CN113158528B - Dynamic modeling method and system for space inflation unfolding structure - Google Patents

Dynamic modeling method and system for space inflation unfolding structure Download PDF

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CN113158528B
CN113158528B CN202110527582.9A CN202110527582A CN113158528B CN 113158528 B CN113158528 B CN 113158528B CN 202110527582 A CN202110527582 A CN 202110527582A CN 113158528 B CN113158528 B CN 113158528B
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inflation
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CN113158528A (en
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孙加亮
金栋平
曹华科
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention relates to a dynamic modeling method and a system of a space inflation and deployment structure, which firstly adopts ALE-ANCF time-varying length thin shell units and a natural coordinate method to carry out dynamic modeling on a shared frame type inflation and deployment satellite system to obtain a rigid-flexible coupling system dynamic model; then, carrying out grid division on a flexible inflation tube in the co-frame type inflation deployment satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of a rigid-flexible coupling system dynamics model; establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model; introducing a kinematic constraint equation into a dynamics equation to obtain a dynamics equation after time domain dispersion, solving and processing an overlong boundary unit to obtain a processed rigid-flexible coupling system dynamics model; finally, by combining an ideal gas equation, a change curve of the expansion length along with the inflation time under different inflation rates is calculated, so that the accuracy of calculation dynamics response can be improved, and an accurate dynamics model can be constructed.

Description

Dynamic modeling method and system for space inflation unfolding structure
Technical Field
The invention relates to the field of modeling of inflatable unfolding structures, in particular to a dynamic modeling method and system of a space inflatable unfolding structure.
Background
In recent years, as the space structure is being developed towards the directions of large size, light weight and complexity, the space inflatable unfolding structure is widely applied to the on-orbit task of the spacecraft by virtue of the advantages of small folding volume, light weight, high unfolding efficiency and the like. Future spatial detection requires a telescope with higher resolution to facilitate deep space detection and research in more fields. The common frame type inflatable unfolding satellite system formed by connecting a plurality of sub-satellites and a central satellite through flexible and unfolding inflatable pipes can meet the requirement of high resolution required by deep space exploration.
However, although the co-frame type inflatable unfolding satellite system can meet the requirement of high resolution, the complex dynamics characteristics of space motion and deformation coupling are involved, the child satellite is difficult to be inflated and unfolded to a target position, the aim of improving the observation resolution can not be achieved through the synthetic aperture, and even the unfolding failure can be caused. In order to accurately describe the motion and deformation conditions in the deployment process of the co-frame type inflatable deployment satellite system, the dynamics of the deployment process of the system needs to be mastered, so that an accurate dynamics model of the deployment process of the system is constructed, and the method is a key technology for ensuring the accurate deployment of the system to a target configuration. Aiming at the dynamic description of a co-frame type inflation and deployment satellite system, a thin-shell unit and a thin-film unit which are described by a traditional absolute node coordinate-based method are adopted for modeling a flexible cylindrical inflation tube in the system, so that the dynamic response of the system deployment process cannot be accurately calculated, and therefore, a satisfactory structural dynamic calculation result is difficult to obtain by means of a traditional modeling method, and the accuracy is low.
Therefore, a method and a system for dynamic modeling of a spatial inflatable unfolding structure are needed at present to improve accuracy of dynamic response in the process of calculating the spatial inflatable unfolding structure and construct an accurate dynamic model of the spatial inflatable unfolding structure.
Disclosure of Invention
The invention aims to provide a dynamic modeling method and a system for a space inflation and deployment structure, which can build an accurate dynamic model for the space inflation and deployment structure and solve the problem that the existing dynamic modeling method can not accurately describe the dynamic characteristics of the coupling of the space motion and deformation of the space inflation and deployment structure in the deployment process.
In order to achieve the above object, the present invention provides the following solutions:
a method of dynamic modeling of a spatially inflated deployed structure, comprising the steps of:
performing dynamic modeling on the shared frame type inflatable unfolding satellite system by adopting an ALE-ANCF time-varying length thin shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamic model;
according to the rigid-flexible coupling system dynamics model, performing grid division on flexible inflation tubes in the co-frame type inflation and deployment satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model;
Establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector;
introducing the kinematic constraint equation into a dynamics equation, setting a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and carrying out iteration solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model;
and calculating dynamic response in the expansion process of the flexible inflation tube according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain a change curve of the expansion length of the flexible inflation tube along with the inflation time under different inflation rates.
Optionally, the dynamic modeling is performed on the co-frame type inflatable deployment satellite system by adopting an ALE-ANCF time-varying length thin-shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamic model, which specifically comprises the following steps:
modeling a flexible inflation tube in the co-frame type inflation and deployment satellite system by adopting the ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamics model;
Modeling rigid satellites and sub-satellites in the shared frame type inflatable unfolding satellite system by adopting a natural coordinate method to obtain a rigid satellite dynamics model;
and combining the flexible inflation tube dynamic model and the rigid satellite dynamic model to obtain a rigid-flexible coupling system dynamic model.
Optionally, modeling the flexible inflation tube in the co-frame type inflation and deployment satellite system by adopting the ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamics model, which specifically comprises the following steps:
performing configuration description on the ALE-ANCF time-varying length thin-shell unit according to the position vector of any point on the ALE-ANCF time-varying length thin-shell unit to obtain a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit;
introducing a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit by using a Lagrange multiplier method to obtain a dynamic equation of the ALE-ANCF time-varying length thin-shell unit, and determining a geometric relationship of the micro elements on the ALE-ANCF time-varying length thin-shell unit;
establishing a local curve coordinate system and a local Cartesian coordinate system on the ALE-ANCF time-varying length thin-shell unit to obtain a conversion matrix between the local curve coordinate system and the local Cartesian coordinate system, and combining the geometric relationship of the microelements on the ALE-ANCF time-varying length thin-shell unit to obtain a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit;
The flexible inflation tube is discretized into a plurality of inflation tube units by adopting a finite element assembly method, the inflation tube units and nodes are numbered orderly, and the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the inflation tube units are assembled into a new matrix according to the numbering sequence of the inflation tube units, so that the dynamic model parameters of the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the flexible inflation tube are obtained, and the flexible inflation tube dynamic model is obtained.
Optionally, the co-frame type inflatable and unfolding satellite system comprises 1 rigid satellite, 3 sub-satellites uniformly distributed around the rigid satellite, and flexible inflatable tubes connecting the rigid satellite and the sub-satellites, wherein an unfolding end of each flexible inflatable tube is respectively connected with each sub-satellite after inflatable and unfolding, and a folding end of each flexible inflatable tube is respectively connected with the rigid satellite.
Optionally, the ALE-ANCF time-varying length thin-shell unit includes a plurality of nodes, each node has a plurality of generalized coordinates, two sides of the ALE-ANCF time-varying length thin-shell unit each have 1 substance coordinate, a movement state and a deformation state of the flexible inflation tube in the inflation and deployment process are described by a mother unit mapping mode, and the mother unit is a mapping unit with regular shape and unchanged length in the ALE-ANCF time-varying length thin-shell unit.
Optionally, the meshing of the flexible inflation tube according to the rigid-flexible coupling system dynamics model to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model specifically includes:
grid division is carried out on the flexible inflation tube according to the rigid-flexible coupling system dynamics model, so that a plurality of divided flexible inflation tube grid units are obtained;
determining initial node position vectors and initial generalized velocity vectors of all flexible inflation tube grid cells according to grid size conditions of the flexible inflation tube grid cells;
and calculating the initial generalized coordinate vector and the initial generalized velocity vector of each flexible inflation tube grid unit according to the initial node position vector and the initial generalized velocity vector of each flexible inflation tube grid unit, so as to obtain the initial generalized coordinate vector and the initial generalized velocity vector of the rigid-flexible coupling system dynamics model.
Optionally, the establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector specifically includes:
Determining boundary conditions of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector;
and establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the boundary condition.
Optionally, introducing the kinematic constraint equation into a dynamics equation, setting a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and performing iterative solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model, which specifically comprises:
introducing the kinematic constraint equation into the dynamic equation by using Lagrangian multipliers, and setting simulation iteration step length to obtain the dynamic equation after time domain dispersion;
carrying out iterative solution on the dynamic equation after the time domain dispersion by adopting a generalized alpha algorithm;
in the iterative solving process, processing the boundary overlong unit in a node inserting mode to obtain a processed rigid-flexible coupling system dynamics model; the boundary overlong unit is a unit which is positioned at the boundary of the rigid-flexible coupling system dynamics model and has a length greater than an average length value.
Optionally, calculating a dynamic response in the deployment process of the flexible inflation tube according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain a change curve of the deployment length of the flexible inflation tube along with the inflation time under different inflation rates, wherein the method specifically comprises the following steps:
calculating the numerical relation between the pressure and the volume in the flexible gas tube according to the ideal gas equation and the processed rigid-flexible coupling system dynamics model;
given a constant inflation rate, adopting a generalized alpha algorithm to simulate and calculate to obtain a change curve of the expansion length of the flexible inflation tube along with inflation time at the constant inflation rate;
and adjusting the inflation rate, controlling other parameters to be unchanged, and substituting a plurality of different inflation rates into the simulation process in sequence to obtain a change curve of the expansion length of the flexible inflation tube along with the inflation time under different inflation rates.
The invention also provides a dynamic modeling system of the space inflation and deployment structure, which comprises:
the dynamic model building module is used for carrying out dynamic modeling on the shared frame type inflatable unfolding satellite system by adopting an ALE-ANCF time-varying length thin shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamic model;
The initial generalized vector acquisition module is used for meshing flexible inflation tubes in the co-frame type inflation and deployment satellite system according to the rigid-flexible coupling system dynamics model to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model;
the kinematic constraint equation building module is used for building a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized speed vector;
the dynamics model processing module is used for introducing the kinematics constraint equation into a dynamics equation, setting a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and carrying out iteration solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model;
and the dynamic response calculation module is used for calculating the dynamic response in the unfolding process of the flexible inflation tube according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain the change curve of the unfolding length of the flexible inflation tube along with the inflation time under different inflation rates.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a dynamic modeling method and a dynamic modeling system for a space inflation and deployment structure, which can accurately describe dynamic characteristics of range motion and deformation coupling of a flexible inflation tube in the space inflation and deployment structure in the deployment process by an ALE-ANCF time-varying length thin-shell unit, and are more suitable for dynamic modeling of the space inflation and deployment structure. The dynamic equation is obtained through the kinematic constraint equation of the rigid-flexible coupling system dynamic model, the dynamic equation is solved, the overlong boundary unit is processed, the ideal gas equation and the processed rigid-flexible coupling system dynamic model are utilized to calculate the dynamic response of the flexible inflation tube in the unfolding process, the change curve of the unfolding length of the flexible inflation tube along with the inflation time under different inflation rates is obtained through simulation, so that the dynamic response of the space inflation unfolding structure is obtained, the problem that the dynamic characteristics of the space inflation unfolding structure in the unfolding process cannot be accurately described by the existing modeling method is solved, the accuracy of the dynamic response of the space inflation unfolding structure in the unfolding process is improved, the dynamic model of the space inflation unfolding structure is obtained, and the dynamic characteristics of the space inflation unfolding structure are accurately described.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a dynamic modeling method for a space-inflated deployment structure according to embodiment 1 of the present invention;
fig. 2 is a schematic structural diagram of a co-frame type inflatable satellite platform according to embodiment 1 of the present invention; fig. 2 (a) is a front view of a structure of a co-frame type inflatable and expandable satellite platform, and fig. 2 (b) is a top view of a structure of a co-frame type inflatable and expandable satellite platform;
FIG. 3 is a schematic diagram showing the deformation of ALE-ANCF time-varying length thin-shell units according to embodiment 1 of the present invention;
FIG. 4 is a partial view of an initial configuration of an ALE-ANCF time-varying length thin-shell unit as provided in example 1 of the present invention;
FIG. 5 is a schematic diagram of a rigid satellite model constructed by the natural coordinate method according to embodiment 1 of the present invention;
FIG. 6 is a schematic diagram illustrating grid division of flexible inflatable tubes in a co-frame inflatable deployment satellite platform according to embodiment 1 of the present invention;
FIG. 7 is a graph showing the deployment length of a flexible inflation tube according to embodiment 1 of the present invention as a function of inflation time;
FIG. 8 is a graph showing the expansion rate of the flexible inflation tube according to embodiment 1 of the present invention
FIG. 9 is a graph showing the deployment length of a flexible inflation tube as a function of inflation time for different inflation rates provided in example 1 of the present invention;
fig. 10 is a schematic structural diagram of a dynamic modeling system of a space-inflated deployment structure according to embodiment 2 of the present invention.
Reference numerals illustrate:
the system comprises a 1-rigid satellite, a 2-sub-satellite, a 3-flexible gas filled tube, a 4-folded end, a 5-unfolded end, a 6-flexible gas filled tube grid unit, a 7-dynamics model building module, an 8-initial generalized vector acquisition module, a 9-kinematics constraint equation building module, a 10-dynamics model processing module and an 11-dynamics response calculation module.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a dynamic modeling method and a system for a space inflation and deployment structure, which are used for carrying out dynamic modeling on a shared frame type inflation and deployment satellite system by adopting an ALE-ANCF time-varying length thin-shell unit, wherein the ALE-ANCF time-varying length thin-shell unit can accurately describe the dynamic characteristics of range motion and deformation coupling of a flexible inflation tube in the space inflation and deployment structure in the deployment process, so that an accurate dynamic model is obtained, the method is suitable for constructing dynamic models of space inflation and deployment structures in various forms, the accuracy of computational dynamic response is effectively improved, and the problem that the existing dynamic modeling method cannot accurately describe the dynamic characteristics of the space motion and deformation coupling of the space inflation and deployment structure in the deployment process is solved.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1
As shown in fig. 1, the present embodiment provides a dynamic modeling method for a space inflatable unfolding structure, which specifically includes the following steps:
s1, dynamically modeling a shared frame type inflatable deployment satellite system by adopting an ALE-ANCF time-varying length thin shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamic model;
As shown in fig. 2, the co-frame type inflatable and unfolding satellite system comprises 1 rigid satellite 1 positioned in the center, 3 sub-satellites 2 uniformly distributed around the rigid satellite 1, and 3 flexible inflatable tubes 3 for connecting the rigid satellite 1 and the sub-satellites 2, wherein the total number of the flexible inflatable tubes 3 is 3, two ends of each flexible inflatable tube 3 are respectively provided with an unfolding end 5 and a folding end 4, the unfolding ends 5 of the 3 flexible inflatable tubes 3 are respectively connected with the sub-satellites 2 after being inflated and unfolded, and the folding ends 4 are respectively and directly connected with the rigid satellite 1, namely, the 3 sub-satellites 2 are uniformly connected to the 3 outer surfaces of the rigid satellite 1 through the 3 flexible inflatable tubes 3. That is, one end, i.e. the unfolding end 5, of the flexible inflation tube 3 of the 3 sub-satellites 2 is fixedly connected with the surface of the sub-satellites 2, and the other end, i.e. the folding end 4, is inflated and unfolded from the inside of the central rigid satellite 1, so that the joint of the flexible inflation tube 3 and the rigid satellite 1 is in a folded state, and the rest is in an inflated and unfolded state, and the unfolding process of the co-frame type inflated and unfolded satellite system involves dynamic characteristics of spatial movement and deformation coupling.
The step S1 specifically comprises the following steps:
s1.1, modeling a flexible inflation tube 3 in the co-frame type inflation and deployment satellite system by adopting the ALE-ANCF time-varying length thin-shell unit to obtain a dynamic model of the flexible inflation tube 3; the method specifically comprises the following steps:
In this embodiment, as shown in fig. 3, the ALE-ANCF time-varying length thin-shell unit includes 4 nodes, namely A, B, C and D, and each node has 9 generalized coordinates, namely 9 generalized coordinates are counted in the parent unit, the initial configuration and the current configuration for the same node, and 1 substance coordinate is respectively disposed at two ends of the ALE-ANCF time-varying length thin-shell unit, the motion state and the deformation state of the flexible inflatable tube 3 in the inflation and deployment process are described by the parent unit mapping method, the parent unit is a mapping unit with a regular shape and a constant length in the ALE-ANCF time-varying length thin-shell unit, and because the shape of the initial configuration of the ALE-ANCF time-varying length thin-shell unit is irregular, and the current configuration is changed in length, it is difficult to perform volume integral calculation on the ALE-ANCF time-varying length thin-shell unit by adopting the parent unit mapping method, and finally, the motion state and deformation state of the ALE-ANCF time-varying length thin-shell unit are determined by the lagrangian sub-method, and the dynamic equation of the ALE-ANCF time-varying length thin-shell unit is established by the lagrange sub-law, and the geometry equation of the strain equation of the ALE-ANCF time-varying length of the flexible inflatable tube is obtained in the inflation and the time-varying length of the flexible tube is obtained.
S1.1.1, performing configuration description on the ALE-ANCF time-varying length thin-shell unit according to a position vector of any point on the ALE-ANCF time-varying length thin-shell unit to obtain a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit; the method specifically comprises the following steps:
under the current configuration, the generalized coordinates and the position coordinates of any point of the ALE-ANCF variable-length thin-shell unit are respectively marked as q and r, and two substance coordinates m capable of changing the axial length are introduced 1 And m 2 Generalized coordinates of ALE-ANCF time-varying length thin-shell unit areWherein (1)>Describing generalized node coordinates of ALE-ANCF time-varying length thin-shell units for absolute node coordinates, T is a matrix transpose, and q A ,q B ,q C ,q D Coordinate information respectively representing 4 nodes in the ALE-ANCF time-varying length thin-shell unit is respectively composed of a global position vector of each node and slope vectors of the nodes along local coordinates x and y. Similarly, generalized coordinates of the initial configuration of the ALE-ANCF time-varying thin-shell unit and position coordinates of any point are respectively marked as q 0 And r 0 。
In the global coordinate system O-XYZ in fig. 3, the position vector of any point P on the ALE-ANCF time-varying length thin-shell element is:wherein N is e And the interpolation functions of the ALE-ANCF time-varying length thin-shell units described by absolute node coordinates are respectively represented by the coordinates of the parent units of the ALE-ANCF time-varying length thin-shell units, and the value ranges are-1 to 1. In addition, the spatial position coordinates r of any point in the ALE-ANCF time-varying length thin-shell element are labeled in FIG. 3.
The position vector r of any point is subjected to partial derivative on time t to obtain a generalized speed vector of any point on an ALE-ANCF time-varying length thin-shell unitAnd generalized acceleration vector->The method comprises the following steps of:
wherein,as a function of the shape of ALE-ANCF time-varying length thin-shell units, anInterpolation matrix N representing ALE-ANCF time-varying length thin-shell elements e For ". Cndot." in parentheses, partial derivatives, are calculated>And->Generalized velocity and acceleration for ALE-ANCF time-varying length thin-shell unitsRepresents an additional term caused by the mass flow of the flexible structure, and +.>Respectively the substance coordinates m 1 ,m 2 Partial derivatives over time t, respectively representing the rate of change of the substance coordinates at the nodes of the ALE-ANCF time-varying length thin-shell element, +.>Representing the generalized velocity of the node on the ALE-ANCF time-varying length thin-shell element.
S1.1.2, introducing a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit by adopting a Lagrangian multiplier method, obtaining a dynamic equation of the ALE-ANCF time-varying length thin-shell unit, and determining a geometric relationship of the microelements on the ALE-ANCF time-varying length thin-shell unit; the method specifically comprises the following steps:
considering the kinematic constraint phi of the ALE-ANCF time-varying length thin-shell unit, and obtaining the dynamic equation of the ALE-ANCF time-varying length thin-shell unit according to the Lagrange multiplier method as
Wherein M is a Representing the quality matrix of the ALE-ANCF time-varying length thin-shell element,generalized acceleration of ALE-ANCF time-varying length thin-shell element, F a An additional inertial force column vector representing ALE-ANCF time-varying length thin-shell element, F e Representing the elastic force column vector of ALE-ANCF time-varying length thin-shell unit, F f Generalized external force column vector representing ALE-ANCF time-varying length thin-shell element, +.>The jacobian matrix representing the constraint equation, λ represents the lagrangian multiplier. The calculation formula is as follows:
wherein S represents the area of the middle face of the parent cell, D represents the mapping matrix between the parent cell and the ALE-ANCF time-varying length thin-shell cell, N represents the shape function of the ALE-ANCF time-varying length thin-shell cell, D represents the differential operator, D (·) represents the differential of "·" in brackets, V is the volume of the ALE-ANCF time-varying length thin-shell cell, V 0 Representing the volume of the parent unit, ρ is the density of the ALE-ANCF time-varying length thin-shell unit, c is the thickness of the ALE-ANCF time-varying length thin-shell unit, f represents the external force exerted on the ALE-ANCF time-varying length thin-shell unit, E ε And E is κ Respectively ALE-ANCF time-varying length thinThe elastic coefficient matrix of the shell unit, q represents the generalized coordinates of the ALE-ANCF time-varying length shell unit, epsilon represents the strain vector, kappa and kappa of the ALE-ANCF time-varying length shell unit 0 The curvature vectors in the current and initial configurations of the faces in the ALE-ANCF time-varying length shell element are shown, respectively.
S1.1.3, establishing a local curve coordinate system and a local Cartesian coordinate system on the ALE-ANCF time-varying length thin-shell unit to obtain a conversion matrix between the local curve coordinate system and the local Cartesian coordinate system, and combining the geometric relationship of the microelements on the ALE-ANCF time-varying length thin-shell unit to obtain a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit; the method specifically comprises the following steps:
fig. 4 is a partial view of an initial configuration of an ALE-ANCF time-varying length thin-shell unit provided in this embodiment. As shown in FIG. 4, a local curve coordinate system (g) is established at any point P on the ALE-ANCF time-varying length thin-shell element 0 ) 1 -(g 0 ) 2 -n 0 And a local Cartesian coordinate system (e 0 ) 1 -(e 0 ) 2 -(e 0 ) 3 (hereinafter, the local curve coordinate system and the local cartesian coordinate system are referred to as local coordinate systems), and the calculation formulas of the coordinate axes of the two local coordinate systems are respectively:
wherein r is 0 Representing the position coordinates, n, of any point P in the initial configuration of an ALE-ANCF time-varying length thin-shell element 0 The unit normal vector of the midpoint P of the initial configuration of the ALE-ANCF time-varying length thin-shell unit is represented, I I.I.I. represents the vector ". Sum" in double vertical lines, and "×" represents the cross multiplication of two vectors;
Taking a point N near the point P, obtaining two points according to the arc length infinitesimal between the two points PNThe numerical relationship between the local coordinate systems is (g 0 ) 1 dξ+(g 0 ) 2 dη＝(e 0 ) 1 dx 0 +(e 0 ) 2 dy 0 ；
Wherein dζ and dη respectively represent a local curve coordinate system (g 0 ) 1 -(g 0 ) 2 -n 0 The upper coordinate component, dx 0 ,dy 0 Representing a local Cartesian coordinate system (e 0 ) 1 -(e 0 ) 2 -(e 0 ) 3 Coordinate components of (a);
from algebraic relations, the relation between the coordinate components of two local coordinate systems is:
wherein a and b respectively represent the arc lengths of the AB and AD sides in the initial configuration, and θ represents the coordinate axis (g) 0 ) 1 Sum (g) 0 ) 2 Included angle between T 0 A transformation matrix representing a local curvilinear coordinate system and a local cartesian coordinate system;
according to the geometric relationship of the microelements on the ALE-ANCF time-varying length thin-shell unit, the strain tensor of the ALE-ANCF time-varying length thin-shell unit is obtained as follows:
wherein ε ε Representing the strain tensor, r, of an ALE-ANCF time-varying length thin-shell element ,(·) And r 0,(·) Respectively r and r 0 Partial derivatives, T, of the element ". Cndot." in brackets 0 A transformation matrix representing a local curvilinear coordinate system and a local cartesian coordinate system;
further, the strain vector of the ALE-ANCF time-varying length thin-shell element can be obtained as:
ε＝[ε 11 ε 22 2ε 12 ] T ；
wherein ε 11 And epsilon 22 Indicating tensile strain, ε 12 Represents shear strain;
according to the transformation matrix between the two local coordinate systems of the local curve coordinate system and the local Cartesian coordinate system, obtaining the curvature tensor of the ALE-ANCF time-varying length thin-shell unit under the initial configuration as follows through the differential geometric relationThe curvature tensor of ALE-ANCF time-varying length thin-shell element in the current configuration is +.>
Wherein n represents the unit normal vector of the current configuration of the ALE-ANCF time-varying length thin-shell unit, r ,(*)(·) And r 0,(*)(·) Represents r and r 0 Respectively and sequentially obtaining partial derivatives, T, of elements ' x ' and ' · 0 A transformation matrix representing a local curvilinear coordinate system and a local cartesian coordinate system;
will T 0 The algebraic expression of the ALE-ANCF time-varying length thin-shell unit is carried into the curvature tensor of the ALE-ANCF time-varying length thin-shell unit, so that the curvature vectors of the ALE-ANCF time-varying length thin-shell unit in the initial configuration and the current configuration are respectively kappa 0 ＝[(κ 0 ) 11 (κ 0 ) 22 2(κ 0 ) 12 ] T And κ= [ κ ] 11 κ 22 2κ 12 ] T ；
Wherein, (kappa) 11 And (kappa) 22 Representing the transverse bending curvature component (κ) 12 Representing the torsional curvature component.
And S1.1.4, dispersing the flexible gas tube 3 into a plurality of gas tube units by adopting a finite element assembly method, orderly numbering the gas tube units and nodes, and assembling generalized coordinates, generalized speed, mass matrix, elastic force, additional inertia force and generalized external force of the gas tube units into a new matrix according to the numbering sequence of the gas tube units to obtain dynamic model parameters of the generalized coordinates, generalized speed, mass matrix, elastic force, additional inertia force and generalized external force of the flexible gas tube 3, thereby obtaining a dynamic model of the flexible gas tube 3.
Modeling a flexible inflation tube 3 in a shared frame type inflation and deployment satellite system by adopting ALE-ANCF time-varying length thin shell units, and sequentially numbering all inflation tube units and nodes by a finite element assembly method by dispersing the flexible inflation tube 3 into a plurality of inflation tube units; then according to the serial number sequence of the inflation tube units, the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the inflation tube units are assembled into a new matrix, and finally the generalized coordinates q of the flexible inflation tube 3 are obtained f Generalized speedMass matrix M, elastic force F e Additional inertial force F a And a generalized external force Q.
Further, consider the kinematic constraint Φ (q f T) =0, the kinetic equation of the flexible inflation tube 3 can be obtained
Wherein,represents the generalized acceleration of the flexible inflation tube 3, λ represents the lagrangian multiplier, and t represents time.
S1.2, modeling a rigid satellite 1 and a sub-satellite 2 in the shared frame type inflatable expansion satellite system by adopting a natural coordinate method to obtain a dynamic model of the rigid satellite 1; the method specifically comprises the following steps:
a rigid satellite 1 and a sub-satellite 2 in a co-frame type inflatable spread satellite system are respectively described by adopting a natural coordinate method, and fig. 5 shows a schematic diagram of a rigid satellite 1 model constructed by utilizing the natural coordinate method. As shown in fig. 5, the rigid body satellite 1 has a regular hexagonal prism shape.
Coordinate position of any point on rigid satellite 1Is arranged as
Wherein r is i And r j Respectively represent the centroids C of the rigid satellites 1 0 And global position coordinates of j points on the surface of the rigid satellite 1, u and v represent two unit vectors which are not coplanar with each other, q r Representing generalized coordinates of rigid satellite 1, I 3 Is a 3-order identity matrix, A is a constant matrix, and a 1 、a 2 And a 3 Related, a 1 、a 2 And a 3 Position coordinate vector [ La ] in local coordinate system through point P 1 ,a 2 ,a 3 ] T Obtained, L represents centroid C 0 Distance from the j point on the surface of the rigid satellite 1;
at the centroid C of rigid satellite 1 0 Establishing a local Cartesian coordinate system C- ζηζ, and calculating to obtain the position coordinate of any point on the rigid satellite 1 in the local coordinate systemWherein the upper horizontal line represents the coordinates of the vector in the local coordinate system;
according to the virtual work generated by the inertia force, the constant mass matrix calculation expression describing the rigid body satellite 1 by the natural coordinate method is obtained as follows:
wherein M is s A constant mass matrix representing the rigid body satellite 1, V ' representing the volume of the rigid body satellite 1, d representing the differential operator, d (V ') representing the differential of the volume of the rigid body satellite 1, ρ ' representing the density of the rigid body satellite 1, T representing the matrix transpose, I 3 Is a 3-order identity matrix, A is a constant matrix, and a 1 、a 2 And a 3 Related, a 1 、a 2 And a 3 Position coordinate vector [ La ] in local coordinate system through point P 1 ,a 2 ,a 3 ] T Obtained, L represents centroid C 0 He GangThe distance between the j points of the surface of the body satellite 1.
And S1.3, combining the dynamic model of the flexible gas tube 3 with the dynamic model of the rigid satellite 1 to obtain a dynamic model of the rigid-flexible coupling system.
The invention provides an ALE-ANCF time-varying length thin-shell unit for the first time based on any Lagrange-Euler description method (Arbitrary Lagrangian Eulerlian, ALE) and an absolute node coordinate method (Absolute Nodal Coordinate Formulation, ANCF), wherein the absolute node coordinate method defines the node coordinates of the ALE-ANCF time-varying length thin-shell unit under global coordinates, a slope vector is adopted to replace the node corner coordinates in the traditional finite element, and a derived system dynamics equation has the characteristics of constant quality matrix, no centrifugal force and the like, so that the calculation efficiency and the calculation precision can be improved. In any Lagrange-Euler description method, the grid nodes move flexibly, can move along with a moving object and can be fixed, and the deformation process of the flexible inflatable tube 3 can be accurately described by introducing two material coordinates and the new ALE-ANCF time-varying length thin-shell unit. The flexible inflatable tube 3 in the common frame type inflatable and unfolding satellite system is modeled by adopting an ALE-ANCF time-varying length thin shell unit, and the rigid body satellite 1 and the sub-satellite 2 in the common frame type inflatable and unfolding satellite system are modeled by adopting a natural coordinate method, so that a dynamic model of a rigid-flexible coupling system is obtained, and the problem that the dynamic modeling method in the prior art cannot accurately describe the dynamic characteristics of spatial movement and deformation coupling involved in the unfolding process of the spatial inflatable and unfolding structure is solved.
Step S2, according to the rigid-flexible coupling system dynamics model, carrying out grid division on a flexible inflation tube 3 in the co-frame type inflation and deployment satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model, wherein the method specifically comprises the following steps:
step S2.1, carrying out grid division on the flexible inflatable tube 3 according to the rigid-flexible coupling system dynamics model to obtain a plurality of divided flexible inflatable tube grid units 6, as shown in FIG. 6;
s2.2, determining initial node position vectors and initial generalized velocity vectors of the flexible inflation tube grid cells 6 according to grid size conditions of the flexible inflation tube grid cells 6;
step S2.3, calculating initial generalized coordinate vectors q of the flexible inflation tube grid units 6 according to the initial node position vectors and the initial generalized velocity vectors of the flexible inflation tube grid units 6 0 And an initial generalized velocity vectorThereby obtaining the initial generalized coordinate vector of the flexible gas tube 3 in the rigid-flexible coupling system dynamics modelAnd an initial generalized velocity vector +.>Wherein (q) 0 ) D Representing the initial generalized coordinate vector of the flexible inflation tube 3, (q) 0 ) f And (q) 0 ) r Representing the initial generalized coordinates of the flexible inflatable tube 3, < >>Represents the initial generalized velocity vector,/-for the flexible inflation tube 3>And->Representing the initial generalized velocity component of the flexible gas tube 3, T representing the matrix transpose.
Step S3, establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector, wherein the kinematic constraint equation comprises the following steps of:
s3.1, determining boundary conditions of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector;
because the dynamic model of the rigid-flexible coupling system is in a vacuum state and in a zero gravity environment, the whole system is in a completely free state, 6 rigid body inherent constraints are arranged in each rigid body satellite 1 and are divided into numerical constraints and vertical constraints, and the numerical constraint expression is |r i -r j |=l, |u|=1, |v|=1, and the vertical constraint expression is (r i -r j )⊥u,(r i -r j )⊥v,u⊥v。
S3.2, establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the boundary condition;
based on the boundary condition of the rigid-flexible coupling system dynamics model, a kinematic constraint equation phi (q S T) =0. In this embodiment, one end of the flexible inflation tube 3 is hinged to the terminal star 2, and the rigid body inherent constraint is divided into numerical constraint of unit vectors of 3 coordinate axes of the local coordinate system and vertical constraint of 3 coordinate axes of the local coordinate system, the rigid body satellite 1 has 12 degrees of freedom, and the generalized coordinate of the rigid body satellite 1 is q r ＝[q 1 … q 12 ] T Further, the kinematic constraint equation Φ of the rigid body satellite 1 is written as:
wherein q 1 -q 12 Specific generalized coordinate values of the rigid satellites 1 are respectively denoted as q S L represents the center of mass C of the rigid body satellite 1 0 And the distance between the j points of the surface of the rigid body satellite 1.
Thus, a kinematic constraint equation Φ (q S ,t)＝0，q S The specific generalized coordinate value of the rigid body satellite 1 is shown, and t is time.
Step S4, introducing the kinematic constraint equation into a dynamic equation, setting a simulation iteration step length to obtain a dynamic equation after time domain dispersion, and carrying out iterative solution and overlong boundary unit processing on the dynamic equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamic model, wherein the method specifically comprises the following steps of:
s4.1, introducing the kinematic constraint equation into a dynamic equation by utilizing Lagrangian multipliers, and setting simulation iteration step length to obtain the dynamic equation after time domain dispersion; the method specifically comprises the following steps:
Kinematic constraint equation Φ (q) of rigid-flexible coupled system dynamics model by Lagrangian multiplier λ S Introducing t) =0 into a dynamic equation of a dynamic model of the rigid-flexible coupling system, solving the dynamic equation by adopting a generalized alpha algorithm, and setting a simulation iteration step h to obtain the dynamic equation of the time domain discrete co-frame type inflatable unfolding satellite system, wherein the dynamic equation is as follows:
wherein,representing the generalized coordinate column vector of the system obtained by the n+1th step iteration after the discrete differential equation,/>A system generalized velocity column vector,/-obtained by n+1th step iteration after the discrete of differential equation>Represents the generalized acceleration column vector lambda of the system obtained by n+1st step iteration after the dispersion of the differential equation n+1 Represents the lagrangian multiplier vector and satisfies the following relationship:
where a, beta and gamma are vector parameters of the algorithm,h represents the step size of the simulation iteration,representing the system generalized coordinate column vector obtained by the nth iteration after the discrete differential equation,/the system generalized coordinate column vector is obtained by the nth iteration after the discrete differential equation>And (3) representing a system generalized velocity column vector obtained by the n-th iteration after the differential equation is discrete, wherein n represents the number of iteration steps.
S4.2, carrying out iterative solution on the dynamic equation after time domain dispersion by adopting a generalized alpha algorithm; the method specifically comprises the following steps:
In the embodiment, the simulation iteration step h is valued to be 0.0001, the generalized alpha algorithm is adopted to solve the discrete form kinetic equation, and the increment delta q of the generalized coordinate column vector of the system is obtained by calculation S And the delta lambda of Lagrangian multiplier vector, generalized coordinate column vector of the systemAnd Lagrangian multiplier vector lambda n+1 The results obtained from the previous iteration can be updated as follows:
wherein,representing the generalized coordinate column vector of the system obtained by the n+1th step iteration after the discrete differential equation,/>Representing the generalized coordinate column vector of the system, delta q, obtained by the nth iteration after the discrete of the differential equation S Represents the increment, lambda, of the generalized coordinate column vector of the system n+1 Represents the Lagrangian multiplier vector, lambda n Represents the Lagrangian multiplier vector in the previous iteration, Δλ represents the Lagrangian multiplier vectorAnd (5) increasing.
It should be noted that, in this embodiment, the simulation iteration step h is set to 0.0001, which is a preferred value, and only the value of the set iteration step h is illustrated, which is not unique, and should not be taken as a limitation on the protection scope of the present invention, but may be other values, and may be set by itself according to the actual situation.
S4.3, in the iterative solving process, processing the units with overlong boundaries in a node inserting mode to obtain a processed rigid-flexible coupling system dynamics model; the boundary overlong unit is a unit which is positioned at the boundary of the rigid-flexible coupling system dynamics model and has a length greater than an average length value.
In this embodiment, in order to avoid that the length of the boundary unit of the co-frame type inflatable and expandable satellite system is too long due to the expansion of the co-frame type inflatable and expandable satellite system, in the iterative solution process of step S4.2, the boundary too long unit is processed by adopting a node inserting method.
Substance coordinate m of inserting new node inside boundary overlong unit insert Interpolation function N by ALE-ANCF time-varying length thin-shell element e The sum-form function N can obtain all node information of the boundary unit insertion, including generalized coordinates q of the insertion node insert Generalized speed of insertion nodeAnd generalized acceleration of the inserted node->The calculated expression is:
wherein,a rate of change of the substance coordinates representing the inserted node, < + >>Acceleration representing the material coordinates of the inserted node, +.>And->Respectively indicate->And N T Partial derivatives of the element ". Cndot.,>representation->Partial derivatives of the element ". Cndot.,>and describing generalized node coordinates of the ALE-ANCF time-varying length thin-shell unit for absolute node coordinates, wherein ζ and η are parent unit coordinates of the ALE-ANCF time-varying length thin-shell unit respectively, and T represents matrix transposition. />
Step S5, calculating dynamic response in the unfolding process of the flexible inflatable tube 3 according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain a change curve of the unfolding length of the flexible inflatable tube 3 along with the inflation time under different inflation rates, wherein the method specifically comprises the following steps:
S5.1, calculating the numerical relation between the pressure and the volume in the flexible gas tube 3 according to the ideal gas equation and the processed rigid-flexible coupling system dynamics model;
in this embodiment, the ideal gas equation expression used is:
wherein P represents pressure, V a Represents the volume of the charge gas, M represents the mass of the charge gas, M g The molar mass of the gas is represented by R, the gas constant is represented by R, and the ambient temperature is represented by T.
According to the processed rigid-flexible coupling system dynamics model, the ideal gas equation expression is utilized to obtain the pressure P and the volume V in the flexible gas tube 3 a Is a numerical relationship of (a).
S5.2, giving a constant inflation rate, and adopting a generalized alpha algorithm to simulate and calculate to obtain a change curve of the expansion length of the flexible inflation tube 3 along with inflation time under the constant inflation rate; the method specifically comprises the following steps:
simulation using MATLAB software by numerical relationship of volume and pressure in flexible inflation tube 3, in this example, given a constant inflation rate of v=5×10 -4 g/s, the ambient temperature is T=300K, the gas filled is nitrogen, the generalized alpha algorithm is adopted, and simulation calculation is carried out to obtain a change curve of the expansion length of the flexible inflation tube 3 in the inflation and expansion process of the co-frame type inflation and expansion satellite system along with the inflation time, as shown in fig. 7. It is further possible to calculate the development speed of the flexible inflation tube 3 during the development of the system as a function of the inflation time, as shown in fig. 8.
S5.3, adjusting the inflation rate, controlling other parameters to be unchanged, and substituting a plurality of different inflation rates into the simulation process in sequence to obtain a change curve of the expansion length of the flexible inflation tube 3 along with the inflation time under different inflation rates; the method specifically comprises the following steps:
the constant aeration rate in step S5.2 was v=5×10 -4 g/s is respectively enlarged to 2 times and 4 times of the originalTwo new inflation rates were obtained, v1=1×10, respectively -3 g/s、v2＝2×10 -3 g/S, controlling other system parameters to be kept unchanged, and obtaining the influence rule of three inflation rates v, v1 and v2 on the inflation tube expansion length by using the same method in the step S5.2 to obtain a graph of the expansion length of the flexible inflation tube 3 along with the inflation time under different inflation rates as shown in fig. 9. The observation of the curve shows that the larger the inflation rate is, the shorter the flexible inflation tube 3 is unfolded to the target length, so that the inflation time is further controlled, and the flexible inflation tube 3 can be precisely controlled to be unfolded to the target length.
The dynamic characteristics of the range motion and deformation coupling of the flexible inflatable tube 3 in the space inflation and deployment structure during the deployment process can be accurately described through the ALE-ANCF time-varying length thin-shell unit, and the dynamic modeling method is more suitable for dynamic modeling of the space inflation and deployment structure. The dynamic equation is obtained through the kinematic constraint equation of the rigid-flexible coupling system dynamic model, the dynamic equation is solved, the overlong boundary unit is processed, the ideal gas equation and the processed rigid-flexible coupling system dynamic model are utilized to calculate the dynamic response of the flexible inflatable tube 3 in the unfolding process, the change curve of the unfolding length of the flexible inflatable tube 3 along with the inflation time under different inflation rates is obtained through simulation, so that the dynamic response of a more accurate space inflation unfolding structure is obtained, the problem that the dynamic characteristics of the space inflation unfolding structure in the unfolding process cannot be accurately described by the existing modeling method is solved, the accuracy of the dynamic response of the space inflation unfolding structure in the unfolding process is improved, the dynamic model of the more accurate space inflation unfolding structure is obtained, and the dynamic characteristics of the space inflation unfolding structure are more accurately described.
Example 2
As shown in fig. 10, the present embodiment proposes a dynamic modeling system for a space-inflated deployment structure, specifically including:
the dynamics model building module 7 is used for carrying out dynamics modeling on the shared frame type inflatable unfolding satellite system by adopting an ALE-ANCF time-varying length thin shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamics model;
the initial generalized vector acquisition module 8 is used for carrying out grid division on the flexible inflation tube 3 in the co-frame type inflation and deployment satellite system according to the rigid-flexible coupling system dynamics model to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model;
a kinematic constraint equation establishing module 9, configured to establish a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector;
the dynamics model processing module 10 is configured to introduce the kinematic constraint equation into a dynamics equation, set a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and perform iteration solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model;
The dynamic response calculation module 11 is configured to calculate a dynamic response in the deployment process of the flexible inflation tube 3 according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjust the inflation rate to obtain a change curve of the deployment length of the flexible inflation tube 3 with respect to the inflation time at different inflation rates.
In this specification, all embodiments are mainly described and are different from other embodiments, and the same similar parts between the embodiments are mutually referred to. The principles and embodiments of the present invention have been described in this specification with reference to specific examples, the description of which is only for the purpose of aiding in understanding the method of the present invention and its core ideas; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (8)

1. A method of dynamic modeling of a spatially inflated deployed structure, comprising the steps of:
performing dynamic modeling on the shared frame type inflatable unfolding satellite system by adopting an ALE-ANCF time-varying length thin shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamic model;
According to the rigid-flexible coupling system dynamics model, performing grid division on flexible inflation tubes in the co-frame type inflation and deployment satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model;
establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector;
introducing the kinematic constraint equation into a dynamics equation, setting a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and carrying out iteration solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model;
according to an ideal gas equation and the processed rigid-flexible coupling system dynamics model, calculating dynamics response in the flexible inflation tube unfolding process, and adjusting inflation rates to obtain a change curve of the unfolding length of the flexible inflation tube along with inflation time under different inflation rates;
the method for dynamically modeling the shared frame type inflatable unfolding satellite system by adopting the ALE-ANCF time-varying length thin shell unit and the natural coordinate method to obtain a rigid-flexible coupling system dynamic model comprises the following steps:
Modeling a flexible inflation tube in a co-frame type inflation and deployment satellite system by adopting an ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamics model;
modeling rigid satellites and sub-satellites in the shared frame type inflatable unfolding satellite system by adopting a natural coordinate method to obtain a rigid satellite dynamics model;
combining the flexible inflation tube dynamic model and the rigid satellite dynamic model to obtain a rigid-flexible coupling system dynamic model;
modeling a flexible inflation tube in a co-frame type inflation and deployment satellite system by adopting an ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamics model, wherein the modeling comprises the following steps:
performing configuration description on the ALE-ANCF time-varying length thin-shell unit according to the position vector of any point on the ALE-ANCF time-varying length thin-shell unit to obtain a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit;
introducing a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit by using a Lagrange multiplier method to obtain a dynamic equation of the ALE-ANCF time-varying length thin-shell unit, and determining a geometric relationship of the micro elements on the ALE-ANCF time-varying length thin-shell unit;
Establishing a local curve coordinate system and a local Cartesian coordinate system on the ALE-ANCF time-varying length thin-shell unit to obtain a conversion matrix between the local curve coordinate system and the local Cartesian coordinate system, and combining the geometric relationship of the microelements on the ALE-ANCF time-varying length thin-shell unit to obtain a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit;
the flexible inflation tube is discretized into a plurality of inflation tube units by adopting a finite element assembly method, the inflation tube units and nodes are numbered orderly, and the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the inflation tube units are assembled into a new matrix according to the numbering sequence of the inflation tube units, so that the dynamic model parameters of the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the flexible inflation tube are obtained, and the flexible inflation tube dynamic model is obtained.
2. The dynamic modeling method of a space inflation and deployment structure according to claim 1, wherein the co-frame type inflation and deployment satellite system comprises 1 rigid satellite, 3 sub-satellites uniformly distributed around the rigid satellite and the flexible inflation tubes connecting the rigid satellite and the sub-satellites, the deployment end of each flexible inflation tube is respectively connected with each sub-satellite after inflation and deployment, and the deployment end is respectively connected with the rigid satellite.
3. The dynamic modeling method of a space-inflated and expanded structure according to claim 1, wherein the ALE-ANCF time-varying length thin-shell unit comprises a plurality of nodes, each node has a plurality of generalized coordinates, and each of two sides of the ALE-ANCF time-varying length thin-shell unit has 1 substance coordinate, and the motion state and the deformation state of the flexible inflatable tube in the inflation and expansion process are described by a mother unit mapping mode, wherein the mother unit is a mapping unit with regular shape and unchanged length in the ALE-ANCF time-varying length thin-shell unit.
4. The dynamic modeling method of a space inflation and deployment structure according to claim 1, wherein the meshing of the flexible inflation tubes in the co-frame type inflation and deployment satellite system is performed according to the rigid-flexible coupling system dynamic model to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamic model, and the method specifically comprises the following steps:
grid division is carried out on the flexible inflation tube according to the rigid-flexible coupling system dynamics model, so that a plurality of divided flexible inflation tube grid units are obtained;
determining initial node position vectors and initial generalized velocity vectors of all flexible inflation tube grid cells according to grid size conditions of the flexible inflation tube grid cells;
And calculating the initial generalized coordinate vector and the initial generalized velocity vector of each flexible inflation tube grid unit according to the initial node position vector and the initial generalized velocity vector of each flexible inflation tube grid unit, so as to obtain the initial generalized coordinate vector and the initial generalized velocity vector of the rigid-flexible coupling system dynamics model.
5. The method for dynamic modeling of a spatial inflatable unfolding structure according to claim 1, wherein the establishing a kinematic constraint equation of the rigid-flexible coupling system dynamic model according to the initial generalized coordinate vector and the initial generalized velocity vector specifically comprises:
determining boundary conditions of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized velocity vector;
and establishing a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the boundary condition.
6. The method for modeling dynamics of a space inflation and deployment structure according to claim 1, wherein the steps of introducing the kinematic constraint equation into the dynamics equation, setting a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and performing iterative solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model, specifically include:
Introducing the kinematic constraint equation into the dynamic equation by using Lagrangian multipliers, and setting simulation iteration step length to obtain the dynamic equation after time domain dispersion;
carrying out iterative solution on the dynamic equation after the time domain dispersion by adopting a generalized alpha algorithm;
in the iterative solving process, processing the boundary overlong unit in a node inserting mode to obtain a processed rigid-flexible coupling system dynamics model; the boundary overlong unit is a unit which is positioned at the boundary of the rigid-flexible coupling system dynamics model and has a length greater than an average length value.
7. The method for dynamic modeling of a spatial inflatable deployment structure according to claim 1, wherein the calculating the dynamic response of the flexible inflatable tube during deployment according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate, and obtaining a change curve of the deployment length of the flexible inflatable tube with respect to inflation time at different inflation rates, specifically comprises:
calculating the numerical relation between the pressure and the volume in the flexible gas tube according to the ideal gas equation and the processed rigid-flexible coupling system dynamics model;
Given a constant inflation rate, adopting a generalized alpha algorithm to simulate and calculate to obtain a change curve of the expansion length of the flexible inflation tube along with inflation time at the constant inflation rate;
and adjusting the inflation rate, controlling other parameters to be unchanged, and substituting a plurality of different inflation rates into the simulation process in sequence to obtain a change curve of the expansion length of the flexible inflation tube along with the inflation time under different inflation rates.
8. A system for dynamic modeling of a space-filling, deployment structure, comprising:
the dynamic model building module is used for carrying out dynamic modeling on the shared frame type inflatable unfolding satellite system by adopting an ALE-ANCF time-varying length thin shell unit and a natural coordinate method to obtain a rigid-flexible coupling system dynamic model;
the initial generalized vector acquisition module is used for meshing flexible inflation tubes in the co-frame type inflation and deployment satellite system according to the rigid-flexible coupling system dynamics model to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamics model;
the kinematic constraint equation building module is used for building a kinematic constraint equation of the rigid-flexible coupling system dynamics model according to the initial generalized coordinate vector and the initial generalized speed vector;
The dynamics model processing module is used for introducing the kinematics constraint equation into a dynamics equation, setting a simulation iteration step length to obtain a dynamics equation after time domain dispersion, and carrying out iteration solution and overlong boundary unit processing on the dynamics equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamics model;
the dynamic response calculation module is used for calculating dynamic response in the unfolding process of the flexible inflation tube according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain a change curve of the unfolding length of the flexible inflation tube along with the inflation time at different inflation rates;
the method for dynamically modeling the shared frame type inflatable unfolding satellite system by adopting the ALE-ANCF time-varying length thin shell unit and the natural coordinate method to obtain a rigid-flexible coupling system dynamic model comprises the following steps:
modeling a flexible inflation tube in a co-frame type inflation and deployment satellite system by adopting an ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamics model;
modeling rigid satellites and sub-satellites in the shared frame type inflatable unfolding satellite system by adopting a natural coordinate method to obtain a rigid satellite dynamics model;
Combining the flexible inflation tube dynamic model and the rigid satellite dynamic model to obtain a rigid-flexible coupling system dynamic model;
modeling a flexible inflation tube in a co-frame type inflation and deployment satellite system by adopting an ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamics model, wherein the modeling comprises the following steps:
performing configuration description on the ALE-ANCF time-varying length thin-shell unit according to the position vector of any point on the ALE-ANCF time-varying length thin-shell unit to obtain a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit;
introducing a kinematic constraint equation of the ALE-ANCF time-varying length thin-shell unit by using a Lagrange multiplier method to obtain a dynamic equation of the ALE-ANCF time-varying length thin-shell unit, and determining a geometric relationship of the micro elements on the ALE-ANCF time-varying length thin-shell unit;
establishing a local curve coordinate system and a local Cartesian coordinate system on the ALE-ANCF time-varying length thin-shell unit to obtain a conversion matrix between the local curve coordinate system and the local Cartesian coordinate system, and combining the geometric relationship of the microelements on the ALE-ANCF time-varying length thin-shell unit to obtain a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit;
The flexible inflation tube is discretized into a plurality of inflation tube units by adopting a finite element assembly method, the inflation tube units and nodes are numbered orderly, and the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the inflation tube units are assembled into a new matrix according to the numbering sequence of the inflation tube units, so that the dynamic model parameters of the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the generalized external force of the flexible inflation tube are obtained, and the flexible inflation tube dynamic model is obtained.
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