CN109165475A - The method for improving finite element grid local cypher quality - Google Patents
The method for improving finite element grid local cypher quality Download PDFInfo
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- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract
Present invention discloses the methods for improving finite element grid local cypher quality, it include: encryption partiting step, region to be encrypted is determined on the prime area by finite element two-dimensional cell grid dividing, in region to be encrypted, it is smaller by grid cell, the higher finite element two-dimensional cell grid of density treats encryption section and carries out encryption division, and after encrypted division, there are triangular elements for the outer region in region to be encrypted.Triangular element removes step, select a triangular element, select one or the several grid cell adjacent with the triangular element, the triangular element and grid cell collectively constitute transitional region, transitional region has the profile of quadrangle, in transitional region, former triangular element and grid cell are eliminated, fills up the transitional region with several quadrilateral units again.Each of outer region for region to be encrypted triangular element successively executes triangle and removes step, until all triangular elements are removed and finish.
Description
Technical field
The present invention relates to the application technologies of finite element, are locally adding more specifically to two-dimensional cell finite element grid
Removal wherein method of the triangular element to improve mesh quality when close.
Background technique
Finite element is a kind of numerical technique to solve partial differential equation problem approximate solution in mathematics.To entire when solution
Problem area is decomposed, and each subregion just becomes basic unit, and this basic unit is known as finite element.In setting for automobile
It during meter and test, can be graded as early as possible to components and complete vehicle structure performance using FInite Element, quickly discovery is set
The weak link of meter proposes suggestions on Optimization, components experimental quantities and test number (TN) is reduced, to shorten development time and drop
Low development cost improve the maturity of product.
The type selection of the basic unit of finite element meshing timesharing has analysis precision important influence.In automobile
In design process, the basic unit of the finite element used is mainly two-dimensional cell.The grid dividing of two-dimensional cell is general in engineering
What it is all over application is quadrilateral units and triangular element, and the differentiation of grid is mainly embodied on the shape function of interpolation.Triangle
Unit strains the first derivative for displacement, therefore the strain in unit can only be constant, simulation due to using linear interpolation function
Strain gradient will generate very big error when very big, so the stress obtained by the strain also generate therewith it is very big
Error.Therefore in practical projects, if the maximum stress or strain on part are appeared precisely on triangular element, usually
The regional area grid must be repartitioned, try to remove triangular mesh, therefore triangular mesh accounts for total-grid number
The ratio of amount is to measure the major criterion of an engineering project grid dividing quality.It is same in automotive design engineering,
In the finite element grid divided, the quantity of triangular mesh is few as far as possible, and the quantity of triangular mesh accounts for whole nets
The ratio of lattice quantity is lower, then grid dividing quality is higher.
When carrying out FEM meshing, commercially available business finite element software, these business finite elements are mainly used
Software has with powerful gridding method function, fast automatic can generate various two-dimensional cell grids.But often
Due to being influenced by the characteristic curve of part curved surface, some triangular elements can be still left in some local transitional regions, to drop
The quality of low whole grid dividing.At this time, it may be necessary to which by virtue of experience skill removes the networks of triangle of these regional areas to engineer
Lattice.Currently, removal triangular mesh work mainly by engineer by virtue of experience, be manually removed.The work of artificial removal
It is lower to make efficiency, and unstable result, and final grid dividing result has very strong individual difference, different engineerings
The result that teacher divides is different, this is unfavorable for the standardization of overall work.
In addition, often also being needed in partial zones after generating basic two-dimensional cell grid by business finite element software
The grid dividing that domain is more refined.The size of grid affects the precision of calculating and calculates cost.On the one hand wish
As far as possible using coarse grid to reduce the memory space for calculating time and calculated result in relatively accurate situation.On the other hand again
Wish to improve computational accuracy as far as possible under limited calculating cost.In practical projects, it will usually soft using business finite element
The part grid thicker in vehicle Surface Creation calculates time and memory space to save.But it is being easy to produce stress or strain
Regional area or engineer pay special attention to a certain regional area, it is necessary to the regional area carry out unit refinement, thus
It solves computational accuracy and calculates the contradiction between cost.During mesh refinement, as the refinement of grid may make carefully
The part of change increases many triangular elements newly.Currently, these newly-increased triangular elements are also required to carry out by artificial mode
Removal.Since the finite element unit at refinement position is more, the quantity of newly-increased triangular element is also more, removes work
Larger workload, efficiency are lower.
Summary of the invention
The present invention propose it is a kind of can with standardized program, by the method for the removal triangular mesh that software auxiliary is realized, with
Promote the closed quality of finite element grid part.
An embodiment according to the present invention proposes a kind of method for improving finite element grid local cypher quality, including such as
Under step:
Partiting step is encrypted, region to be encrypted is determined on the prime area by finite element two-dimensional cell grid dividing,
It is smaller by grid cell in region to be encrypted, the higher finite element two-dimensional cell grid of density treat encryption section into
Row encryption divides, and after encrypted division, there are triangular elements for the outer region in region to be encrypted；
Triangular element removes step, selects a triangular element, select adjacent with the triangular element one or
The several grid cells of person, the triangular element and one or several grid cells collectively constitute transitional region, the transition region
Domain has the profile of quadrangle, in transitional region, eliminates former triangular element and one or several grid cells, uses number again
A quadrilateral units fill up the transitional region；
Each of outer region for region to be encrypted triangular element successively executes the triangle removal step
Suddenly, until all triangular elements are removed and finish.
In one embodiment, in transitional region, several quadrilateral units be according to the mass center of the transitional region with
And the triangular element vertex and determine.
In one embodiment, the size for the grid cell that the quantity of the quadrilateral units in transitional region and encryption divide
Correlation, the size for encrypting the grid cell of division is the 1/n of former grid cell size, then in transitional region quadrilateral units number
It measures S (n) are as follows:
Wherein n is the ratio of the size for the grid cell that encryption divides and the size of former grid cell, and N is natural number.
In one embodiment, encryption stroke is carried out in region to be encrypted by commercially available commercial finite element processing software
Point.
In one embodiment, it encrypts in partiting step, by the prime area of finite element two-dimensional cell grid dividing
Upper determination region to be encrypted, in region to be encrypted, by the refined net unit of 1/2 having a size of former grid cell to be encrypted
Region carries out encryption division, and after encrypted division, there are triangular elements for the outer region in region to be encrypted.
In one embodiment, former grid cell is rectangular element, and refined net unit is having a size of former grid cell 1/2
Rectangular mesh unit；
After encrypted division, there are right angled triangle units for the outer region in region to be encrypted.
In one embodiment, triangular element removal step includes:
A right angled triangle unit is selected, a right-angled trapezium unit adjacent with the right angled triangle unit is selected,
The right angled triangle unit and the right-angled trapezium unit collectively constitute transitional region, and transitional region has rectangle outer profile；
The bevel edge for removing right angled triangle unit, retains the rectangle outer profile of transitional region；
Determine the centroid position A of transitional region, the midpoint B for the right-angle side for determining former right-angled trapezium unit, determining original
Two vertex positions C and D of the bevel edge of right angled triangle unit；
AB, AC, AD distinguish line, and transitional region is divided into a rectangular element and two right-angled trapezium units, rectangle
Unit and right-angled trapezium unit are quadrilateral units, and three quadrilateral units fill up the transitional region.
The method of raising finite element grid local cypher quality of the invention has the advantage that
1) partition process is simple: the grid cell on triangular element and periphery only being needed to be repartitioned；
2) versatility is good: since the grid cell in local refinement region is usually based on rectangular element, for all squares
Shape refinement region can be gone to handle with this method, can not theoretically stay a triangular element；
3) engineering application value is high: it can be applied to all engineering projects simulated using two-dimensional cell using this method,
Either curved surface or plane components can be general
4) simulation accuracy is high: after being handled by this method, will locally not have triangular element, and not only be mentioned by tessellated mesh
High computational accuracy, and improve by removal triangular element the confidence level of calculated result.
Detailed description of the invention
The above and other feature of the present invention, property and advantage will pass through description with reference to the accompanying drawings and examples
And become apparent, identical appended drawing reference always shows identical feature in the accompanying drawings, in which:
Fig. 1 discloses the process of the method for the raising finite element grid local cypher quality of an embodiment according to the present invention
Figure.
Fig. 2 a- Fig. 2 g discloses the method for the raising finite element grid local cypher quality of an embodiment according to the present invention
Specific implementation process.
Fig. 3 a, Fig. 3 b and Fig. 3 c disclose the raising finite element grid local cypher quality of an embodiment according to the present invention
Method under different encryption ratios transitional region division situation.
Fig. 4 a, Fig. 4 b and Fig. 4 c disclose the raising finite element grid local cypher quality of an embodiment according to the present invention
Practical situations of the method on components schematic diagram.
Specific embodiment
Refering to what is shown in Fig. 1, Fig. 1 discloses the raising finite element grid local cypher quality of an embodiment according to the present invention
Method flow chart.The method of raising finite element grid local cypher quality of the invention includes two steps:
S1, encryption partiting step.Area to be encrypted is determined on the prime area by finite element two-dimensional cell grid dividing
Domain, smaller by grid cell in region to be encrypted, the higher finite element two-dimensional cell grid of density treats encryption section
Encryption division is carried out, after encrypted division, there are triangular elements for the outer region in region to be encrypted.In general, encryption divides
Step is to carry out encryption division in region to be encrypted by commercially available commercial finite element processing software.
S2, triangular element remove step.A triangular element is selected, one adjacent with the triangular element is selected
Or several grid cells, the triangular element and one or several grid cells collectively constitute transitional region, the transition
Region has the profile of quadrangle, in transitional region, eliminates former triangular element and one or several grid cells, uses again
Several quadrilateral units fill up the transitional region.
Triangular element removal step S2 is repeatedly executed, for each of the outer region in region to be encrypted triangle
Shape unit successively executes above-mentioned triangle removal step, until all triangular elements are removed and finish.
In one embodiment, in the triangular element removal step for each triangular element, transitional region
In several quadrilateral units be to be determined according to the mass center of transitional region and the vertex of triangular element.
The quantity of quadrilateral units in transitional region is related to the size of grid cell that encryption divides, and encrypts division
The size of grid cell is the 1/n of former grid cell size, then in transitional region quadrilateral units quantity S (n) are as follows:
Wherein n is the ratio of the size for the grid cell that encryption divides and the size of former grid cell, and N is natural number.It needs
It is noted that ratio n herein refers to the ratio of the side length of grid cell, the ratio of area is not referred to.
A specific example is named, is commented with simulating certain car body structure performance the high velocity impact of side during
Valence.Initial finite element grid unit is mainly the rectangular mesh that side length is 8mm, for centre gangway thermoforming metal plate and bottom plate
Between there are two weld seams to be the collision area of high spot reviews, since bonding wire model foundation is more fine, by this two weld seams
The mesh refinement of region is at the rectangular mesh that side length is 4mm in favor of evaluation.It is limited that raising of the invention is described in conjunction with Fig. 2
The implementation procedure of the method for first grid local cypher quality.Fig. 2 a- Fig. 2 g discloses the raising of an embodiment according to the present invention
The specific implementation process of the method for finite element grid local cypher quality.
For the embodiment, encrypt in partiting step, by the original area of finite element two-dimensional cell grid dividing
Determine that region to be encrypted, the region to be encrypted are exactly two weld seams place between centre gangway thermoforming metal plate and bottom plate on domain
Region.Prime area is divided by the two-dimensional cell grid that side length is 8mm.Fig. 2 a discloses the state, the void in Fig. 2 a
The region that line is confined is exactly region 102 to be encrypted.It should be noted that finite element two-dimensional cell mentioned here, refers to work
Journey plate or the part of similar type in practice.The characteristics of this kind of part is that have the length of a dimension much smaller than in addition in size
The length of the length of two dimensions and the small dimension remains unchanged.At this moment the middle face of the plate can be taken, i.e., by a three dimensional panel
It is converted to a two-dimensional surface, then the grid division on the two-dimensional surface.In Fig. 2 a and subsequent description, for plane
It is illustrated, in practical projects, method of the invention is not limited to plane, and the curved surface of slightly radian is also can be using this
Invention.Furthermore in Fig. 2 a and subsequent description, grid cell is by taking rectangular mesh as an example.In practical projects, it carries out
When the mesh refinement refinement of part, the refined net after usual original mesh and refinement is all rectangle, therefore is had by taking rectangle as an example
There is widest applicability.But method of the invention is not limited to the grid of rectangle, quadrangle of the shape close to rectangle
It can be encrypted using method of the invention.
In region to be encrypted, by the refined net unit of 1/2 having a size of former grid cell, i.e. the side length square that is 4mm
Shape unit treats encryption section and carries out encryption division.The step of encryption divides by commercially available commercial finite element processing software into
Row.Result after encryption divides is as shown in Figure 2 b.It is all that rectangle adds in the centre in region 102 to be encrypted with reference to Fig. 2 b
Fine grid, i.e. side length are the rectangular mesh of 4mm.But the outer region in region 102 to be encrypted, due to original grid (side
The rectangular mesh of a length of 8mm) transition and linkage relationship, there is triangular element.With reference to shown in Fig. 2 b, in the embodiment
In, there is right angled triangle unit, and matches with right angled triangle unit in the outer region in region 102 to be encrypted
Right-angled trapezium unit.These right angled triangle units and right-angled trapezium unit are to carry out grid by commercial finite element processing software
It is automatically generated after encryption.Right-angled trapezium unit is quadrilateral units, has preferable precision for simulated strain.But it is straight
Angle triangular element is triangular element, and the precision in terms of simulated strain is poor, next needs to remove these triangle lists
Member.
In this embodiment, triangular element removal step includes following process:
A right angled triangle unit is selected, a right-angled trapezium unit adjacent with the right angled triangle unit is selected.
In the embodiment shown in Fig. 2 b, selection be the right angled triangle unit T1 of arrow meaning and it is adjacent thereto, share bevel edge
Right-angled trapezium unit.The right angled triangle unit and the right-angled trapezium unit collectively constitute transitional region, and transitional region has
Rectangle outer profile.In the embodiment shown in Fig. 2 b, which is exactly an original rectangular mesh (side length 8mm
Rectangular mesh).Fig. 2 c further discloses the structure of transitional region, and transitional region includes a right angled triangle unit and one
A right-angled trapezium unit, the two share bevel edge.Transitional region itself has the outer profile of rectangle.
For the transitional region, the bevel edge of right angled triangle unit is removed, the rectangle outer profile of transitional region is retained.It determines
The centroid position A of transitional region, the midpoint B of the right-angle side of determining former right-angled trapezium unit, determining former right angled triangle list
Two vertex positions C and D of the bevel edge of member.With reference to shown in Fig. 2 d.
AB, AC, AD distinguish line, and transitional region is divided into a rectangular element and two right-angled trapezium units, refer to
Shown in Fig. 2 e.Rectangular element and right-angled trapezium unit are quadrilateral units, and three quadrilateral units fill up the transitional region.
In this way, first triangular element removal finishes.
It is removed followed by second triangular element of selection.In this embodiment, second triangle is being selected
When unit, it can select to be formed by the transitional region triangle list symmetrical with the transitional region where first right angled triangle
Member.In this embodiment, second right angled triangle unit T2 is selected to be located on the right side of first right angled triangle unit T1
Right angled triangle unit.It includes that a right angled triangle and one are straight that right angled triangle unit T2, which is formed by transitional region also,
Angle is trapezoidal.The right-angled trapezium and the right-angled trapezium of right angled triangle T1 share right-angle side, which is also two mistakes
Cross the symmetry axis in region.
Triangular element removal step is equally executed to right angled triangle unit T2.Result after processing refers to Fig. 2 f institute
Show.
Triangular element removal step is successively executed to all right angled triangle units, until all right angled triangles
Unit is processed to be finished, and treated, and result is as shown in Figure 2 g.
Above embodiment is illustrated so that the size of refined net is the 1/2 of original mesh as an example.Implement in others
In example, the size of refined net and the size of original mesh can be other ratios.And the quadrilateral units in transitional region
Quantity and the size of grid cell that encryption divides it is related, the size for encrypting the grid cell of division is original grid cell size
1/n, then in transitional region quadrilateral units quantity S (n) are as follows:
Fig. 3 a, Fig. 3 b and Fig. 3 c disclose the raising finite element grid local cypher quality of an embodiment according to the present invention
Method under different encryption ratios transitional region division situation.Fig. 3 a discloses the case where ratio is 2, i.e., previously described
State.Fig. 3 b discloses the case where ratio is 3, and transitional region is divided into 6 grid cells, including four rectangular elements and
Two right-angled trapezium units.Fig. 3 c discloses the case where ratio is 4, and transitional region is divided into 8 grid cells, including four
Rectangular element and four right-angled trapezium units.
Fig. 4 a, Fig. 4 b and Fig. 4 c disclose the raising finite element grid local cypher quality of an embodiment according to the present invention
Practical situations of the method on components schematic diagram.Fig. 4 a discloses the initial shape divided according to original mesh
State, two dashed regions therein indicate region to be encrypted.Fig. 4 b disclose using commercially available commercial finite element processing software into
It can see triangular element as a result, remaining unchanged in Fig. 4 b after row encryption division, commercially available commercialization finite element processing software carries out
Encryption can generate triangular element after dividing.Fig. 4 c is disclosed using raising finite element grid local cypher quality of the invention
Method removes the state after triangular element, and final grid cell structure is similar with state shown in Fig. 2 g.
It being calculated by finite element software, the grid divided automatically by business software is due to there is a large amount of triangular elements, and three
Angular strain value out is 0, is not inconsistent with actual conditions.Actual maximum strain should be 5.1%, and with method of the invention
After processing, triangular element is eliminated, maximum strain is 6.1%, is more nearly actual value.The present invention is replaced with quadrilateral units
The position of triangular element is changed.Found out in the case where local refinement grid by this example, if will with this method
The numerical value for the maximum strain that triangular element obtains after all removing and position will be more accurate
The method of raising finite element grid local cypher quality of the invention has the advantage that
1) partition process is simple: the grid cell on triangular element and periphery only being needed to be repartitioned；
2) versatility is good: since the grid cell in local refinement region is usually based on rectangular element, for all squares
Shape refinement region can be gone to handle with this method, can not theoretically stay a triangular element；
3) engineering application value is high: it can be applied to all engineering projects simulated using two-dimensional cell using this method,
Either curved surface or plane components can be general
4) simulation accuracy is high: after being handled by this method, will locally not have triangular element, and not only be mentioned by tessellated mesh
High computational accuracy, and improve by removal triangular element the confidence level of calculated result.
Above-described embodiment, which is available to, to be familiar with person in the art to realize or use the present invention, and is familiar with this field
Personnel can make various modifications or variation, thus this to above-described embodiment without departing from the present invention in the case of the inventive idea
The protection scope of invention is not limited by above-described embodiment, and should meet inventive features that claims are mentioned most
On a large scale.
Claims (7)
1. a kind of method for improving finite element grid local cypher quality characterized by comprising
Encrypt partiting step, region to be encrypted determined on the prime area by finite element two-dimensional cell grid dividing, to
Smaller by grid cell in encryption section, the higher finite element two-dimensional cell grid of density is treated encryption section and is added
Close division, after encrypted division, there are triangular elements for the outer region in region to be encrypted；
Triangular element removes step, selects a triangular element, selects one or the number adjacent with the triangular element
A grid cell, the triangular element and one or several grid cells collectively constitute transitional region, transitional region tool
There is the profile of quadrangle, in transitional region, former triangular element and one or several grid cells is eliminated, again with several four
Side shape unit fills up the transitional region；
Each of outer region for region to be encrypted triangular element successively executes the triangle removal step,
Until all triangular elements are removed and finish.
2. improving the method for finite element grid local cypher quality as described in claim 1, which is characterized in that
In transitional region, several quadrilateral units are the tops of the mass center and the triangular element according to the transitional region
It puts and determines.
3. improving the method for finite element grid local cypher quality as described in claim 1, which is characterized in that in transitional region
Quadrilateral units quantity and the size of grid cell that encryption divides it is related, it is former for encrypting the size of the grid cell of division
The 1/n of grid cell size, then in transitional region quadrilateral units quantity S (n) are as follows:
Wherein n is the ratio of the size for the grid cell that encryption divides and the size of former grid cell, and N is natural number.
4. improving the method for finite element grid local cypher quality as described in claim 1, which is characterized in that by commercially available
Commercial finite element processing software carries out encryption division in region to be encrypted.
5. improving the method for finite element grid local cypher quality as described in claim 1, which is characterized in that encryption divides step
In rapid, region to be encrypted is determined on the prime area by finite element two-dimensional cell grid dividing, in region to be encrypted, by
The 1/2 refined net unit having a size of former grid cell treats encryption section and carries out encryption division, after encrypted division, to
There are triangular elements for the outer region of encryption section.
6. improving the method for finite element grid local cypher quality as claimed in claim 5, which is characterized in that
Former grid cell is rectangular element, and refined net unit is the rectangular mesh unit having a size of former grid cell 1/2；
After encrypted division, there are right angled triangle units for the outer region in region to be encrypted.
7. improving the method for finite element grid local cypher quality as claimed in claim 6, which is characterized in that the triangle
Unit removes step
A right angled triangle unit is selected, a right-angled trapezium unit adjacent with the right angled triangle unit is selected, this is straight
Angle triangular element and the right-angled trapezium unit collectively constitute transitional region, and transitional region has rectangle outer profile；
The bevel edge for removing right angled triangle unit, retains the rectangle outer profile of transitional region；
Determine the centroid position A of transitional region, the midpoint B for the right-angle side for determining former right-angled trapezium unit, determining former right angle
Two vertex positions C and D of the bevel edge of triangular element；
AB, AC, AD distinguish line, and transitional region is divided into a rectangular element and two right-angled trapezium units, rectangular element
It is quadrilateral units with right-angled trapezium unit, three quadrilateral units fill up the transitional region.
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| CN111931457A (en) * | 2020-09-27 | 2020-11-13 | 北京智芯仿真科技有限公司 | Multilayer integrated circuit electromagnetic field calculation method and device based on mixed order finite element |
| CN114329519A (en) * | 2021-12-10 | 2022-04-12 | 中广核风电有限公司 | Grid encryption method and device based on terrain gradient |
| CN114329520A (en) * | 2021-12-10 | 2022-04-12 | 中广核风电有限公司 | Grid encryption method and device based on wake flow of wind turbine |
| CN116127862A (en) * | 2022-12-12 | 2023-05-16 | 中广核风电有限公司 | Structured grid encryption method and device suitable for large-gradient terrain numerical analysis |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111931457A (en) * | 2020-09-27 | 2020-11-13 | 北京智芯仿真科技有限公司 | Multilayer integrated circuit electromagnetic field calculation method and device based on mixed order finite element |
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| CN114329519A (en) * | 2021-12-10 | 2022-04-12 | 中广核风电有限公司 | Grid encryption method and device based on terrain gradient |
| CN114329520A (en) * | 2021-12-10 | 2022-04-12 | 中广核风电有限公司 | Grid encryption method and device based on wake flow of wind turbine |
| CN116127862A (en) * | 2022-12-12 | 2023-05-16 | 中广核风电有限公司 | Structured grid encryption method and device suitable for large-gradient terrain numerical analysis |
| CN116127862B (en) * | 2022-12-12 | 2024-01-12 | 中广核风电有限公司 | Structured grid encryption method and device suitable for large-gradient terrain numerical analysis |
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