A space thin film antenna system dynamics simulation method, system, computer and storage medium based on absolute nodal coordinate method

Abstract

This invention discloses a dynamic simulation method, system, computer, and storage medium for a space thin-film antenna system based on the absolute nodal coordinate method. The space thin-film antenna is simplified into a rigid-flexible coupled multibody system composed of a flexible support frame, a tensioned cable net, and a thin-film reflector. Nonlinear cable elements are introduced between the frame and the thin film as connections. The flexible frame and the non-bending stiffness thin film are divided into elements based on the absolute nodal coordinate method. According to the theory of continuum mechanics and the principle of virtual work, a dynamic model of the flexible frame-cable net-thin film coupled multibody system under pretension is established. A form-finding strategy for gentle slope loading is proposed. The generalized -α implicit time integration algorithm is used to solve the dynamic equations of this system, obtaining curves showing the displacement and vibration attenuation of the space thin-film antenna under impact disturbance as a function of time. This invention provides a new dynamic modeling model for large-scale space thin-film antenna systems and offers researchers in this field more comprehensive data and image data.

Description

Technical Field

[0001] This invention relates to multibody system dynamics modeling technology, specifically a spatial thin-film antenna system dynamics simulation method, system, computer, and storage medium based on the absolute node coordinate method. Background Technology

[0002] As large-scale space structures in aerospace develop towards lighter weight, larger size, and higher flexibility, space thin-film antennas, with their characteristics of light weight, high packing ratio, and high surface precision requirements, have become core equipment for future high-resolution Earth observation and deep space exploration missions. These structures typically consist of a flexible support frame, a tensioned cable net, and a thin-film reflector, belonging to a typical rigid-flexible coupled multibody system, exhibiting high flexibility, low damping, and strong geometric nonlinearity. During on-orbit operation, the structure is highly susceptible to large-amplitude vibrations caused by attitude maneuvers or environmental thermal shocks, severely affecting the antenna's pointing accuracy and electrical performance.

[0003] In existing dynamic modeling studies, the traditional floating coordinate system method often introduces errors due to its approximate assumptions when dealing with strongly nonlinear problems involving large rotations and large deformations. Furthermore, there is a lack of dynamic studies on flexible frame-cable-net-film structures with rigid-flexible coupling. Therefore, establishing a simulation method capable of accurately describing the complex dynamic characteristics of space thin-film antenna systems is of significant engineering importance for improving the surface accuracy of large-scale space thin-film structures. Summary of the Invention

[0004] This invention proposes a dynamic simulation method, system, computer, and storage medium for a space thin-film antenna system based on the absolute node coordinate method.

[0005] The technical solution to achieve the purpose of this invention is: a dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method, comprising the following steps:

[0006] Step 1: Construct a rigid-flexible coupled multibody physical model of the space thin-film antenna system. The system includes an outer flexible support frame, an inner metal reflective film, and a tensioned cable net connecting the two. Set the geometric parameters, material parameters, and mesh parameters of each component, and set the motion parameters applied to the model.

[0007] Step 2: For the flexible support frame, the mass matrix, generalized elastic force vector, and tangent stiffness matrix of the beam element are derived using the absolute nodal coordinate method; for the thin film reflector, a thin film element with no bending stiffness is constructed using the absolute nodal coordinate method, and its mass matrix, generalized elastic force vector, and tangent stiffness matrix are derived; for the tensioned cable net, it is simplified into a massless nonlinear two-node cable element, and its generalized elastic force vector and tangent stiffness matrix are derived.

[0008] Step 3: Assemble the mass matrix, generalized elastic force vector, and tangent stiffness matrix of each unit into the overall mass matrix, overall generalized elastic force vector, and overall tangent stiffness matrix of the system, respectively; introduce Rayleigh damping that is linearly related to the system mass matrix and the overall tangent stiffness matrix to reflect the energy dissipation characteristics of the structure; and establish the overall dynamic equation of the flexible frame-cable net-membrane coupled system based on the first kind of Lagrange equation.

[0009] Step 4: Use the form-finding strategy of gentle slope loading to determine the initial equilibrium state of the system. Use the generalized α method to solve the dynamic equation of the flexible frame-cable net-membrane coupled system. Through iterative calculation, obtain the displacement, velocity and acceleration of each unit node at each time step. Visualize the obtained data to obtain the curves of the displacement of the membrane center and the frame side beam center as a function of time, as well as the curves of the tension of the key connecting cable as a function of time.

[0010] Furthermore, in step 1, the geometric parameters, material parameters, and mesh parameters are set. The specific method is as follows:

[0011] (1) Geometric parameters:

[0012] Geometric parameters of the flexible support frame: The length of the undeformed beam element is l, the cross-sectional area is A, and the moment of inertia is I;

[0013] Geometric parameters of the metal reflective film: the length of the film is a, the width is b, and the thickness is h;

[0014] The geometric parameters of the tensioned cable net are: the initial natural length of the cable is l0, and the cross-sectional area is A0;

[0015] (2) Material parameters:

[0016] The density of the frame material is ρ b The elastic modulus is E b ;

[0017] The density of the thin film material is ρ m The elastic modulus is E m Poisson's ratio is ;

[0018] The elastic modulus of the cable is E0;

[0019] (3) Mesh parameters:

[0020] The supporting frame is divided into N1 beam elements along its length; the metal reflective film is divided into N2×N3 film elements along the orthogonal direction of the plane.

[0021] Furthermore, in step 2, for the flexible support frame, a three-dimensional Euler-Bernoulli beam element based on the absolute nodal coordinate method is used to describe it, and its mass matrix, generalized elastic force vector, and tangent stiffness matrix are derived. The specific method is as follows:

[0022] a) Based on the global inertial coordinate system O-XYZ, any point on the central axis of the beam element... Use global absolute position vector Represented as:

[0023] ;

[0024] In the formula , , These are the position components in each direction; The shape function matrix of the beam element is represented by a cubic Hermite interpolation polynomial, specifically defined as:

[0025] ;

[0026] in for The components of the form functions of the identity matrix are:

[0027] ;

[0028] Where normalized coordinates x is the coordinate of any point P on the central axis of the beam element in the beam element coordinate system when the flexible beam is undeformed;

[0029] The generalized nodal coordinate array of the beam element consists of the generalized coordinates of two nodes i and j, with a total of 12 degrees of freedom:

[0030] ;

[0031] Wherein, the generalized coordinates of any node k (k = i, j) of the beam element It contains 6 scalar components:

[0032] ;

[0033] in, This represents the translational displacement component of node k in the beam element along the direction m. The first derivative of the translational displacement component x of node k in the direction m of the beam element is given.

[0034] b) The kinetic energy of the beam element Expressed as the volume integral of the kinetic energy of a infinitesimal element:

[0035] ;

[0036] velocity interpolation relationship Substituting and rearranging, we get:

[0037] ;

[0038] This yields the uniform mass matrix of the beam element. :

[0039] ;

[0040] c) Define elongation ratio The axial tangent vector of the beam element Modulus length:

[0041] ;

[0042] The Green-Lagrange strain tensor is used to describe the axial strain of beam elements under large deformation. :

[0043] ;

[0044] Axial tensile strain energy of beam element for:

[0045] ;

[0046] Through the curvature of the space curve The exact expression for the square of the curvature of a three-dimensional curve, used to calculate bending deformation energy, is as follows:

[0047] ;

[0048] Using Lagrange identities Expanded into a form that is easier for computers to solve:

[0049] ;

[0050] Bending strain energy of beam element for:

[0051] ;

[0052] The generalized elastic force vector of the variational element is obtained by considering the total strain energy. :

[0053] ;

[0054] (d) Axial strain energy Find the variational form, considering The generalized axial tensile force is obtained as follows:

[0055] ;

[0056] Bending generalized force with respect to the square of curvature To find the variation, using the chain rule, the result can be decomposed into the sum of four terms:

[0057] ;

[0058] The specific expansions of each item are as follows:

[0059] The first item originates from Molecular variation:

[0060] ;

[0061] The second item originates from Variation of the denominator (for) (differentiation)

[0062] ;

[0063] The third item originates from Molecular variation:

[0064] ;

[0065] The fourth item originates from Variation of the denominator (for) (differentiation)

[0066] ;

[0067] The tangent stiffness matrix of the beam element is obtained by taking partial derivatives.

[0068] .

[0069] Furthermore, in step 2, for the thin film reflecting surface, an absolute nodal coordinate method thin film element with no bending stiffness is constructed, and its mass matrix, generalized elastic force vector, and tangent stiffness matrix are derived. The specific method is as follows:

[0070] a) Based on the global inertial coordinate system O-XYZ, the global absolute position vector of any point P on the neutral surface of the thin film unit is... Through the shape function matrix With the generalized node coordinate array of the element To indicate:

[0071] ;

[0072] To facilitate numerical solutions to the subsequent dynamic equations, the shape functions of the thin film unit cells are normalized, and normalized coordinates are introduced. and ,in ;

[0073] The thin film unit consists of 4 nodes, among which The generalized coordinates of each node contain an absolute position vector. and along the coordinate axes and Tangential gradient vector of direction and single node Generalized coordinate vector Defined as:

[0074] ;

[0075] Generalized nodal coordinate array of the entire thin film unit It is assembled from the coordinates of 4 nodes and contains a total of 36 degrees of freedom:

[0076] ;

[0077] Shape function matrix Represented as:

[0078] ;

[0079] in, for The identity matrix; scalar form functions The specific expression is as follows:

[0080] ;

[0081] According to the definition of continuum mechanics, the absolute velocity vector of a thin film unit... We can obtain this directly by differentiating the position vector:

[0082] ;

[0083] The kinetic energy of the thin film unit Defined as the volume integral of the kinetic energy of a infinitesimal element:

[0084] ;

[0085] This yields the uniform mass matrix of the thin film unit. :

[0086] ;

[0087] b) The thin film unit only undergoes in-plane tensile and shear deformation, with no bending strain energy; the Green-Lagrange strain tensor is used to describe the in-plane deformation. :

[0088] ;

[0089] Where the gradient vector matrix , for identity matrix:

[0090] ;

[0091] In the formula, , , , ;

[0092] Using the generalized Hooke's law, the in-plane tensile shear strain energy can be written as:

[0093] ;

[0094] in, Here is the matrix of elastic coefficients under plane stress:

[0095] ;

[0096] The explicit expression for the generalized elastic force vector of the thin film unit is obtained as follows:

[0097] ;

[0098] The tangent stiffness matrix of the thin film element is obtained by taking partial derivatives.

[0099] .

[0100] Furthermore, in step 2, the tensioned cable net is simplified into a massless nonlinear two-node cable element, and its generalized elastic force vector and tangent stiffness matrix are derived. The specific method is as follows:

[0101] Nodes on the cable unit connection frame and nodes on the thin film The absolute position vectors in the global coordinate system are respectively and ;

[0102] The instantaneous geometric length of the cable element for:

[0103] ;

[0104] Engineering strain of cable for:

[0105] ;

[0106] strain energy of cable element The function is defined as a piecewise function:

[0107] ;

[0108] Based on the principle of virtual work, the generalized elastic force vector generated by the cable element on the system is obtained by taking the partial derivative of the strain energy with respect to the generalized coordinates. :

[0109] ;

[0110] Define the direction unit vector of the cable. The axial tension within the cable is The nodal forces generated by the cable at both ends are as follows:

[0111] ;

[0112] Tangential stiffness matrix of cable element :

[0113] ;

[0114] This matrix contains the elastic stiffness caused by the material's elasticity. and geometric stiffness caused by internal forces .

[0115] Furthermore, in step 3, Rayleigh damping, which is linearly related to the system mass matrix and the overall tangent stiffness matrix, is introduced to reflect the energy dissipation characteristics of the structure. Based on the Lagrange equation, the overall dynamic equation of the flexible frame-cable net-membrane coupled system is established. The specific method is as follows:

[0116] Integrating the mechanical contributions of the frame, membrane, and tensioned cable net, and based on the first kind of Lagrange equation, the global dynamic differential-algebraic equations (DAE) system for the flexible frame-cable net-membrane coupled system are established as follows:

[0117] ;

[0118] In the formula: M is the mass matrix assembled from the frame beam element and the membrane element;

[0119] The generalized acceleration vector of the system;

[0120] This is the complete constraint equation vector of the system, mainly describing the fixed boundary conditions at the corner points of the frame and the rigid connection constraints between frame elements;

[0121] Let be the Jacobian matrix of the constraint equations;

[0122] These are the Lagrange multiplier vectors corresponding to the constraints;

[0123] The overall generalized elastic force vector of the system is formed by the superposition of the generalized elastic force vectors of each element:

[0124] ;

[0125] It is a generalized external force vector that includes gravity, external impact loads, and control forces;

[0126] To simulate energy dissipation within the structure and suppress high-frequency numerical noise, Rayleigh damping is introduced, with damping force... Assume:

[0127] ;

[0128] in The overall tangent stiffness matrix of the system is assembled from the tangent stiffness matrices of each element;

[0129] and These are the Rayleigh mass damping coefficient and the stiffness damping coefficient, respectively;

[0130] After introducing the damping term, the dynamic equation is corrected to:

[0131] .

[0132] Further, in step 4, the initial equilibrium state of the system is determined using a form-finding strategy with gentle slope loading. The dynamic equations of the flexible frame-cable net-membrane coupled system are solved using the generalized α method. The displacement, velocity, and acceleration of each element node at each time step are obtained through iterative calculation. The obtained data are visualized to obtain curves showing the displacement of the membrane center and the frame edge beam center over time, as well as curves showing the tension of the key connecting cables over time. The specific method is as follows:

[0133] (1) Shape-finding strategy for gentle slope loading

[0134] Let the initial geometric spacing of the cable nodes be... The target pretension coefficient is Then the natural length as a function of time t changes as follows:

[0135] ;

[0136] in Loading time;

[0137] along with As the cable gradually shortens, tension drives system deformation; utilizing generalized - The numerical dissipation characteristics of the algorithm and the introduced Rayleigh damping dissipate the kinetic energy of the system during the loading process, enabling it to converge smoothly to the equilibrium position.

[0138] (2) Utilizing generalized - The algorithm is used to solve the problem.

[0139] At the start of each time step, the initial values ​​of the generalized displacement and velocity at the next time step are estimated based on the generalized displacement, velocity and acceleration at the previous time step, and the initial value of the generalized acceleration at the next time step is estimated accordingly. Then, the state variables of the intermediate time layer are calculated based on the numerical dissipation parameters and substituted into the dynamic differential-algebraic equations to calculate the residual vector.

[0140] Then, it enters the Newton-Raphson iterative loop to solve the incremental equations of system dynamics and the nonlinear constraint equations. In each loop, the increment is calculated and the velocity and position coordinates are updated until the generalized displacement increment calculation results in the iterative loop meet the set accuracy requirements, and then the iterative loop is exited.

[0141] Finally, update the acceleration and Lagrange multipliers, and proceed to the next time step calculation until the time step calculation results of the entire dynamic simulation reach the set total time requirement;

[0142] (3) Data visualization processing

[0143] In MATLAB, the time matrix, displacement matrix, and connecting cable tension matrix are visualized to obtain curves showing the displacement of the membrane center and the frame side beam center over time, as well as the tension of the key connecting cables over time.

[0144] A dynamic simulation system for a space thin-film antenna system based on the absolute node coordinate method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method, thereby realizing the dynamic simulation of the space thin-film antenna system based on the absolute node coordinate method.

[0145] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method, thereby realizing the dynamic simulation of the space thin-film antenna system based on the absolute node coordinate method.

[0146] A computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, it implements the aforementioned method for dynamic simulation of a space thin-film antenna system based on the absolute node coordinate method, thereby realizing the dynamic simulation of a space thin-film antenna system based on the absolute node coordinate method.

[0147] Compared with the prior art, the present invention has the following significant advantages: (1) The absolute node coordinate method is used to establish a multibody dynamic model of the flexible frame, tensioned cable net and thin film reflector. In this method, the position vector and its gradient under the global coordinate system are directly used as generalized coordinates. The small deformation approximation assumption of the traditional floating coordinate system method is abandoned. It can accurately describe the spatial bending deformation of the frame with a large aspect ratio and the large deformation coupling characteristics of the whole structure. Therefore, the absolute node coordinate method has better processing capability for studying spatial thin film antennas with strong geometric nonlinearity. (2) The thin film system is discretized by thin film units without bending stiffness. The out-of-plane bending term is eliminated, which effectively eliminates the non-physical bending stiffness that is easily introduced by traditional modeling and greatly improves the physical reality of thin film dynamics calculation. (3) Considering the influence of stiffness singularity in the initial stress-free state of the flexible multibody system, a gentle slope loading form-finding strategy is proposed. By applying the pretension to the system in a way that increases with time, not only is the initial equilibrium configuration without singularity obtained stably, but the elastic feedback deformation of the cable tension on the flexible frame is also accurately captured. Attached Figure Description

[0148] Figure 1 This is a flowchart of the present invention.

[0149] Figure 2 This is a schematic diagram of the frame beam unit of a thin-film antenna structure.

[0150] Figure 3 This is a schematic diagram of a thin-film antenna structure.

[0151] Figure 4 This is a schematic diagram of a flexible frame-cable net-film system.

[0152] Figure 5 This is a schematic diagram of the initial equilibrium state of the system after shape-finding analysis.

[0153] Figure 6 This is a graph showing the displacement of the membrane center node and the side beam center node as a function of time during the shape-finding process.

[0154] Figure 7 The flowchart of the generalized -α method iterative process for solving the equation.

[0155] Figure 8 This is a graph showing the change of the first-order out-of-plane modal frequency of the system with the average tension of the cable net.

[0156] Figure 9 This is a graph showing the change of the first-order out-of-plane modal frequency of the system with the elastic modulus of the thin film.

[0157] Figure 10 This is a graph showing the displacement of the membrane center node and the frame side beam center node as a function of time.

[0158] Figure 11 This is a graph showing the tension of the key connecting cable over time. Detailed Implementation

[0159] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0160] like Figure 1 As shown, the present invention provides a simulation method for the dynamic response of a thin-film antenna structure based on the absolute nodal coordinate method, comprising the following steps:

[0161] Step 1: Construct a rigid-flexible coupled multi-body physical model of the space thin-film antenna system. The system includes an outer flexible support frame, an inner metallic reflective film, and a tensioned cable net connecting the two. Set the geometric parameters, material parameters, and mesh parameters of each component, and set the motion parameters applied to the model. The specific method is as follows:

[0162] (1) Geometric parameters:

[0163] Geometric parameters of the flexible support frame: The length of the undeformed beam element is l, the cross-sectional area is A, and the moment of inertia is I;

[0164] Geometric parameters of the metal reflective film: the length of the film is a, the width is b, and the thickness is h;

[0165] The geometric parameters of the tensioned cable net are: the initial natural length of the cable is l0, and the cross-sectional area is A0;

[0166] (2) Material parameters:

[0167] The density of the frame material is ρ b The elastic modulus is E b ;

[0168] The density of the thin film material is ρ m The elastic modulus is E m Poisson's ratio is ;

[0169] The elastic modulus of the cable is E0;

[0170] (3) Mesh parameters:

[0171] The supporting frame is divided into N1 beam elements along its length; the metal reflective film is divided into N2×N3 film elements along the orthogonal direction of the plane.

[0172] Step 2: For the flexible support frame, derive its mass matrix and generalized elastic force matrix; for the thin film reflector, construct a thin film element with no bending stiffness using the absolute nodal coordinate method, and derive its mass matrix and generalized elastic force matrix; for the tensioned cable net, simplify it into a massless nonlinear two-node cable element, and derive its generalized internal force vector and tangent stiffness matrix. The specific method is as follows:

[0173] (1) The specific method for deriving the mass matrix, generalized elastic force vector, and tangent stiffness matrix of the beam element is as follows:

[0174] a) Based on the global inertial coordinate system O-XYZ, any point on the central axis of the beam element... Use global absolute position vector Represented as:

[0175] ;

[0176] In the formula , , These are the position components in each direction; The shape function matrix of the beam element is represented by a cubic Hermite interpolation polynomial, specifically defined as:

[0177] ;

[0178] in for The components of the form functions of the identity matrix are:

[0179] ;

[0180] Where normalized coordinates x is the coordinate of any point P on the central axis of the beam element in the beam element coordinate system when the flexible beam is undeformed;

[0181] The generalized nodal coordinate array of the beam element consists of the generalized coordinates of two nodes i and j, with a total of 12 degrees of freedom:

[0182] ;

[0183] Wherein, the generalized coordinates of any node k (k = i, j) of the beam element It contains 6 scalar components:

[0184] ;

[0185] in, This represents the translational displacement component of node k in the beam element along the direction m. The first derivative of the translational displacement component x of node k in the direction m of the beam element is given.

[0186] b) The kinetic energy of the beam element Expressed as the volume integral of the kinetic energy of a infinitesimal element:

[0187] ;

[0188] velocity interpolation relationship Substituting and rearranging, we get:

[0189] ;

[0190] This yields the uniform mass matrix of the beam element. :

[0191] ;

[0192] c) Define elongation ratio The axial tangent vector of the beam element Modulus length:

[0193] ;

[0194] The Green-Lagrange strain tensor is used to describe the axial strain of beam elements under large deformation. :

[0195] ;

[0196] Axial tensile strain energy of beam element for:

[0197] ;

[0198] Through the curvature of the space curve The exact expression for the square of the curvature of a three-dimensional curve, used to calculate bending deformation energy, is as follows:

[0199] ;

[0200] Using Lagrange identities The above equation can be expanded into a form that is easier for a computer to solve:

[0201] ;

[0202] Bending strain energy of beam element for:

[0203] ;

[0204] The generalized elastic force vector of the variational element is obtained by considering the total strain energy. :

[0205] ;

[0206] (d) Axial strain energy Find the variational form, considering The generalized axial tensile force is obtained as follows:

[0207] ;

[0208] Bending generalized force with respect to the square of curvature To find the variation, using the chain rule, the result can be decomposed into the sum of four terms:

[0209] ;

[0210] The specific expansions of each item are as follows:

[0211] The first item originates from Molecular variation:

[0212] ;

[0213] The second item originates from Variation of the denominator (for) (differentiation)

[0214] ;

[0215] The third item originates from Molecular variation:

[0216] ;

[0217] The fourth item originates from Variation of the denominator (for) (differentiation)

[0218] ;

[0219] The tangent stiffness matrix of the beam element is obtained by taking partial derivatives.

[0220] .

[0221] (2) The specific method for deriving the mass matrix, generalized elastic force vector, and tangent stiffness matrix of the thin film unit is as follows:

[0222] a) such as Figure 3 Based on the global inertial coordinate system O-XYZ, the global absolute position vector of any point P on the neutral surface of the thin film unit is determined. Through the shape function matrix With the generalized node coordinate array of the element To indicate:

[0223] ;

[0224] To facilitate numerical solutions to the subsequent dynamic equations, the shape functions of the thin film unit cells are normalized, and normalized coordinates are introduced. and ,in ;

[0225] The thin film unit consists of 4 nodes, among which The generalized coordinates of each node contain an absolute position vector. and along the coordinate axes and Tangential gradient vector of direction and single node Generalized coordinate vector Defined as:

[0226] ;

[0227] Generalized nodal coordinate array of the entire thin film unit It is assembled from the coordinates of 4 nodes and contains a total of 36 degrees of freedom:

[0228] ;

[0229] Shape function matrix Represented as:

[0230] ;

[0231] in, for The identity matrix; scalar form functions The specific expression is as follows:

[0232] ;

[0233] According to the definition of continuum mechanics, the absolute velocity vector of a thin film unit... We can obtain this directly by differentiating the position vector:

[0234] ;

[0235] The kinetic energy of the thin film unit Defined as the volume integral of the kinetic energy of a infinitesimal element:

[0236] ;

[0237] This yields the uniform mass matrix of the thin film unit. :

[0238] ;

[0239] b) The thin film unit only undergoes in-plane tensile and shear deformation, with no bending strain energy; the Green-Lagrange strain tensor is used to describe the in-plane deformation. :

[0240] ;

[0241] Where the gradient vector matrix , for identity matrix:

[0242] ;

[0243] In the formula, , , , ;

[0244] Using the generalized Hooke's law, the in-plane tensile shear strain energy can be written as:

[0245] ;

[0246] in, Here is the matrix of elastic coefficients under plane stress:

[0247] ;

[0248] The explicit expression for the generalized elastic force vector of the thin film unit is obtained as follows:

[0249] ;

[0250] The tangent stiffness matrix of the thin film element is obtained by taking partial derivatives.

[0251] .

[0252] (3) For tensioned cable nets, they are simplified into massless nonlinear two-node cable elements. Their generalized internal force vector and tangent stiffness matrix are derived using the following method:

[0253] Nodes on the cable unit connection frame and nodes on the thin film The absolute position vectors in the global coordinate system are respectively and ;

[0254] The instantaneous geometric length of the cable element for:

[0255] ;

[0256] Engineering strain of cable for:

[0257] ;

[0258] strain energy of cable element The function is defined as a piecewise function:

[0259] ;

[0260] Based on the principle of virtual work, the generalized elastic force vector generated by the cable element on the system is obtained by taking the partial derivative of the strain energy with respect to the generalized coordinates. :

[0261] ;

[0262] Define the direction unit vector of the cable. The axial tension within the cable is The nodal forces generated by the cable at both ends are as follows:

[0263] ;

[0264] Tangential stiffness matrix of cable element :

[0265] ;

[0266] This matrix contains the elastic stiffness caused by the material's elasticity. and geometric stiffness caused by internal forces .

[0267] Step 3: Introduce Rayleigh damping, which is linearly related to the system mass matrix and the overall tangent stiffness matrix, to reflect the energy dissipation characteristics of the structure. Combined with the internal force contributions of the nonlinear cable elements, establish the overall dynamic equation of the flexible frame-cable net-membrane coupled system based on the Lagrange equation. The specific method is as follows:

[0268] Integrating the mechanical contributions of the frame, membrane, and tensioned cable net, and based on the first kind of Lagrange equation, the global dynamic differential-algebraic equations (DAE) system for the flexible frame-cable net-membrane coupled system are established as follows:

[0269] ;

[0270] In the formula: M is the mass matrix assembled from the frame beam element and the membrane element;

[0271] The generalized acceleration vector of the system;

[0272] This is the complete constraint equation vector of the system, mainly describing the fixed boundary conditions at the corner points of the frame and the rigid connection constraints between frame elements;

[0273] Let be the Jacobian matrix of the constraint equations;

[0274] These are the Lagrange multiplier vectors corresponding to the constraints;

[0275] The overall generalized elastic force vector of the system is formed by the superposition of the generalized elastic force vectors of each element:

[0276] ;

[0277] It is a generalized external force vector that includes gravity, external impact loads, and control forces;

[0278] To simulate energy dissipation within the structure and suppress high-frequency numerical noise, Rayleigh damping is introduced, with damping force... Assume:

[0279] ;

[0280] in The overall tangent stiffness matrix of the system is assembled from the tangent stiffness matrices of each element;

[0281] and These are the Rayleigh mass damping coefficient and the stiffness damping coefficient, respectively;

[0282] After introducing the damping term, the dynamic equation is corrected to:

[0283] .

[0284] Step 4: The initial equilibrium state of the system is determined using a gentle slope loading form-finding strategy. The generalized α method is employed to solve the dynamic equations of the flexible frame-cable net-membrane coupled system. Through iterative calculations, the displacement, velocity, and acceleration of each element node at each time step are obtained. The obtained data are then visualized to obtain curves showing the displacement of the membrane center and the frame edge beam center over time, as well as the tension of the key connecting cables over time. The specific method is as follows:

[0285] (1) Shape-finding strategy for gentle slope loading

[0286] Let the initial geometric spacing of the cable nodes be... The target pretension coefficient is Then the natural length as a function of time t changes as follows:

[0287] ;

[0288] in Loading time;

[0289] along with As the cable gradually shortens, tension drives system deformation; utilizing generalized - The numerical dissipation characteristics of the algorithm and the introduced Rayleigh damping dissipate the kinetic energy of the system during the loading process, enabling it to converge smoothly to the equilibrium position.

[0290] (2) Utilizing generalized - The algorithm is used to solve the problem.

[0291] At the start of each time step, the initial values ​​of the generalized displacement and velocity at the next time step are estimated based on the generalized displacement, velocity and acceleration at the previous time step, and the initial value of the generalized acceleration at the next time step is estimated accordingly. Then, the state variables of the intermediate time layer are calculated based on the numerical dissipation parameters, and the residual vector is calculated by substituting them into the dynamic differential-algebraic equations after the active control strategy is introduced.

[0292] Then, it enters the Newton-Raphson iterative loop to solve the incremental equations of system dynamics and the nonlinear constraint equations. In each loop, the increment is calculated and the velocity and position coordinates are updated until the generalized displacement increment calculation results in the iterative loop meet the set accuracy requirements, and then the iterative loop is exited.

[0293] Finally, update the acceleration and Lagrange multipliers, and proceed to the next time step calculation until the time step calculation results of the entire dynamic simulation reach the set total time requirement.

[0294] (3) Data visualization processing

[0295] In MATLAB, the time matrix, displacement matrix, and connecting cable tension matrix are visualized to obtain curves showing the displacement of the membrane center and the frame side beam center over time, as well as the tension of the key connecting cables over time.

[0296] This invention also proposes a dynamic simulation system for a space thin-film antenna system based on the absolute node coordinate method, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method, thereby realizing the dynamic simulation of the space thin-film antenna system based on the absolute node coordinate method.

[0297] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method, thereby realizing the dynamic simulation of the space thin-film antenna system based on the absolute node coordinate method.

[0298] A computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, it implements the aforementioned method for dynamic simulation of a space thin-film antenna system based on the absolute node coordinate method, thereby realizing the dynamic simulation of a space thin-film antenna system based on the absolute node coordinate method.

[0299] Example

[0300] To verify the effectiveness of the present invention, the following embodiments were carried out.

[0301] This embodiment uses MATLAB to calculate the dynamic response of a space thin-film antenna system based on the absolute nodal coordinate method. The specific method is as follows:

[0302] Step 1: In this embodiment, the rigid-flexible coupled thin-film antenna system uses the system parameter settings shown in Table 1. The simulation environment is set to simulate low-damping conditions in space (…). The operating condition is set to be in At time 1, a pulse force with an amplitude of 20 N and a duration of 0.005 s is applied to the geometric center node of the thin film in the negative direction of the Z-axis.

[0303] Table 1 System parameter settings used in this embodiment

[0304]

[0305] Step 2: For the flexible support frame, a three-dimensional Euler-Bernoulli beam element based on the absolute nodal coordinate method is used for discretization, and its mass matrix and generalized elastic force matrix are derived. For the thin film reflector, a thin film element with no bending stiffness based on the absolute nodal coordinate method is constructed for discretization, and its mass matrix and generalized elastic force matrix are derived. For the tension cable net connecting the frame and the thin film, it is simplified into a massless nonlinear two-node cable element, a piecewise strain energy function with unidirectional force characteristics is defined, and its generalized internal force vector and tangential stiffness matrix are derived. Proceed to Step 3.

[0306] Step 3: Introduce Rayleigh damping, which is linearly related to the system mass matrix and the overall tangent stiffness matrix, to reflect the energy dissipation characteristics of the structure. Combine the internal force contribution of the nonlinear cable element, establish the overall dynamic equation of the flexible frame-cable net-membrane coupled system based on the Lagrange equation, and proceed to step 4.

[0307] Step 4: Use the form-finding strategy of gentle slope loading to determine the initial equilibrium state of the system. Use the generalized α method to solve the dynamic equations of the flexible frame-cable net-membrane coupled system. Through iterative calculation, obtain the displacement, velocity, and acceleration of each unit node at each time step. Visualize the obtained data to obtain the curves of the displacement of the membrane center and the frame side beam center as a function of time, as well as the curves of the tension of the key connecting cables as a function of time.

[0308] For such rigid-flexible coupled systems, applying full pretension directly at the initial moment can easily lead to sudden and severe acceleration at the thin-film nodes, causing computational divergence. Therefore, this paper adopts a gradual loading strategy to achieve the form-finding of the system. The form-finding process is set during the simulation time. This is performed internally. The natural length of the cable unit is controlled. The pretension is applied smoothly by varying the pretension over time. Let the initial geometric spacing of the cable nodes be... The target pretension coefficient is (Using 0.995 in this study), the function of natural length is:

[0309]

[0310] in This refers to the loading time.

[0311] along with As the cable gradually shortens, tension drives system deformation. Utilizing a generalized... The algorithm's numerical dissipation characteristics and the introduced Rayleigh damping dissipate the kinetic energy of the system during loading, enabling it to smoothly converge to the equilibrium position. Figure 5 As shown, the displacement curves of the membrane midpoint in the Z direction and the frame side beam midpoint in the Y direction during the shape-finding process are as follows: Figure 6 As shown.

[0312] During the form-finding process and subsequent simulations, the generalized α method was used to solve the dynamic equations of the flexible frame-cable net-membrane coupled system. Through iterative calculations, the displacement, velocity, and acceleration of each element node at each time step were obtained. The iterative process is as follows: Figure 7 As shown.

[0313] By adjusting the natural length shortening factor of the connecting cable, five different pretensioning conditions were set within the range of 0.999 to 0.991 to simulate the mechanical state change of the cable net from relaxation to tension. For each condition, the first-order out-of-plane diaphragm mode frequency of the system was extracted as an index to measure the effective out-of-plane stiffness of the system.

[0314] from Figure 8 Simulation results show that the first out-of-plane modal frequency of the system is highly sensitive to changes in internal tension. As the average tension of the cable net increases from 3.6 N (corresponding to a factor of 0.999) to 32.4 N (corresponding to a factor of 0.991), the first out-of-plane modal frequency of the system increases from 10.81 Hz to 20.94 Hz, an increase of nearly 100%. This indicates that under the current configuration, the dynamic stiffness of the thin film is highly dependent on the internal pre-tension field.

[0315] The overall stiffness of the flexible frame-cable net-membrane system is essentially a nonlinear superposition of the material's elastic stiffness and the geometric stiffness generated by the pretension. While maintaining a constant cable net pretension, the elastic modulus of the membrane material was also parametrically analyzed. Simulations were performed to calculate the variation of the system's first-order out-of-plane modal frequency when the membrane's elastic modulus varied within the range of 1.0 to 5.0 GPa. Figure 9As shown, compared to the significant effect of cable tension on the system frequency, the influence of the thin film elastic modulus on the first out-of-plane modal frequency is relatively weak. Within the simulation range, as the thin film elastic modulus increases significantly from 1 GPa to 5 GPa, the first out-of-plane modal frequency of the system does not increase substantially. This phenomenon reflects that the stiffness of such large flexible spatial structures under tension is mainly due to the geometric stiffness provided by the pretension field, while the elastic stiffness determined by material properties accounts for a small proportion and is secondary. This means that in engineering design, attempting to increase the antenna fundamental frequency simply by using high-modulus materials has very limited benefits, while actively controlling the stiffness by adjusting the pretension level is a more efficient technical approach.

[0316] Figure 10 The time history responses of the Z-direction displacement at the center node of the membrane and the Y-direction displacement at the center node of the side beam are shown. Under impact, the membrane deforms rapidly, and as the external force disappears, the system enters the free vibration stage. The vibration frequency, calculated from the actual vibration period of the system by measuring the time interval between adjacent peaks in the displacement curve, shows that although the displacement response of the rigid frame side beam has a small amplitude, its vibration frequency is twice the fundamental frequency of the membrane. This phenomenon reflects the vibration transmission of the tensioned overall structure. When the membrane undergoes a complete vibration cycle, whether it deforms outward in a positive or negative direction, it leads to an increase in the length of the boundary cables, thereby increasing the tension within the cables. Therefore, each up-and-down fluctuation of the membrane corresponds to two peak fluctuations in the cable tension. The frame, as the boundary support, directly bears the driving force of the cable tension. Therefore, the frame is actually excited at twice the membrane frequency. This phenomenon demonstrates that the ANCF model established in this paper successfully captures the coupling relationship between the cable net tension and the structure during large deformation.

[0317] Figure 11 The dynamic changes in tension of the key connecting cable (closest to the impact point) are shown. During the intense vibration phase following the impact, the cable tension fluctuates around its initial equilibrium value. Corresponding to the frame vibration, the cable tension also exhibits a characteristic of twice the membrane frequency. This indicates that although there is nonlinear frequency harmonic transmission within the system, the pretension ensures that the cable net remains taut throughout the dynamic process, without slackening.

[0318] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0319] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A dynamic simulation method for a space thin-film antenna system based on the absolute nodal coordinate method, characterized in that, Includes the following steps: Step 1: Construct a rigid-flexible coupled multibody physical model of the space thin-film antenna system. The system includes an outer flexible support frame, an inner metal reflective film, and a tensioned cable net connecting the two. Set the geometric parameters, material parameters, and mesh parameters of each component, and set the motion parameters applied to the model. Step 2: For the flexible support frame, the mass matrix, generalized elastic force vector, and tangent stiffness matrix of the beam element are derived using the absolute nodal coordinate method; for the thin film reflector, a thin film element with no bending stiffness is constructed using the absolute nodal coordinate method, and its mass matrix, generalized elastic force vector, and tangent stiffness matrix are derived; for the tensioned cable net, it is simplified into a massless nonlinear two-node cable element, and its generalized elastic force vector and tangent stiffness matrix are derived. Step 3: Assemble the mass matrix, generalized elastic force vector, and tangent stiffness matrix of each unit into the overall mass matrix, overall generalized elastic force vector, and overall tangent stiffness matrix of the system, respectively; introduce Rayleigh damping that is linearly related to the system mass matrix and the overall tangent stiffness matrix to reflect the energy dissipation characteristics of the structure; and establish the overall dynamic equation of the flexible frame-cable net-membrane coupled system based on the first kind of Lagrange equation. Step 4: Use the form-finding strategy of gentle slope loading to determine the initial equilibrium state of the system. Use the generalized α method to solve the dynamic equation of the flexible frame-cable net-membrane coupled system. Through iterative calculation, obtain the displacement, velocity and acceleration of each unit node at each time step. Visualize the obtained data to obtain the curves of the displacement of the membrane center and the frame side beam center as a function of time, as well as the curves of the tension of the key connecting cable as a function of time.

2. The dynamic simulation method for a space thin-film antenna system based on the absolute nodal coordinate method according to claim 1, characterized in that, Step 1: Set the geometric parameters, material parameters, and mesh parameters. The specific method is as follows: (1) Geometric parameters: Geometric parameters of the flexible support frame: The length of the undeformed beam element is l, the cross-sectional area is A, and the moment of inertia is I; Geometric parameters of the metal reflective film: the length of the film is a, the width is b, and the thickness is h; Geometric parameters of the tensioned cable net: the initial natural length of the cable is l0, and the cross-sectional area is A0; (2) Material parameters: The density of the frame material is ρ b The elastic modulus is E b ; The density of the thin film material is ρ m The elastic modulus is E m Poisson's ratio is ; The elastic modulus of the cable is E0; (3) Mesh parameters: The supporting frame is divided into N1 beam elements along its length; the metal reflective film is divided into N2×N3 film elements along the orthogonal direction of the plane.

3. The dynamic simulation method for a space thin-film antenna system based on the absolute nodal coordinate method according to claim 1, characterized in that, In step 2, for the flexible support frame, a three-dimensional Euler-Bernoulli beam element based on the absolute nodal coordinate method is used to describe it, and its mass matrix, generalized elastic force vector, and tangent stiffness matrix are derived. The specific method is as follows: a) Based on the global inertial coordinate system O-XYZ, any point on the central axis of the beam element... Use global absolute position vector Represented as: ； In the formula , , These are the position components in each direction; The shape function matrix of the beam element is represented by a cubic Hermite interpolation polynomial, specifically defined as: ； in for The components of the form functions of the identity matrix are: ； Where normalized coordinates x is the coordinate of any point P on the central axis of the beam element in the beam element coordinate system when the flexible beam is undeformed; The generalized nodal coordinate array of the beam element consists of the generalized coordinates of two nodes i and j, with a total of 12 degrees of freedom: ； Wherein, the generalized coordinates of any node k (k = i, j) of the beam element It contains 6 scalar components: ； in, This represents the translational displacement component of node k in the beam element along the direction m. The first derivative of the translational displacement component x of node k in the direction m of the beam element is given. b) The kinetic energy of the beam element Expressed as the volume integral of the kinetic energy of a infinitesimal element: ； velocity interpolation relationship Substituting and rearranging, we get: ； This yields the uniform mass matrix of the beam element. : ； c) Define elongation ratio The axial tangent vector of the beam element Modulus length: ； The Green-Lagrange strain tensor is used to describe the axial strain of beam elements under large deformation. : ； Axial tensile strain energy of beam element for: ； Through the curvature of the space curve The exact expression for the square of the curvature of a three-dimensional curve, used to calculate bending deformation energy, is: ； Using Lagrange identities Expanded into a form that is easier for computers to solve: ； Bending strain energy of beam element for: ； The generalized elastic force vector of the variational element is obtained by considering the total strain energy. : ； Axial strain energy Find the variational form, considering The generalized axial tensile force is obtained as follows: ； Bending generalized force with respect to the square of curvature To find the variation, using the chain rule, the result can be decomposed into the sum of four terms: ； The specific expansion formulas for each item are as follows: The first item originates from Molecular variation: ； The second item originates from Variation of the denominator (for) (differentiation) ； The third item originates from Molecular variation: ； The fourth item originates from Variation of the denominator (for) (differentiation) ； The tangent stiffness matrix of the beam element is obtained by taking partial derivatives. 。 4. The dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method according to claim 1, characterized in that, In step 2, for the thin film reflecting surface, an absolute nodal coordinate method thin film element with no bending stiffness is constructed, and its mass matrix, generalized elastic force vector, and tangent stiffness matrix are derived. The specific method is as follows: a) Based on the global inertial coordinate system O-XYZ, the global absolute position vector of any point P on the neutral surface of the thin film unit is... Through the shape function matrix With the generalized node coordinate array of the element To indicate: ； To facilitate numerical solutions to the subsequent dynamic equations, the shape functions of the thin film unit cells are normalized, and normalized coordinates are introduced. and ,in ; The thin film unit consists of 4 nodes, among which The generalized coordinates of each node contain an absolute position vector. and along the coordinate axes and Tangential gradient vector of direction and single node Generalized coordinate vector Defined as: ； Generalized nodal coordinate array of the entire thin film unit It is assembled from the coordinates of 4 nodes and contains a total of 36 degrees of freedom: ； Shape function matrix Represented as: ； in, for The identity matrix; scalar form functions The specific expression is as follows: ； According to the definition of continuum mechanics, the absolute velocity vector of a thin film unit... We can obtain this directly by differentiating the position vector: ； The kinetic energy of the thin film unit Defined as the volume integral of the kinetic energy of a infinitesimal element: ； This yields the uniform mass matrix of the thin film unit. : ； b) The thin film unit only undergoes in-plane tensile and shear deformation, with no bending strain energy; the Green-Lagrange strain tensor is used to describe the in-plane deformation. : ； Where the gradient vector matrix , for identity matrix: ； In the formula, , , , ; Using the generalized Hooke's law, the in-plane tensile shear strain energy can be written as: ； in, Here is the matrix of elastic coefficients under plane stress: ； The explicit expression for the generalized elastic force vector of the thin film unit is obtained as follows: ； The tangent stiffness matrix of the thin film element is obtained by taking partial derivatives. 。 5. The dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method according to claim 1, characterized in that, In step 2, the tensioned cable net is simplified into a massless nonlinear two-node cable element, and its generalized elastic force vector and tangent stiffness matrix are derived. The specific method is as follows: Nodes on the cable unit connection frame and nodes on the thin film The absolute position vectors in the global coordinate system are respectively and ; The instantaneous geometric length of the cable element for: ； Engineering strain of cable for: ； strain energy of cable element The function is defined as a piecewise function: ； Based on the principle of virtual work, the generalized elastic force vector generated by the cable element on the system is obtained by taking the partial derivative of the strain energy with respect to the generalized coordinates. : ； Define the direction unit vector of the cable. The axial tension within the cable is The nodal forces generated by the cable at both ends are as follows: ； Tangential stiffness matrix of cable element : ； This matrix contains the elastic stiffness caused by the material's elasticity. and geometric stiffness caused by internal forces .

6. The dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method according to claim 1, characterized in that, In step 3, Rayleigh damping, which is linearly related to the system mass matrix and the overall tangent stiffness matrix, is introduced to reflect the energy dissipation characteristics of the structure. Based on the Lagrange equation, the overall dynamic equation of the flexible frame-cable net-membrane coupled system is established. The specific method is as follows: Integrating the mechanical contributions of the frame, membrane, and tensioned cable net, and based on the first kind of Lagrange equation, the global dynamic differential-algebraic equations (DAE) system for the flexible frame-cable net-membrane coupled system are established as follows: ； In the formula: M is the mass matrix assembled from the frame beam element and the membrane element; The generalized acceleration vector of the system; This is the complete constraint equation vector of the system, mainly describing the fixed boundary conditions at the corner points of the frame and the rigid connection constraints between frame elements; Let be the Jacobian matrix of the constraint equations; These are the Lagrange multiplier vectors corresponding to the constraints; The overall generalized elastic force vector of the system is formed by the superposition of the generalized elastic force vectors of each element: ； It is a generalized external force vector that includes gravity, external impact loads, and control forces; To simulate energy dissipation within the structure and suppress high-frequency numerical noise, Rayleigh damping is introduced, with damping force... Assume: ； in The overall tangent stiffness matrix of the system is assembled from the tangent stiffness matrices of each element; and These are the Rayleigh mass damping coefficient and the stiffness damping coefficient, respectively; After introducing the damping term, the dynamic equation is corrected to: 。 7. The dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method according to claim 1, characterized in that, Step 4: The initial equilibrium state of the system is determined using a gentle slope loading form-finding strategy. The generalized α method is employed to solve the dynamic equations of the flexible frame-cable net-membrane coupled system. Iterative calculations are used to obtain the displacement, velocity, and acceleration of each element node at each time step. The obtained data is then visualized to obtain curves showing the displacement of the membrane center and the frame edge beam center over time, as well as the tension of the key connecting cables over time. The specific method is as follows: (1) Shape-finding strategy for gentle slope loading Let the initial geometric spacing of the cable nodes be... The target pretension coefficient is Then the natural length as a function of time t changes as follows: ； in Loading time; along with As the cable gradually shortens, tension drives system deformation; utilizing generalized - The numerical dissipation characteristics of the algorithm and the introduced Rayleigh damping dissipate the kinetic energy of the system during the loading process, enabling it to converge smoothly to the equilibrium position. (2) Utilizing generalized - The algorithm is used to solve the problem. At the start of each time step, the initial values ​​of the generalized displacement and velocity at the next time step are estimated based on the generalized displacement, velocity and acceleration at the previous time step, and the initial value of the generalized acceleration at the next time step is estimated accordingly. Then, the state variables of the intermediate time layer are calculated based on the numerical dissipation parameters and substituted into the dynamic differential-algebraic equations to calculate the residual vector. Then, it enters the Newton-Raphson iterative loop to solve the incremental equations of system dynamics and the nonlinear constraint equations. In each loop, the increment is calculated and the velocity and position coordinates are updated until the generalized displacement increment calculation results in the iterative loop meet the set accuracy requirements, and then the iterative loop is exited. Finally, update the acceleration and Lagrange multipliers, and proceed to the next time step calculation until the time step calculation results of the entire dynamic simulation reach the set total time requirement; (3) Data visualization processing In MATLAB, the time matrix, displacement matrix, and connecting cable tension matrix are visualized to obtain curves showing the displacement of the membrane center and the frame side beam center over time, as well as the tension of the key connecting cables over time.

8. A dynamic simulation system for a space thin-film antenna system based on the absolute node coordinate method, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the dynamic simulation method for a space thin-film antenna system based on the absolute node coordinate method as described in any one of claims 1 to 7, thereby realizing the dynamic simulation of the space thin-film antenna system based on the absolute node coordinate method.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the dynamic simulation method for a spatial thin-film antenna system based on the absolute node coordinate method as described in any one of claims 1 to 7, thereby realizing the dynamic simulation of a spatial thin-film antenna system based on the absolute node coordinate method.

10. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the dynamic simulation method for a spatial thin-film antenna system based on the absolute node coordinate method as described in any one of claims 1 to 7, thereby realizing the dynamic simulation of a spatial thin-film antenna system based on the absolute node coordinate method.

Images