CN105426592B - A kind of Electrostatic deformation film reflector surface antenna analysis method - Google Patents
A kind of Electrostatic deformation film reflector surface antenna analysis method Download PDFInfo
- Publication number
- CN105426592B CN105426592B CN201510752953.8A CN201510752953A CN105426592B CN 105426592 B CN105426592 B CN 105426592B CN 201510752953 A CN201510752953 A CN 201510752953A CN 105426592 B CN105426592 B CN 105426592B
- Authority
- CN
- China
- Prior art keywords
- film
- ith
- displacement
- increment
- matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Aerials With Secondary Devices (AREA)
Abstract
The invention belongs to Radar Antenna System fields, specifically provide a kind of Electrostatic deformation film reflector surface antenna analysis method.Film reflector face finite element model is initially set up, the function that electrostatic force is expressed as to Displacement of elemental node is applied in model, and then exponential type step increment method mode carries out model solution and obtains film reflector facial disfigurement.Result is accurate compared with prior art for the film reflector facial disfigurement obtained using the present invention, computational efficiency higher.
Description
Technical field
The invention belongs to Radar Antenna System fields, are related to a kind of Electrostatic deformation that consideration deformation of thin membrane influences electrostatic force
Film reflector surface antenna rapid analysis method.Specifically a kind of Electrostatic deformation film reflector surface antenna analysis method, for accurate
Quick deformation of the analysed film under electrostatic force, wherein solving the exponential type step increment method mode that Nonlinear System of Equations uses
With generality.
Background technology
The operation principle of Electrostatic deformation film reflector surface antenna (ECDMA) is in the film reflector face and control for being coated with metal layer
Apply different voltage (general film be equivalent zero gesture face, electrode is high potential) on electrode processed, generate electrostatic force to film into
Row stretch, to make film formed have a fixed-focus diameter than reflecting surface.Since electrode voltage can be carried out in real time by power supply
Adjustment, and then can realize that the timely compensation to reflecting surface shape surface error, ECDMA just have been a concern from scheme proposition.It is beautiful
The Electrostatic deformation film reflector surface antenna development that state NASA began to bore 4.88m early in 1979, until SRS in 2004
Technologies companies cooperate with Northrop Grumman, just have developed Electrostatic deformation film reflector truly
Face deployable antenna 5m bore model machines.
For the precision for ensureing under electrostatic film Antenna Operation state, it is necessary to accurately calculate electrostatic force suffered by film.For
Electrostatic force computational problem suffered by film involved in ECDMA, foreign literature generally assume that deformation of thin membrane amount counter film interpolar away from being
One a small amount of, to directly be acquired using capacity plate antenna formula.However, due to Film stiffness very little, load effect is lower generally
Large deformation, thus deformation of thin membrane can change film interpolar away from, it is necessary to capacity plate antenna formula is improved.The finite elements such as Ansys are soft
Part has the ability of two couplings of analysis, can solve electrostatic force computational problem suffered by film, however since modeling is complicated, finally
The error of model foundation there is no method to accurately control.
Invention content
The purpose of the present invention is being directed to the problem of deformation of thin membrane present in electrostatic film speculum influences electrostatic force, carry
A kind of Electrostatic deformation film reflector surface antenna rapid analysis method that consideration deformation of thin membrane influences electrostatic force is supplied；With finite element
It is programmed using Matlab based on method and deformation analysis is carried out to film, consider that membrane structure geometrical non-linearity is asked in analytic process
It inscribes, while electrostatic force being expressed as to the function of Displacement of elemental node, carry out using exponential type load mode when Incremental SAT, realize
Consider that deformation of thin membrane quickly analyzes the Electrostatic deformation film reflector surface antenna that electrostatic force influences.
To achieve the above object, the present invention provides a kind of Electrostatic deformation film reflector surface antenna analysis method, technologies
Scheme is：A kind of Electrostatic deformation film reflector surface antenna analysis method, includes the following steps：
Step 101：According to the bore D of electrostatic film reflecting surfaceaFilm reflector face finite element model is established with focal length f, is used
Plane triangle film unit carries out mesh generation to film reflector face, amounts to N number of film unit, M node；
Step 102：Input the power convergence criterion that each step equilibrium iteration needs when film reflector face finite element model solves
With increment total number J=ab, wherein a and b are exponential type incremental step controlling elements, give each film unit prestressing force σ0=
[σx0 σy0 σxy0]T, wherein σx0、σy0And σxy0The respectively prestress value in the directions film unit x, the directions y and the directions xy, electrode
Voltage value is U, and initial displacement vector is δ, and δ is zero column vector of 3 × M rows；
Step 103：Enable i=0, j=ai, wherein i is incremental computations number, and j is increment, starts step 104 to step 107
Ith incremental computations；
Step 104：Film unit number is indicated with e, is analyzed N number of film unit successively, is calculated ith incremental computations and open
Global stiffness matrix K when the beginningi, equivalent force vector FiWith load vectors Ri；
Step 105：Utilize the Nonlinear System of Equations K of full Newton-Raphson solutions by iterative method ith incremental computationsiΔ
δi=Ri-Fi, wherein Δ δiThe displacement value gone out for ith incremental computations；
Step 106：Enable δ=δ+Δ δi, i.e., displacement superposed obtain total shift value by what ith incremental computations obtained；
Step 107：Judge whether to complete the calculating of all increments：If j≤J, i=i+1, j=a are enabledi, go to step 104；
If j ＞ J, terminate incremental computations, go to step 108；
Step 108：According to result of calculation output node motion vector δ and element stress vector σ；
Step 109；Judge whether deformed film reflector face precision meets the requirements, precision is unsatisfactory for requiring then to change thin
Film prestressing force or initial voltage value re-start analysis；Precision is met the requirements, and terminates the analysis of electrostatic film reflector antenna.
Above-mentioned steps 104 include the following steps：
Step 201：It is the number number of film unit to enable e=1, e, starts e-th of film unit analysis, and step is shown in concrete analysis
Rapid 202- steps 210；
Step 202：Read in e-th of unit information, including global coordinate system lower film cell node position coordinates a={ x1 y1
z1 x2 y2 z2 x3 y3 z3}T, the displacement increment Δ a={ u of node1 v1 w1 u2 v2 w2 u3 v3 w3}T；
Step 203：It according to cell node position coordinates, converts it under local coordinate system, calculates ith increment e
The stiffness matrix of a film unit wherein A is the area of film unit, and t is film thickness,For film unit elastic matrix, wherein E is thin flexible film modulus, and μ is Poisson's ratio, BLFor line
Property the strain and relational matrix of displacement, be matrix BLTransposed matrix, T be matrix transposition symbol；M is element stress square
Battle array, G are node coordinate function, GTFor the transposed matrix of matrix G；
Step 204：By cell matrixIt is transformed into global coordinate system, and is assembled into ith incremental computations global stiffness square
Battle array KiIn；
Step 205：Calculate the equivalent force vector of e-th of film unit of ith incrementWherein=DBLΔa+
σ0For element stress matrix；
Step 206：By the equivalent force vector of unitIt is transformed into global coordinate system, is assembled into ith increment totality equivalent force
Vectorial FiIn；
Step 207：Calculate e-th of film unit load vector of ith increment under film unit global coordinate systemWherein Ax、AyAnd AzRespectively film unit face
Projection of the product in global coordinate system on the face YOZ, XOZ and XOY, qx、qyAnd qzRespectively film unit area power is in X, Y and Z axis
Projection on direction indicates face electrostatic force suffered by ith e-th of film unit of increment, and expression is wherein is load increment controlling elements, and ε is permittivity of vacuum, and U is electrode voltage value, and d is thin
The initial spacing of film unit and electrode, ω are Displacement of elemental node function, and expression is wherein
δl、δm、δnDisplacement for film unit node relative to electrode normal direction；
Step 208：By e-th of film unit load vector of ith incrementIt is assembled into overall load vector RiIn；
Step 209：Judge whether to complete the analysis of all film units：If e≤N enables e=e+1, step 202 is gone to；If
E ＞ N, then the calculating of end unit matrix, goes to step 210；
Step 210：Complete the global stiffness matrix K of ith incrementi, equivalent force vector FiWith total load head vector RiIt calculates.
Above-mentioned steps 105, include the following steps：
Step 301：It is equilibrium iteration number to enable k=1, k, and the equilibrium iteration for starting Nonlinear System of Equations solves, specific to change
Generation, which calculates, sees step 302- steps 310；
Step 302：Enable Ki,k=Ki, Ki,kFor the Bulk stiffness matrix of ith incremental computations kth time equilibrium iteration, solve
System of linear equations Ki,kΔδi,k=Ri, Δ δi,kFor ith incremental computations kth time equilibrium iteration modal displacement；
Step 303：Acquire ith incremental computations kth time equilibrium iteration modal displacement Δ δi,k；
Step 304：Node coordinate is updated by the modal displacement acquired；
Step 305：According to step 104, the Bulk stiffness matrix of ith incremental computations+1 equilibrium iteration of kth is calculated
Ki,k+1With equivalent force vector Fi,k+1；
Step 306：Solve system of linear equations Ki,k+1Δδi,k+1=Ri-Fi,k+1, Δ δi,k+1For ith incremental computations kth+1
The modal displacement of secondary equilibrium iteration；
Step 307：Acquire the displacement δ of ith increment+1 equilibrium iteration of kthi,k+1；
Step 308：JudgeWhether the convergence criterion of power is met,For power in practical calculate
Relative error magnitudes：IfThen result meets the convergence criterion of power, terminates equilibrium iteration, arrives step 309；It is no
Then, k=k+1 is enabled, step 303 is gone to；
Step 309：Will be displacement superposed during equilibrium iteration, ith increment total displacement is obtained, even δi=Δ δi,1+
Δδi,2...+Δδi,k+1；
Step 310：Complete the solution of ith increment.
Beneficial effects of the present invention：Compared with prior art, the present invention considers that electrostatic force is the letter of film modal displacement
Number analyzes influence of the deformation of thin membrane to electrostatic force in the calculating of Electrostatic deformation film reflector surface antenna model, improves model
The accuracy of calculating.Simultaneously because the present invention acquires electrostatic force in the form of function, avoid complex model establishes process,
Computational accuracy and efficiency can be improved.
The present invention is described in further details below with reference to attached drawing.
Description of the drawings
Fig. 1 Electrostatic deformation film reflector surface antennas analyze overview flow chart；
The step flow chart of Fig. 2 steps 104；
The flow chart of Fig. 3 steps 105；
The finite element model that Fig. 4 is established according to reflecting surface structure parameter.
Specific implementation mode
A kind of Electrostatic deformation film reflector surface antenna analysis method as shown in Figure 1, it is characterized in that：Including at least following step
Suddenly：
Step 101：According to the bore D of electrostatic film reflecting surfaceaFilm reflector face finite element model is established with focal length f, is used
Plane triangle film unit carries out mesh generation to film reflector face, amounts to N number of film unit, M node；
Step 102：Input the power condition of convergence that each step equilibrium iteration needs when film reflector face finite element model solves
With increment total score step number mesh J=ab, wherein a and b are exponential type incremental step controlling elements, give each film unit prestressing force
σ0=[σx0 σy0 σxy0]T, wherein σx0、σy0And σxy0The respectively prestress value in the directions film unit x, the directions y and the directions xy,
Electrode voltage value U and initial displacement vector δ, δ are zero column vector of 3 × M rows；
Step 103：Enable i=0, j=ai, wherein i is incremental computations number, and j is increment, starts ith incremental computations packet
Include the calculating of step 104- steps 107；
Step 104：Film unit number number is indicated with e, analyzes N number of film unit successively, calculates ith incremental computations
Global stiffness matrix K when beginningi, equivalent force vector FiWith load vectors Ri, specific calculating process is shown in step 201- steps 210；
Step 105：Utilize the Nonlinear System of Equations K of full Newton-Raphson solutions by iterative method ith incrementiΔδi=
Ri-Fi, wherein Δ δiFor the displacement value that ith incremental computations go out, equilibrium iteration number is indicated with k during iterative solution,
Specific calculate sees step 301- steps 310；
Step 106：Enable δ=δ+Δ δi, i.e., displacement superposed obtain total shift value by what ith incremental computations obtained；
Step 107：Judge whether to complete the calculating of all increments：If j≤J, i=i+1, j=a are enabledi, go to step 104；
If j ＞ J, terminate incremental computations, go to step 108；
Step 108：According to result of calculation output node motion vector δ and element stress vector σ；
Step 109：Judge whether deformed film reflector face precision meets the requirements, precision is unsatisfactory for requiring then to change thin
Film prestressing force or initial voltage value re-start analysis；Precision is met the requirements, and terminates the analysis of electrostatic film reflector antenna.
As shown in Fig. 2, the step 104, and in particular to following steps：
Step 201：It is the number number of film unit to enable e=1, e, starts e-th of film unit analysis, and step is shown in concrete analysis
202- steps 210；
Step 202：Read in e-th of unit information, including global coordinate system lower film cell node position coordinates a={ x1 y1
z1 x2 y2 z2 x3 y3 z3}T, the displacement increment Δ a={ u of node1 v1 w1 u2 v2 w2 u3 v3 w3}T；
Step 203：It according to cell node position coordinates, converts it under local coordinate system, calculates ith increment e
The stiffness matrix of a film unit wherein A is the area of film unit, and t is film thickness,For film unit elastic matrix, wherein E is thin flexible film modulus, and μ is Poisson's ratio, BLIt is linear
The relational matrix of strain and displacement is matrix BLTransposed matrix, M be element stress matrix, G be node coordinate function, be
With the relevant matrix of cell node coordinate, GTFor the transposed matrix of matrix G；
Step 204：By cell matrixIt is transformed into global coordinate system, and is assembled into ith increment global stiffness matrix Ki
In；
Step 205：Calculate the equivalent force vector of e-th of film unit of ith incrementWherein σ=DBLΔa+σ0
For element stress matrix；
Step 206：By the equivalent force vector of unitIt is transformed into global coordinate system, is assembled into ith increment totality equivalent force
Vectorial FiIn；
Step 207：Calculate e-th of film unit load vector of ith increment under film unit global coordinate systemWherein Ax、AyAnd AzRespectively film unit face
Projection of the product in global coordinate system on the face YOZ, XOZ and XOY, qx、qyAnd qzRespectively film unit area power is in X, Y and Z axis
Projection on direction indicates face electrostatic force suffered by ith e-th of film unit of increment, and expression is wherein is load increment controlling elements, and ε is permittivity of vacuum, and U is electrode voltage value, and d is thin
The initial spacing of film unit and electrode, ω are Displacement of elemental node function, and expression is wherein
δl、δm、δnDisplacement for film unit node relative to electrode normal direction；
Step 208：By e-th of film unit load vector of ith incrementIt is assembled into overall load vector RiIn；
Step 209：Judge whether to complete the analysis of all film units：If e≤N enables e=e+1, step 202 is gone to；If
E ＞ N, then the calculating of end unit matrix, goes to step 210；
Step 210：Complete the global stiffness matrix K of ith incrementi, equivalent force vector FiWith total load head vector RiIt calculates.
As shown in figure 3, the step 105, and in particular to following steps：
Step 301：It is equilibrium iteration number to enable k=1, k, and the equilibrium iteration for starting Nonlinear System of Equations solves, specific to change
Generation, which calculates, sees step 302- steps 310；
Step 302：Enable Ki,k=Ki, Ki,kFor the Bulk stiffness matrix of ith incremental computations kth time equilibrium iteration, solve
System of linear equations Ki,kΔδi,k=Ri, Δ δi,kFor ith incremental computations kth time equilibrium iteration modal displacement；
Step 303：Acquire ith incremental computations kth time equilibrium iteration modal displacement Δ δi,k；
Step 304：Node coordinate is updated by the modal displacement acquired；
Step 305：According to step 104, the Bulk stiffness matrix of ith incremental computations+1 equilibrium iteration of kth is calculated
Ki,k+1With equivalent force vector Fi,k+1；
Step 306：Solve system of linear equations Ki,k+1Δδi,k+1=Ri-Fi,k+1, Δ δi,k+1For ith incremental computations kth+1
The modal displacement of secondary equilibrium iteration；
Step 307：Acquire the displacement δ of ith increment+1 equilibrium iteration of kthi,k+1；
Step 308：JudgeWhether the convergence criterion of power is met,For power in practical calculate
Relative error magnitudes：IfThen result meets the convergence criterion of power, terminates equilibrium iteration, arrives step 309；It is no
Then, k=k+1 is enabled, step 303 is gone to；
Step 309：Will be displacement superposed during equilibrium iteration, ith increment total displacement is obtained, even Δ δi=Δ
δi,1+Δδi,2...+Δδi,k+1；
Step 310：Complete the solution of ith increment.
Advantages of the present invention can be further illustrated by following emulation experiment：
Simulated conditions：
Electrostatic deformation film reflector plane materiel material uses isotropism Kapton, thin-film material parameter：Thickness t=25
μm, elastic modulus E=2.17GPa, Poisson's ratio μ=3.14, thermalexpansioncoefficientα=29 × 10-6/℃；Reflecting surface structure parameter：Mouthful
Diameter Da=2m, focal length f → ∞；Calculate relevant parameter：Power convergence criterion β=0.001, incremental step controlling elements a=2, b=
13, permittivity of vacuum ε=8.85 × 10-12F/m, electrode voltage U=2000V, film and the initial spacing d=20mm of electrode.Root
According to finite element model such as Fig. 4 that reflecting surface structure parameter is established, N=600 film unit, M=331 node, reflection are shared
Face periphery is fixed, and the structural initial pre stress of T=-0.01 DEG C of Δ, i.e. σ are given in film0=[σx0 σy0 σxy0]T=[Et α Δ T Et α
ΔT 0]T.In order to embody the accuracy and efficiency of this method, divide herein with electrostatic mechanical coupling modular program in ansys softwares
Analysis is compared.Result of calculation is extracted to be carried out along 11 radial representational modal displacements of the same busbar in film reflector face
Compare, and counted two methods under the same conditions and calculated example required time, as a result such as table 1.
1 comparison of computational results of table
Unit/mm
It falls into a trap in the 64 bit manipulation systems of processor Intel Core i3-3240 CPU@3.40GHz, memory 8G and counts in stating
Example under identical power convergence criterion, utilizes the Electrostatic deformation film reflector surface antenna analysis method in the present invention to calculate the time
Reduce 46.4s, computational efficiency significantly improves under the premise of ensureing precision.The reason is that ansys electrostatic mechanical coupling modules point
Analysis needs to carry out calculating separately for displacement structure field and electrostatic field, and analyzes electrostatic field and need to divide more electric field unit；
The present invention then omits the calculating of complicated finite element modeling process and electrostatic field substantially.
To sum up, the present invention considers that electrostatic force is the function of film modal displacement, in Electrostatic deformation film reflector surface antenna
Model analyzes influence of the deformation of thin membrane to electrostatic force in calculating, and improves the accuracy of model calculating.Simultaneously because of the invention
Electrostatic force is acquired in the form of function, avoid complex model establishes process, can improve computational accuracy and efficiency.
There is no the part described in detail to belong to the well known conventional means of the industry in present embodiment, does not chat one by one here
It states.The foregoing examples are only illustrative of the present invention, does not constitute the limitation to protection scope of the present invention, every and sheet
Invent it is same or analogous design all belong to the scope of protection of the present invention within.
Claims (2)
1. a kind of Electrostatic deformation film reflector surface antenna analysis method, it is characterised in that：Include the following steps：
Step 101：According to the bore D of electrostatic film reflecting surfaceaFilm reflector face finite element model is established with focal length f, with plane three
Angular film unit carries out mesh generation to film reflector face, amounts to N number of film unit, M node；
Step 102：Input the power convergence criterion β and increasing that each step equilibrium iteration needs when film reflector face finite element model solves
Measure total number J=ab, wherein a and b are exponential type incremental step controlling elements, give each film unit prestressing force σ0=[σx0
σy0σxy0]T, wherein σx0、σy0And σxy0The respectively prestress value in the directions film unit x, the directions y and the directions xy, electrode voltage value
For U, initial displacement vector is δ, and δ is zero column vector of 3 × M rows；
Step 103：Enable i=0, j=ai, wherein i is incremental computations number, and j is increment, starts step 104 to the i-th of step 107
Secondary incremental computations；
Step 104：Film unit number is indicated with e, analyzes N number of film unit successively, when calculating ith incremental computations and starting
Global stiffness matrix Ki, equivalent force vector FiWith load vectors Ri；
Step 105：Utilize the Nonlinear System of Equations K of full Newton-Raphson solutions by iterative method ith incremental computationsiΔδi=
Ri-Fi, wherein Δ δiThe displacement value gone out for ith incremental computations；
Step 106：Enable δ=δ+Δ δi, i.e., displacement superposed obtain total shift value by what ith incremental computations obtained；
Step 107：Judge whether to complete the calculating of all increments：If j≤J, i=i+1, j=a are enabledi, go to step 104；If j ＞
J then terminates incremental computations, goes to step 108；
Step 108：According to result of calculation output node motion vector δ and element stress vector σ；
Step 109；Judge whether deformed film reflector face precision meets the requirements, precision is unsatisfactory for requiring that then to change film pre-
Stress or initial voltage value re-start analysis；Precision is met the requirements, and terminates the analysis of electrostatic film reflector antenna；
Wherein step 104 includes the following steps：
Step 201：It is the number number of film unit to enable e=1, e, starts e-th of film unit analysis, and step is shown in concrete analysis
202- steps 210；
Step 202：Read in e-th of unit information, including global coordinate system lower film cell node position coordinates c=
{x1y1z1x2y2z2x3y3z3}T, the displacement increment Δ c={ u of node1v1w1u2v2w2u3v3w3}T；
Step 203：It according to cell node position coordinates, converts it under local coordinate system, calculates ith e-th of film of increment
The stiffness matrix of unitWherein A is the area of film unit, and t is film thickness,For film unit elastic matrix, wherein E is thin flexible film modulus, and μ is Poisson's ratio, BLFor line
Property the strain and relational matrix of displacement,For matrix BLTransposed matrix, T be matrix transposition symbol；M is element stress square
Battle array, G are node coordinate function, GTFor the transposed matrix of matrix G；
Step 204：By cell matrixIt is transformed into global coordinate system, and is assembled into ith incremental computations global stiffness matrix Ki
In；
Step 205：Calculate the equivalent force vector of e-th of film unit of ith incrementWherein σ=DBLΔa+σ0For
Element stress matrix；
Step 206：By the equivalent force vector of unitIt is transformed into global coordinate system, is assembled into ith increment totally equivalent force vector
FiIn；
Step 207：Calculate e-th of film unit load vector of ith increment under film unit global coordinate systemWherein Ax、AyAnd AzRespectively film unit face
Projection of the product in global coordinate system on the face YOZ, XOZ and XOY, qx、qyAnd qzRespectively film unit area power is in X, Y and Z axis
Projection on direction,Indicate that face electrostatic force suffered by ith e-th of film unit of increment, expression areWhereinFor load increment controlling elements, ε is permittivity of vacuum, and U is electrode voltage value, and d is film
The initial spacing of unit and electrode, ω are Displacement of elemental node function, and expression isWherein δl、
δm、δnDisplacement for film unit node relative to electrode normal direction；
Step 208：By e-th of film unit load vector of ith incrementIt is assembled into overall load vector RiIn；
Step 209：Judge whether to complete the analysis of all film units：If e≤N enables e=e+1, step 202 is gone to；If e ＞
N, then the calculating of end unit matrix, goes to step 210；
Step 210：Complete the global stiffness matrix K of ith incrementi, equivalent force vector FiWith total load head vector RiIt calculates.
2. a kind of Electrostatic deformation film reflector surface antenna analysis method according to claim 1, it is characterised in that：Wherein step
105 include the following steps：
Step 301：It is equilibrium iteration number to enable k=1, k, and the equilibrium iteration for starting Nonlinear System of Equations solves, specific iteration meter
Step 302- steps 310 are shown in calculation；
Step 302：Enable Ki,k=Ki, Ki,kFor the Bulk stiffness matrix of ith incremental computations kth time equilibrium iteration, linear side is solved
Journey group Ki,kΔδi,k=Ri, Δ δi,kFor ith incremental computations kth time equilibrium iteration modal displacement；
Step 303：Acquire ith incremental computations kth time equilibrium iteration modal displacement Δ δi,k；
Step 304：Node coordinate is updated by the modal displacement acquired；
Step 305：According to step 104, the Bulk stiffness matrix K of ith incremental computations+1 equilibrium iteration of kth is calculatedi,k+1With
Equivalent force vector Fi,k+1；
Step 306：Solve system of linear equations Ki,k+1Δδi,k+1=Ri-Fi,k+1, Δ δi,k+1It is flat for ith incremental computations kth+1 time
The modal displacement for the iteration that weighs；
Step 307：Acquire the displacement δ of ith increment+1 equilibrium iteration of kthi,k+1；
Step 308：JudgeWhether the convergence criterion of power is met,It is missed for the opposite of power in practical calculate
Difference：IfThen result meets the convergence criterion of power, terminates equilibrium iteration, arrives step 309；Otherwise, k=is enabled
K+1 goes to step 303；
Step 309：Will be displacement superposed during equilibrium iteration, ith increment total displacement is obtained, even Δ δi=Δ δi,1+Δ
δi,2...+Δδi,k+1；
Step 310：Complete the solution of ith increment.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510752953.8A CN105426592B (en) | 2015-11-06 | 2015-11-06 | A kind of Electrostatic deformation film reflector surface antenna analysis method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510752953.8A CN105426592B (en) | 2015-11-06 | 2015-11-06 | A kind of Electrostatic deformation film reflector surface antenna analysis method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105426592A CN105426592A (en) | 2016-03-23 |
| CN105426592B true CN105426592B (en) | 2018-10-12 |
Family
ID=55504801
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510752953.8A Active CN105426592B (en) | 2015-11-06 | 2015-11-06 | A kind of Electrostatic deformation film reflector surface antenna analysis method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105426592B (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106156429B (en) * | 2016-07-05 | 2019-04-26 | 西安电子科技大学 | A kind of Electrostatic deformation film antenna finite element modeling method based on information in kind |
| CN106250588B (en) * | 2016-07-21 | 2019-05-17 | 西安电子科技大学 | A kind of Electrostatic deformation film reflector face based on osculating element looks for shape to look for state method |
| CN106295035B (en) * | 2016-08-16 | 2019-04-30 | 西安电子科技大学 | The Electrostatic deformation film antenna shape adjustment method of optimization is cooperateed with bitter end position based on voltage |
| CN108197352B (en) * | 2017-12-14 | 2020-07-31 | 中国科学院西安光学精密机械研究所 | Accurate surface shape calculation method for large-aperture reflector |
| CN108110432B (en) * | 2017-12-18 | 2020-03-10 | 中国电子科技集团公司第五十四研究所 | Reflector antenna panel blocking method and reflector antenna |
| CN111046538B (en) * | 2019-11-26 | 2023-11-07 | 中国科学院空间应用工程与技术中心 | Voltage distribution method and system of electrostatic force actuating mechanism |
| CN114139410A (en) * | 2021-10-19 | 2022-03-04 | 青岛科技大学 | Electrostatic force applying method and system considering deformation of electrode surface and thin film reflecting surface |
| CN114065434B (en) * | 2021-11-22 | 2024-02-13 | 青岛科技大学 | Method for analyzing deformation of film reflecting surface of electrostatically formed film antenna |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103678810A (en) * | 2013-12-17 | 2014-03-26 | 西安电子科技大学 | Electrode layout method of static formed film antenna |
| CN104123421A (en) * | 2014-07-31 | 2014-10-29 | 西安电子科技大学 | Electrostatic forming film reflecting surface form design method based on mechanical and electrical field coupling |
-
2015
- 2015-11-06 CN CN201510752953.8A patent/CN105426592B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103678810A (en) * | 2013-12-17 | 2014-03-26 | 西安电子科技大学 | Electrode layout method of static formed film antenna |
| CN104123421A (en) * | 2014-07-31 | 2014-10-29 | 西安电子科技大学 | Electrostatic forming film reflecting surface form design method based on mechanical and electrical field coupling |
Non-Patent Citations (3)
| Title |
|---|
| Surface Configuration Design of Cable-Network Reflectors Considering the Radiation Pattern;Yali Zong等;《IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION》;20140630;第62卷(第6期);论文第3163-3173页 * |
| 静电成形薄膜反射面可展开天线形面分析理论与制作方法研究;刘超;《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》;20141115(第11期);论文第15-49页 * |
| 静电成形薄膜反射面可展开天线研究;童浙夫;《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》;20110716(第8期);论文第9-33页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105426592A (en) | 2016-03-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105426592B (en) | A kind of Electrostatic deformation film reflector surface antenna analysis method | |
| Zhang et al. | Kinematic reliability analysis of robotic manipulator | |
| Zhang et al. | Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method | |
| Li et al. | Dynamics of a deployable mesh reflector of satellite antenna: form-finding and modal analysis | |
| Percy et al. | Application of matrix displacement method to linear elastic analysisof shells of revolution. | |
| Higa et al. | Stress and strain in silicon electrode models | |
| Man et al. | Semi-analytical analysis for piezoelectric plate using the scaled boundary finite-element method | |
| CN107160401B (en) | Method for solving problem of joint angle deviation of redundant manipulator | |
| Toi et al. | Finite element analysis of two-dimensional electrochemical–mechanical response of ionic conducting polymer–metal composite beams | |
| Qi et al. | Multi-objective optimization of parallel tracking mechanism considering parameter uncertainty | |
| Javani et al. | Free vibration of arbitrary thick FGM deep arches using unconstrained higher-order shear deformation theory | |
| Hao et al. | A novel adaptive force control method for IPMC manipulation | |
| CN109325284B (en) | Honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty | |
| Rouzegar et al. | A refined finite element method for bending of smart functionally graded plates | |
| Anh et al. | Nonlinear vibration and geometric optimization of nanocomposite multilayer organic solar cell under wind loading | |
| Qiao et al. | Structure, design, and modeling of an origami-inspired pneumatic solar tracking system for the NPU-phonesat | |
| CN108090306A (en) | A kind of deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain | |
| CN110826208B (en) | Pneumatic numerical simulation accelerated convergence method | |
| Wei et al. | Real-time thermal deformation compensation method for active phased array antenna panels | |
| CN108182330A (en) | A kind of method that the response of flexible rectangular thin plate Rigid-flexible Coupling Dynamics is calculated based on B-spline | |
| Zhang et al. | Stress effect on self-limiting lithiation in silicon-nanowire electrode | |
| CN106168999B (en) | A kind of Electrostatic deformation film antenna force finding method based on Entity measurement information | |
| CN104850683B (en) | The method that material crack tip stress fields coefficient is calculated based on weak form quadrature member method | |
| CN106156429B (en) | A kind of Electrostatic deformation film antenna finite element modeling method based on information in kind | |
| CN109446557A (en) | A kind of random aeroelastic system method for analyzing stability based on probabilistic density evolution |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |