CN108446507A - Elastic body grid deformation method based on grid quality feedback optimization - Google Patents
Elastic body grid deformation method based on grid quality feedback optimization Download PDFInfo
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Abstract
The invention provides an elastic body grid deformation method based on grid quality feedback optimization, which comprises the following steps: step S100: constructing an elastic body grid deformation model containing the elastic modulus E of the grid unit according to the elastic strain generated by the grid unit in the elastic body grid and the stress state sigma of the grid unit after the elastic body grid to be deformed is deformed by an external force; step S200: a grid quality feedback value for the grid cell is established,Qe∈ [0, 1)), the constrained elastic modulus E', E ═ Q is obtainedeE; step S300: and substituting the constraint elastic modulus into the to-be-deformed elastic body grid deformation model to obtain a constraint equation, and solving the constraint equation to obtain a deformed grid node coordinate with grid quality feedback optimization. The definition of the elastic modulus E in the established deformation model of the elastomer mesh to be deformed is improved, so that the robustness of the obtained deformation equation of the elastomer mesh is improved, the elastomer mesh has wide applicability, and the deformation capability and the mesh quality of the mesh during large deformation can be effectively improved.
Description
Technical field
The invention belongs to engineering design fields, relate generally to a kind of elastomer grid change feedback optimized based on mesh quality
Shape method.
Background technology
In increasingly complicated engineering problem emulation, it is often necessary to the Unsteady Flow problem for including moving boundaries is solved,
Especially as the fast development of Fluid Mechanics Computation, grid deforming method has become the crucial skill of support Unsteady Flow emulation
Art.Distortion of the mesh can be based on existing mesh node information and deformation algorithm, be calculated inside grid according to the variation of moving boundary
Warp mesh just can be obtained without changing network topology relationship in the displacement of node.It shakes in engineering design field, such as Free Surface
Dynamic, wing aerodynamic elasticity, fluid structurecoupling, flight vehicle aerodynamic profile optimization design etc., user can utilize mesh deformation technique pair
The calculating grid of research object reuses, and can improve design efficiency and reduce the calculating error that replacement lengths are come.
Currently, studying more grid deforming method, there are two classifications：Physical model method and algebraic approach (also referred to as mathematical interpolation
Method).Wherein physical model method is the grid deforming method based on physical model, and the governing equation established by solving model obtains
Deformed mesh coordinate, preferably still modeling process is complicated for deformation effect, mainly has：Spring analogy method and elastomer method；And
Algebraic approach is to realize distortion of the mesh according to the coordinate information of grid node, and efficiency is higher but stability is bad, mainly has：It is radial
Basis Function Method and Delaunay background grid interpolation methods.To sum up various grid deforming methods, elastomer method treat as distortion of the mesh
Elastic fluid mechanics problem solves, and distortion of the mesh ability, mesh quality and Partial controll will be better than spring analogy method, diameter
To other methods such as Basis Function Method and Delaunay background grid interpolation methods.But in the large deformation problem of moving boundaries, bullet
The robustness of property volumetric mesh deformation method is poor, when especially being applied to the grid cell of near moving boundaries, can often lead
Illegal " negative volume " unit is caused to occur, i.e. the topological structure of grid destroys, and distortion of the mesh is caused to fail too early.This
Outside, although existing elastomer method can proceed to distortion of the mesh largely, Severe distortion can occur for Individual cells, deformation
Mesh quality is poor afterwards, cannot be satisfied the stability requirement of numerical computations.
Invention content
A kind of elastomer grid deforming method feedback optimized based on mesh quality that an aspect of of the present present invention provides, should
Method easily leads to Individual cells Severe distortion when solving existing elastomer grid deforming method poor robustness, large deformation, influences
The technical issues of computational stability.
Referring to Fig. 1, the elastomer grid deforming method feedback optimized based on mesh quality provided by the invention, including it is following
Step：
Step S100：After being deformed by external force according to elastomer grid to be deformed, grid cell generate elastic strain ε and
The stress state σ of grid cell builds the elastomer grid distorted pattern to be deformed of the elastic modulus E containing grid cell；
Elastomer grid herein includes the grid cell of multiple interconnections.The endpoint of each grid cell is known as grid section
Point.
Step S200：Establish the mesh quality value of feedback Q of grid celle,Qe∈ [0,1), wherein L/r is
Baker mesh quality parameters, X are constant, when grid cell is two-dimentional triangleWhen grid cell is three-dimensional four sides
When bodyObtain constraint elastic modulus E ', E'=QeE；
Step S300：Constraint elasticity modulus is substituted into elastomer grid distorted pattern to be deformed and obtains constraint equation, is asked
Constraint equation is solved, mesh point coordinate after the deformation for having mesh quality feedback optimized is obtained, is obtained according to mesh point coordinate
Deformed elastomer grid.
Method provided by the invention is redefined by treating the elastic modulus E in flexible elastomer distortion of the mesh model,
Increase quality feedback value in elastic modulus E, the topological structure to effectively prevent grid occurs to break near moving boundaries
It is bad, improve the robustness of distortion of the mesh.Avoid the generation of mesh distortion.The step of not being described in detail above by existing method i.e.
It can.
Preferably, Q when grid cell quality is preferablee→0；Q when grid cell is second-ratee→1。
Further, step S100 includes the following steps：
Step S110：Parse the coordinate of all grid nodes and opening up for all grid cells in elastomer grid to be deformed
Relationship is flutterred, the displacement vector U (x, y, z) that arbitrary mess node (x, y, z) generates under external force in elastomer grid is defined
=(u, v, w), wherein u, v, w are respectively that grid node (x, y, z) existsThe displacement component in three directions, elastomer
The elastic stress tensor of grid inner mesh unit meets
Step S120：Grid cell meets linear movement law：
Wherein, ε is the strain regime of grid cell.In text ()TIt indicates to turn order.；
Step S130：According to generalized Hooke law, can obtain：
σ=λ Tr (ε) I+2 μ ε (2)
Wherein, λ and μ is the Lame＆1＆ constants for representing elastic mesh material properties,E is
Elasticity modulus and ν are Poisson's ratio, Tr (ε)=εx+εy+εz, σ is the stress state of grid cell, and I indicates unit vector；
Step S140：Elastomer grid distorted pattern is obtained according to formula (1) and (2)：
Wherein,E is elasticity modulus and ν is Poisson's ratio.
Further, the step of solution constraint equation in step S300, includes the following steps：
Step S310：Using elastomer grid to be deformed as finite element grid, establishes finite element equation and solve constraint equation；
Step S320：The boundary condition of elastomer distortion of the mesh is established, boundary condition includes by force boundary condition and displacement
Boundary condition；
Step S330：The linear algebraic equation systems after distortion of the mesh are solved, the change for having mesh quality feedback optimized is obtained
Shape mesh point coordinate.
Further, the method for solving linear algebric equation group is Gauss-Seidel iteration method.
Referring to Fig. 1 specifically, the elastomer grid deforming method feedback optimized based on mesh quality provided by the invention, packet
Include following steps：
Step 1 builds elastomer grid deformation equation to be deformed：
(1) grid to be deformed is imported, the coordinate information of all nodes of grid to be deformed and opening up for all units are parsed
Flutter relationship.
(2) define elastomer in arbitrary mess node (x, y, z) displacement vector U (x, y, z)=(u, v, w), wherein u,
V, w is respectively that grid node (x, y, z) existsThe displacement component in three directions.
According to the basic principle of Elasticity, if applying an external force, all sections inside grid to elastomer grid
Point will produce elastic stress, and then elastic strain occurs, and grid node is caused to be subjected to displacement variation, to which grid system reaches again
To equilibrium state.
(3) under the effect of external force, the elastic stress tensor that elastomer grid generates meets for definition：
Wherein, σ is the stress state of grid cell, σx, σyAnd σzRespectively stress point of the direct stress along cartesian coordinate system
Amount, τxy、τzyAnd τxzThe respectively components of stress of the shear stress along cartesian coordinate system.HereinIndicate divergence.
(4) under the action of elastic stress, the state for the elastic strain ε that elastomer grid generates is expressed as：
Wherein, ε is the strain regime of grid cell, εx, εyAnd εzRespectively normal strain answers variation along cartesian coordinate system
Amount, γxy、γzyAnd γxzRespectively component of the shearing strain along cartesian coordinate system.
Under the action of elastic stress, elastic strain can occur for elastomer grid, to obtain the above-mentioned table about strain stress
It states.
(5) expression formula of displacement vector U and elastic strain ε, grid cell is combined to meet linear movement law：
(6) in distortional elastomer, stress and strain meets generalized Hooke law, has after arrangement：
σ=λ Tr (ε) I+2 μ ε (7)
Wherein, λ and μ is the Lame＆1＆ constants for representing elastic mesh material properties,E is
Elasticity modulus and ν are Poisson's ratio, Tr (ε)=εx+εy+εz, σ is the stress state of grid cell, and I indicates unit vector.
(7) in summary elastomer grid deformable modeling process, can obtain the expression formula of grid node displacement vector U：
Wherein, Lame＆1＆ constants λ and μ can be indicated with elastic modulus E and Poisson's ratio ν.
In elastomer grid deforming method, elastic modulus E and Poisson's ratio ν play key player, they are controlled respectively
The rigidity and grid degree of compressibility of unit, it is similar with the stiffness coefficient K in spring analogy method.Specifically, E is Hooke's law
Middle proportionality constant, E values are bigger, and material stiffness is stronger, and variation degree of the grid cell in deformation process is with regard to smaller, and ν usually takes
Constant in [- 1,0.5].
Step 2, the mesh quality for introducing grid cell are feedback optimized.
(1) first against two-dimentional triangular mesh unit, the expression formula of Baker mesh quality parameters is
Wherein, l1、l2And l3For the length of side of triangular mesh, r is triangle inscribed circle radius, L=(l1+l2+l3)/3, S
For triangle area.From the above equation, we can see thatWhen grid cell quality is preferableGrid cell quality
The value of poorer parameter L/r is bigger.
(2) and then for the three-dimensional tetrahedron element in unstrctured grid, the expression formula of Baker mesh quality parameters is
Wherein, r is the tetrahedron inscribe radius of a ball, and V is tetrahedral volume, and L is all length of side l of tetrahedron elementiIt is flat
Mean value, SiFor tetrahedron arbitrary surfaces area.From the above equation, we can see thatWhen grid cell quality is preferableThe value of the poorer parameter L/r of grid cell quality is bigger.
(3) parameter L/r is normalized, obtains the value of feedback Q of mesh qualitye, expression formula is
Wherein, when grid cell is two-dimentional triangleFor three-dimensional tetrahedron whenFrom the above equation, we can see that Qe
∈ [0,1), the Q when grid cell quality is preferablee→ 0, Q when grid cell is second-ratee→1。
(4) the feedback optimized value Q of mesh quality is finally introduced in elastomer grid distorted patterne, by constraining each net
The elastic modulus E of lattice unit, obtain based on the feedback optimized constraint elastic modulus E of mesh quality ', expression formula is
Comparison improves front and back elastic modulus E and E', by mesh quality value of feedback QeAdjustment, matter can be improved as possible
The elasticity modulus for measuring poor unit makes it avoid continuing to deteriorate when deforming serious, enhances elastomer grid to a certain extent
The robustness of deformation.
Step 3, elastomer grid deformation equation solve.Existing finite element method can also be used.
(1) regard elastomer grid to be deformed as finite element grid, establish finite element equation and solve grid node displacement
Variation equation (i.e. constraint equation, i.e.,Wherein, )。
(2) boundary condition of elastomer distortion of the mesh is established, including by force boundary condition and displacement boundary conditions.
(3) boundary condition is introduced to the finite element equation established, the i.e. finite element equation and perimeter strip of simultaneous distortion of the mesh
Part solves the linear algebraic equation systems i.e. formula (8) of distortion of the mesh, and wherein variable E is substituted into formula (12), obtains updated net
Lattice node coordinate.
It is solved with the method for solving linear algebric equation group, such as Gauss-Seidel iteration method.
Referring to Fig. 2, another aspect of the present invention additionally provides a kind of elastomer grid deformation device based on geometrical constraint,
It is characterised in that it includes：
Strain stress module 100, after being deformed by external force according to elastomer grid to be deformed, inside elastomer grid
The stress state σ for the elastic strain ε and grid cell that grid cell generates, elastic modulus E of the structure containing grid cell wait becoming
Shape elastomer grid distorted pattern；
Feedback module 200, the mesh quality value of feedback Q for establishing grid celle,Qe∈ [0,1),
In, L/r is Baker mesh quality parameters, and X is constant, when grid cell is two-dimentional triangleWhen grid cell is
When three-dimensional tetrahedronObtain constraint elastic modulus E ', E'=QeE；
Module 300 is solved, constraint elasticity modulus is substituted into elastomer grid distorted pattern to be deformed and obtains constraint equation,
Constraint equation is solved, mesh point coordinate after the deformation for having mesh quality feedback optimized is obtained, is obtained according to mesh point coordinate
To deformed elastomer grid.
Further, strain stress module, including：
Topography module, for parsing the coordinate of all grid nodes and all grid cells in elastomer grid to be deformed
Topological relation, define elastomer grid in arbitrary mess node (x, y, z) generate under external force displacement vector U (x,
Y, z)=(u, v, w), wherein u, v, w is respectively that grid node (x, y, z) existsThe displacement component in three directions, bullet
Property volume mesh inner mesh unit elastic stress tensor meet
Linear movement module meets linear movement law for grid cell：
Wherein, ε is the strain regime of grid cell,
εx, εyAnd εzRespectively normal strain is along the component of cartesian coordinate system, γxy、γyzAnd γxzRespectively shearing strain is sat along Descartes
Mark the component of system；
Stress state module, for that according to generalized Hooke law, can obtain：
σ=λ Tr (ε) I+2 μ ε (2)
Wherein, λ and μ is the Lame＆1＆ constants for representing elastic mesh material properties,E is
Elasticity modulus, ν are Poisson's ratio, Tr (ε)=εx+εy+εz, σ is the stress state of grid cell, and I indicates unit vector；
Distorted pattern module, for obtaining elastomer grid distorted pattern according to formula (1) and (2)：
Wherein,E is elasticity modulus and ν is Poisson's ratio.
Further, module is solved, including：
Finite-element module, for using elastomer grid to be deformed as finite element grid, establishing finite element equation solution
Constraint equation；
Boundary condition module, the boundary condition for establishing elastomer distortion of the mesh, boundary condition include stress perimeter strip
Part and displacement boundary conditions；
Algebraic solution module is obtained for solving the deformed linear algebraic equation systems of grid cell with mesh quality
Feedback optimized warp mesh node coordinate.
Further, the method for solving linear algebric equation group is Gauss-Seidel iteration method.
Further, Q when grid cell quality is preferablee→0；Q when grid cell is second-ratee→1。
It has the advantage that compared with the prior art：
The elastomer grid deforming method feedback optimized based on mesh quality provided by the invention, by being waited for what is established
The definition of elastic modulus E in flexible elastomer distortion of the mesh model is improved, and improves gained elastomer distortion of the mesh side
The robustness of journey, makes it have wide applicability, and the deformability and mesh quality of grid when can effectively improve large deformation are
It solves the Unsteady Flow problem comprising moving boundaries and improves stronger support.Both the number of unqualified unit can have been reduced
Amount, can be modified all grid cells the time that unqualified unit can also be delayed to occur.
The elastomer grid deforming method feedback optimized based on mesh quality provided by the invention becomes for elastomer grid
Shape is in the large deformation problem of moving boundaries, 1) grid cell of near moving boundaries is susceptible to illegal " negative volume " unit
The shortcomings that destroying mesh topology；2) the shortcomings that individual grid cells are easy excessive compression or stretching and Severe distortion occur,
The feedback optimized of grid cell mass parameter is introduced, the maximum distortion ability of distortion of the mesh has both been enhanced, has also ensured deformation
Preferable stability in the process, preferably solves the above problem.
The elastomer grid deforming method feedback optimized based on mesh quality provided by the invention, utilizes the matter of grid cell
Amount evaluation parameter (such as Baker mesh qualities parameter) constrains poor grid cell, prevent its during overall deformation to
The direction of distortion continues to deform, to improve this method robustness.
The elastomer grid deforming method feedback optimized based on mesh quality provided by the invention, this method are particularly suitable for
Unstrctured grid (main includes two-dimentional triangular mesh and three-dimensional tetrahedral grid) deformation.Pass through the distortion of the mesh of high robust
Method realizes the reuse purpose for calculating grid, outside Free Surface vibration, wing aerodynamic elasticity, fluid structurecoupling, flight vehicle aerodynamic
The Engineering Simulations such as shape optimization design field has important application value.
Description of the drawings
Fig. 1 is the elastomer grid deforming method flow schematic block feedback optimized based on mesh quality provided by the invention
Figure；
Fig. 2 is the elastomer grid deformation device structural schematic diagram feedback optimized based on mesh quality provided by the invention；
Fig. 3 is that two-dimentional NACA0012 aerofoil profiles initial mesh model handled in preferred embodiment 1 provided by the invention is shown
It is intended to, wherein (a) is the global grid of grid model, it is (b) the moving boundaries surface mesh of grid model；
Fig. 4 is that mesh quality of the preferred embodiment 1 provided by the invention in wide-angle pitching movement becomes with pitch angle
Change curve synoptic diagram, wherein (a) is the change curve of average meshes quality, it is (b) change curve of minimum grid quality；
Fig. 5 is the contrast schematic diagram of the grid at trailing edge in typical pitch angle of preferred embodiment 1 provided by the invention, wherein
(a) it is existing elastomer grid deforming method acquired results in 10 ° of pitch angles；(b) preferred embodiment of the present invention 1 is bowed at 10 °
The acquired results when elevation angle；(c) it is existing elastomer grid deforming method acquired results in 50 ° of pitch angles；(d) present invention is preferred
The acquired results in 50 ° of pitch angles of embodiment 1；(e) existing elastomer grid deforming method acquired results in 90 ° of pitch angles；
(f) acquired results in 90 ° of pitch angles of the preferred embodiment of the present invention 1；
Fig. 6 is that three-dimensional ONERA M6 wing initial mesh models handled in preferred embodiment 2 provided by the invention are shown
It is intended to, wherein (a) is the global grid of grid model, it is (b) the moving boundaries surface mesh of grid model；
Fig. 7 is that mesh quality of the preferred embodiment 2 provided by the invention in wide-angle pitching movement becomes with pitch angle
Change curve synoptic diagram, wherein (a) is the change curve of average meshes quality, it is (b) change curve of minimum grid quality.
Specific implementation mode
Below in conjunction with two specific embodiments, clear, complete description is carried out to technical scheme of the present invention, it is clear that
Described embodiment is only a part of the embodiment of the present invention, instead of all the embodiments.Implementation based on the present invention
Example, other embodiment obtained by those of ordinary skill in the art without making creative efforts belong to this hair
The range of bright protection.
It is two specific embodiments that inventor provides below, the non-structural triangle list of two dimension of general significance is respectively adopted
Member and three-dimension unstructure tetrahedral grid unit.Two embodiments are carried out especially by the following steps：
Step 1 establishes elastomer grid distorted pattern.
(1) grid to be deformed is imported, the topological relation of the coordinate information and all units of all nodes of grid is parsed, this
The initial mesh model of inventive embodiments 1 is as shown in figure 3, the initial mesh model of embodiment 2 is as shown in Figure 6；
(2) displacement vector for defining arbitrary mess node (x, y, z) is U (x, y, z)=(u, v, w), and wherein u, v, w distinguishes
Exist for grid node (x, y, z)The displacement component in three directions.
(3) hypothesis elastomer grid is because the effect of external force deforms, the elastic stress tensor of inner mesh unit
Meet Conservation Relationship, i.e.,
(4) under the action of elastic stress, elastic strain ε occurs for elastomer grid cell；
(5) elastomer grid cell meets linear movement law,
(6) stress and strain of elastomer grid cell meets generalized Hooke law, σ=λ Tr (ε) I+2 μ ε (2)；
(7) distorted pattern of elastomer grid to be deformed is established,
(8) Lame＆1＆ constants λ and μ elastic modulus Es and Poisson's ratio ν are indicated, i.e.,
(9) in this example, elastic modulus E>0, Poisson's ratio ν=0.3.
Step 2, the mesh quality for introducing grid cell are feedback optimized.
(1) it is directed to the non-structural triangular mesh unit of two dimension, establishes Baker mesh quality parameters
(2) it is directed to three-dimension unstructure tetrahedral grid unit, establishes Baker mesh quality parameters
(3) parameter L/r is normalized, obtains the value of feedback Q of mesh qualitye,
(4) the feedback optimized value Q of mesh quality of grid cell is introduced in elastic modulus Ee, by improved springform
Amount isSo far it establishes based on the feedback optimized elastomer grid distorted pattern of mesh quality.
Step 3, elastomer grid deformation equation solve.
(1) the elastomer grid that will be deformed regards finite element grid as, establishes finite element method grid node displacement
The equation of variation.
(2) displacement boundary conditions of elastomer distortion of the mesh are established, translation, rotation and the extensional deformation of moving boundaries are included
Three kinds of forms of motion.
(3) displacement boundary conditions are introduced to the finite element equation established, solving grid using Gauss-Seidel iteration method becomes
The linear algebraic equation systems of shape obtain updated mesh point coordinate, complete elastomer distortion of the mesh.
The application includes three above step：The mesh quality established elastomer grid distorted pattern, introduce grid cell
Feedback optimized and elastomer grid deformation equation solution.In addition, for convenience of comparison introducing mesh quality before and after feedback optimized
Warp mesh robustness additionally establishes mesh quality parameter, passes through comparative illustration introducing mesh quality changing after feedback optimized
Into the technique effect of effect compared with the prior art.
Step 4 establishes mesh quality parameter.
(1) it is directed to the three-dimension unstructure tetrahedral grid unit of the present embodiment, establishes mesh quality parameter as follows
Wherein, λ=V/ ξ, V are tetrahedron element volume, and ξ is that the equilateral triangle built with the cell-average surface area forms
Equilateral tetrahedron volume, liFor the tetrahedral arbitrary length of side, SiFor tetrahedral arbitrary plane area.
From the above equation, we can see that fsize-shape∈ (0,1], the f when grid cell quality is preferablesize-shape→ 1, grid cell matter
F when measuring poorsize-shape→0。
(2) in turn, with the comprehensive parameters f of each unitsize-shapeBased on, from the average level and minimum of mesh quality
Two levels of extreme value, establish average meshes quality fmeanWith minimum grid quality fmin, expression formula is
Wherein, Ne is grid cell number.
Step 5, comparison introduce the feedback optimized front and back warp mesh robustness of mesh quality.
(1) the mesh quality parameter established by step 4 is it is found that fmeanAnd fminNumerical value it is bigger, the robustness of grid is got over
By force, it can be used for quantifying the robustness of comparation and assessment warp mesh.
(2) existing elastomer grid deforming method is known as classical way, the present invention is carried to simplify statement herein
The elastomer grid deforming method feedback optimized based on mesh quality supplied is known as improved method.
(3) it is directed to classical way and improved method, embodiment 1 is respectively completed and is transported in wide-angle pitching by initial mesh model
Distortion of the mesh under dynamic, the robustness based on mesh quality parameter comparison warp mesh.
Fig. 4 is in the embodiment of the present invention 1, and 1/4 string point of the grid model by original state around NACA0012 aerofoil profiles makees pitching
Movement, maximum pitch angle are αmax=90 °, mesh quality with rotation angle α result of variations, wherein (a) be average meshes
Quality (b) is minimum grid quality.Under the basic average meshes quality and minimum grid quality that can be seen that improved method
Reduction of speed rate is less than classical way, especially with obvious effects to minimum grid quality improvement.The average meshes quality of ordinate in figure
fmeanAnd minimum grid quality fminIt is obtained by formula (8).
Fig. 5 is in the embodiment of the present invention 1, and grid model is in 10 °, 50 ° and 90 ° of typical pitch angle, NACA0012 aerofoil profiles
Grid profiles versus at trailing edge as a result, wherein (a) be existing elastomer grid deforming method in 10 ° of pitch angles obtained by tie
Fruit；(b) acquired results in 10 ° of pitch angles of the preferred embodiment of the present invention 1；(c) be existing elastomer grid deforming method at 50 °
Acquired results when pitch angle；(d) acquired results in 50 ° of pitch angles of the preferred embodiment of the present invention 1；(e) existing elastomer grid
Deformation method acquired results in 90 ° of pitch angles；(f) acquired results in 90 ° of pitch angles of the preferred embodiment of the present invention 1.Substantially
As can be seen that with the gradual increase of aerofoil profile pitch angle, the grid cell of classical way is sent out because of the stretching of moving boundaries
Distortion of the mesh amount at raw deformation, especially aerofoil profile trailing edge is maximum, but the distortion of the mesh of improved method is not obvious.
Fig. 7 is in the embodiment of the present invention 2, and 1/4 string point of the grid model by original state around ONERA M6 Airfoil Sections is made
Pitching movement, maximum pitch angle are αmax=40 °, mesh quality with rotation angle α result of variations, wherein (a) is average
Mesh quality (b) is minimum grid quality.The average meshes quality f of ordinate in figuremeanAnd minimum grid quality fmin
It is obtained by formula (8).
The fall off rate of the basic average meshes quality that can be seen that improved method and minimum grid quality is less than classics side
Method, it is especially with obvious effects to minimum grid quality improvement.It illustrates, in 39 ° of pitch angle, the deformation net of classical way
" negative volume " unit, which have occurred, in lattice causes deformation to fail, but the mesh topology of improved method is still complete.
Those skilled in the art will be clear that the scope of the present invention is not limited to example discussed above, it is possible to be carried out to it
Several changes and modification, the scope of the present invention limited without departing from the appended claims.Although oneself is through in attached drawing and explanation
The present invention is illustrated and described in book in detail, but such illustrate and describe only is explanation or schematical, and not restrictive.
The present invention is not limited to the disclosed embodiments.
By to attached drawing, the research of specification and claims, those skilled in the art can be in carrying out the present invention
Understand and realize the deformation of the disclosed embodiments.In detail in the claims, term " comprising " is not excluded for other steps or element,
And indefinite article "one" or "an" be not excluded for it is multiple.The certain measures quoted in mutually different dependent claims
The fact does not mean that the combination of these measures cannot be advantageously used.Any reference marker in claims is not constituted pair
The limitation of the scope of the present invention.
Claims (10)
1. a kind of elastomer grid deforming method feedback optimized based on mesh quality, which is characterized in that include the following steps：
Step S100：After being deformed by external force according to elastomer grid to be deformed, the elastomer grid inner mesh unit production
The stress state σ of raw elastic strain ε and grid cell builds the elastomer net to be deformed of the elastic modulus E containing grid cell
Lattice distorted pattern；
Step S200：Establish the mesh quality value of feedback Q of the grid celle,Qe∈ [0,1), wherein L/r is
Baker mesh quality parameters, X are constant, when grid cell is two-dimentional triangleWhen grid cell is three-dimensional four sides
When bodyObtain constraint elastic modulus E ', E'=QeE；
Step S300：The constraint elasticity modulus is substituted into the elastomer grid distorted pattern to be deformed and obtains constraint side
Journey solves the constraint equation, mesh point coordinate after the deformation for having mesh quality feedback optimized is obtained, according to grid node
Coordinate obtains deformed elastomer grid.
2. the elastomer grid deforming method feedback optimized based on mesh quality according to claim 1, which is characterized in that
The step S100 includes the following steps：
Step S110：Parse the coordinate of all grid nodes and opening up for all grid cells in the elastomer grid to be deformed
Flutter relationship, define arbitrary mess node (x, y, z) generates under external force in the elastomer grid displacement vector U (x,
Y, z)=(u, v, w), wherein u, v, w is respectively that grid node (x, y, z) existsThe displacement component in three directions, institute
The elastic stress tensor for stating elastomer grid inner mesh unit meets
Step S120：The grid cell meets linear movement law：
Wherein, ε is the strain regime of grid cell,
εx, εyAnd εzRespectively component of the normal strain along cartesian coordinate system；
Step S130：According to generalized Hooke law, can obtain：
σ=λ Tr (ε) I+2 μ ε (2)
Wherein, λ and μ is the Lame＆1＆ constants for representing elastic mesh material properties,E is elasticity
Modulus, ν are Poisson's ratio, Tr (ε)=εx+εy+εz, σ is the stress state of grid cell, and I indicates unit vector；
Step S140：Elastomer grid distorted pattern is obtained according to formula (1) and (2)：
Wherein,E is elasticity modulus and ν is Poisson's ratio.
3. the elastomer grid deforming method feedback optimized based on mesh quality according to claim 1, which is characterized in that
The step of constraint equation is solved in the step S300, includes the following steps：
Step S310：Using the elastomer grid to be deformed as finite element grid, establishes finite element equation and solve constraint side
Journey；
Step S320：The boundary condition of the elastomer distortion of the mesh is established, boundary condition includes by force boundary condition and displacement
Boundary condition；
Step S330：The deformed linear algebraic equation systems of the grid cell are solved, are obtained feedback optimized with mesh quality
Warp mesh node coordinate.
4. the elastomer grid deforming method feedback optimized based on mesh quality according to claim 3, which is characterized in that
The method of the solving linear algebric equation group is Gauss-Seidel iteration method.
5. the elastomer grid deforming method feedback optimized based on mesh quality according to claim 1, which is characterized in that
Q when the grid cell quality is preferablee→0；The Q when grid cell is second-ratee→1。
6. a kind of elastomer grid deformation device feedback optimized based on mesh quality, which is characterized in that including：
Strain stress module, after being deformed by external force according to elastomer grid to be deformed, the elastomer grid intranet
The stress state σ for the elastic strain ε and grid cell that lattice unit generates builds the to be deformed of the elastic modulus E containing grid cell
Elastomer grid distorted pattern；
Feedback module, the mesh quality value of feedback Q for establishing the grid celle,Qe∈ [0,1), wherein
L/r is Baker mesh quality parameters, and X is constant, when grid cell is two-dimentional triangleWhen grid cell is three
When tieing up tetrahedronObtain constraint elastic modulus E ', E'=QeE。
Module is solved, the constraint elasticity modulus is substituted into the elastomer grid distorted pattern to be deformed and obtains constraint side
Journey solves the constraint equation, mesh point coordinate after the deformation for having mesh quality feedback optimized is obtained, according to grid node
Coordinate obtains deformed elastomer grid.
7. the elastomer grid deformation device feedback optimized based on mesh quality according to claim 6, which is characterized in that
The strain stress module, including：
Topography module, for parsing the coordinate of all grid nodes and all grid cells in the elastomer grid to be deformed
Topological relation, define the displacement vector U that arbitrary mess node (x, y, z) generates under external force in the elastomer grid
(x, y, z)=(u, v, w), wherein u, v, w are respectively that grid node (x, y, z) existsThe displacement component in three directions,
The elastic stress tensor of the elastomer grid inner mesh unit meets
Linear movement module meets linear movement law for the grid cell：
Wherein, ε is the strain regime of grid cell,
εx, εyAnd εzRespectively component of the normal strain along cartesian coordinate system；
Stress state module, for that according to generalized Hooke law, can obtain：
σ=λ Tr (ε) I+2 μ ε (2)
Wherein, λ and μ is the Lame＆1＆ constants for representing elastic mesh material properties,E is elasticity
Modulus, ν are Poisson's ratio, Tr (ε)=εx+εy+εz, σ is the stress state of grid cell；
Distorted pattern module, for obtaining elastomer grid distorted pattern according to formula (1) and (2)：
Wherein,E is elasticity modulus and ν is Poisson's ratio.
8. the elastomer grid deformation device feedback optimized based on mesh quality according to claim 6, which is characterized in that
The solution module, including：
Finite-element module, for using the elastomer grid to be deformed as finite element grid, establishing finite element equation solution
Constraint equation；
Boundary condition module, the boundary condition for establishing the elastomer distortion of the mesh, boundary condition include stress perimeter strip
Part and displacement boundary conditions；
Algebraic solution module is obtained for solving the deformed linear algebraic equation systems of the grid cell with mesh quality
Feedback optimized warp mesh node coordinate.
9. the elastomer grid deformation device feedback optimized based on mesh quality according to claim 6, which is characterized in that
The method of the solving linear algebric equation group is Gauss-Seidel iteration method.
10. the elastomer grid deformation device feedback optimized based on mesh quality according to claim 6, feature exist
In Q when the grid cell quality is preferablee→0；The Q when grid cell is second-ratee→1。
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| CN114996858A (en) * | 2022-07-14 | 2022-09-02 | 中国空气动力研究与发展中心计算空气动力研究所 | Aircraft simulation method and device, terminal equipment and storage medium |
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