CN109102570A - A kind of modeling method of three-dimensional finite element model - Google Patents
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Abstract
A kind of modeling method of three-dimensional finite element model, for similar electromagnetic railgun, three-phase bus slot, research object as power cable line tunnel, 3D solid with object based on plane symmetrical structure feature object, when establishing finite element model, initially set up two-dimensional model, finite elements division is carried out using triangular mesh again, two-dimensional finite element model is subjected to segmentation stretching along the symmetrical axial direction of plane, segmental stretching starts point is determined with different location where main object each in 3D solid, and axially also carrying out grid dividing during stretching, then after 3-D geometric model is formed, corresponding three-dimensional finite element model also generates simultaneously, the finite element model generated is stretched in this way using prismatic mesh, its mesh quality is better than the tetrahedral grid that conventional method uses, both the modeling time is saved, It in turn ensures mesh quality, provides a kind of completely new thinking for the modeling method of Numerical Calculation of Electromagnetic Fields three-dimensional finite element model.
Description
Technical field
A kind of modeling method of three-dimensional finite element model of the present invention is related to Numerical Calculation of Electromagnetic Fields and electrical theory technology neck
Domain.
Background technique
It is three-dimensional real for research object as similar electromagnetic railgun, three-phase bus slot, power cable line tunnel
Body characteristics are: containing the entity of similar guide rail, bus, this plane symmetrical structure of cable;And armature, line tower are not
Plane symmetrical structure.When carrying out 3 D electromagnetic field finite element numerical and calculating, first have to establish entity 3-D geometric model and
Finite element model just can be carried out finite element equation numerical solution.Conventional modeling method is, according to the entity structure of object, directly
It connects and establishes 3-D geometric model, by taking electromagnetic railgun as an example, i.e., establish guide rail, armature, air packet threedimensional model respectively, then to whole
A threedimensional model carries out FEM meshing, and irregular said three-dimensional body uses the free subdivision of tetrahedral grid, such not advise
Then structure causes mesh quality not can guarantee.
Summary of the invention
For the deficiency of the above method, the present invention provides a kind of modeling method of three-dimensional finite element model, for similar electricity
Magnetic railgun, three-phase bus slot, research object as power cable line tunnel, there is plane symmetrical structure feature object to be
The 3D solid of main object initially sets up two-dimensional model when establishing finite element model, then using triangular mesh into
Row finite elements divide, and two-dimensional finite element model are stretched along the symmetrical axial direction of plane, and during stretching in axis
To grid dividing is also carried out, then after 3-D geometric model is formed, corresponding three-dimensional finite element model also generates simultaneously, draws in this way
The finite element model of generation is stretched using prismatic mesh, and mesh quality is better than the tetrahedral grid that conventional method uses.
Both the modeling time is saved, in turn ensures mesh quality, is mentioned for the modeling method of Numerical Calculation of Electromagnetic Fields three-dimensional finite element model
For a kind of completely new thinking.
The technical scheme adopted by the invention is as follows:
A kind of modeling method of three-dimensional finite element model, for three with object based on plane symmetrical structure feature object
Entity is tieed up, two-dimensional model is initially set up, carries out FEM meshing, then by two-dimensional finite element model along plane symmetry axis
To direction, segmentation stretching is carried out, respectively with nonbody object positions other in 3D solid, determines segmental stretching starts
Point, and axial grid dividing is carried out when stretching;After the completion of stretching specified length, 3-D geometric model is formed, accordingly
Three-dimensional finite element model also generates simultaneously, no longer needs to re-start grid dividing to three-dimensional entity model.
A kind of modeling method of three-dimensional finite element model, comprising the following steps:
Step 1: for the 3D solid object modeled, to have the master of plane symmetrical structure feature in 3D solid
Body object is reference target, establishes the two-dimensional model of the element containing each section;
Step 2: to two-dimensional model, finite elements division being carried out using triangular mesh, generates two-dimensional finite element model;
Step 3: along the symmetrical axial direction of plane, segmentation stretching being carried out to two-dimensional finite element model, with main body each in 3D solid
Different location determines segmental stretching starts point where object, and axial grid dividing is carried out when stretching;
Step 4: according to the total length of 3D solid, after the completion of stretching, three-dimensional entity model and corresponding three-dimensional finite element model
It has been be formed simultaneously that, finite element model is then made of prismatic mesh, according to the real material attribute of objects different in entity, to not
Finite elements with computational domain carry out material parameter setting.
Using a kind of modeling method of three-dimensional finite element model of the present invention, the finite element model of generation is stretched using three
Prism grid, mesh quality are better than the tetrahedral grid that conventional method uses, and both save the modeling time, in turn ensure grid
Quality.
Using a kind of modeling method of three-dimensional finite element model of the present invention, no longer need to re-start net to three-dimensional entity model
Lattice divide, and both save the modeling time, in turn ensure preferable mesh quality.
Using a kind of modeling method of three-dimensional finite element model of the present invention, it is applied to plane symmetrical structure characteristic body
The three-dimensional entity model of object based on body, for example, electromagnetic railgun, three-phase bus slot or power cable line tunnel three
Tie up finite element model modeling.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples:
Fig. 1 is double-layer guide rail electromagnetic railgun schematic diagram.
Fig. 2 is railgun two dimensional model figure.
Fig. 3 is the finite element model figure after two dimensional model is divided using triangular mesh.
Fig. 4 is threedimensional model generated after the stretching for the first time of segmentation along the z-axis direction, and wherein Fig. 4 (a) is to generate after stretching
Three-dimensional finite element model figure, Fig. 4 (b) is the 3-D geometric model that generates after stretching.
Fig. 5 is threedimensional model generated after second of stretching of segmentation along the z-axis direction, and wherein Fig. 5 (a) is to generate after stretching
Three-dimensional finite element model figure, Fig. 5 (b) is the 3-D geometric model that generates after stretching.
Fig. 6 is threedimensional model generated after segmentation third time stretching along the z-axis direction, and wherein Fig. 6 (a) is to generate after stretching
Three-dimensional finite element model figure, Fig. 6 (b) is the 3-D geometric model that generates after stretching.
Fig. 7 is to be segmented threedimensional model generated after the 4th stretching along the z-axis direction, and wherein Fig. 7 (a) is to generate after stretching
Three-dimensional finite element model figure, Fig. 7 (b) is the 3-D geometric model that generates after stretching.
Fig. 8 is to be segmented threedimensional model generated after the 5th stretching along the z-axis direction, and wherein Fig. 8 (a) is to generate after stretching
Three-dimensional finite element model figure, Fig. 8 (b) is the 3-D geometric model that generates after stretching.
Fig. 9 is to be segmented threedimensional model generated after the 6th stretching along the z-axis direction, and wherein Fig. 9 (a) is to generate after stretching
Three-dimensional finite element model figure, Fig. 9 (b) is the 3-D geometric model that generates after stretching.
Figure 10 is to be segmented threedimensional model generated after the 7th stretching along the z-axis direction, and wherein Figure 10 (a) is raw after stretching
At three-dimensional finite element model figure, Figure 10 (b) is the 3-D geometric model that generates after stretching.
Figure 11 is cable tunnel schematic diagram in engineering.
Figure 12 is cable tunnel two dimensional model figure.
Figure 13 is the finite element model figure after two dimensional model is divided using triangular mesh.
Figure 14 is threedimensional model generated after the stretching for the first time of segmentation along the z-axis direction, and wherein Figure 14 (a) is raw after stretching
At three-dimensional finite element model figure, Figure 14 (b) is the 3-D geometric model that generates after stretching.
Figure 15 is threedimensional model generated after second of stretching of segmentation along the z-axis direction, and wherein Figure 15 (a) is raw after stretching
At three-dimensional finite element model figure, Figure 15 (b) is the 3-D geometric model that generates after stretching.
Figure 16 is threedimensional model generated after segmentation third time stretching along the z-axis direction, and wherein Figure 16 (a) is raw after stretching
At three-dimensional finite element model figure, Figure 16 (b) is the 3-D geometric model that generates after stretching.
Figure 17 is to be segmented threedimensional model generated after the 4th stretching along the z-axis direction, and wherein Figure 17 (a) is raw after stretching
At three-dimensional finite element model figure, Figure 17 (b) is the 3-D geometric model that generates after stretching.
Figure 18 is to be segmented threedimensional model generated after the 5th stretching along the z-axis direction, and wherein Figure 18 (a) is raw after stretching
At three-dimensional finite element model figure, Figure 18 (b) is the 3-D geometric model that generates after stretching.
Specific embodiment
A kind of modeling method of three-dimensional finite element model, for object based on plane symmetrical structure feature object
3D solid, initially set up two-dimensional model, carry out FEM meshing, then by two-dimensional finite element model along plane pair
Claim axial direction, carry out segmentation stretching, respectively with nonbody object positions other in 3D solid, determines that segmentation stretches
Initial point, and axial grid dividing is carried out when stretching;After the completion of stretching specified length, 3-D geometric model is formed, accordingly
Three-dimensional finite element model also generate simultaneously, no longer need to re-start grid dividing to three-dimensional entity model.
The above method specifically includes the following steps:
Step 1: for the 3D solid object modeled, to have the master of plane symmetrical structure feature in 3D solid
Body object is reference target, establishes the two-dimensional model of the element containing each section.
Step 2: to two-dimensional model, finite elements division being carried out using triangular mesh, generates two dimensional finite element mould
Type;
Step 3: along the symmetrical axial direction of plane, segmentation stretching being carried out to two-dimensional finite element model, with main body each in 3D solid
Different location determines segmental stretching starts point where object, and axial grid dividing is carried out when stretching.
Step 4: according to the total length of 3D solid, after the completion of stretching, three-dimensional entity model and corresponding three-dimensional finite element
Model has been formed simultaneously, and finite element model is then made of prismatic mesh, according to the real material attribute of objects different in entity,
Material parameter setting is carried out to the finite elements of different computational domains.
Embodiment 1:
By taking electromagnetic railgun as an example, the double-deck electromagnetic railgun schematic diagram is as shown in Figure 1, the double-deck electromagnetic railgun 3D solid contains two
A upper strata guide rail 1, two lower floor guide rail 2, upper layer armature 3, lower layer's armature 4, wherein guide rail is copper product, armature is aluminum material.
In the object entity, upper strata guide rail 1, lower floor guide rail 2 have plane symmetrical structure, and longitudinal direction iszAxis direction is plane pair
Claim axial direction, and upper layer armature 3, lower layer's armature 4 are different due to moving speed, present position is different, in this example in hypothesis
Layer armature space upright position is preceding, and lower layer's armature is rear, and the two position overlaps in vertical direction.In addition,
When carrying out the calculating of electromagnetic finite element numerical value, other than establishing railgun ontology model, it is also necessary to establish and surround railgun mould
The air body region of type.Therefore complete model includes upper and lower level guide rail, upper and lower level armature, air section.Carry out three-dimensional finite element
The description of model modeling implementation process:
(1): foundation includes the two dimensional model of the guide rail, the armature, air, as shown in Fig. 2, yellow area is four armatures
Two-dimensional section, green area be armature section, gray area is air part.
(2): two dimensional model being subjected to finite elements division using triangular mesh, as shown in figure 3, generating two dimensional finite element
Model.
(3): edgezThe two dimensional finite element areal model of Fig. 3 is carried out segmentation stretching, by track, armature, front and back by axis direction
The starting point for holding air section to stretch respectively as segmentation, and axial grid dividing is carried out when stretching, each grid is three
Prism elements.The specific steps are the guide rail front end stretched first armature sectional positions forward to appearance position, as shown in figure 4,
Fig. 4 (a) is to be formed by three-dimensional finite element model after stretching for the first time;Display is three-dimensional geometry mould after stretching in Fig. 4 (b)
Type shows that wherein green portion is a part of upper and lower level track, transparent region in order to distinguish different zones with different colours
For air part.Stretching is then proceeded by, is stretched to the armature sectional position of appearance position rearward for the second time, as shown in figure 5,
Fig. 5 (a) is to be formed by three-dimensional finite element model after stretching for the second time;Display is three-dimensional geometry mould after stretching in Fig. 5 (b)
Type, wherein green portion is a part of upper and lower level guide rail, and yl moiety is a part of upper layer armature, and transparent region is sky
Gas.Third time continues to be stretched to upper layer armature geometrical model end position, as shown in fig. 6, Fig. 6 (a) is institute after third time stretching
The three-dimensional finite element model of formation;Display is 3-D geometric model after stretching in Fig. 6 (b), and wherein green portion is upper and lower level
A part of guide rail, yl moiety are complete upper layer armature and section bottom armature, and transparent region is air.Continue to draw for 4th time
Lower layer's armature geometrical model end position is extended to, as shown in fig. 7, Fig. 7 (a) is formed by three-dimensional finite element after stretching for the 4th time
Model;Display is 3-D geometric model after stretching in Fig. 7 (b), and wherein green portion is a part of upper and lower level guide rail, yellow
Part is complete upper layer armature and complete lower layer's armature, transparent region are air.Continue to be stretched to lower layer's armature geometry for 5th time
Model end position, as shown in figure 8, Fig. 8 (a) is formed by three-dimensional finite element model after stretching for the 5th time;It is shown in Fig. 8 (b)
Show the 3-D geometric model after stretching, wherein green portion is complete upper and lower level guide rail, and yl moiety is the upper and lower
Armature, transparent region are air.Continue stretched back air region 6th time, as shown in figure 9, Fig. 9 (a) is the 6th stretching
After be formed by three-dimensional finite element model;Display is 3-D geometric model after stretching in Fig. 9 (b), and wherein green portion is upper
Lower floor guide rail, yl moiety are the upper and lower armature, and transparent region contains the new stretched next air in rear end.7th time to
The stretched front end air region in front end, as shown in Figure 10, Figure 10 (a) are formed by three-dimensional finite element mould after stretching for the 7th time
Type;Display is 3-D geometric model after stretching in Figure 10 (b), wherein including guide rail and armature, transparent region contains front and back
The air at end.As shown in Figure 10, it after the completion of seven stretchings, that is, forms comprising upper and lower level guide rail, upper and lower level armature, surround track
The three-dimensional finite element model of the air of big gun, entire three-dimensional finite element model all use prismatic mesh.
(4): the setting of material properties is carried out to the grid in each region in newly-generated three-dimensional finite element model, by guide rail area
Material parameter, that is, the relative permeability and resistivity of domain Three-D limited unit are set as the international unit parameter of copper product, such as opposite
Magnetic conductivity is 1, and resistivity is 1.7e-8 Ω m;By the material parameter, that is, relative permeability and electricity of armature area three-dimensional finite elements
Resistance rate is set as the international unit parameter of aluminum material, and if relative permeability is 1, resistivity is 2.7e-8 Ω m;By air section
Material parameter, that is, relative permeability of Three-D limited unit is set as 1.
By above method by two dimensional model stretch generate threedimensional model, by Figure 10 it can be seen that, when railgun geometrical model
While generation, three-dimensional finite element model also generates simultaneously, and the shape of grid is tri-prism element, carries out unit to new model
After material properties setting, it can be directly used in the calculating of electromagnetic finite element numerical value.Conventional method is directly to establish three-dimensional geometry
Model, then it is unified carry out mesh generation, due to the asymmetry of model structure in zoning, can only using tetrahedral grid into
Row subdivision, and subdivision process is unable to control the grid density of each region.And the method for the present invention is established in two-dimensional finite element model
When, the control of grid density can be carried out to each region, and continue to carry out density control to grid during stretching along axial direction, work as life
After three-dimensional finite element model, grid is also to generally believe that convergence is better than the triangular prism of tetrahedral grid in numerical value calculating
Grid preferably controls the quality of grid, and since drawing process generates geometrical model and finite element model simultaneously, shortens
The time that threedimensional model is built up.
Embodiment 2:
Cable tunnel signal is as shown in figure 11 in engineering, the entity object structure feature are as follows: include different voltages grade, difference
The power cable of arrangement mode;And air in cable run bracket and tunnel concrete wall, tunnel.Along cable and tunnel
Road extending direction iszAxis, wherein power cable and tunnel wall, air section arezPlane symmetrical structure in axis direction, and
Bracket has one every a distance, is not plane symmetrical structure.By taking cable tunnel as an example, implementation process description is carried out:
(1): establish the power cable section of different voltages grade difference arrangement mode, bracket, tunnel wall, air section two
Dimension module, as shown in figure 12.
(2): two dimensional model being subjected to finite elements division using triangular mesh, as shown in figure 13, generates two-dimensional finite
Meta-model.
(3): edgezThe two-dimensional finite element model of Figure 13 is carried out segmentation stretching by axis positive direction, respectively with back air, branch
The starting point that frame position and front end air position are stretched as segmentation, and axial grid dividing is carried out when stretching.
The specific steps are stretched tunnel back air regions first, and as shown in figure 14, Figure 14 (a) is to be formed by after stretching for the first time
Three-dimensional finite element model;Display is 3-D geometric model after stretching in Figure 14 (b), and entire transparent region is air part.The
Succeeding stretch is to first bracket cross section appearance position, and as shown in figure 15, Figure 15 (a) is to form Three-D limited after stretching for the second time
Meta-model;3-D geometric model after stretching is shown as in Figure 15 (b), wherein green area is different voltages grade cable run,
Transparent region is air and tunnel wall.Third time is stretched to the other side sectional position after first bracket occurs completely, such as
Shown in Figure 16, Figure 16 (a) is to form three-dimensional finite element model after third time stretches;It is shown as three-dimensional several after stretching in Figure 16 (b)
What model, wherein green area is different voltages grade cable run, and blue region is cable bearer, transparent region be air and
Tunnel wall.It is stretched to bracket other side cable run extended end portion position 4th time, as shown in figure 17, Figure 17 (a) is the 4th
Three-dimensional finite element model is formed after secondary stretching;3-D geometric model after stretching is shown as in Figure 17 (b), wherein green area is not
With voltage class cable run, blue region is cable bearer, and transparent region is air and tunnel wall.5th stretched tunnel
Road front end air region, as shown in figure 18, Figure 18 (a) form three-dimensional finite element model after stretching for the 5th time;It is shown in Figure 18 (b)
It is shown as 3-D geometric model after stretching, wherein green area is different voltages grade cable run, and blue region is cable bearer,
Transparent region is air section and tunnel wall in tunnel front and back end and tunnel.According to the above process, sequentially generate back air,
Tunnel wall, each voltage class cable run, bracket, front end air three-dimensional finite element model, entire three-dimensional finite element model
All prismatic meshs.
(4): the setting of material properties is carried out to the grid in each region in newly-generated three-dimensional finite element model, to cable area
Its relative permeability and resistivity for using material is respectively set according to construction of cable feature, to the grid of every part-structure in domain;
To the corresponding relative permeability and resistivity for using material of grid setting of stent area;For tunnel wall and air section
It is 1 that relative permeability, which is arranged, in grid.
By above method by two dimensional model stretch generate threedimensional model, by Figure 18 it can be seen that, when cable tunnel etc. calculates
While region whole geometrical model generates, three-dimensional finite element model also generates simultaneously, and the shape of grid is tri-prism element,
Each zoning is carried out to new model, such as each layer of cable body, bracket, air, tunnel wall, the setting of grid material attribute
Afterwards, it can be directly used in the calculating of electromagnetic finite element numerical value.Conventional method be directly establish 3-D geometric model, then unify into
Row mesh generation can only carry out subdivision, and subdivision due to the asymmetry of model structure in zoning using tetrahedral grid
Process is unable to control the grid density of each region.And the method for the present invention is when two-dimensional finite element model is established, it can be to each region
The control of grid density is carried out, and continues to carry out density control to grid during stretching along axial direction, when generation three-dimensional finite element
After model, grid be also generally believe numerical value calculating in convergence be better than tetrahedral grid prismatic mesh, preferably
The quality of grid is controlled, and since drawing process generates geometrical model and finite element model simultaneously, shortens threedimensional model and builds
At time.
Claims (3)
1. a kind of modeling method of three-dimensional finite element model, it is characterised in that: for plane symmetrical structure feature object
Based on object 3D solid, initially set up two-dimensional model, carry out FEM meshing, then by two dimensional finite element mould
Type carries out segmentation stretching along the symmetrical axial direction of plane, respectively with nonbody object positions other in 3D solid, determines
Segmental stretching starts point, and axial grid dividing is carried out when stretching;After the completion of stretching specified length, 3-D geometric model
It is formed, corresponding three-dimensional finite element model also generates simultaneously, no longer needs to re-start grid dividing to three-dimensional entity model.
2. a kind of modeling method of three-dimensional finite element model, it is characterised in that the following steps are included:
Step 1: for the 3D solid object modeled, to have the master of plane symmetrical structure feature in 3D solid
Body object is reference target, establishes the two-dimensional model of the element containing each section;
Step 2: to two-dimensional model, finite elements division being carried out using triangular mesh, generates two-dimensional finite element model;
Step 3: along the symmetrical axial direction of plane, segmentation stretching being carried out to two-dimensional finite element model, with main body each in 3D solid
Different location determines segmental stretching starts point where object, and axial grid dividing is carried out when stretching;
Step 4: according to the total length of 3D solid, after the completion of stretching, three-dimensional entity model and corresponding three-dimensional finite element model
It has been be formed simultaneously that, finite element model is then made of prismatic mesh, according to the real material attribute of objects different in entity, to not
Finite elements with computational domain carry out material parameter setting.
3. a kind of modeling method of three-dimensional finite element model as described in claims 1 or 2, it is characterised in that: be applied to tool
There is the three-dimensional entity model of object based on plane symmetrical structure feature object.
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