CN113255196A - Grid optimization method, grid generator and storage medium - Google Patents

Grid optimization method, grid generator and storage medium Download PDF

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CN113255196A
CN113255196A CN202110755948.8A CN202110755948A CN113255196A CN 113255196 A CN113255196 A CN 113255196A CN 202110755948 A CN202110755948 A CN 202110755948A CN 113255196 A CN113255196 A CN 113255196A
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value
stress
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CN113255196B (en
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赵佳欣
李会江
张军飞
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Zwcad Software Co ltd
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    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
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Abstract

The invention discloses a grid optimization method, a grid generator and a storage medium, comprising the following steps: step S1, obtaining an initial grid generated by a grid generator, carrying out static analysis on the initial grid to obtain a stress field of the initial grid, judging whether the stress field meets the calculation requirement, and if not, executing step S2; step S2, calculating the estimation error of the initial grid to obtain a metric tensor field on the grid node of the initial grid; step S3, calculating the eigenvalue of the measurement tensor field of each grid node, acquiring the constraint size of the grid node, and generating an optimized grid according to the constraint size; and step S4, the optimized grid is set as an initial grid, and the step S1 is executed again for the next iteration until the initial grid meets the preset requirement. The method automatically adjusts the grid size, generates the grid meeting the preset requirement, performs iterative calculation, saves the calculation resource, improves the calculation precision and simultaneously improves the calculation efficiency.

Description

Grid optimization method, grid generator and storage medium
Technical Field
The present invention relates to the field of data processing technologies, and in particular, to a mesh optimization method, a mesh generator, and a computer-readable storage medium.
Background
With the continuous development of the CAE simulation technology, how to simultaneously improve the calculation efficiency and the calculation accuracy is an urgent problem to be solved. Currently available methods include the use of parallel computing, high performance computers, improving the efficiency of solving algorithms, and the like.
The grid division can also improve the calculation efficiency and the calculation precision at the same time. In areas needing fine calculation, such as stress concentration and large deformation areas, small-scale grid units are used, and in areas needing no fine calculation, large-scale grid units can be used, so that the purposes of saving calculation resources and improving calculation efficiency are achieved. But how to reasonably partition the grid, the prediction needs, and the areas that do not require elaborate computation is very dependent on the processing experience of the engineer.
As shown in fig. 1, which is a geometric model, the tetrahedral mesh generated by the mesh generator under the constraint size of mesh size 10 contains 2392 mesh cells. Fig. 2 is a stress simulation result obtained after setting model material properties, fixing boundary conditions and applying a load based on the grid stress value diagram of fig. 1, and it can be seen that the maximum stress value is only 209 Mpa. According to experience and formula analysis, the stress value has a larger difference from the true value, the reasonable degree of grid division is limited, and optimization is still needed.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a grid optimization method, which can automatically adjust the grid size, generate a grid meeting the preset requirements, perform iterative computation, save the computation resources, improve the computation precision and simultaneously improve the computation efficiency.
The second objective of the present invention is to provide a grid generator, which executes the above-mentioned grid optimization method, automatically adjusts the grid size, generates a grid meeting the preset requirements, iterates the calculation, saves the calculation resources, improves the calculation accuracy, and simultaneously improves the calculation efficiency.
The third objective of the present invention is to provide a storage medium, which executes the above-mentioned grid optimization method, automatically adjusts the grid size, generates a grid meeting the preset requirements, performs iterative computation, saves the computation resources, and improves the computation accuracy and the computation efficiency.
One of the purposes of the invention is realized by adopting the following technical scheme:
a mesh optimization method comprising the steps of:
step S1, obtaining an initial grid generated by a grid generator, and carrying out static analysis on the initial grid to obtain a stress field of the initial grid; judging whether the stress field meets a preset requirement, if not, executing a step S2;
step S2, calculating the estimation error of the initial grid to obtain a metric tensor field on the grid node of the initial grid;
step S3, calculating the eigenvalue of the measurement tensor field of each grid node, and acquiring the constrained dimension of the grid node; generating an optimized grid according to the constraint size;
and step S4, the optimized grid is made to be an initial grid, and the step S1 is executed again for the next iteration until the initial grid meets the preset requirement.
Further, the step S2 of calculating the estimation error of the initial grid to obtain the metric tensor field on the grid node of the initial grid includes the following steps:
step S21, calculating the stress gradient value of each grid node and all the connection nodes
Figure 608511DEST_PATH_IMAGE001
According to said stress gradient value
Figure 405696DEST_PATH_IMAGE002
And calculating the average stress value gradient by the number of the connection nodes
Figure 453287DEST_PATH_IMAGE003
(ii) a The connection nodes are nodes for connecting the grid nodes;
step S22, order
Figure 567306DEST_PATH_IMAGE004
Representing connected grid nodes
Figure 700347DEST_PATH_IMAGE005
And a connection node
Figure 301224DEST_PATH_IMAGE006
Grid connection lines according to each grid node
Figure 468900DEST_PATH_IMAGE007
Average stress value gradient of
Figure 762609DEST_PATH_IMAGE003
And a connection node
Figure 117367DEST_PATH_IMAGE008
Average stress value gradient of
Figure 53093DEST_PATH_IMAGE009
Calculating grid connection lines
Figure 809696DEST_PATH_IMAGE004
Is estimated error of
Figure 271377DEST_PATH_IMAGE010
；
Step S23, calculating the grid connection line
Figure 519956DEST_PATH_IMAGE004
Length change value of
Figure 243061DEST_PATH_IMAGE011
Wherein
Figure 870483DEST_PATH_IMAGE012
Is a preset maximum error value;
step S24, according to the length change value of each grid connecting line
Figure 286421DEST_PATH_IMAGE013
Computing a field of metric tensors for each grid node
Figure 756716DEST_PATH_IMAGE014
。
Further, the step S21 includes the following steps:
step S211, order
Figure 768666DEST_PATH_IMAGE004
Representing connected grid nodes
Figure 765441DEST_PATH_IMAGE015
And a connection node
Figure 103012DEST_PATH_IMAGE008
Grid connection line, grid node
Figure 795025DEST_PATH_IMAGE005
And a mesh node
Figure 125512DEST_PATH_IMAGE016
Has a stress gradient value of
Figure 730455DEST_PATH_IMAGE017
Computing said mesh nodes
Figure 222617DEST_PATH_IMAGE005
With all connecting nodes connecting the grid nodes
Figure 933084DEST_PATH_IMAGE008
Stress gradient value of
Figure 552415DEST_PATH_IMAGE018
Wherein
Figure 258203DEST_PATH_IMAGE019
As a mesh node
Figure 62211DEST_PATH_IMAGE005
The value of the stress of (a) is,
Figure 338602DEST_PATH_IMAGE020
to connect nodes
Figure 10892DEST_PATH_IMAGE008
The stress value of (a);
step S212, calculating grid node
Figure 587498DEST_PATH_IMAGE021
With all connecting nodes
Figure 421462DEST_PATH_IMAGE006
Average stress value gradient of
Figure 106521DEST_PATH_IMAGE022
The average stress value gradient is the grid node
Figure 799146DEST_PATH_IMAGE023
With all connecting nodes
Figure 479526DEST_PATH_IMAGE024
Average value of the gradient of stress values.
Further, the average stress value gradient is calculated by the following formula:
Figure 235124DEST_PATH_IMAGE025
wherein
Figure 876321DEST_PATH_IMAGE026
Representation and grid node
Figure 890413DEST_PATH_IMAGE015
Connected connection node
Figure 176032DEST_PATH_IMAGE008
A collection of (a).
Further, the grid connection lines in the step S22
Figure 617378DEST_PATH_IMAGE027
Is estimated error of
Figure 745871DEST_PATH_IMAGE010
Calculated by the following formula:
Figure 48807DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 703779DEST_PATH_IMAGE003
as a mesh node
Figure 456972DEST_PATH_IMAGE005
The gradient of the average stress value of (a),
Figure 509696DEST_PATH_IMAGE029
to connect nodes
Figure 600012DEST_PATH_IMAGE006
The gradient of the average stress value of (a),
Figure 329065DEST_PATH_IMAGE004
as a mesh node
Figure 112213DEST_PATH_IMAGE005
And a connection node
Figure 90664DEST_PATH_IMAGE006
The grid connection lines of (1).
Further, in step S24, the metric tensor field is calculated by the following formula
Figure 984671DEST_PATH_IMAGE014
：
Figure 224023DEST_PATH_IMAGE030
Wherein the content of the first and second substances,
Figure 928805DEST_PATH_IMAGE031
representation and grid node
Figure 378240DEST_PATH_IMAGE015
Connected connection node
Figure 823741DEST_PATH_IMAGE008
A collection of (a).
Further, the tensor field of metrics
Figure 183178DEST_PATH_IMAGE014
Is a 3 x 3 symmetric matrix for computing the transformation of the spatial coordinate system of the triangle elements, with the expression:
Figure 308129DEST_PATH_IMAGE032
wherein the content of the first and second substances,
Figure 995593DEST_PATH_IMAGE033
in order to be a characteristic value of the image,
Figure 231402DEST_PATH_IMAGE034
in order to be a matrix of rotations,
Figure 445346DEST_PATH_IMAGE035
is the transpose of the rotation matrix; the mesh node
Figure 491931DEST_PATH_IMAGE005
Is the characteristic value
Figure 650379DEST_PATH_IMAGE033
Average value of (a).
Further, the step S1 of determining whether the stress field optimized grid of the initial grid meets a preset requirement includes the following steps:
step S11, judging whether the stress field of the initial grid meets the calculation requirement, if so, outputting the initial grid, and if not, executing step S12;
and step S12, judging whether the iteration number of the optimized grid is not less than a threshold value, if the iteration number is less than the threshold value, executing step S2 to carry out the next iteration, and if the iteration number is not less than the threshold value, outputting the initial grid.
The second purpose of the invention is realized by adopting the following technical scheme:
a mesh generator comprising a plurality of processors, a memory, and a computer program stored on the memory and executable on the processors, the plurality of processors implementing a mesh optimization method as described in any one of the above to generate a mesh when executing the computer program.
The third purpose of the invention is realized by adopting the following technical scheme:
a computer readable storage medium having stored thereon a computer program which, when executed, implements a mesh optimization method as recited in any one of the above.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a grid optimization method, a grid generator and a computer readable storage medium, which are used for calculating an estimation error and a measurement tensor field of grid nodes of a grid, obtaining constraint sizes of the grid nodes according to the measurement tensor field, automatically adjusting the grid sizes according to a simulation result and a requirement on simulation precision, and generating an optimized grid meeting a preset requirement through multiple iterations, so that the calculation precision of simulation software is improved, calculation resources are saved, and the calculation efficiency is improved.
Drawings
FIG. 1 is a diagram of a tetrahedral mesh generated under a constraint size with a mesh size of 10;
FIG. 2 is a schematic illustration of a static analysis of the tetrahedral mesh of FIG. 1;
FIG. 3 is a schematic flow chart of a first embodiment of the present invention;
FIG. 4 is a flowchart illustrating a step S2 according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a grid obtained from a first iteration according to a first embodiment of the present invention;
fig. 6 is a schematic diagram of grid stress values obtained by a first iteration according to a first embodiment of the present invention;
FIG. 7 is a grid obtained from a third iteration according to the first embodiment of the present invention;
fig. 8 is a diagram illustrating grid stress values obtained by a third iteration according to the first embodiment of the present invention;
FIG. 9 is a grid obtained from a fifth iteration according to a first embodiment of the present invention;
fig. 10 is a diagram illustrating grid stress values obtained by the fifth iteration according to the first embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and the detailed description, and it should be noted that any combination of the embodiments or technical features described below can be used to form a new embodiment without conflict.
Example one
As shown in fig. 3, the present application provides a grid optimization method, which automatically adjusts the grid size, generates a grid meeting the simulation requirements, performs iterative computation, saves the computation resources, improves the computation accuracy, and improves the computation efficiency.
Specifically, the method comprises the following steps:
step S1, obtaining an initial grid generated by a grid generator, and carrying out static analysis on the initial grid to obtain a stress field of the initial grid; judging whether the stress field of the initial grid meets a preset requirement or not, and if not, executing a step S2; and if so, outputting the initial grid.
The mesh generator is an existing mesh generator, and triangular, quadrangular, tetrahedral or hexahedral mesh division of a geometric model is realized according to a mesh division algorithm of a Delaunay-frontier marching method (Delaunay-AFT). As shown in fig. 2, the static force analysis is performed on the grid to obtain a stress field of the corresponding grid.
Judging whether the stress field of the initial grid meets preset requirements or not, and the method comprises the following steps:
step S11, judging whether the initial grid stress field meets the calculation requirement, if so, outputting the initial grid, and if not, executing step S12; the calculation requirements may include requirements for maximum stress values, etc., which may be set by the operator according to the actual situation.
And step S12, judging whether the iteration number of the initial grid is not less than a threshold value, if the iteration number is less than the threshold value, executing the step S2 on the initial grid for the next iteration, and if the iteration number is not less than the threshold value, outputting the initial grid.
Step S2, calculating the estimation error of the initial grid to obtain a metric tensor field on the grid node of the initial grid;
specifically, as shown in fig. 4, the step S2 further includes the following steps:
step S21, calculating the stress gradient of each grid node and all the connecting nodes
Figure 440612DEST_PATH_IMAGE002
Calculating the average stress gradient according to the stress gradient and the number of the connection nodes
Figure 40221DEST_PATH_IMAGE003
(ii) a The connection nodes are nodes connecting the grid nodes. Each grid node stores a corresponding stress field, so that a stress gradient exists between each grid node and the connecting node
Figure 506974DEST_PATH_IMAGE002
. In the grid, each grid node is connected with a plurality of connecting nodes, different stress gradients exist on the node, and therefore the average stress gradient of the stress gradients of the node and all the connecting nodes needs to be calculated
Figure 640802DEST_PATH_IMAGE003
。
The method of calculating the mean stress gradient is as follows:
step S211, order
Figure 483993DEST_PATH_IMAGE004
Representing connected grid nodes
Figure 547895DEST_PATH_IMAGE036
And a connection node
Figure 326495DEST_PATH_IMAGE008
Grid connection line, grid node
Figure 193957DEST_PATH_IMAGE007
And a mesh node
Figure 325992DEST_PATH_IMAGE016
Has a stress gradient value of
Figure 493668DEST_PATH_IMAGE017
Computing said mesh nodes
Figure 177591DEST_PATH_IMAGE005
With all connecting nodes connecting the grid nodes
Figure 814240DEST_PATH_IMAGE008
Stress gradient value of
Figure 733654DEST_PATH_IMAGE018
Wherein
Figure 769219DEST_PATH_IMAGE037
As a mesh node
Figure 624042DEST_PATH_IMAGE015
The value of the stress of (a) is,
Figure 731675DEST_PATH_IMAGE038
to connect nodes
Figure 471092DEST_PATH_IMAGE008
The stress value of (a).
Step S212, calculating grid node
Figure 488727DEST_PATH_IMAGE005
With all connecting nodes
Figure 639086DEST_PATH_IMAGE008
Average stress value gradient of
Figure 719168DEST_PATH_IMAGE039
The average stress value gradient is the grid node
Figure 245965DEST_PATH_IMAGE007
With all connecting nodes
Figure 727893DEST_PATH_IMAGE006
Average value of the gradient of stress values of;
Figure 49152DEST_PATH_IMAGE025
wherein
Figure 6744DEST_PATH_IMAGE040
Representation and grid node
Figure 79175DEST_PATH_IMAGE005
Connected connection node
Figure 930456DEST_PATH_IMAGE008
A collection of (a).
Step S22, order
Figure 173350DEST_PATH_IMAGE041
Representing connected grid nodes
Figure 618238DEST_PATH_IMAGE042
And a connection node
Figure 486836DEST_PATH_IMAGE008
Grid connection lines according to the average stress value gradient of each grid node
Figure 943357DEST_PATH_IMAGE003
And
Figure 871998DEST_PATH_IMAGE029
calculating grid connection lines
Figure 538603DEST_PATH_IMAGE041
Is estimated error of
Figure 696046DEST_PATH_IMAGE043
(ii) a The grid connecting line
Figure 256340DEST_PATH_IMAGE027
Is estimated error of
Figure 103686DEST_PATH_IMAGE043
Calculated by the following formula:
Figure 382221DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 467988DEST_PATH_IMAGE022
as a mesh node
Figure 899101DEST_PATH_IMAGE042
The gradient of the average stress value of (a),
Figure 169545DEST_PATH_IMAGE029
to connect nodes
Figure 420529DEST_PATH_IMAGE006
The gradient of the average stress value of (a),
Figure 575567DEST_PATH_IMAGE027
as a mesh node
Figure 110454DEST_PATH_IMAGE044
And a connection node
Figure 302532DEST_PATH_IMAGE016
The grid connection lines of (1).
Step S23, calculating the grid connection line
Figure 555658DEST_PATH_IMAGE004
Length change value of
Figure 983229DEST_PATH_IMAGE011
Wherein
Figure 391863DEST_PATH_IMAGE045
Is a preset maximum error value; given an acceptable maximum error value
Figure 738531DEST_PATH_IMAGE012
Calculating the grid connection line
Figure 432948DEST_PATH_IMAGE046
The length change value of (2). If the maximum error value is greater than the estimation error, that is
Figure 788843DEST_PATH_IMAGE047
Indicating that the estimated error is less than the acceptable maximum error value, grid connection lines
Figure 49055DEST_PATH_IMAGE046
Can be lengthened. Conversely, if the maximum error value is greater than the estimation error,
Figure 832203DEST_PATH_IMAGE048
indicating that the estimated error is greater than the maximum acceptable error, the grid connection lines need to be shortened
Figure 669709DEST_PATH_IMAGE027
To reduce estimation errors
Figure 314448DEST_PATH_IMAGE043
。
Step S24, according to the length change value of each grid connecting line
Figure 944012DEST_PATH_IMAGE013
Computing a field of metric tensors for each grid node
Figure 645865DEST_PATH_IMAGE049
. Calculating the metric tensor field by the following formula
Figure 970667DEST_PATH_IMAGE014
：
Figure 668364DEST_PATH_IMAGE050
Wherein the content of the first and second substances,
Figure 637588DEST_PATH_IMAGE031
representation and grid node
Figure 762539DEST_PATH_IMAGE021
Connected connection node
Figure 450004DEST_PATH_IMAGE006
A collection of (a).
Step S3, calculating the eigenvalue of the measurement tensor field of each grid node, and acquiring the constrained dimension of the grid node; generating an optimized grid according to the constraint size;
the measurement tensor field of the grid node is a symmetrical matrix of 3 multiplied by 3, which is used for calculating the transformation of the space coordinate system of the triangular unit, and the expression is as follows:
Figure 561179DEST_PATH_IMAGE051
wherein the content of the first and second substances,
Figure 899757DEST_PATH_IMAGE033
in order to be a characteristic value of the image,
Figure 946341DEST_PATH_IMAGE052
is a 3 x 3 rotation matrix,
Figure 370369DEST_PATH_IMAGE035
is the transpose of the rotation matrix. The mesh node
Figure 285236DEST_PATH_IMAGE005
Is the characteristic value
Figure 243700DEST_PATH_IMAGE033
Average value of (a).
The characteristic value is measured
Figure 710454DEST_PATH_IMAGE033
The average value of (a) is substituted into the mesh generator in step S1, and an optimized mesh is generated using a mesh division algorithm of Delaunay-frontier marching (Delaunay-AFT).
And step S4, the optimized grid is made to be an initial grid, and the step S1 is executed again for the next iteration until the initial grid meets the preset requirement.
As shown in fig. 5 to 10, schematic diagrams of embodiments provided by the present invention are respectively isotropic meshes obtained through one, three, and five iterations, where the number of meshes is 2623, 2877, and 2920 in order, the corresponding maximum stress values are 490MPa, 528MPa, and 651MPa, and each iteration is closer to the true value, so that a better simulation result is obtained without significantly increasing the number of units.
According to the grid optimization method, the estimation error and the measurement tensor field of the grid nodes of the grid are calculated, the constraint size of the grid nodes is obtained according to the measurement tensor field, the grid size is automatically adjusted according to the simulation result and the requirement on the simulation precision, the optimized grid meeting the preset requirement is generated through multiple iterations, the calculation precision of simulation software is improved, meanwhile, the calculation resources are saved, and the calculation efficiency is improved.
Example two
The present application further provides a grid generator, which is provided with a plurality of processors, a memory, and a computer program stored on the memory and capable of running on the processors, wherein the plurality of processors implement the grid optimization method according to the first embodiment when executing the computer program, so as to generate a grid. The grid generator generates grid units with corresponding sizes according to grid constraint conditions set by space by using a grid division algorithm of a Delaunay-frontier marching method (Delaunay-AFT).
EXAMPLE III
The embodiment of the present invention further provides a computer-readable storage medium, where the storage medium stores computer-executable instructions, and the computer-executable instructions can execute the mesh optimization method described in the first embodiment of the present invention. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a Flash Memory (Flash Memory), a hard disk (hard disk Drive, abbreviated as HDD), a Solid State Drive (SSD), or the like; the storage medium may also comprise a combination of memories of the kind described above.
It should be noted that the above-mentioned numbers of the embodiments of the present invention are merely for description, and do not represent the merits of the embodiments. And the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, apparatus, article, or method. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, apparatus, article, or method that comprises the element.
The grid generator, the computer-readable storage medium and the method in the foregoing embodiments are based on two aspects of the same inventive concept, and the method implementation process has been described in detail in the foregoing, so that those skilled in the art can clearly understand the structure and implementation process of the system in this implementation according to the foregoing description, and for the brevity of the description, no further description is provided here.
The above embodiments are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited thereby, and any insubstantial changes and substitutions made by those skilled in the art based on the present invention are within the protection scope of the present invention.

Claims (10)

1. A mesh optimization method, comprising the steps of:
step S1, obtaining an initial grid generated by a grid generator, carrying out static analysis on the initial grid to obtain a stress field of the initial grid, judging whether the stress field of the initial grid meets a preset requirement, and if not, executing step S2;
step S2, calculating the estimation error of the initial grid to obtain a metric tensor field on the grid node of the initial grid;
step S3, calculating the eigenvalue of the measurement tensor field of each grid node, and acquiring the constrained dimension of the grid node; generating an optimized grid according to the constraint size;
and step S4, the optimized grid is made to be an initial grid, and the step S1 is executed again for the next iteration until the initial grid meets the preset requirement.
2. The trellis optimization method of claim 1, wherein the step S2 of calculating the estimation error of the initial trellis to obtain the metric tensor field on the trellis node of the initial trellis comprises the steps of:
step S21, calculating the stress gradient value of each grid node and all the connection nodes
Figure 893566DEST_PATH_IMAGE001
According to said stress gradient value
Figure 592400DEST_PATH_IMAGE001
And calculating the average stress value gradient by the number of the connection nodes
Figure 620530DEST_PATH_IMAGE002
(ii) a The connection nodes are nodes for connecting the grid nodes;
step S22, order
Figure 381813DEST_PATH_IMAGE003
Representing connected grid nodes
Figure 301228DEST_PATH_IMAGE004
And a connection node
Figure 339722DEST_PATH_IMAGE005
Grid connection lines according to each grid node
Figure 725704DEST_PATH_IMAGE006
Average stress value gradient of
Figure 567758DEST_PATH_IMAGE002
And a connection node
Figure 575684DEST_PATH_IMAGE007
Gradient of mean stress value
Figure 186794DEST_PATH_IMAGE008
Calculating grid connection lines
Figure 822306DEST_PATH_IMAGE003
Is estimated error of
Figure 823760DEST_PATH_IMAGE009
；
Step S23, calculating the grid connection line
Figure 84977DEST_PATH_IMAGE010
Length change value of
Figure 35746DEST_PATH_IMAGE011
Wherein
Figure 153744DEST_PATH_IMAGE012
Is a preset maximum error value;
step S24, according to the length change value of each grid connecting line
Figure 455543DEST_PATH_IMAGE013
Computing a field of metric tensors for each grid node
Figure 661397DEST_PATH_IMAGE014
。
3. The mesh optimization method of claim 2, wherein said step S21 includes the steps of:
step S211, order
Figure 43837DEST_PATH_IMAGE015
Representing connected grid nodes
Figure 18221DEST_PATH_IMAGE016
And a connection node
Figure 728688DEST_PATH_IMAGE007
Grid connection line, grid node
Figure 862866DEST_PATH_IMAGE016
And a mesh node
Figure 53807DEST_PATH_IMAGE005
Has a stress gradient value of
Figure 123395DEST_PATH_IMAGE017
Computing said mesh nodes
Figure 649054DEST_PATH_IMAGE016
With all connecting nodes connecting the grid nodes
Figure 337655DEST_PATH_IMAGE018
Stress gradient value of
Figure 304474DEST_PATH_IMAGE019
Wherein
Figure 607280DEST_PATH_IMAGE020
As a mesh node
Figure 433284DEST_PATH_IMAGE016
The value of the stress of (a) is,
Figure 112527DEST_PATH_IMAGE021
to connect nodes
Figure 292709DEST_PATH_IMAGE018
The stress value of (a);
step S212, calculating grid node
Figure 969678DEST_PATH_IMAGE004
With all connecting nodes
Figure 814137DEST_PATH_IMAGE007
Average stress value gradient of
Figure 31492DEST_PATH_IMAGE002
The average stress value gradient is the grid node
Figure 972903DEST_PATH_IMAGE004
With all connecting nodes
Figure 430560DEST_PATH_IMAGE005
Average value of the gradient of stress values.
4. The mesh optimization method of claim 3, wherein the average stress value gradient is calculated by the following formula:
Figure 152529DEST_PATH_IMAGE023
wherein
Figure 111258DEST_PATH_IMAGE024
Representation and grid node
Figure 782541DEST_PATH_IMAGE025
Connected connection node
Figure 863630DEST_PATH_IMAGE007
A collection of (a).
5. The mesh optimization method of claim 3, wherein said mesh connection lines in step S22
Figure 10577DEST_PATH_IMAGE015
Is estimated error of
Figure 317538DEST_PATH_IMAGE026
Calculated by the following formula:
Figure 358175DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 360897DEST_PATH_IMAGE002
as a mesh node
Figure 729561DEST_PATH_IMAGE025
The gradient of the average stress value of (a),
Figure 357989DEST_PATH_IMAGE029
to connect nodes
Figure 3865DEST_PATH_IMAGE005
The gradient of the average stress value of (a),
Figure 426756DEST_PATH_IMAGE015
as a mesh node
Figure 95766DEST_PATH_IMAGE006
And a connection node
Figure 59043DEST_PATH_IMAGE005
The grid connection lines of (1).
6. The trellis optimization method of claim 2, wherein the metric tensor field is calculated in the step S24 by the following formula
Figure 765617DEST_PATH_IMAGE030
：
Figure 297093DEST_PATH_IMAGE032
Wherein the content of the first and second substances,
Figure 702666DEST_PATH_IMAGE033
representation and grid node
Figure 485946DEST_PATH_IMAGE025
Connected connection node
Figure 293365DEST_PATH_IMAGE007
A collection of (a).
7. The mesh optimization method of claim 6, wherein the tensor field of metrics
Figure 995741DEST_PATH_IMAGE034
Is a 3 x 3 symmetric matrix for computing the transformation of the spatial coordinate system of the triangle elements, with the expression:
Figure 436081DEST_PATH_IMAGE035
wherein the content of the first and second substances,
Figure 678844DEST_PATH_IMAGE036
in order to be a characteristic value of the image,
Figure 544032DEST_PATH_IMAGE037
in order to be a matrix of rotations,
Figure 230359DEST_PATH_IMAGE038
is the transpose of the rotation matrix; the mesh node
Figure 672842DEST_PATH_IMAGE006
Is the characteristic value
Figure 467098DEST_PATH_IMAGE036
Average value of (a).
8. The grid optimization method of claim 4, wherein the step of determining whether the stress field of the initial grid meets a preset requirement in step S1 comprises the steps of:
step S11, judging whether the stress field of the initial grid meets the calculation requirement, if so, outputting the initial grid, and if not, executing step S12;
and step S12, judging whether the iteration number of the initial grid is not less than a threshold value, if the iteration number is less than the threshold value, executing step S2 to carry out the next iteration, and if the iteration number is not less than the threshold value, outputting the initial grid.
9. A mesh generator comprising a plurality of processors, a memory, and a computer program stored on the memory and executable on the processors, the plurality of processors implementing the mesh optimization method of any one of claims 1 to 8 when executing the computer program.
10. A computer-readable storage medium, having stored thereon a computer program which, when executed, implements the mesh optimization method of any one of claims 1 to 8.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114734640A (en) * 2022-04-22 2022-07-12 上海大学 Printing path generation method, computer equipment and storage medium

Citations (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5923329A (en) * 1996-06-24 1999-07-13 National Research Council Of Canada Method of grid generation about or within a 3 dimensional object
US6106561A (en) * 1997-06-23 2000-08-22 Schlumberger Technology Corporation Simulation gridding method and apparatus including a structured areal gridder adapted for use by a reservoir simulator
US20030206178A1 (en) * 2002-05-01 2003-11-06 Microsoft Corporation Systems and methods for providing signal-specialized parametrization
CN101833789A (en) * 2010-01-26 2010-09-15 南京师范大学 Discrete algorithm for tetrahedral mesh considering feature constraint
CN102222150A (en) * 2011-07-12 2011-10-19 上海理工大学 Full-stress structure topological optimization design method based on continuous phase step reference stress
CN107958124A (en) * 2017-12-06 2018-04-24 哈尔滨工业大学深圳研究生院 A kind of mixed-scale coupling process based on distribution mode of contact stresses optimization
CN109242972A (en) * 2018-08-14 2019-01-18 重庆大学 A kind of double normal mesh model method for fairing based on apex feature
CN109408870A (en) * 2018-09-13 2019-03-01 广州中国科学院工业技术研究院 A kind of topological net generation method and electronic equipment based on boundary constraint
US20190304180A1 (en) * 2016-06-08 2019-10-03 Technische Universität München Method and System for Generating a Mesh
CN111079326A (en) * 2019-11-20 2020-04-28 杭州电子科技大学 Two-dimensional anisotropic grid unit measurement tensor field smoothing method
WO2020097216A1 (en) * 2018-11-09 2020-05-14 Autodesk, Inc. Macrostructure topology generation with physical simulation for computer aided design and manufacturing
CN112464349A (en) * 2020-12-08 2021-03-09 中南建筑设计院股份有限公司 Single-layer free-form surface space grid optimization method

Patent Citations (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5923329A (en) * 1996-06-24 1999-07-13 National Research Council Of Canada Method of grid generation about or within a 3 dimensional object
US6106561A (en) * 1997-06-23 2000-08-22 Schlumberger Technology Corporation Simulation gridding method and apparatus including a structured areal gridder adapted for use by a reservoir simulator
US20030206178A1 (en) * 2002-05-01 2003-11-06 Microsoft Corporation Systems and methods for providing signal-specialized parametrization
CN101833789A (en) * 2010-01-26 2010-09-15 南京师范大学 Discrete algorithm for tetrahedral mesh considering feature constraint
CN102222150A (en) * 2011-07-12 2011-10-19 上海理工大学 Full-stress structure topological optimization design method based on continuous phase step reference stress
US20190304180A1 (en) * 2016-06-08 2019-10-03 Technische Universität München Method and System for Generating a Mesh
CN107958124A (en) * 2017-12-06 2018-04-24 哈尔滨工业大学深圳研究生院 A kind of mixed-scale coupling process based on distribution mode of contact stresses optimization
CN109242972A (en) * 2018-08-14 2019-01-18 重庆大学 A kind of double normal mesh model method for fairing based on apex feature
CN109408870A (en) * 2018-09-13 2019-03-01 广州中国科学院工业技术研究院 A kind of topological net generation method and electronic equipment based on boundary constraint
WO2020097216A1 (en) * 2018-11-09 2020-05-14 Autodesk, Inc. Macrostructure topology generation with physical simulation for computer aided design and manufacturing
CN111079326A (en) * 2019-11-20 2020-04-28 杭州电子科技大学 Two-dimensional anisotropic grid unit measurement tensor field smoothing method
CN112464349A (en) * 2020-12-08 2021-03-09 中南建筑设计院股份有限公司 Single-layer free-form surface space grid optimization method

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
SYLVAIN ROUSSEAU等: "Metric tensor for multicomponent edge detection", 《2010 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING》 *
TAKASHI TORIU 等: "Image smoothing using a metric tensor for an affine invariant scale space", 《2014 4TH INTERNATIONAL CONFERENCE ON IMAGE PROCESSING THEORY, TOOLS AND APPLICATIONS (IPTA)》 *
吴禄慎 等: "基于区域划分和三角网格优化的基段选择算法", 《计算机工程与设计》 *
赵佳欣 等: "基于自适应各向异性网格拓扑优化法的仿真分析", 《机械设计》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114734640A (en) * 2022-04-22 2022-07-12 上海大学 Printing path generation method, computer equipment and storage medium
CN114734640B (en) * 2022-04-22 2024-01-16 上海大学 Printing path generation method, computer equipment and storage medium

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