performed. The merging rule is to traverse all block domains, and if the boundaries of two domains have shared corners, and the degree of boundary sharing exceeds a certain threshold, then merge the two domains into a new block domain. Wherein, the threshold can be set according to actual conditions.

Fig. 10 is a schematic diagram of domain merging of most shared edge blocks. As shown in Figure 10, the edges of domain 1 and domain 2 share corner points, and the sharing exceeds the threshold, so domain 1 and domain 2 are merged; similarly, domain 3 and domain 4 also meet the conditions for merging, and domain 3 Merged with domain 4.

Finally, island block domain merging is performed. After the above merging, the number of block domains has decreased significantly, but there are still some isolated grid units or block domains in the model, which are not merged or completely contained by other block domains. These grid units and block domains are called island blocks. area. The merging algorithm rule of the island block domain is to identify isolated units or completely contained block domains, and merge them into the largest adjacent sub-domain.

Figure 11(A) and Figure 11(B) are schematic diagrams of merging island block domains. As shown in Figure 11(A), isolated unit 1 and isolated unit 2 are contained by large block domain 3 and large block domain 4, respectively, and domain 5 is contained by large block domain 6, so the isolated unit 1 is merged into the large block domain In domain 3, the isolated unit 2 is merged into the bulk domain 4, and domain 5 is merged into the bulk domain 6. The merging result is shown in Figure 11(B).

Fig. 20 is a schematic diagram of the combined final result of the nine-hole grid model. As shown in Figure 20, the model undergoes block-domain adaptive merging to obtain a certain number of sub-domains.

Step S2.3, generating the final subdomain boundary. After the above merging, the model is divided into several quadrilateral subdomains, but the boundary shape is more complex, which is not conducive to expression. Take all the corner points on the boundaries of these subdomains as feature points, keep these feature points and adjust them.

Fig. 12 is a schematic diagram of feature point adjustment. The rule of feature point adjustment is that the feature points of the outer boundary remain unchanged, and the feature points of the inner boundary are adjusted to the limit position of the boundary. As shown in Figure 12, the square point is a feature point and needs to be adjusted, and the small circle point is a general boundary point and does not need to be adjusted.

Figure 21 is a schematic diagram of the adjusted feature points of the nine-hole plate grid model. As shown in Figure 21, the feature points are retained and adjusted to obtain the adjusted feature points.

After the feature point adjustment is completed, the feature points are connected into a quadrilateral domain. The connection steps are as described in steps S2.3.1 to S2.3.3.

Step S2.3.1, traversing all the inner boundary feature points and outer boundary feature points, connecting the nearest inner boundary feature points and outer boundary feature points with a straight line;

Step S2.3.2, traversing all the inner boundary feature points, connecting the nearest inner boundary feature points with a straight line to obtain a certain number of N polygons, and the value of N is 4 to 20;

Step S2.3.3, according to the method of dividing the polygon into quadrilaterals, generate straight lines inside the N-gons obtained in the above steps, and generate new sub-domains, which are the final sub-domains, and all of them are quadrilateral domains.

Fig. 22 is a schematic diagram of the final subdomain boundary of the nine-hole grid model. As shown in Figure 22, the adjusted feature points are connected to obtain several quadrilateral final sub-domains.

Step S3, generation and optimization of the two-dimensional parameter domain model, the process is as described in steps S3.1-3.2.

Step S3.1, generation of the two-dimensional parameter model, including control point interpolation in the boundary curve control point reverse sum domain. Perform B-spline curve fitting on the final subdomain boundary points obtained in step S2 to obtain initial control points, and then perform node insertion, upgrade, and splicing on the curve so that it is unified with the node vectors of the adjacent subdomain boundary curves and The same order, thus the final boundary control point is obtained. The initial internal control points are obtained by performing intra-domain control point interpolation on the boundary control points.

Fig. 13 is a schematic diagram of U- and V-directed ruled surfaces, and Fig. 14 is a schematic diagram of control points in a quadrilateral domain. As shown in Figure 13, the initial internal control points are generated using Coons surface interpolation theory, and four spline curves P(u,0), P(u,1), P(0,v) surrounded by a closed quadrilateral domain are set, P(1,v), u,v∈[0,1], the corresponding control vertices are The four corner points are P(0,0), P(0,1), P(1,0), P(1,1), as shown below. The control points in the four-sided surface domain are obtained as follows:

Step S3.2, model adjustment and optimization. After the above model generation process, the output results are the internal control points of the volume parameterized model, but these control points have defects such as distortion and self-intersection, which affect the subsequent analysis, so the control points need to be rationally optimized.

Fig. 15 is a flow chart of volume parameterized mesh quality optimization. According to the process shown in Figure 15, the control points in the obtained initialized grid model are divided and conquered, each point control of the model is recorded as T ^H , and the number of times is set to α=H, respectively for each control point Integrating constraint equations for optimization and solution, the value of α is reduced by 1 every time it is solved, and the solution is continued until α=1, and the final optimization is completed, and finally the volume parameterized model is obtained and output.

[Example 2]

In this second embodiment, descriptions of the same algorithms and steps as those in the first embodiment are omitted.

Figure 23 is an example diagram of the operation of the L-shaped plate model with holes. The model is an L-shaped plate with four through-holes regularly distributed on it. As shown in Figure 23, the grid models obtained from the finite element analysis software are merged , feature point retention and adjustment, and feature point connection to obtain several quadrilateral final sub-domains. According to these final sub-domains, two-dimensional parameter models are generated, adjusted and optimized, and volume parameterization suitable for isogeometric analysis can be obtained and output. Model.

[Embodiment 3]

Figure 24 is an example diagram of the operation of the model of a foot-shaped plate with holes. The model is a foot-shaped plate with a large through-hole and three small through-holes distributed on it. After merging the grid models, retaining and adjusting feature points, and connecting feature points, several quadrilateral final sub-domains are obtained. According to these final sub-domains, two-dimensional parameter models are generated, adjusted and optimized to obtain and output suitable for isogeometric Analytical volume parametric models.

[Example 4]

Figure 25 is an example diagram of the operation of the random nine-hole plate model. The model is a square plate with nine through-holes irregularly distributed on it. As shown in Figure 25, the grid model obtained from the finite element analysis software is passed through Combine, retain and adjust feature points, and connect feature points to obtain several quadrilateral final subdomains. Based on these final subdomains, perform two-dimensional parameter model generation, adjustment and optimization to obtain and output volume parameters suitable for isogeometric analysis model.

Function and effect of embodiment

According to the parametric model reconstruction algorithm of the four-sided finite element grid model provided by the present invention, in Embodiment 1, the volume parameterized model reconstruction based on the four-sided finite element grid model is performed on the nine-hole plate model, and the result is shown in Figure 22 It is shown that the number of subdomains can be effectively reduced through the merging step, and then a certain number of quadrilateral final subdomains can be obtained through the steps of feature point retention and adjustment, feature point connection, etc., and a two-dimensional parameterized model is generated for the boundaries of these subdomains , optimization and adjustment, the volume parameterized model can be obtained and exported, which can be applied to subsequent isogeometric analysis. Similarly, in Embodiment 2, Embodiment 3 and Embodiment 4, the algorithm provided by the present invention can run smoothly, reduce the number of unit grids and obtain the final sub-domain, and finally generate, optimize and The volume parameterized model can be obtained and output by the operation of adjustment. These volume parameterized models have the advantages of concise expression, global smoothness, and easy integration with CAD, and can be used for subsequent isogeometric analysis.

The above embodiments are only used to illustrate the implementation and operation results of the parametric model reconstruction algorithm of the four-sided finite element mesh model provided by the present invention, but the present invention is not limited to the above-mentioned embodiments, for other types of porous The algorithm provided by the invention is also effective for plate structures and general structures with fewer grid units in the grid model.

Claims (6)

1. A parametric model reconstruction algorithm of a four-sided finite element mesh model, which is used to carry out volume parametric model reconstruction applicable to isogeometric analysis to a quadrilateral mesh model, wherein the quadrilateral mesh model is transformed by finite element software The created model is divided into quadrilateral grids, and the numbers and node coordinates of all quadrilateral grid units in the quadrilateral grid model are used as input information for the implementation of the parametric model reconstruction algorithm. The algorithm is characterized in that, Including the following steps: Step S1, according to the input information, reconstruct the topological relationship between quadrilateral grid units, including unit adjacency relationship and unit arrangement relationship; Step S2, according to the topological relationship obtained in step S1, perform grid unit normative merging and block domain adaptive merging to obtain the final sub-domain and the final sub-domain boundary; Step S3: Obtain a two-dimensional parameter domain model by performing reverse calculation of boundary control points and intra-domain control point interpolation on the final subdomain obtained in step S2, and adjust and optimize the control points in the two-dimensional parameter domain model , to obtain a volume parameterized model suitable for isogeometric analysis; Wherein, step S2 specifically includes the following steps: Step S2.1, grid unit canonical merging, combining the UV growth algorithm and the relative edge growth algorithm, performing canonical merging of the quadrilateral grid units to obtain a certain number of basic block domains; Step S2.2, carry out block domain self-adaptive merging on the basic block domain obtained in step S2.1, including fully shared edge block domain merging, most shared edge block domain merging and island block domain merging, to obtain a certain number of child area; Step S2.3, taking all the corner points on the boundary of the sub-domain obtained in step S2.2 as feature points, retaining the feature points, keeping the feature points of the outer boundary unchanged, and adjusting the feature points of the inner boundary to the boundary The rule of the extreme position adjusts the feature points; connects the adjusted feature points with a straight line to generate a new four-sided domain, and obtains the final sub-domain and the corresponding final sub-domain boundary. 2. the parametric model rebuilding algorithm of quadrilateral finite element mesh model according to claim 1, is characterized in that, described step S1 comprises the steps: Step S1.1, extracting basic information including the unit number and the node coordinates by analyzing the information table of the unit number and the information table of the node coordinates of the quadrilateral grid unit; Step S1.2, traversing all the quadrilateral grid units, analyzing the shared information of nodes and edges of the quadrilateral grid units, obtaining all common edge information and identifying the adjacency relationship between the quadrilateral grid units; Step S1.3, select a quadrilateral grid unit as the starting point, search for the arrangement relationship of the quadrilateral grid units from two mutually perpendicular directions according to the adjacency information, and the two directions are respectively defined as the U direction and V direction; Step S1.4, classify all quadrilateral grid units, set the quadrilateral grid units located on the boundary line as boundary quadrilaterals, and the rest as internal quadrilaterals; the boundary quadrilaterals containing boundary corner points are set as boundary corners point quadrilaterals, and the rest are boundary general quadrilaterals; The quadrilateral whose number of adjacent quadrilaterals at the midpoint of the internal quadrilateral is not equal to the number of side adjacent quadrilaterals, and the quadrilateral whose number of adjacent quadrilaterals in the boundary quadrilateral is not less than the number of side adjacent quadrilaterals is defined as a characteristic quadrilateral, and The nodes whose surrounding quadrilaterals are all characteristic quadrilaterals are defined as characteristic nodes, and the characteristic quadrilaterals and the characteristic nodes are marked; among them, the definition of adjacent points is that two quadrilaterals have and only have one common node, and the definition of adjacent sides Two quadrilaterals have one and only two common nodes, and two quadrilaterals whose vertices are adjacent or sides are adjacent are called adjacent quadrilaterals. 3. The parametric model reconstruction algorithm of the quadrilateral finite element mesh model according to claim 2, wherein, in step S2.1, the UV growth algorithm comprises the following steps: According to the unit arrangement relationship described in step S2.1, select the starting quadrilateral, and merge along the U direction and the V direction of the starting quadrilateral respectively until both directions meet the characteristic quadrilateral, and the merging ends . 4. The parametric model reconstruction algorithm of four-sided finite element mesh model according to claim 2, is characterized in that, in step S2.1, described relative edge growth algorithm comprises the steps: In the process of merging the unit grid specifications, when the U direction and V direction of the quadrilateral cannot be judged, the quadrilateral is used as the initial quadrilateral, and the initial quadrilateral is selected according to the unit adjacency relationship described in step S1. The two adjacent sides are used as the starting side, and the adjacent quadrilateral of the side opposite to the starting side is grown until both sides in the growing direction belong to the characteristic quadrilateral, and the merging ends. 5. The parametric model reconstruction algorithm of the quadrilateral finite element grid model according to claim 1, wherein in step S2.3, the connection steps of the feature points are: Step S2.3.1, traversing all the inner boundary feature points and outer boundary feature points, connecting the nearest inner boundary feature points and outer boundary feature points with a straight line; Step S2.3.2, traversing all the inner boundary feature points, connecting the nearest inner boundary feature points with a straight line to obtain a certain number of N polygons, and the value of N is 4 to 20; Step S2.3.3, generating straight lines inside the N-gon according to the method of dividing the polygon into quadrilaterals to generate new sub-domains, so that the sub-domains are all quadrilateral domains. 6. the parametric model reconstruction algorithm of quadrilateral finite element mesh model according to claim 1, is characterized in that: In step S3, the method of inverting the boundary control points is: performing B-spline curve fitting on the boundary points on the final subdomain boundary obtained in the step S2 to obtain initial control points, and then knotting the curve Insert, upgrade, and splicing, so that it is unified and of the same order as the node vectors of the adjacent subdomain boundary curves, so as to obtain the final boundary control points; The method of control point interpolation in the described domain is: according to the Coons surface theory, set four spline curves P(u,0) surrounded by a closed four-sided domain, P(u,1), P(0,v), P( 1, v), u, v∈[0,1], P(1,1), the corresponding control vertices are The four corner points are P(0,0), P(0,1), P(1,0), P(1,1), as shown in the figure below, the control points in the four-sided surface domain are obtained as follows: