CN105426592A - Electrostatically formed film reflecting surface antenna analysis method - Google Patents

Abstract

The invention belongs to the technical field of radar antennas, and particularly provides an electrostatically formed film reflecting surface antenna analysis method. The method comprises the following steps: firstly, establishing a film reflecting surface finite element model, expressing electrostatic force into an element node displacement function to be exerted into a model, and then conducting model solution by applying an exponential type increment loading manner to obtain film reflecting surface deformation. Compared with the prior art, the film reflecting surface deformation obtained by adopting the method is accurate in result and relatively high in computational efficiency.

Description

A kind of Electrostatic deformation film reflector surface antenna analytical approach

Technical field

The invention belongs to Radar Antenna System field, relate to a kind of Electrostatic deformation film reflector surface antenna rapid analysis that deformation of thin membrane affects electrostatic force of considering.A specifically Electrostatic deformation film reflector surface antenna analytical approach, for the distortion of accurate express-analysis film under electrostatic forcing, the exponential type step increment method mode wherein solving Nonlinear System of Equations employing has ubiquity.

Background technology

The principle of work of Electrostatic deformation film reflector surface antenna (ECDMA) on the film reflector face being coated with metal level and control electrode, applies different voltage (general film is equivalent zero gesture face, electrode is high potential), produce electrostatic force to stretch to film, thus make film formation have the reflecting surface that focuses footpath ratio.Because electrode voltage can be adjusted in real time by power supply, and then can realize the timely compensation to reflecting surface shape surface error, ECDMA proposes just to receive much concern from scheme always.U.S. NASA just started the Electrostatic deformation film reflector surface antenna development of bore 4.88m as far back as 1979, until SRSTechnologies company in 2004 cooperates with NorthropGrumman, just have developed Electrostatic deformation film reflector face deployable antenna 5m bore model machine truly.

For ensureing the precision under electrostatic film Antenna Operation state, electrostatic force suffered by necessary accurate Calculation film.For electrostatic force computational problem suffered by the film related in ECDMA, foreign literature generally supposes that the relative film die opening of deformation of thin membrane amount is an a small amount of, thus directly application capacity plate antenna formula is tried to achieve.But, because Film stiffness is very little, under load effect, be generally large deformation, therefore deformation of thin membrane can change film die opening, be necessary to improve capacity plate antenna formula.The finite element softwares such as Ansys have the ability of analysis two coupling, can solve electrostatic force computational problem suffered by film, but due to modeling complexity, the error that final mask is set up there is no method and accurately controls.

Summary of the invention

The object of the invention is problem electrostatic force affected for the deformation of thin membrane existed in electrostatic film catoptron, provide a kind of Electrostatic deformation film reflector surface antenna rapid analysis that deformation of thin membrane affects electrostatic force of considering; Based on Finite Element Method, utilize Matlab to programme deformation analysis is carried out to film, membrane structure GEOMETRICALLY NONLINEAR is considered in analytic process, electrostatic force is expressed as the function of Displacement of elemental node simultaneously, adopt exponential type load mode when carrying out Incremental SAT, realize the Electrostatic deformation film reflector surface antenna express-analysis considering that deformation of thin membrane affects electrostatic force.

For achieving the above object, the invention provides a kind of Electrostatic deformation film reflector surface antenna analytical approach, its technical scheme is: a kind of Electrostatic deformation film reflector surface antenna analytical approach, comprises the steps:

Step 101: according to the bore D of electrostatic film reflecting surface _aset up film reflector face finite element model with focal distance f, with plane triangle film unit, stress and strain model is carried out to film reflector face, amount to N number of film unit, a M node;

Step 102: the power convergence criterion that when input film reflector face finite element model solves, each step equilibrium iteration needs and increment total number J=a ^b, wherein a and b is exponential type incremental step controlling elements, given each film unit prestress σ ₀=[σ _x0σ _y0σ _xy0] ^t, wherein σ _x0, σ _y0and σ _xy0be respectively the prestress value in film unit x direction, y direction and xy direction, electrode voltage value is U, and initial displacement vector is δ, δ is zero column vector that 3 × M is capable;

Step 103: make i=0, j=a ⁱ, wherein i is incremental computations number of times, and j is increment, starts i-th incremental computations of step 104 to step 107;

Step 104: film unit numbering represents with e, analyzes N number of film unit successively, calculates global stiffness matrix K when i-th incremental computations starts _i, equivalent force vector F _iwith load vectors R _i;

Step 105: the Nonlinear System of Equations K utilizing full Newton-Raphson solution by iterative method i-th incremental computations _iΔ δ _i=R _i-F _i, wherein Δ δ _iit is the displacement value that i-th incremental computations goes out;

Step 106: make δ=δ+Δ δ _i, what obtain by i-th incremental computations displacement superposedly obtains total shift value;

Step 107: the calculating having judged whether all increments: if j≤J, make i=i+1, j=a ⁱ, forward step 104 to; If j > is J, then terminates incremental computations, forward step 108 to;

Step 108: according to result of calculation output node motion vector δ and element stress vector σ;

Step 109; Judge whether the film reflector surface accuracy after being out of shape meets the demands, precision does not meet the demands and then changes film prestress or initial voltage value, re-starts analysis; Precision meets the demands, and terminates the analysis of electrostatic film reflector antenna.

Above-mentioned steps 104 comprises the steps:

Step 201: make e=1, e is the numbering number of film unit, starts e film unit analysis, and step 202-step 210 is shown in concrete analysis;

Step 202: read in e unit information, comprises film unit node location coordinate a={x under global coordinate system ₁y ₁z ₁x ₂y ₂z ₂x ₃y ₃z ₃} ^t, the displacement increment Δ a={u of node ₁v ₁w ₁u ₂v ₂w ₂u ₃v ₃w ₃} ^t;

Step 203: according to cell node position coordinates, under being transformed into local coordinate system, calculates the stiffness matrix of i-th increment e film unit wherein A is the area of film unit, and t is film thickness, $D=\frac{E}{1-{\mathrm{\μ}}^2}\left[\begin{array}{ccc}1& \mathrm{\μ}& 0\\ \mathrm{\μ}& 1& 0\\ 0& 0& \frac{1-\mathrm{\μ}}{2}\end{array}\right]$ For film unit elastic matrix, wherein E is thin flexible film modulus, and μ is Poisson ratio, B _lfor the relational matrix of linear strain and displacement, for matrix B _ltransposed matrix, T is transpose of a matrix symbol; M is element stress matrix, and G is node coordinate function, G ^tfor the transposed matrix of matrix G;

Step 204: by cell matrix be transformed into global coordinate system, and be assembled into i-th incremental computations global stiffness matrix K _iin;

Step 205: calculate i-th increment e film unit equivalent force vector wherein=DB _lΔ a+ σ ₀for element stress matrix;

Step 206: by unit equivalent force vector be transformed into global coordinate system, be assembled into i-th increment overall equivalent force vector F _iin;

Step 207: calculate i-th increment e the film unit load vector under film unit global coordinate system $R_i^e=\frac{1}{3}{\mathrm{Aq}}_i^e{\left\{A_x{q}_x{A}_y{q}_y{A}_z{q}_z{A}_x{q}_x{A}_y{q}_y{A}_z{q}_z{A}_x{q}_x{A}_y{q}_y{A}_z{q}_z\right\}}^T,$ Wherein A _x, A _yand A _zbe respectively the projection of film unit area in global coordinate system on YOZ, XOZ and XOY face, q _x, q _yand q _zbe respectively the projection of film unit area power on X, Y and Z-direction, represent face electrostatic force suffered by i-th increment e film unit, expression is wherein for load increment controlling elements, ε is permittivity of vacuum, and U is electrode voltage value, and d is the initial separation of film unit and electrode, and ω is Displacement of elemental node function, and expression is wherein δ _l, δ _m, δ _nfor film unit node is relative to the displacement of electrode normal direction;

Step 208: by i-th increment e film unit load vector be assembled into overall load vector R _iin;

Step 209: the analysis having judged whether all film units: if e≤N, then make e=e+1, forward step 202 to; If e > is N, then the calculating of end unit matrix, forwards step 210 to;

Step 210: the global stiffness matrix K completing i-th increment _i, equivalent force vector F _iwith total load (TL) vector R _icalculate.

Above-mentioned steps 105, comprises the steps:

Step 301: make k=1, k is equilibrium iteration number of times, and the equilibrium iteration starting Nonlinear System of Equations solves, and concrete iterative computation is shown in step 302-step 310;

Step 302: make K _i,k=K _i, K _i,kbe the Bulk stiffness matrix of i-th incremental computations kth time equilibrium iteration, solve system of linear equations K _i,kΔ δ _i,k=R _i, Δ δ _i,kbe i-th incremental computations kth time equilibrium iteration nodal displacement;

Step 303: try to achieve i-th incremental computations kth time equilibrium iteration nodal displacement Δ δ _i,k;

Step 304: upgrade node coordinate by the nodal displacement of trying to achieve;

Step 305: according to step 104, calculates the Bulk stiffness matrix K of i-th incremental computations kth+1 equilibrium iteration _{i, k+1}with equivalent force vector F _{i, k+1};

Step 306: solve system of linear equations K _{i, k+1}Δ δ _{i, k+1}=R _i-F _{i, k+1}, Δ δ _{i, k+1}it is the nodal displacement of i-th incremental computations kth+1 equilibrium iteration;

Step 307: the displacement δ trying to achieve i-th increment kth+1 equilibrium iteration _{i, k+1};

Step 308: judge whether meet the convergence criterion of power, relative error magnitudes for power in actual computation: if then result meets the convergence criterion of power, terminates equilibrium iteration, to step 309; Otherwise, make k=k+1, forward step 303 to;

Step 309: displacement superposed by equilibrium iteration process, obtains i-th increment total displacement, even δ _i=Δ δ _{i, 1}+ Δ δ _{i, 2}...+Δ δ _{i, k+1};

Step 310: complete solving of i-th increment.

Beneficial effect of the present invention: compared with prior art, the present invention considers that electrostatic force is the function of film nodal displacement, in Electrostatic deformation film reflector surface antenna model calculates, analyze the impact of deformation of thin membrane on electrostatic force, improves the accuracy that model calculates.Simultaneously because electrostatic force is tried to achieve with the form of function by the present invention, avoid the process of establishing of complex model, computational accuracy and efficiency can be improved.

Below with reference to accompanying drawing, the present invention is described in further details.

Accompanying drawing explanation

Fig. 1 Electrostatic deformation film reflector surface antenna analyzes overview flow chart;

The flow chart of steps of Fig. 2 step 104;

The process flow diagram of Fig. 3 step 105;

The finite element model that Fig. 4 sets up according to reflecting surface structure parameter.

Embodiment

An Electrostatic deformation film reflector surface antenna analytical approach, is characterized in that: at least comprise the steps: as shown in Figure 1

Step 101: according to the bore D of electrostatic film reflecting surface _aset up film reflector face finite element model with focal distance f, with plane triangle film unit, stress and strain model is carried out to film reflector face, amount to N number of film unit, a M node;

Step 102: the power condition of convergence that when input film reflector face finite element model solves, each step equilibrium iteration needs and increment total score step number order J=a ^b, wherein a and b is exponential type incremental step controlling elements, given each film unit prestress σ ₀=[σ _x0σ _y0σ _xy0] ^t, wherein σ _x0, σ _y0and σ _xy0be respectively the prestress value in film unit x direction, y direction and xy direction, electrode voltage value U and initial displacement vector δ, δ are zero column vector that 3 × M is capable;

Step 103: make i=0, j=a ⁱ, wherein i is incremental computations number of times, and j is increment, starts the calculating that i-th time incremental computations comprises step 104-step 107;

Step 104: film unit numbering number e represents, analyzes N number of film unit successively, calculates global stiffness matrix K when i-th incremental computations starts _i, equivalent force vector F _iwith load vectors R _i, concrete computation process is shown in step 201-step 210;

Step 105: the Nonlinear System of Equations K utilizing full Newton-Raphson solution by iterative method i-th increment _iΔ δ _i=R _i-F _i, wherein Δ δ _ibe the displacement value that i-th incremental computations goes out, represent equilibrium iteration number of times in iterative process with k, concrete calculating sees step 301-step 310;

Step 106: make δ=δ+Δ δ _i, what obtain by i-th incremental computations displacement superposedly obtains total shift value;

Step 107: the calculating having judged whether all increments: if j≤J, make i=i+1, j=a ⁱ, forward step 104 to; If j > is J, then terminates incremental computations, forward step 108 to;

Step 108: according to result of calculation output node motion vector δ and element stress vector σ;

Step 109: judge whether the film reflector surface accuracy after being out of shape meets the demands, precision does not meet the demands and then changes film prestress or initial voltage value, re-starts analysis; Precision meets the demands, and terminates the analysis of electrostatic film reflector antenna.

As shown in Figure 2, described step 104, is specifically related to following steps:

Step 201: make e=1, e is the numbering number of film unit, starts e film unit analysis, and step 202-step 210 is shown in concrete analysis;

Step 202: read in e unit information, comprises film unit node location coordinate a={x under global coordinate system ₁y ₁z ₁x ₂y ₂z ₂x ₃y ₃z ₃} ^t, the displacement increment Δ a={u of node ₁v ₁w ₁u ₂v ₂w ₂u ₃v ₃w ₃} ^t;

Step 203: according to cell node position coordinates, under being transformed into local coordinate system, calculates the stiffness matrix of i-th increment e film unit wherein A is the area of film unit, and t is film thickness, $D=\frac{E}{1-{\mathrm{\μ}}^2}\left[\begin{array}{ccc}1& \mathrm{\μ}& 0\\ \mathrm{\μ}& 1& 0\\ 0& 0& \frac{1-\mathrm{\μ}}{2}\end{array}\right]$ For film unit elastic matrix, wherein E is thin flexible film modulus, and μ is Poisson ratio, B _lfor the relational matrix of linear strain and displacement, for matrix B _ltransposed matrix, M is element stress matrix, and G is node coordinate function, is the matrix relevant to cell node coordinate, G ^tfor the transposed matrix of matrix G;

Step 204: by cell matrix be transformed into global coordinate system, and be assembled into i-th increment global stiffness matrix K _iin;

Step 205: calculate i-th increment e film unit equivalent force vector wherein σ=DB _lΔ a+ σ ₀for element stress matrix;

Step 206: by unit equivalent force vector be transformed into global coordinate system, be assembled into i-th increment overall equivalent force vector F _iin;

Step 207: calculate i-th increment e the film unit load vector under film unit global coordinate system $R_i^e=\frac{1}{3}{\mathrm{Aq}}_i^e{\left\{A_x{q}_x{A}_y{q}_y{A}_z{q}_z{A}_x{q}_x{A}_y{q}_y{A}_z{q}_z{A}_x{q}_x{A}_y{q}_y{A}_z{q}_z\right\}}^T,$ Wherein A _x, A _yand A _zbe respectively the projection of film unit area in global coordinate system on YOZ, XOZ and XOY face, q _x, q _yand q _zbe respectively the projection of film unit area power on X, Y and Z-direction, represent face electrostatic force suffered by i-th increment e film unit, expression is wherein for load increment controlling elements, ε is permittivity of vacuum, and U is electrode voltage value, and d is the initial separation of film unit and electrode, and ω is Displacement of elemental node function, and expression is wherein δ _l, δ _m, δ _nfor film unit node is relative to the displacement of electrode normal direction;

Step 208: by i-th increment e film unit load vector be assembled into overall load vector R _iin;

Step 209: the analysis having judged whether all film units: if e≤N, then make e=e+1, forward step 202 to; If e > is N, then the calculating of end unit matrix, forwards step 210 to;

Step 210: the global stiffness matrix K completing i-th increment _i, equivalent force vector F _iwith total load (TL) vector R _icalculate.

As shown in Figure 3, described step 105, is specifically related to following steps:

Step 301: make k=1, k is equilibrium iteration number of times, and the equilibrium iteration starting Nonlinear System of Equations solves, and concrete iterative computation is shown in step 302-step 310;

Step 302: make K _i,k=K _i, K _i,kbe the Bulk stiffness matrix of i-th incremental computations kth time equilibrium iteration, solve system of linear equations K _i,kΔ δ _i,k=R _i, Δ δ _i,kbe i-th incremental computations kth time equilibrium iteration nodal displacement;

Step 303: try to achieve i-th incremental computations kth time equilibrium iteration nodal displacement Δ δ _i,k;

Step 304: upgrade node coordinate by the nodal displacement of trying to achieve;

Step 305: according to step 104, calculates the Bulk stiffness matrix K of i-th incremental computations kth+1 equilibrium iteration _{i, k+1}with equivalent force vector F _{i, k+1};

Step 306: solve system of linear equations K _{i, k+1}Δ δ _{i, k+1}=R _i-F _{i, k+1}, Δ δ _{i, k+1}it is the nodal displacement of i-th incremental computations kth+1 equilibrium iteration;

Step 307: the displacement δ trying to achieve i-th increment kth+1 equilibrium iteration _{i, k+1};

Step 308: judge whether meet the convergence criterion of power, relative error magnitudes for power in actual computation: if then result meets the convergence criterion of power, terminates equilibrium iteration, to step 309; Otherwise, make k=k+1, forward step 303 to;

Step 309: displacement superposed by equilibrium iteration process, obtains i-th increment total displacement, even Δ δ _i=Δ δ _{i, 1}+ Δ δ _{i, 2}...+Δ δ _{i, k+1};

Step 310: complete solving of i-th increment.

Advantage of the present invention can be further illustrated by following emulation experiment:

Simulated conditions:

Electrostatic deformation film reflector plane materiel material adopts isotropy Kapton, membraneous material parameter: thickness t=25 μm, elastic modulus E=2.17GPa, Poisson ratio μ=3.14, thermalexpansioncoefficientα=29 × 10 ^-6/ DEG C; Reflecting surface structure parameter: bore D _a=2m, focal distance f → ∞; Calculate correlation 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 electrode initial separation d=20mm.The finite element model set up according to reflecting surface structure parameter is as Fig. 4, and total N=600 film unit, M=331 node, reflecting surface periphery is fixed, the structural initial pre stress of given Δ T=-0.01 DEG C in film, i.e. σ ₀=[σ _x0σ _y0σ _xy0] ^t=[Et α Δ TEt α Δ T0] ^t.In order to embody the accuracy and efficiency of this method, contrast with electrostatic mechanical coupling modular program analysis in ansys software herein.11 representational nodal displacements that result of calculation is extracted along film reflector face same bus radial direction compare, and have added up two kinds of methods under the same conditions and calculate this example required time, and result is as table 1.

Table 1 comparison of computational results

Unit/mm

At processor IntelCorei3-3240CPU3.40GHz, the 64 bit manipulation systems of internal memory 8G are fallen into a trap to count in and are stated example, under identical power convergence criterion, utilize the Electrostatic deformation film reflector surface antenna analytical approach in the present invention to decrease 46.4s computing time, under the prerequisite ensureing precision, counting yield significantly improves.Reason is the calculating respectively that ansys electrostatic mechanical coupling module analysis needs to carry out displacement structure field and electrostatic field, and analyzes electrostatic field and need to divide more electric field unit; The present invention then omits complicated finite element modeling process and the calculating of electrostatic field substantially.

To sum up, the present invention considers that electrostatic force is the function of film nodal displacement, in Electrostatic deformation film reflector surface antenna model calculates, analyze the impact of deformation of thin membrane on electrostatic force, improves the accuracy that model calculates.Simultaneously because electrostatic force is tried to achieve with the form of function by the present invention, avoid the process of establishing of complex model, computational accuracy and efficiency can be improved.

The part do not described in detail in present embodiment belongs to the known conventional means of the industry, does not describe one by one here.More than exemplifying is only illustrate of the present invention, does not form the restriction to protection scope of the present invention, everyly all belongs within protection scope of the present invention with the same or analogous design of the present invention.

Claims (3)

1. an Electrostatic deformation film reflector surface antenna analytical approach, is characterized in that: comprise the steps:

Step 101: according to the bore D of electrostatic film reflecting surface _aset up film reflector face finite element model with focal distance f, with plane triangle film unit, stress and strain model is carried out to film reflector face, amount to N number of film unit, a M node;

Step 102: the power convergence criterion β that when input film reflector face finite element model solves, each step equilibrium iteration needs and increment total number J=a ^b, wherein a and b is exponential type incremental step controlling elements, given each film unit prestress σ ₀=[σ _x0σ _y0σ _xy0] ^t, wherein σ _x0, σ _y0and σ _xy0be respectively the prestress value in film unit x direction, y direction and xy direction, electrode voltage value is U, and initial displacement vector is, δ is zero column vector that 3 × M is capable;

Step 103: make i=0, j=a ⁱ, wherein i is incremental computations number of times, and j is increment, starts i-th incremental computations of step 104 to step 107;

Step 104: film unit numbering represents with e, analyzes N number of film unit successively, calculates global stiffness matrix K when i-th incremental computations starts _i, equivalent force vector F _iwith load vectors R _i;

Step 105: the Nonlinear System of Equations K utilizing full Newton-Raphson solution by iterative method i-th incremental computations _iΔ δ _i=R _i-F _i, wherein Δ δ _iit is the displacement value that i-th incremental computations goes out;

Step 106: make δ=δ+Δ δ _i, what obtain by i-th incremental computations displacement superposedly obtains total shift value;

Step 107: the calculating having judged whether all increments: if j≤J, make i=i+1, j=a ⁱ, forward step 104 to; If j > is J, then terminates incremental computations, forward step 108 to;

Step 108: according to result of calculation output node motion vector δ and element stress vector σ;

Step 109; Judge whether the film reflector surface accuracy after being out of shape meets the demands, precision does not meet the demands and then changes film prestress or initial voltage value, re-starts analysis; Precision meets the demands, and terminates the analysis of electrostatic film reflector antenna.

2. a kind of Electrostatic deformation film reflector surface antenna analytical approach according to claim 1, is characterized in that: wherein step 104 comprises the steps:

Step 201: make e=1, e is the numbering number of film unit, starts e film unit analysis, and step 202-step 210 is shown in concrete analysis;

Step 202: read in e unit information, comprises film unit node location coordinate a={x under global coordinate system ₁y ₁z ₁x ₂y ₂z ₂x ₃y ₃z ₃} ^t, the displacement increment Δ a={u of node ₁v ₁w ₁u ₂v ₂w ₂u ₃v ₃w ₃} ^t;

Step 203: according to cell node position coordinates, under being transformed into local coordinate system, calculates the stiffness matrix of i-th increment e film unit wherein A is the area of film unit, and t is film thickness, $D=\frac{E}{1-{\mathrm{\μ}}^2}\left[\begin{array}{ccc}1& \mathrm{\μ}& 0\\ \mathrm{\μ}& 1& 0\\ 0& 0& \frac{1-\mathrm{\μ}}{2}\end{array}\right]$ For film unit elastic matrix, wherein E is thin flexible film modulus, and μ is Poisson ratio, B _lfor the relational matrix of linear strain and displacement, for matrix B _ltransposed matrix, T is transpose of a matrix symbol; M is element stress matrix, and G is node coordinate function, G ^tfor the transposed matrix of matrix G;

Step 204: by cell matrix be transformed into global coordinate system, and be assembled into i-th incremental computations global stiffness matrix K _iin;

Step 205: calculate i-th increment e film unit equivalent force vector wherein σ=DB _lΔ a+ σ ₀for element stress matrix;

Step 206: by unit equivalent force vector be transformed into global coordinate system, be assembled into i-th increment overall equivalent force vector F _iin;

Step 207: calculate i-th increment e the film unit load vector under film unit global coordinate system $R_i^e=\frac{1}{3}{\mathrm{Aq}}_i^e{\left\{A_x{q}_x{A}_y{q}_y{A}_z{q}_z{A}_x{q}_x{A}_y{q}_y{A}_z{q}_z{A}_x{q}_x{A}_y{q}_y{A}_z{q}_z\right\}}^T,$ Wherein A _x, A _yand A _zbe respectively the projection of film unit area in global coordinate system on YOZ, XOZ and XOY face, q _x, q _yand q _zbe respectively the projection of film unit area power on X, Y and Z-direction, represent face electrostatic force suffered by i-th increment e film unit, expression is wherein for load increment controlling elements, ε is permittivity of vacuum, and U is electrode voltage value, and d is the initial separation of film unit and electrode, and ω is Displacement of elemental node function, and expression is wherein δ _l, δ _m, _nfor film unit node is relative to the displacement of electrode normal direction;

Step 208: by i-th increment e film unit load vector be assembled into overall load vector R _iin;

Step 209: the analysis having judged whether all film units: if e≤N, then make e=e+1, forward step 202 to; If e > is N, then the calculating of end unit matrix, forwards step 210 to;

Step 210: the global stiffness matrix K completing i-th increment _i, equivalent force vector F _iwith total load (TL) vector R _icalculate.

3. a kind of Electrostatic deformation film reflector surface antenna analytical approach according to claim 1, is characterized in that: wherein step 105 comprises the steps:

Step 301: make k=1, k is equilibrium iteration number of times, and the equilibrium iteration starting Nonlinear System of Equations solves, and concrete iterative computation is shown in step 302-step 310;

Step 302: make K _i,k=K _i, K _i,kbe the Bulk stiffness matrix of i-th incremental computations kth time equilibrium iteration, solve system of linear equations K _i,kΔ δ _i,k=R _i, Δ δ _i,kbe i-th incremental computations kth time equilibrium iteration nodal displacement;

Step 303: try to achieve i-th incremental computations kth time equilibrium iteration nodal displacement Δ δ _i,k;

Step 304: upgrade node coordinate by the nodal displacement of trying to achieve;

Step 305: according to step 104, calculates the Bulk stiffness matrix K of i-th incremental computations kth+1 equilibrium iteration _{i, k+1}with equivalent force vector F _{i, k+1};

Step 306: solve system of linear equations K _{i, k+1}Δ δ _{i, k+1}=R _i-F _{i, k+1}, Δ δ _{i, k+1}it is the nodal displacement of i-th incremental computations kth+1 equilibrium iteration;

Step 307: the displacement δ trying to achieve i-th increment kth+1 equilibrium iteration _{i, k+1};

Step 308: judge whether meet the convergence criterion of power, relative error magnitudes for power in actual computation: if then result meets the convergence criterion of power, terminates equilibrium iteration, to step 309; Otherwise, make k=k+1, forward step 303 to;

Step 309: displacement superposed by equilibrium iteration process, obtains i-th increment total displacement, even Δ δ _i=Δ δ _{i, 1}+ Δ δ _{i, 2}...+Δ δ _{i, k+1};

Step 310: complete solving of i-th increment.