Method for optimizing topological structure of net-shaped deployable antenna cable net

Abstract

The invention discloses a net-shaped deployable antenna cable net topological structure optimization method, which comprises the steps of determining geometric parameters, material parameters and electrical parameters of a net-shaped antenna, and calculating an ideal antenna far-area electric field; assigning the number of cable net optimization nodes of the mesh antenna, generating uniformly distributed nodes under the assigned number in the aperture surface of the mesh antenna, and generating an initial value of an optimization model; performing shape finding on the optimization model and calculating the electrical performance of the reflecting surface of the mesh antenna after shape finding to obtain an optimized mesh antenna cable network topological structure; and changing the number of network cable optimization nodes of the mesh antenna, performing network cable topological structure optimization on multiple groups of mesh antennas, comparing multiple groups of optimization results, and selecting an optimal topological structure under the optimal number of nodes. According to the invention, the electrical performance target of high gain and low sidelobe level can be realized under the condition of a small number of nodes, and meanwhile, the uniformity of tension distribution of the cable section is ensured.

Description

Technical Field

[0001] The present invention is applicable to the structural design of a mesh deployable antenna, and specifically is a method for optimizing the topological structure of a mesh deployable antenna. Background Art

[0002] The mesh deployable antenna consists of front and rear cable mesh surfaces and a deployable structure. Compared with solid surface antennas, the mesh deployable antenna has unique advantages. It can cover a large space range with a small amount of material while meeting the strength requirements, and has a high storage rate. The structure of the mesh reflector antenna mainly includes a metal reflective wire mesh used to reflect electromagnetic waves, a deployable structure, and a cable mesh system that stretches the entire antenna structure into a predetermined shape. The side on which the metal wire mesh is laid is the reflective surface, and the surface accuracy of the mesh surface directly affects the electrical performance of the antenna.

[0003] When designing the reflector mesh using the traditional regular grid design method, the number of rings is determined by the geometric approximation error δ rms The upper limit of is taken as the benchmark. According to the number of rings, the aperture surface of the parabola is divided into N rings of regular triangles, and then projected onto the parabola. This method only considers the geometric approximation error on the entire reflection surface, and does not consider the error distribution.

[0004] Existing studies have shown that when the root mean square error of the reflector is the same, different error distributions will have different effects on the gain and sidelobe level of the antenna. The cable net reflector is composed of several triangular patches that approximate a standard parabola, and there are principle errors. At present, there are many optimization design methods for ensuring the electrical and structural performance of antennas, but most of them are optimized based on the number of sub-rings or the radius of the sub-rings as optimization variables. There are still large restrictions on the number of nodes and node positions, which may cause the model to fall into a local optimal solution or miss the global optimal solution.

[0005] Therefore, it is necessary to propose an optimization design method with fewer design variable restrictions and more comprehensive objectives, so as to obtain a mesh reflector antenna grid structure with good structural and electrical performance in a larger search space. Summary of the invention

[0006] In order to solve the above-mentioned defects existing in the prior art, the purpose of the present invention is to provide a method for designing a mesh reflector antenna cable net topology structure based on the optimization of electrical performance and structural performance, so as to obtain a cable net structure with uniform rope tension, high gain and low side lobe level in a larger search space, so that the optimized structure has good structural performance and electrical performance.

[0007] The present invention is achieved through the following technical solutions.

[0008] One aspect of the present invention provides a method for optimizing the topological structure of a mesh deployable antenna line, comprising the following steps:

[0009] Determine the geometric parameters, material parameters and electrical parameters of the mesh deployable antenna, and calculate the far-zone electric field of the ideal antenna;

[0010] Specify the number of mesh antenna line optimization nodes, generate the specified number of uniformly distributed nodes within the mesh antenna aperture plane, and generate the initial value of the optimization model;

[0011] Based on the initial value of the optimization model, the optimization model is shape-finded and the electrical performance of the mesh antenna reflector after shape-finding is calculated to obtain the optimized mesh antenna line grid topology structure;

[0012] Change the number of optimized nodes of the mesh antenna cable network, optimize the cable network topology of multiple groups of mesh antennas, compare multiple groups of optimization results, and select the optimal topology with the optimal number of nodes.

[0013] Preferably, the geometric parameters include antenna aperture, focal length and offset distance; the material parameters include material density, Poisson's ratio, elastic modulus and cross-sectional area of ​​the cable net, deployable structure and film; and the electrical parameters include operating frequency and feed source parameters.

[0014] Preferably, generating initial values ​​of the optimization model includes:

[0015] Determine the coordinates of the connection between the cable net boundary and the deployable structure as the fixed node coordinates, and give the value range of the free node coordinates;

[0016] Determine the minimum distance between points;

[0017] Generate a new node through iteration, determine whether the node is within the aperture plane, and check whether the minimum distance between the new node and the existing node is greater than the preset minimum distance threshold; if both conditions are met, retain and store the node, otherwise regenerate the node until a sufficient number of nodes are generated or the maximum number of iterations is reached;

[0018] If the maximum number of iterations is reached and still not enough nodes are generated, the value of the minimum distance between points is reduced;

[0019] After the iteration is completed, the initial value of the optimization model is obtained, that is, the evenly distributed nodes under the specified number.

[0020] Preferably, the topological structure of the mesh antenna line surface is optimized, and the shape-finding of the optimization model includes solving the optimization model using a finite element analysis method to achieve uniform distribution of cable force; the calculation of the electrical performance of the mesh antenna reflector surface after shape-finding includes adopting a physical optics method to approximately calculate the electrical performance of the deformed reflector surface antenna using Taylor expansion.

[0021] Preferably, the optimization model is form-finding, including:

[0022] Project the nodes in the aperture plane onto the upper and lower mesh surfaces to obtain the coordinates of the nodes on the upper and lower mesh surfaces;

[0023] According to the coordinates of the upper and lower mesh nodes, the topological relationship is calculated using the Delaunay algorithm, and a three-dimensional finite element model of the mesh reflector antenna is established in ANSYS;

[0024] Given the initial stress of the cable-membrane structure, constraints are imposed on the deployable structure, and static analysis is performed to extract the node coordinates, cable tension, and membrane strain in the equilibrium state.

[0025] When calculating equilibrium, the length of the cable segment is calculated using the node coordinates, and the original length of the cable segment is calculated based on the strain;

[0026] Calculate the difference between the mesh node coordinates in the equilibrium state and the initial design value;

[0027] According to the global equilibrium equation of the cable-membrane reflection surface, the sensitivity matrix of the node position relative to the original length of the cable segment and the unstretched length of the three sides of the membrane in the equilibrium state, as well as the sensitivity matrix of the unstretched length relative to the stress are calculated;

[0028] Solve the optimization model to find a set of form-finding results that are closer to the specified stress state;

[0029] Update the unstretched length in the finite element model of the reflecting surface in the equilibrium state to find a new equilibrium state;

[0030] Repeat the steps of solving the mechanical optimization model to find a new equilibrium state until the convergence criteria are met.

[0031] Preferably, the calculating of the electrical performance of the reflective surface of the mesh antenna after shape finding includes:

[0032] Divide the mesh surface of the mesh antenna after shape finding into a grid, and extract the reflector surface nodes, units and shape function information;

[0033] Calculate the first-order and second-order coefficient matrices of the overall electrical performance and obtain the displacement vector of the node relative to the ideal parabola;

[0034] Calculate the far-field electric field vector matrix caused by structural deformation; substitute the far-field observation point position vector to calculate the actual far-field electric field of the deformed reflector antenna;

[0035] Calculate the gain and sidelobe level according to the far-zone electric field, and calculate the objective function;

[0036] Solve the comprehensive optimization model until the global optimal solution of the mesh expandable antenna network topology structure under the number of nodes is found.

[0037] The invention adopts the above technical solution, which has the following beneficial effects:

[0038] The calculation of the objective function in the optimization process of this optimization method consists of two parts: form-finding and electrical performance calculation. In the form-finding process, the optimization model is solved based on the nonlinear finite element method to ensure that the cable force is distributed as evenly as possible; in the electrical performance calculation process, the physical optics method is used to approximate the electrical performance of the deformable reflector antenna using the Taylor expansion. This optimization method can generate evenly distributed nodes with any number of nodes, and improve the antenna gain and reduce the sidelobe level by optimizing the node position. The present invention can achieve the electrical performance goals of high gain and low sidelobe level with a small number of nodes, while ensuring the structural performance of evenly distributed cable force. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute an improper limitation of the present invention. In the drawings:

[0040] Figure 1 It is a flow chart of the optimization design of mesh antenna topology;

[0041] Figure 2 It is a flow chart that generates a specified number of evenly distributed nodes;

[0042] Figure 3 It is a schematic diagram of a specified number of evenly distributed nodes;

[0043] Figure 4 is a mesh antenna shape-finding flow chart corresponding to steps 301-309;

[0044] Figure 5 It is a schematic diagram of the finite element model of the ring truss cable net antenna;

[0045] Figure 6 is a flow chart of electrical performance calculation corresponding to steps 310-313 and step 101;

[0046] Figure 7 The traditional design method and the present invention obtain Comparison of electric fields in the surface and far zones. DETAILED DESCRIPTION

[0047] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The exemplary embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0048] like Figure 1As shown, the present invention proposes a method for optimizing the topological structure of a deployable mesh antenna cable net based on electrical performance and structural performance optimization, which takes the weighted sum of the mesh antenna gain and the sidelobe level as the objective function, and optimizes the node position given the number of nodes. Taking the annular truss-type deployable cable net antenna as an example, the method specifically includes the following steps:

[0049] Step 101: Determine the geometric parameters, material parameters and electrical parameters of the mesh deployable antenna, and calculate the far-zone electric field of the ideal antenna.

[0050] The geometric parameters include the antenna's aperture, focal length and offset distance; the material parameters include the material density, Poisson's ratio, elastic modulus and cross-sectional area of ​​the cable net, wire mesh and deployable structure; the electrical parameters include the operating frequency band and feed source parameters.

[0051] The electric field in the far zone of an ideal antenna Calculated according to the following formula:

[0052]

[0053] Where j represents the imaginary unit, k represents the spatial wave number, is the vector of the far observation point, The vector representing the source point, and represents vector The unit vector of represents the unit vector, η represents the free space wave impedance, is the surface current density, and Σ represents the reflection surface.

[0054] Step 102: specifying the number of mesh antenna optimization nodes and generating the initial value of the optimization model, that is, generating a specified number of uniformly distributed nodes within the mesh antenna aperture plane.

[0055] like Figure 2 As shown in the flow chart, step 102 specifically includes the following steps:

[0056] Step 201: Determine the coordinates of the connection between the cable net boundary and the deployable structure as fixed node coordinates, and give the value range of the free node coordinates x i ∈(x min ,x max ),y i ∈(y min ,y max ), where (x i ,y i ) is any free coordinate, x min ,x max For x i The maximum and minimum values ​​of y i Same reason.

[0057] Step 202: Determine the minimum distance d between points min , the number of nodes on the aperture surface is N. Theoretically, there should be a minimum distance d between points. min , so that all points are evenly distributed in the aperture surface, and the minimum distance d between all points is at d min Floating in a small range. min It can be estimated by solving the following formula

[0058]

[0059] Among them, S is the area of ​​the aperture surface, N is the number of all nodes in the aperture surface, and N out is the number of boundary nodes.

[0060] Due to the randomness of the node generation process, the d can be adjusted according to the actual operation results. min .

[0061] Step 203: Repeat the iteration to generate a new node, and determine whether the new node is within the aperture plane, and whether the minimum distance d between the new node and the existing points is greater than the minimum distance d between the points. min If both conditions are met, the node is retained and stored, otherwise the node is regenerated until a sufficient number of nodes are generated or the maximum number of iterations is reached.

[0062] Step 204: If the maximum number of iterations is reached and a sufficient number of nodes are still not generated, the minimum distance d between points needs to be reduced. min The value of

[0063] Step 205: After the iteration is completed, a specified number of uniformly distributed nodes within the mesh antenna aperture plane is obtained; Figure 3 The figure shows that 62 nodes are evenly distributed within the 1m antenna aperture.

[0064] Step 103: performing shape finding on the optimized model and calculating the electrical performance of the mesh antenna reflector after shape finding to obtain an optimized mesh antenna line grid topology structure.

[0065] With the initial value of the optimization model obtained in step 102, and with high gain and low sidelobe level as the optimization target, the optimization model is optimized under the condition of ensuring the uniformity of the rope tension as much as possible, and a cable net topology structure with good electrical and structural performance is obtained. The optimization model is as follows:

[0066]

[0067] Among them, X is the coordinate set of free nodes in the optimized aperture plane, x1, y1...x n ,y nis the coordinate of the free node in the optimized aperture plane, gain is the antenna gain, sl is the sidelobe level, σ A is the aperture surface, and the constraint condition indicates that all the optimized node coordinates are within the aperture surface.

[0068] The optimization solution of the objective function f(X)=-gain+sl in the optimization model includes two parts: shape finding and electrical performance calculation of the reflection surface after shape finding.

[0069] like Figure 4 As shown, the shape-finding steps are as follows:

[0070] Step 301: Project the two-dimensional node coordinates in the aperture plane onto the upper and lower cable mesh surfaces to obtain the upper and lower mesh surface node coordinates;

[0071] Step 302: Based on the coordinates of the upper and lower mesh nodes, the topological relationship is calculated using the Delaunay algorithm, and a three-dimensional finite element model of the mesh reflector antenna is established in ANSYS; the finite element model of the ring truss cable net antenna is shown in Figure 5 As shown;

[0072] Step 303: Given the initial stress of the cable-membrane structure, constraints are imposed on the deployable structure, static analysis is performed, node coordinates, cable tension and membrane strain under equilibrium state are extracted, and the above process is saved as a script file;

[0073] Step 304: Calculate the length L of the cable segment at equilibrium based on the geometric relationship, and calculate the original length L0 of the cable segment based on the strain;

[0074] L = [(x1-x2) T (x1-x2)] 1 / 2 (4)

[0075] L0=L / (1+ε) (5)

[0076] Among them, x1, x2 are the position vectors of nodes 1 and 2, ε c is the cable element strain.

[0077] Step 305: Calculate the difference ΔX between the grid node coordinates in the equilibrium state and the initial design value;

[0078] ΔX=X-X0(6)

[0079] where X=[(x1′,y1′,z1′),(x2′,y2′,z2′),......(x n ′,y n ′,z n ′)] are the coordinates of the free nodes at equilibrium, X0=[(x1,y1,z1),(x2,y2,z2),......(x n ,yn ,z n )] are the initial design free node coordinates.

[0080] Step 306: Calculate the sensitivity matrix K of the node position relative to the original length (including the original length of the cable segment and the unstretched length of the three sides of the membrane) under the equilibrium state according to the global equilibrium equation of the cable-membrane reflection surface through finite element analysis. X and the sensitivity matrix K of the unstretched length with respect to stress σ , the calculation method is as follows:

[0081] Sensitivity matrix K X , calculated by the following formula:

[0082] K X =-K m -1 k l (7)

[0083] Among them, K m and K l are the tangent matrices obtained by assembling the stiffness matrices of the cable and membrane elements, respectively;

[0084] K σ =K s -K d K m -1 K l (8)

[0085] Among them, K σ and K s is the corresponding tangent matrix obtained by assembling the cable and membrane element geometry matrices;

[0086] Step 307: Solve the following mechanical optimization model to find a set of ΔL0 that makes the stress closer to the specified stress state;

[0087]

[0088] Among them, σ(L0) is the stress state after form finding, σ c To specify the stress distribution state, g(L0)=H T H, H = [h1, h2, ... h n ] T , is the axial coordinate difference of the i-th reflection surface node, (x i ,y i , z i ) is the coordinate of the i-th node on the reflection surface, n is the number of nodes, and f is the focal length of the upper surface.

[0089] Step 308: Update the unstretched length L0=L0+ΔL0 in the finite element model of the reflection surface in the equilibrium state, and perform static analysis to find a new equilibrium state.

[0090] Step 309: Repeat steps 307 to 308 until the convergence criterion is met;

[0091] like Figure 6 As shown in the figure, the electrical performance calculation process is as follows:

[0092] Step 310: Divide the mesh surface of the mesh antenna after shape finding into a grid, and extract the reflector surface nodes, units and shape function information;

[0093] Step 311: Calculate the first-order and second-order coefficient matrices of the overall electrical performance;

[0094] The first-order coefficient matrix H1 is calculated as follows:

[0095]

[0096] Where A is the finite element grouping operation, m represents the total number of elements, e represents a certain element in the obtained finite element model, and h1 e is the first-order coefficient of a unit in the finite element model, and its calculation formula is as follows:

[0097]

[0098] cosθ′=cosθ s +cosθ (12)

[0099] Among them, θ represents the position vector of the far-field observation point, θ′ represents the spherical coordinate component of a point in the feed source coordinate system; θ s is the spherical coordinate component of the point in the feed source coordinate system when no deformation occurs;

[0100] The second-order coefficient matrix H2 is calculated by the following formula:

[0101]

[0102] Among them, h2 e is the second-order coefficient of a unit in the finite element model, Calculated by the following formula:

[0103]

[0104] Step 312: Obtain the node displacement vector Δz relative to the ideal parabola, that is, the displacement column vector of all nodes on the reflection surface in the z-axis direction;

[0105] Step 313: Calculate the far-field electric field vector matrix due to structural deformation

[0106]

[0107] Among them, r is the distance from the observation point to the origin of the coordinate system;

[0108] Substitute the far-field electric field vector matrix of the far-field observation point position vector into

[0109]

[0110] in, is the far-field observation point position vector.

[0111] The actual far-field electric field of the deformable reflector antenna is calculated by the following formula:

[0112]

[0113] in, is the electric field in the far zone of the ideal reflecting surface;

[0114] Step 314: Calculate the gain gain and the sidelobe level sl according to the far-field electric field, and calculate the objective function f(X):

[0115] f(X)=-gain+sl (18)

[0116] Step 315: Solve the comprehensive optimization model until the global optimal solution of the mesh expandable antenna network topology structure under the number of nodes is found.

[0117] Step 105: Change the number of optimized nodes of the mesh antenna cable network, optimize the cable network topology structure of multiple groups of mesh antennas, comprehensively compare the multiple groups of optimization results, and select the optimal topology structure with the optimal number of nodes.

[0118] The present invention can further illustrate its advantages in electrical performance through simulation experiments:

[0119] 1. Experimental conditions:

[0120] The aperture D of the forward-fed mesh antenna is 5m, the focal length of the antenna is 3m, the operating frequency is 3GHZ, and an electric dipole is used as the feed source. The material parameters are shown in Table 1.

[0121] Table 1: Material parameters of the positive-feedback ring truss

[0122]

[0123] The above specific implementation steps are programmed using software Python, Matlab and ANSYS.

[0124] 2. Experimental results

[0125] The topological structure optimized by the present invention is compared with the traditional three-way grid structure. The electric field comparison of the far area is shown in Figure 7 The experimental comparison results are shown in Table 2.

[0126] Table 2: Experimental performance comparison

[0127]

[0128] From the above experimental comparison results, it can be seen that the optimized 64-node cable net antenna can significantly reduce the sidelobe level and greatly reduce the number of cable net nodes when the gain variation range is extremely small. Therefore, it is not the case that the more nodes there are, the closer the whole is to the standard parabola, and the better the electrical performance of the reflector antenna. On the contrary, too many nodes will cause unnecessary random errors. Therefore, the method of the present invention can achieve the electrical performance goals of high gain and low sidelobe level, while ensuring the structural performance of uniform stress distribution.

[0129] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A method for optimizing the topology structure of a mesh deployable antenna network, characterized in that: The steps include: Determine the geometric parameters, material parameters and electrical parameters of the mesh antenna, and calculate the far-zone electric field of the ideal antenna; Specify the number of mesh antenna line optimization nodes, generate the specified number of uniformly distributed nodes within the mesh antenna aperture plane, and generate the initial value of the optimization model; Based on the initial value of the optimization model, the optimization model is form-finded and the electrical performance of the mesh antenna reflector after the form-finding is calculated to obtain the optimized mesh antenna line grid topology structure; Change the number of optimized nodes of the mesh antenna cable network, optimize the cable network topology of multiple groups of mesh antennas, compare multiple groups of optimization results, and select the optimal topology with the optimal number of nodes.

2. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 1, characterized in that: The geometric parameters include antenna aperture, focal length and offset distance; the material parameters include material density, Poisson's ratio, elastic modulus and cross-sectional area of ​​the cable net, deployable structure and film; and the electrical parameters include operating frequency and feed source parameters.

3. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 1, characterized in that: The far-field electric field of an ideal antenna is calculated according to the following formula Where j represents the imaginary unit, k represents the spatial wave number, is the vector of the far observation point, The vector representing the source point, and represents vector The unit vector of represents the unit vector, η represents the free space wave impedance, is the surface current density, and ∑ represents the reflection surface.

4. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 1, characterized in that: Generate initial values ​​for the optimization model, including: Determine the coordinates of the connection between the cable net boundary and the deployable structure as the fixed node coordinates, and give the value range of the free node coordinates; Determine the minimum distance between points; Generate a new node through iteration, determine whether the node is within the aperture plane, and check whether the minimum distance between the new node and the existing node is greater than the preset minimum distance threshold; if both conditions are met, retain and store the node, otherwise regenerate the node until a sufficient number of nodes are generated or the maximum number of iterations is reached; If the maximum number of iterations is reached and still not enough nodes are generated, the value of the minimum distance between points is reduced; After the iteration is completed, the initial value of the optimization model is obtained, that is, the evenly distributed nodes under the specified number.

5. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 4, characterized in that: Determine the minimum distance d between points min , calculated using the following formula: Among them, S is the area of ​​the aperture surface, N is the number of all nodes in the aperture surface, and N out is the number of boundary nodes.

6. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 1, characterized in that: The topological structured model of the antenna network is as follows: Find X=[(x1,y1),(x2,y2),......,(x n ,y n )] Min f(X)=-gain+sl S.t.X∈σ A Among them, X is the coordinate set of free nodes in the optimized aperture plane, x1, y1...x n ,y n is the coordinate of the free node in the optimized aperture plane, gain is the antenna gain, sl is the sidelobe level, σ A is the aperture surface, and the constraint condition indicates that all the optimized node coordinates are within the aperture surface.

7. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 1, characterized in that: The topological structure of the mesh antenna line mesh surface is optimized, and the shape finding of the optimization model includes solving the optimization model by a finite element analysis method to achieve uniform distribution of cable force; the calculation of the electrical performance of the mesh antenna reflector surface after shape finding includes using a physical optics method to approximately calculate the electrical performance of the deformed reflector surface antenna using a Taylor expansion.

8. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 7, characterized in that: Perform form-finding on the optimized model, including: Project the nodes in the aperture plane onto the upper and lower mesh surfaces to obtain the coordinates of the nodes on the upper and lower mesh surfaces; According to the coordinates of the upper and lower mesh nodes, the topological relationship is calculated using the Delaunay algorithm, and a three-dimensional finite element model of the mesh reflector antenna is established in ANSYS; Given the initial stress of the cable-membrane structure, constraints are imposed on the deployable structure, and static analysis is performed to extract the node coordinates, cable tension, and membrane strain in the equilibrium state. When calculating equilibrium, the length of the cable segment is calculated using the node coordinates, and the original length of the cable segment is calculated based on the strain; Calculate the difference between the mesh node coordinates in the equilibrium state and the initial design value; According to the global equilibrium equation of the cable-membrane reflection surface, the sensitivity matrix of the node position relative to the original length of the cable segment and the unstretched length of the three sides of the membrane in the equilibrium state, as well as the sensitivity matrix of the unstretched length relative to the stress are calculated; Solve the optimization model to find a set of form-finding results that are closer to the specified stress state; Update the unstretched length in the finite element model of the reflecting surface in the equilibrium state to find a new equilibrium state; Repeat the steps of solving the mechanical optimization model to find a new equilibrium state until the convergence criteria are met.

9. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 7, characterized in that: The calculation of the electrical performance of the reflector surface of the mesh antenna after shape finding includes: Divide the mesh surface of the mesh antenna after shape finding into a grid, and extract the reflector surface nodes, units and shape function information; Calculate the first-order and second-order coefficient matrices of the overall electrical performance and obtain the displacement vector of the node relative to the ideal parabola; Calculate the far-field electric field vector matrix caused by structural deformation; substitute the far-field observation point position vector to calculate the actual far-field electric field of the deformed reflector antenna; Calculate the gain and sidelobe level according to the far-zone electric field, and calculate the objective function; Solve the comprehensive optimization model until the global optimal solution of the mesh expandable antenna network topology structure under the number of nodes is found.

10. The method for optimizing the topology structure of a mesh deployable antenna network according to claim 9, characterized in that: The objective function f(X) is as follows: f(X)=-gain+sl Where gain is the gain and sl is the sidelobe level.

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