CN113158528A - Dynamics modeling method and system for space inflation unfolding structure - Google Patents
Dynamics modeling method and system for space inflation unfolding structure Download PDFInfo
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Abstract
The invention relates to a dynamic modeling method and a dynamic modeling system for a space inflation unfolding structure, wherein firstly, an ALE-ANCF time-varying length thin-shell unit and a natural coordinate method are adopted to carry out dynamic modeling on a common-frame type inflation unfolding satellite system to obtain a rigid-flexible coupling system dynamic model; then, carrying out grid division on flexible inflation tubes in the common-frame type inflation unfolding satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of a rigid-flexible coupling system dynamic model; then establishing a kinematic constraint equation of the rigid-flexible coupling system dynamic model; introducing a kinematic constraint equation into a kinetic equation to obtain a time-domain discretized kinetic equation, solving and performing overlong boundary unit processing to obtain a processed rigid-flexible coupling system kinetic model; and finally, by combining an ideal gas equation, calculating to obtain a change curve of the expansion length along with the inflation time at different inflation rates, so that the accuracy of calculating the dynamic response can be improved, and an accurate dynamic model can be constructed.
Description
Technical Field
The invention relates to the field of inflatable unfolding structure modeling, in particular to a dynamic modeling method and system for a space inflatable unfolding structure.
Background
In recent years, with the development of aerospace structures toward large-scale, light-weight and complex directions, the space inflation 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 space exploration requires telescopes with higher resolution to facilitate deep space exploration and more field research. The requirement of high resolution required by deep space exploration can be met by establishing a common-frame type inflatable expansion satellite system which is formed by connecting a plurality of subsateters and a central satellite through a flexible expandable inflation tube.
However, although the co-frame type inflatable deployment satellite system can meet the requirement of high resolution, the co-frame type inflatable deployment satellite system involves complex dynamics characteristics of spatial motion and deformation coupling, and it is difficult to inflate and deploy the subsatellite to a target position, so that the purpose of improving observation resolution through a synthetic aperture cannot be achieved, and even deployment failure is caused. In order to accurately describe the motion and deformation conditions of the common-frame type inflatable unfolding satellite system in the unfolding process, the dynamic characteristics of the system in the unfolding process need to be mastered, so that an accurate dynamic model of the system in the unfolding process is constructed, and the method is a key technology for ensuring the system to be accurately unfolded to a target configuration. Aiming at the dynamics description of a common-frame type inflatable unfolding satellite system, a flexible cylindrical inflatable tube in the system is modeled by a thin shell unit and a thin film unit which are described by a traditional absolute node coordinate-based method, and the dynamics response of the unfolding process of the system cannot be accurately calculated, so that a satisfactory structural dynamics calculation result is difficult to obtain by the traditional modeling method, and the accuracy is low.
Therefore, a dynamic modeling method and a dynamic modeling system for a space inflation unfolding structure are needed to improve the accuracy of calculating the dynamic response of the space inflation unfolding structure in the unfolding process and construct an accurate dynamic model of the space inflation unfolding structure.
Disclosure of Invention
The invention aims to provide a dynamic modeling method and a dynamic modeling system for a space inflatable unfolding structure, which can be used for establishing an accurate dynamic model for the space inflatable unfolding structure and solving the problem that the existing dynamic modeling method cannot accurately describe the dynamic characteristics of space motion and deformation coupling of the space inflatable unfolding structure in the unfolding process.
In order to achieve the purpose, the invention provides the following scheme:
a dynamic modeling method of a space inflation unfolding structure comprises the following steps:
performing dynamic modeling on the common-frame type inflatable expansion 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 dynamic model, carrying out grid division on flexible inflation tubes in the common-rack type inflation unfolding satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamic model;
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;
introducing the kinematic constraint equation into a kinetic equation, setting a simulation iteration step length to obtain a time-domain discretized kinetic equation, and performing iteration solution and overlong boundary unit processing on the time-domain discretized kinetic equation to obtain a processed rigid-flexible coupling system kinetic model;
and calculating the dynamic response of the flexible inflation tube in the expansion process 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 expansion length of the flexible inflation tube along with the inflation time at different inflation rates.
Optionally, the dynamic modeling is performed on the common-frame type inflatable deployment satellite system by using the ALE-ANCF time-varying length thin-shell unit and the natural coordinate method to obtain a rigid-flexible coupling system dynamic model, which specifically includes:
modeling a flexible inflation tube in the common-rack type inflation unfolding satellite system by adopting the ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamic model;
modeling the rigid body satellite and the subsatellite in the common-frame type inflatable expansion satellite system by adopting a natural coordinate method to obtain a rigid body satellite dynamic model;
and combining the flexible inflation tube dynamic model with the rigid satellite dynamic model to obtain a rigid-flexible coupling system dynamic model.
Optionally, the flexible inflation tube in the common-frame type inflation and deployment satellite system is modeled by using the ALE-ANCF time-varying length thin-shell unit, so as to obtain a dynamic model of the flexible inflation tube, which specifically includes:
according to the position vector of any point on the ALE-ANCF time-varying length thin-shell unit, performing configuration description 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 adopting a Lagrange multiplier method to obtain a kinetic equation of the ALE-ANCF time-varying length thin-shell unit, and determining the geometric relation of the infinitesimal 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 obtaining a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit by combining the geometric relation of the infinitesimal elements on the ALE-ANCF time-varying length thin-shell unit;
the method comprises the steps of dispersing the flexible inflation tube into a plurality of inflation tube units by adopting a finite element assembly method, sequentially numbering the inflation tube units and nodes, assembling the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertial force and the external force of the inflation tube units into a new matrix according to the numbering sequence of the inflation tube units, obtaining the dynamic model parameters of the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertial force and the generalized external force of the flexible inflation tube, and obtaining the dynamic model of the flexible inflation tube.
Optionally, the common-rack type inflatable expansion satellite system includes 1 rigid satellite, 3 flexible inflation tubes uniformly distributed around the rigid satellite and connected to the sub-satellites, wherein an expansion end of each flexible inflation tube is respectively connected to each sub-satellite after being inflated and expanded, and a furling end of each flexible inflation tube is respectively connected to 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, and each of two sides of the ALE-ANCF time-varying length thin-shell unit has 1 material coordinate, and the motion state and the deformation state of the flexible inflation tube during the inflation and deployment process are described in a manner of mapping by a parent unit, where 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.
Optionally, the mesh division is performed on the flexible gas-filled tube 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 mesh division specifically includes:
meshing the flexible inflation tube according to the rigid-flexible coupling system dynamic model to obtain a plurality of divided flexible inflation tube meshing units;
determining an initial node position vector and an initial generalized velocity vector of each flexible inflation tube grid unit according to the grid size condition of the flexible inflation tube grid unit;
and calculating an initial generalized coordinate vector and an 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 dynamic model.
Optionally, 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 includes:
determining a boundary condition of the rigid-flexible coupling system dynamic 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 dynamic model according to the boundary condition.
Optionally, the introducing the kinematic constraint equation into the kinetic equation, setting a simulation iteration step length to obtain a time-domain discretized kinetic equation, and performing iteration solution and overlong boundary unit processing on the time-domain discretized kinetic equation to obtain a processed rigid-flexible coupling system kinetic model specifically includes:
introducing the kinematic constraint equation into a kinetic equation by using a Lagrange multiplier, and setting a simulation iteration step length to obtain a time domain discretized kinetic equation;
iterative solution is carried out on the time domain discretized kinetic equation by adopting a generalized alpha algorithm;
in the iterative solution process, processing the boundary overlong unit by adopting a node insertion mode to obtain a processed rigid-flexible coupling system dynamic model; the boundary overlength unit is a unit which is positioned at the boundary of the rigid-flexible coupling system dynamic model and has a length larger than the average length value.
Optionally, the calculating, according to an ideal gas equation and the processed rigid-flexible coupling system kinetic model, a kinetic response of the flexible inflation tube in the expansion process, and adjusting the inflation rate to obtain a variation curve of the expansion length of the flexible inflation tube with the inflation time at different inflation rates specifically includes:
calculating the numerical relation between the pressure and the volume in the flexible inflation tube according to the ideal gas equation and the processed rigid-flexible coupling system dynamic model;
giving a constant inflation rate, and obtaining a variation curve of the expansion length of the flexible inflation tube along with inflation time at the constant inflation rate by adopting generalized alpha algorithm simulation calculation;
adjusting the inflation rate, controlling other parameters to be kept unchanged, and sequentially substituting a plurality of different inflation rates into the simulation process to obtain the variation curve of the expansion length of the flexible inflation tube along with the inflation time at different inflation rates.
The invention also provides a dynamic modeling system of the space inflation unfolding structure, which comprises the following components:
the dynamic model establishing module is used for performing dynamic modeling on the common-frame type inflatable expansion 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 carrying out grid division on a flexible inflation tube in the common-rack type inflation unfolding satellite system 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;
the kinematic constraint equation establishing module is used for 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;
the dynamic model processing module is used for introducing the kinematic constraint equation into the dynamic equation, setting simulation iteration step length to obtain a dynamic equation after time domain dispersion, and performing iteration solution and overlong boundary unit processing on the dynamic equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamic model;
and the dynamic response calculation module is used for calculating the dynamic response of the flexible inflation tube in the expansion process 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 expansion length of the flexible inflation tube along with the inflation time at 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 inflatable unfolding structure. The dynamic equation is obtained through the kinematic constraint equation of the dynamic model of the rigid-flexible coupling system, solving a kinetic equation and processing an overlong boundary unit, calculating a kinetic response of the flexible inflation tube in the expansion process by using an ideal gas equation and a processed rigid-flexible coupling system kinetic model, simulating to obtain a change curve of the expansion length of the flexible inflation tube along with the inflation time at different inflation rates, therefore, more accurate dynamic response of the space inflatable unfolding structure is obtained, the problem that the existing modeling method cannot accurately describe the dynamic characteristics of the space inflatable unfolding structure in the unfolding process is solved, the accuracy of calculating the dynamic response of the space inflatable unfolding structure in the unfolding process is improved, a more accurate dynamic model of the space inflatable unfolding structure is obtained, and the dynamic characteristics of the space inflatable unfolding structure are more accurately described.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings 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 it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a schematic flow chart of a dynamic modeling method for a space inflation deployment structure provided in embodiment 1 of the present invention;
fig. 2 is a schematic structural diagram of a common-frame inflatable expansion satellite platform according to embodiment 1 of the present invention; fig. 2(a) is a front structural view of the common-frame type inflatable unfolding satellite platform, and fig. 2(b) is a top structural view of the common-frame type inflatable unfolding satellite platform;
fig. 3 is a schematic diagram of a variant of an ALE-ANCF time-varying length thin-shell unit provided in embodiment 1 of the present invention;
FIG. 4 is a partial view of the initial configuration of the ALE-ANCF time varying length thin shell element provided in example 1 of the present invention;
fig. 5 is a schematic diagram of a rigid body satellite model constructed by a natural coordinate method according to embodiment 1 of the present invention;
fig. 6 is a schematic diagram illustrating meshing of flexible inflation tubes in a common-frame type inflatable deployment satellite platform according to embodiment 1 of the present invention;
FIG. 7 is a graph of the deployed length of a flexible inflation tube as a function of inflation time as provided in example 1 of the present invention;
FIG. 8 is a graph of the deployment speed of a flexible inflation tube as a function of inflation time as provided in example 1 of the present invention
FIG. 9 is a graph of the deployed length of a flexible inflation tube as a function of inflation time at different inflation rates as provided in example 1 of the present invention;
FIG. 10 is a schematic structural diagram of a dynamic modeling system for a space inflation deployment structure provided in example 2 of the present invention.
Description of reference numerals:
the dynamic simulation model comprises a rigid body satellite 1, a subsatellite 2, a flexible inflation tube 3, a folding end 4, a unfolding end 5, a flexible inflation tube grid unit 6, a dynamic model building module 7, an initial generalized vector acquisition module 8, a kinematic constraint equation building module 9, a dynamic model processing module 10 and a dynamic response calculation module 11.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a dynamic modeling method and a dynamic modeling system for a space inflation unfolding structure, wherein an ALE-ANCF time-varying length thin-shell unit is adopted to carry out dynamic modeling on a common-frame type inflation unfolding satellite system, and the ALE-ANCF time-varying length thin-shell unit can accurately describe the dynamic characteristics of range motion and deformation coupling experienced by a flexible inflation tube in the space inflation unfolding structure in the unfolding process, so that an accurate dynamic model is obtained.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1
As shown in fig. 1, the present embodiment provides a dynamic modeling method for a space inflation deployment structure, which specifically includes the following steps:
s1, performing dynamic modeling on the common-frame type inflatable expansion 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 common-rack type inflatable unfolding satellite system includes 1 rigid satellite 1 located at the center, 3 subsategories 2 uniformly distributed around the rigid satellite 1, and flexible inflation tubes 3 connecting the rigid satellite 1 and the subsategories 2, the number of the flexible inflation tubes 3 is 3, two ends of each flexible inflation tube 3 are respectively an unfolding end 5 and a folding end 4, the unfolding ends 5 of the 3 flexible inflation tubes 3 are respectively connected with the subsategories 2 after being inflated and unfolded, the folding ends 4 are respectively directly connected with the rigid satellite 1, that is, the 3 subsategories 2 are uniformly connected to 3 outer surfaces of the rigid satellite 1 through the 3 flexible inflation tubes 3. That is to say, one end, namely the unfolding end 5, of the flexible inflation tube 3 of the 3 subsategories 2 is fixedly connected with the surface of the subsatellite 2, and the other end, namely the folding end 4, is inflated and unfolded from the interior of the rigid body satellite 1 at the center, so that the connection part of the flexible inflation tube 3 and the rigid body satellite 1 is in the folding state, and the rest part is in the inflated and unfolded state.
The step S1 specifically includes the following steps:
s1.1, modeling a flexible gas tube 3 in the common-rack type inflatable unfolding satellite system by adopting the ALE-ANCF time-varying length thin-shell unit to obtain a dynamic model of the flexible gas tube 3; the method specifically comprises the following steps:
as shown in fig. 3, in this embodiment, the ALE-ANCF time-varying length thin-shell unit includes 4 nodes, that is, A, B, C and D, and each node has 9 generalized coordinates, that is, the same node has 9 generalized coordinates in total in a parent unit, an initial configuration and a current configuration, and two ends of the ALE-ANCF time-varying length thin-shell unit are respectively provided with 1 material coordinate, the motion state and the deformation state of the flexible gas tube 3 during inflation and deployment are described by way of parent unit mapping, 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, since the shape of the initial configuration of the ALE-ANCF time-varying length thin-shell unit is irregular and the length of the current configuration changes, volume integral calculation is difficult to perform, volume integral calculation is performed on the ALE-ANCF time-varying length thin-shell unit by way of parent unit mapping, finally, a kinematic equation of the ALE-ANCF time-varying length thin-shell unit is determined, a dynamic equation of the ALE-ANCF time-varying length thin-shell unit is established through a Lagrange multiplier method, and an expression of a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit is obtained according to a geometric relation on a micro element of the ALE-ANCF time-varying length thin-shell unit, so that a motion state and a deformation state of the flexible inflation tube 3 in an inflation and deployment process are described.
Step S1.1.1, according to a position vector of any point on the ALE-ANCF time-varying length thin-shell unit, performing configuration description 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:
in the current configuration, the generalized coordinate and the position coordinate of any point of the ALE-ANCF time-varying length thin-shell unit are respectively marked as q and r, and two material coordinates m capable of changing the axial length are introduced1And m2The generalized coordinate of the ALE-ANCF time-varying length thin-shell unit is
Wherein the content of the first and second substances,
describing generalized node coordinates of ALE-ANCF time-varying length thin-shell units for absolute node coordinates, T being matrix transpose, and qA,qB,qC,qDAnd 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 a slope vector of each node along local coordinates x and y. Similarly, the generalized coordinate of the initial configuration of the ALE-ANCF time-varying thin-shell unit and the position coordinate of any point are respectively marked as q0And r0。
Under 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 unit is:
wherein N iseAnd an interpolation function of the ALE-ANCF time-varying length thin-shell unit described by absolute node coordinates, xi and eta are respectively the parent unit coordinates of the ALE-ANCF time-varying length thin-shell unit, and the value ranges are all-1. In addition, the spatial position coordinates r of any point in the ALE-ANCF time varying length thin shell element are marked in fig. 3.
Calculating partial derivative of the position vector r of any point to the time t to obtain generalized velocity vector of any point on the ALE-ANCF time-varying length thin-shell unit
And generalized acceleration vector
Respectively as follows:
wherein the content of the first and second substances,
is a shape function of the ALE-ANCF time-varying length thin-shell cell, and
interpolation matrix N representing ALE-ANCF time-varying length thin-shell elementseThe partial derivative is calculated for "·" in the parentheses,
and
generalized velocity and acceleration for ALE-ANCF time varying length thin shell elements, and
represents an additional term caused by mass flow of the flexible structure, an
Respectively being the material coordinate m1,m2The partial derivatives of time t respectively represent the coordinate change rate of the substance at the nodes of the ALE-ANCF time-varying length thin-shell unit,
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 Lagrange multiplier method to obtain a kinetic equation of the ALE-ANCF time-varying length thin-shell unit, and determining the geometric relation 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, solving the kinetic equation of the ALE-ANCF time-varying length thin-shell unit according to the Lagrange multiplier method into
Wherein M isaRepresenting ALE-ANCF time-varying length thin-walled cellsThe quality matrix is used to determine the quality of the image,
representing the generalized acceleration, F, of an ALE-ANCF time-varying length thin-shelled cellaRepresenting the additional inertial force column vector, F, of the ALE-ANCF time-varying length thin-shell elementeRepresenting the elastic force column vector, F, of the ALE-ANCF time-varying length thin-shell elementfRepresenting the generalized external force column vector of the ALE-ANCF time varying length thin shell element,
represents the jacobian matrix of the constraint equation and λ represents the lagrange multiplier. The calculation formula is as follows:
wherein S represents the area of the middle surface of the mother unit, D represents the mapping matrix between the mother unit and the ALE-ANCF time-varying length thin-shell unit, N represents the shape function of the ALE-ANCF time-varying length thin-shell unit, D represents a differential operator, D (-) represents the differential of "·" in brackets, V is the volume of the ALE-ANCF time-varying length thin-shell unit, and V is0Represents the volume of the mother unit, rho 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 applied on the ALE-ANCF time-varying length thin-shell unit, EεAnd EκRespectively ALE-ANCF time-varying length thin shell unit elastic coefficient matrix, and q representsThe generalized coordinates of the ALE-ANCF time-varying length thin-shell element, epsilon represents the strain vector of the ALE-ANCF time-varying length thin-shell element, kappa and kappa0Respectively representing the curvature vectors of the face in the ALE-ANCF time-varying length thin-shell unit in the current configuration and the initial configuration.
Step S1.1.3, establishing a local curve coordinate system and a local cartesian coordinate system on the ALE-ANCF time-varying length thin-shelled cell to obtain a conversion matrix between the local curve coordinate system and the local cartesian coordinate system, and obtaining a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shelled cell by combining a geometric relationship of a micro-element on the ALE-ANCF time-varying length thin-shelled cell; the method specifically comprises the following steps:
fig. 4 is a partial view of the initial configuration of the ALE-ANCF time-varying length thin shell unit provided in this embodiment. As shown in FIG. 4, a local curvilinear coordinate system (g) is established at any point P on the ALE-ANCF time-varying length thin shell element0)1-(g0)2-n0And a local Cartesian coordinate system (e)0)1-(e0)2-(e0)3(the local curved coordinate system and the local cartesian coordinate system are referred to as local coordinate systems hereinafter), the calculation formulas of the coordinate axes of the two local coordinate systems are respectively:
wherein r is0Represents the position coordinate of any point P in the initial configuration of the ALE-ANCF time-varying length thin-shell unit, n0The unit normal vector of the initial configuration midpoint P of the ALE-ANCF time-varying length thin-shell unit is represented, | | | |, means that the modulo is carried out on the vector "·" in a double vertical line, and "×" represents cross multiplication on the two vectors;
taking a point N near the point P, and obtaining a numerical relation between two local coordinate systems according to the arc length infinitesimal between the PN two points(g0)1dξ+(g0)2dη＝(e0)1dx0+(e0)2dy0；
Wherein d xi and d eta respectively represent a local curve coordinate system (g)0)1-(g0)2-n0Coordinate component of (2), dx0,dy0Respectively representing a local Cartesian coordinate system (e)0)1-(e0)2-(e0)3The coordinate component of (a);
according to the algebraic relation, the relation between the coordinate components of the two local coordinate systems is:
wherein a and b represent the arc lengths of the AB and AD sides in the initial configuration, respectively, and θ represents the coordinate axis (g) of the local coordinate system in the initial configuration0)1And (g)0)2Angle between them, T0A transformation matrix representing a local curvilinear coordinate system and a local cartesian coordinate system;
according to the geometric relation 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 epsilonεRepresenting the strain tensor, r, of an ALE-ANCF time-varying length thin-shell element,(·)And r0,(·)Respectively represent r and r0Partial derivatives, T, of the elements "·" in parentheses0A transformation matrix representing a local curvilinear coordinate system and a local cartesian coordinate system;
further, the strain vector of the thin shell element of the time varying length of ALE-ANCF can be expressed as:
ε＝[ε11 ε22 2ε12]T；
wherein epsilon11And ε22Denotes tensile strain,. epsilon12Represents shear strain;
according to a conversion matrix between two local coordinate systems of a local curve coordinate system and a local Cartesian coordinate system, obtaining the curvature tensor of the ALE-ANCF time-varying length thin-shell unit under the initial configuration through a differential geometrical relationship
The curvature tensor of the ALE-ANCF time-varying length thin-shell unit under the current configuration is
Wherein n represents a unit normal vector of the current configuration of the ALE-ANCF time-varying length thin-shell element, r,(*)(·)And r0,(*)(·)Denotes r and r0Partial derivatives, T, are obtained from the elements ". alpha." and ". cndot." in brackets, respectively0A transformation matrix representing a local curvilinear coordinate system and a local cartesian coordinate system;
will T0The algebraic expression is substituted into the curvature tensor of the ALE-ANCF time-varying length thin-shell unit, and the curvature vectors of the ALE-ANCF time-varying length thin-shell unit under the initial configuration and the current configuration are respectively kappa0＝[(κ0)11 (κ0)22 2(κ0)12]TAnd κ ═ κ11 κ22 2κ12]T；
Wherein, (kappa)11And (kappa)22Represents the transverse bending curvature component (kappa)12Representing a torsional curvature component.
S1.1.4, dispersing the flexible inflation tube 3 into a plurality of inflation tube units by adopting a finite element assembly method, sequentially numbering the inflation tube units and nodes, and assembling the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertial force and the external force of the inflation tube units into a new matrix according to the numbering sequence of the inflation tube units to obtain the dynamic model parameters of the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertial force and the generalized external force of the flexible inflation tube 3, so as to obtain the dynamic model of the flexible inflation tube 3.
The flexible inflation tube 3 in the common-rack type inflation unfolding satellite system is modeled by adopting ALE-ANCF time-varying length thin-shell units, the flexible inflation tube 3 is firstly dispersed into a plurality of inflation tube units by a finite element assembly method, and all the inflation tube units and nodes are sequentially numbered; then according to the serial number sequence of the inflatable tube units, the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertia force and the external force of the inflatable tube units are assembled into a new matrix, and finally the generalized coordinates q of the flexible inflatable tube 3 are obtainedfGeneralized velocity
Mass matrix M, elastic force FeAdditional inertial force FaAnd a generalized external force Q.
Further, consider the kinematic constraint Φ (q) of the flexible inflation tube 3fT) is 0, the kinetic equation of the flexible air tube 3 can be obtained
Wherein the content of the first and second substances,
representing the generalized acceleration of the flexible gas tube 3, λ representing the lagrange multiplier, and t representing time.
S1.2, modeling a rigid body satellite 1 and a subsatellite 2 in the common-frame type inflatable expansion satellite system by adopting a natural coordinate method to obtain a rigid body satellite 1 dynamic model; the method specifically comprises the following steps:
the rigid body satellite 1 and the subsatellite 2 in the common-frame type inflatable expansion satellite system are respectively described by adopting a natural coordinate method, and fig. 5 shows a schematic diagram of a rigid body satellite 1 model constructed by using the natural coordinate method. As shown in fig. 5, the configuration of the rigid body satellite 1 is a regular hexagonal prism shape.
The coordinate position of any point on the rigid body satellite 1 is
Wherein r isiAnd rjRespectively representing the centroids C of the rigid body satellites 10And global position coordinates of a j point on the surface of the rigid body satellite 1, u and v represent two unit vectors which are not coplanar with each other, qrRepresenting generalized coordinates of the rigid body satellite 1, I3Is a 3 rd order identity matrix, A is a constant matrix, and1、a2and a3In connection with, a1、a2And a3Position coordinate vector [ La ] of passing point P in local coordinate system1,a2,a3]TGet that L represents the centroid C0And the distance between the surface j point of the rigid body satellite 1;
at the centroid C of the rigid body satellite 10A local Cartesian coordinate system C-xi eta zeta is established, and the position coordinate of any point in the local coordinate system on the rigid body satellite 1 is obtained through calculation
Wherein 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, a constant quality matrix calculation expression of describing the rigid body satellite 1 by a natural coordinate method is obtained as follows:
wherein M issRepresents the constant mass matrix of the rigid body satellite 1, V ' represents the volume of the rigid body satellite 1, d represents the differential operator, d (V ') represents the differential of the volume of the rigid body satellite 1, ρ ' represents the density of the rigid body satellite 1, T represents the matrix transpose, I3Is a 3 rd order identity matrix, A is a constant matrix, and1、a2and a3In connection with, a1、a2And a3Position coordinate vector [ La ] of passing point P in local coordinate system1,a2,a3]TGet that L represents the centroid C0And the surface j point of the rigid body satellite 1.
And S1.3, combining the flexible inflation tube 3 dynamic model with the rigid body satellite 1 dynamic model to obtain a rigid-flexible coupling system dynamic model.
The invention provides an ALE-ANCF time-varying length thin-shell unit for the first time based on any Lagrange-Eulerian (ALE) description method in combination with an Absolute node Coordinate method (ANCF), wherein the Absolute node Coordinate method defines the node coordinates of the ALE-ANCF time-varying length thin-shell unit under global coordinates, slope vectors are adopted to replace node corner coordinates in a traditional finite unit, a derived system kinetic equation has the characteristics of a constant mass matrix, no centrifugal force and the like, and the calculation efficiency and precision can be improved. In any Lagrange-Euler description method, the grid nodes move flexibly, can move along with the moving object and can also be fixed, and the deformation process of the flexible inflation tube 3 can be accurately described by introducing two material coordinates and the novel ALE-ANCF time-varying length thin-shell unit. The method comprises the steps of adopting an ALE-ANCF time-varying length thin-shell unit to model a flexible inflation tube 3 in the common-frame type inflation unfolding satellite system, and adopting a natural coordinate method to model a rigid satellite 1 and a subsatellite 2 in the common-frame type inflation unfolding satellite system, so that a rigid-flexible coupling system dynamic model is obtained, and the problem that the dynamic modeling method in the prior art cannot accurately describe the dynamic characteristics of space motion and deformation coupling involved in the unfolding process of a space inflation unfolding structure is solved.
Step S2, according to the rigid-flexible coupling system dynamic model, grid division is carried out on the flexible inflation tubes 3 in the common-rack 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 dynamic model, and the method specifically comprises the following steps:
step S2.1, performing grid division on the flexible inflation tube 3 according to the rigid-flexible coupling system dynamic model to obtain a plurality of divided flexible inflation tube grid units 6, as shown in FIG. 6;
s2.2, determining an initial node position vector and an initial generalized velocity vector of each flexible inflation tube grid unit 6 according to the grid size condition of the flexible inflation tube grid unit 6;
s2.3, calculating an initial generalized coordinate vector q of each flexible inflation tube grid unit 6 according to the initial node position vector and the initial generalized velocity vector of each flexible inflation tube grid unit 60And an initial generalized velocity vector
Thereby obtaining an initial generalized coordinate vector of the flexible inflation tube 3 in the rigid-flexible coupling system dynamic model
And an initial generalized velocity vector
Wherein (q)0)DRepresents the initial generalized coordinate vector of the flexible gas tube 3, (q)0)fAnd (q)0)rIndicating the initial generalized coordinates of the flexible gas tube 3,
representing the initial generalized velocity vector of the flexible gas tube 3,
and
representing the initial generalized velocity component of the flexible gas tube 3 and T representing the matrix transpose.
Step S3, 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, and specifically comprising the following steps:
s3.1, determining the boundary condition of the rigid-flexible coupling system dynamic 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 intrinsic constraints are arranged in each rigid body satellite 1 and are divided into numerical constraints and vertical constraints, and the numerical constraints have the expression of | r |i-rjL, | u | ═ 1, | v | ═ 1, and the vertical constraint expression is (r)i-rj)⊥u,(ri-rj)⊥v,u⊥v。
S3.2, establishing a kinematic constraint equation of the rigid-flexible coupling system dynamic model according to the boundary condition;
establishing a kinematic constraint equation phi (q) of the rigid-flexible coupling system dynamic model based on the boundary conditions of the rigid-flexible coupling system dynamic modelSAnd t) is 0. In this embodiment, one end of the flexible inflation tube 3 is connected with the sub-satellite 2 in an articulated manner, the rigid body inherent constraint is divided into a numerical constraint of unit vectors of 3 coordinate axes of a local coordinate system and a 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 qr＝[q1 … q12]TAnd then the kinematic constraint equation Φ for the rigid body satellite 1 is written as:
wherein q is1-q12Are the specific generalized coordinate values of the rigid body satellite 1 respectively and are marked as qSL represents the centroid C of the rigid body satellite 10And the surface j point of the rigid body satellite 1.
Thus, a kinematic constraint equation Φ (q) of the rigid-flexible coupling system dynamics model is obtainedS,t)＝0，qSAnd (3) a specific generalized coordinate value of the rigid body satellite 1 is shown, and t represents time.
Step S4, introducing the kinematic constraint equation into a kinetic equation, setting a simulation iteration step length to obtain a time-domain discretized kinetic equation, and performing iteration solution and overlong boundary unit processing on the time-domain discretized kinetic equation to obtain a processed rigid-flexible coupling system kinetic model, specifically comprising the following steps:
s4.1, introducing the kinematic constraint equation into a kinetic equation by using a Lagrange multiplier, and setting a simulation iteration step length to obtain the kinetic equation after time domain dispersion; the method specifically comprises the following steps:
constraining equation phi (q) for kinematics of rigid-flexible coupled system dynamics model by lagrange multiplier lambdaSAnd t) is 0, the dynamic equation is introduced into a dynamic equation of a rigid-flexible coupling system dynamic model, a generalized alpha algorithm is adopted to solve the dynamic equation, and by setting a simulation iteration step length h, the dynamic equation of the common-frame type inflatable expansion satellite system after time domain dispersion can be obtained as follows:
wherein the content of the first and second substances,
expressing a system generalized coordinate column vector obtained by the iteration of the (n + 1) th step after the dispersion of the differential equation,
expressing a system generalized velocity column vector obtained by the iteration of the (n + 1) th step after the dispersion of the differential equation,
expressing a system generalized acceleration column vector, lambda, obtained by the iteration of the (n + 1) th step after the dispersion of the differential equationn+1Represents a lagrange multiplier vector and satisfies the following relationship:
wherein a, beta and gamma are vector parameters of the algorithm, h represents the simulation iteration step size,
expressing a system generalized coordinate column vector obtained by the nth step iteration after the dispersion of the differential equation,
and (4) representing a system generalized velocity column vector obtained by the nth step iteration after the dispersion of the differential equation, wherein n represents the number of iteration steps.
S4.2, carrying out iterative solution on the time-domain discrete kinetic equation by adopting a generalized alpha algorithm; the method specifically comprises the following steps:
in this embodiment, the simulation iteration step h is set to 0.0001, the discrete-form kinetic equation is solved by using the generalized α algorithm, and the increment Δ q of the generalized coordinate column vector of the system is obtained by calculationSDelta lambda of the sum Lagrange multiplier vector, generalized coordinate column vector of the system
And lagrange multiplier vector lambdan+1The following update can be performed according to the result from the previous iteration:
wherein the content of the first and second substances,
expressing a system generalized coordinate column vector obtained by the iteration of the (n + 1) th step after the dispersion of the differential equation,
expressing the system generalized coordinate column vector, delta q, obtained by the nth step iteration after the dispersion of the differential equationSIncrement, λ, representing a column vector of generalized coordinates of the systemn+1Representing the Lagrange multiplier vector, λnRepresenting the lagrangian multiplier vector in the previous iteration, and delta lambda represents the increment of the lagrangian multiplier vector.
It should be noted that, in this embodiment, the simulation iteration step h is set to 0.0001, which is a preferred value, and the value for setting the iteration step h is merely illustrated, and this value is not only not intended to be a limitation on the scope of the present invention, but also may be other values, and may be set according to the actual situation.
S4.3, in the iterative solution process, processing the boundary overlong unit in a node inserting mode to obtain a processed rigid-flexible coupling system dynamic model; the boundary overlength unit is a unit which is positioned at the boundary of the rigid-flexible coupling system dynamic model and has a length larger than the average length value.
In this embodiment, in order to avoid that the length of the boundary unit of the common-rack inflatable expansion satellite system is too long due to the expansion of the common-rack inflatable expansion satellite system, in the step S4.2 of iterative solution, the boundary too-long unit is processed in a node insertion manner.
Inserting material coordinate m of new node in boundary overlong unitinsertInterpolation function N of time-varying length thin-shell elements by ALE-ANCFeThe sum-form function N can obtain all information of the node inserted by the boundary unit, including the generalized coordinate q of the inserted nodeinsertGeneralized velocity of an inserted node
And generalized acceleration of the intervening nodes
The calculation expression is:
wherein the content of the first and second substances,
indicating the rate of change of the material coordinates of the intervening nodes,
an acceleration representing the coordinates of the material inserted into the node,
and
respectively represent
And NTPartial derivatives are taken of the element "·" in parentheses,
to represent
Partial derivatives are taken of the element "·" in parentheses,
describing generalized node coordinates of the ALE-ANCF time-varying length thin-shell unit for absolute node coordinates, wherein xi and eta are respectively mother unit coordinates of the ALE-ANCF time-varying length thin-shell unit, and T represents matrix transposition.
Step S5, calculating the dynamic response of the flexible inflation tube 3 in the expansion process according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain the variation curve of the expansion length of the flexible inflation tube 3 along with the inflation time at different inflation rates, which specifically comprises the following steps:
s5.1, calculating the numerical relation between the pressure and the volume in the flexible gas-filled pipe 3 according to the ideal gas equation and the processed rigid-flexible coupling system dynamic model;
in this embodiment, the expression of the ideal gas equation is as follows:
wherein P represents pressure, VaRepresenting the volume of the charge gas, M representing the mass of the charge gas, MgRepresents the molar mass of the gas, R represents the gas constant, and T represents the ambient temperature.
According to the processed rigid-flexible coupling system dynamic model, the pressure P and the volume V in the flexible gas-filled tube 3 can be obtained by using the ideal gas equation expressionaThe numerical relationship of (c).
S5.2, giving a constant inflation rate, and obtaining a variation curve of the expansion length of the flexible inflation tube 3 along with inflation time at the constant inflation rate by adopting generalized alpha algorithm simulation calculation; the method specifically comprises the following steps:
the simulation was performed by using MATLAB software based on the numerical relationship between the volume and pressure inside the flexible gas-filled tube 3, wherein v is 5 × 10 for a given constant gas-filling rate-4g/s, the ambient temperature T is 300K, the charged gas is nitrogen, and a generalized α algorithm is adopted, and a curve of the change of the expansion length of the flexible gas tube 3 along with the charging time in the charging and expanding process of the common-rack type charging and expanding satellite system is obtained through simulation calculation, as shown in fig. 7. Further, the curve of the expansion speed of the flexible inflation tube 3 during the expansion process of the system along with the inflation time can be calculated, as shown in fig. 8.
S5.3, adjusting the inflation rate, controlling other parameters to be kept unchanged, and sequentially substituting a plurality of different inflation rates into the simulation process to obtain a variation curve of the expansion length of the flexible inflation tube 3 along with the inflation time at different inflation rates; the method specifically comprises the following steps:
setting the constant inflation rate v in step S5.2 to 5 × 10-4g/s was scaled up to 2 and 4 times, respectively, to obtain two new inflation rates, v1 being 1 × 10-3g/s、v2＝2×10-3g/s and control other system parametersThe number is kept unchanged, and the influence rule of the three inflation rates v, v1 and v2 on the expansion length of the inflation tube is obtained by simulation calculation by the same method in the step S5.2, so as to obtain a graph of the expansion length of the flexible inflation tube 3 along with the change of the inflation time under different inflation rates as shown in FIG. 9. Observing the curve, the larger the inflation rate is, the shorter the time for the flexible inflation tube 3 to expand to the target length is, so that the inflation time is further controlled, and the expansion of the flexible inflation tube 3 to the target length can be accurately controlled.
According to the invention, the dynamic characteristics of range motion and deformation coupling experienced by the flexible gas-filled tube 3 in the space gas-filled unfolding structure in the unfolding process can be accurately described through the ALE-ANCF time-varying length thin-shell unit, and the dynamic model is more suitable for performing dynamic modeling on the space gas-filled unfolding structure. The dynamic equation is obtained through the kinematic constraint equation of the dynamic model of the rigid-flexible coupling system, solving a kinetic equation and processing an overlong boundary unit, calculating the kinetic response of the flexible inflatable tube 3 in the unfolding process by using an ideal gas equation and a processed rigid-flexible coupling system kinetic model, simulating to obtain a change curve of the unfolding length of the flexible inflatable tube 3 along with the inflation time at different inflation rates, therefore, more accurate dynamic response of the space inflatable unfolding structure is obtained, the problem that the existing modeling method cannot accurately describe the dynamic characteristics of the space inflatable unfolding structure in the unfolding process is solved, the accuracy of calculating the dynamic response of the space inflatable unfolding structure in the unfolding process is improved, a more accurate dynamic model of the space inflatable unfolding structure is obtained, and the dynamic characteristics of the space inflatable unfolding structure are more accurately described.
Example 2
As shown in fig. 10, the present embodiment provides a dynamic modeling system for a space inflation deployment structure, which specifically includes:
the dynamic model establishing module 7 is used for performing dynamic modeling on the common-frame type inflatable expansion 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;
an initial generalized vector obtaining module 8, configured to perform mesh division on the flexible gas tubes 3 in the common-frame type inflatable deployment satellite system according to the rigid-flexible coupling system dynamical model to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamical model;
a kinematics constraint equation establishing module 9, configured to establish a kinematics constraint equation of the rigid-flexible coupling system dynamical model according to the initial generalized coordinate vector and the initial generalized velocity vector;
the dynamic model processing module 10 is configured to introduce the kinematic constraint equation into a dynamic equation, set a simulation iteration step length to obtain a time-domain discretized dynamic equation, and perform iteration solution and overlong boundary unit processing on the time-domain discretized dynamic equation to obtain a processed rigid-flexible coupling system dynamic model;
and the dynamic response calculating module 11 is configured to calculate a dynamic response of the flexible inflation tube 3 in the expansion process 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 expansion length of the flexible inflation tube 3 with the inflation time at different inflation rates.
In the present specification, the emphasis points of the embodiments are different from those of the other embodiments, and the same and similar parts among the embodiments may be referred to each other. The principle and the implementation mode of the present invention are explained by applying specific examples in the present specification, and the above descriptions of the examples are only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A dynamic modeling method of a space inflation unfolding structure is characterized by comprising the following steps:
performing dynamic modeling on the common-frame type inflatable expansion 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 dynamic model, carrying out grid division on flexible inflation tubes in the common-rack type inflation unfolding satellite system to obtain an initial generalized coordinate vector and an initial generalized velocity vector of the rigid-flexible coupling system dynamic model;
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;
introducing the kinematic constraint equation into a kinetic equation, setting a simulation iteration step length to obtain a time-domain discretized kinetic equation, and performing iteration solution and overlong boundary unit processing on the time-domain discretized kinetic equation to obtain a processed rigid-flexible coupling system kinetic model;
and calculating the dynamic response of the flexible inflation tube in the expansion process 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 expansion length of the flexible inflation tube along with the inflation time at different inflation rates.
2. The method for dynamically modeling a spatial inflatable deployment structure according to claim 1, wherein the dynamic modeling of the common-frame type inflatable deployment satellite system is performed by using an ALE-ANCF time-varying length thin-shell unit and a natural coordinates method to obtain a rigid-flexible coupling system dynamic model, and specifically comprises:
modeling a flexible inflation tube in the common-rack type inflation unfolding satellite system by adopting the ALE-ANCF time-varying length thin-shell unit to obtain a flexible inflation tube dynamic model;
modeling the rigid body satellite and the subsatellite in the common-frame type inflatable expansion satellite system by adopting a natural coordinate method to obtain a rigid body satellite dynamic model;
and combining the flexible inflation tube dynamic model with the rigid satellite dynamic model to obtain a rigid-flexible coupling system dynamic model.
3. The dynamic modeling method for a space inflation deployment structure according to claim 2, wherein the flexible inflation tube dynamic model is obtained by modeling the flexible inflation tube in the common-rack inflation deployment satellite system by using the ALE-ANCF time-varying length thin-shell unit, and specifically comprises:
according to the position vector of any point on the ALE-ANCF time-varying length thin-shell unit, performing configuration description 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 adopting a Lagrange multiplier method to obtain a kinetic equation of the ALE-ANCF time-varying length thin-shell unit, and determining the geometric relation of the infinitesimal 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 obtaining a strain vector and a curvature vector of the ALE-ANCF time-varying length thin-shell unit by combining the geometric relation of the infinitesimal elements on the ALE-ANCF time-varying length thin-shell unit;
the method comprises the steps of dispersing the flexible inflation tube into a plurality of inflation tube units by adopting a finite element assembly method, sequentially numbering the inflation tube units and nodes, assembling the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertial force and the external force of the inflation tube units into a new matrix according to the numbering sequence of the inflation tube units, obtaining the dynamic model parameters of the generalized coordinates, the generalized speed, the mass matrix, the elastic force, the additional inertial force and the generalized external force of the flexible inflation tube, and obtaining the dynamic model of the flexible inflation tube.
4. The dynamic modeling method of a spatial inflatable deployment structure of claim 2, wherein the common-rack inflatable deployment satellite system comprises 1 of the rigid body satellites, 3 of the subsategories uniformly distributed around the rigid body satellites, and the flexible inflation tubes connecting the rigid body satellites and the subsategories, wherein an expanding end of each flexible inflation tube is connected with each of the subsategories after being inflated and deployed, and a closing end is connected with the rigid body satellites.
5. The method for modeling the dynamics of a spatially inflatable deployment structure according to claim 2, wherein the ALE-ANCF time-varying length thin shell unit comprises a plurality of nodes, each of the nodes has a plurality of generalized coordinates, and each of two sides of the ALE-ANCF time-varying length thin shell unit has 1 material coordinate, and the motion state and the deformation state of the flexible inflation tube during the inflation and deployment process are described by means of a parent unit mapping, wherein 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.
6. The dynamic modeling method for a spatial inflatable deployment structure according to claim 1, wherein the mesh division is performed on the flexible inflatable tube 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 specifically comprises:
meshing the flexible inflation tube according to the rigid-flexible coupling system dynamic model to obtain a plurality of divided flexible inflation tube meshing units;
determining an initial node position vector and an initial generalized velocity vector of each flexible inflation tube grid unit according to the grid size condition of the flexible inflation tube grid unit;
and calculating an initial generalized coordinate vector and an 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 dynamic model.
7. The method according to claim 1, wherein the establishing a kinematic constraint equation of the rigid-flexible coupled system dynamical model according to the initial generalized coordinate vector and the initial generalized velocity vector comprises:
determining a boundary condition of the rigid-flexible coupling system dynamic 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 dynamic model according to the boundary condition.
8. The dynamic modeling method for the spatial inflatable deployment structure of claim 1, wherein the kinematic constraint equation is introduced into a dynamic equation, a simulation iteration step is set to obtain a time-domain discretized dynamic equation, and the time-domain discretized dynamic equation is subjected to iteration solution and overlong boundary unit processing to obtain a processed rigid-flexible coupling system dynamic model, and the method specifically comprises the following steps:
introducing the kinematic constraint equation into a kinetic equation by using a Lagrange multiplier, and setting a simulation iteration step length to obtain a time domain discretized kinetic equation;
iterative solution is carried out on the time domain discretized kinetic equation by adopting a generalized alpha algorithm;
in the iterative solution process, processing the boundary overlong unit by adopting a node insertion mode to obtain a processed rigid-flexible coupling system dynamic model; the boundary overlength unit is a unit which is positioned at the boundary of the rigid-flexible coupling system dynamic model and has a length larger than the average length value.
9. The method according to claim 1, wherein the step of calculating a dynamic response of the flexible inflation tube during the deployment process according to an ideal gas equation and the processed rigid-flexible coupling system dynamic model, and adjusting the inflation rate to obtain a curve of the deployment length of the flexible inflation tube with the change of the inflation time at different inflation rates comprises:
calculating the numerical relation between the pressure and the volume in the flexible inflation tube according to the ideal gas equation and the processed rigid-flexible coupling system dynamic model;
giving a constant inflation rate, and obtaining a variation curve of the expansion length of the flexible inflation tube along with inflation time at the constant inflation rate by adopting generalized alpha algorithm simulation calculation;
adjusting the inflation rate, controlling other parameters to be kept unchanged, and sequentially substituting a plurality of different inflation rates into the simulation process to obtain the variation curve of the expansion length of the flexible inflation tube along with the inflation time at different inflation rates.
10. A system for kinetic modeling of a spatially inflated deployed structure, comprising:
the dynamic model establishing module is used for performing dynamic modeling on the common-frame type inflatable expansion 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 carrying out grid division on a flexible inflation tube in the common-rack type inflation unfolding satellite system 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;
the kinematic constraint equation establishing module is used for 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;
the dynamic model processing module is used for introducing the kinematic constraint equation into the dynamic equation, setting simulation iteration step length to obtain a dynamic equation after time domain dispersion, and performing iteration solution and overlong boundary unit processing on the dynamic equation after time domain dispersion to obtain a processed rigid-flexible coupling system dynamic model;
and the dynamic response calculation module is used for calculating the dynamic response of the flexible inflation tube in the expansion process 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 expansion length of the flexible inflation tube along with the inflation time at different inflation rates.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107122515A (en) * | 2017-03-17 | 2017-09-01 | 北京航空航天大学 | The dynamic analysis method of Sheng Xi transportation systems based on absolute node coordinate method |
| CN107220421A (en) * | 2017-05-18 | 2017-09-29 | 北京理工大学 | A kind of spatial complex flexible structure dynamics of multibody systems modeling and computational methods |
| CN110210047A (en) * | 2019-03-19 | 2019-09-06 | 南京航空航天大学 | Band-like tethered satellite Dynamic model of release construction method |
| CN111177960A (en) * | 2019-12-19 | 2020-05-19 | 南京理工大学 | Thin shell collision contact calculation method based on ANCF |
-
2021
- 2021-05-14 CN CN202110527582.9A patent/CN113158528B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107122515A (en) * | 2017-03-17 | 2017-09-01 | 北京航空航天大学 | The dynamic analysis method of Sheng Xi transportation systems based on absolute node coordinate method |
| CN107220421A (en) * | 2017-05-18 | 2017-09-29 | 北京理工大学 | A kind of spatial complex flexible structure dynamics of multibody systems modeling and computational methods |
| CN110210047A (en) * | 2019-03-19 | 2019-09-06 | 南京航空航天大学 | Band-like tethered satellite Dynamic model of release construction method |
| CN111177960A (en) * | 2019-12-19 | 2020-05-19 | 南京理工大学 | Thin shell collision contact calculation method based on ANCF |
Non-Patent Citations (4)
| Title |
|---|
| HYLDAHL P等: "《A thin plate element based on the combined arbitrary Lagrange-Euler and absolute nodal coordinate formulations》", 《PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS, PART K: JOURNAL OF MULTI-BODY DYNAMICS》, vol. 227, no. 3, 22 April 2013 (2013-04-22), pages 211 - 219 * |
| 孙加亮等: "《空间充气展开共机架结构动力学建模研究》", 《第18 届全国非线性振动暨第15 届全国非线性动力学和运动稳定性学术会议（NVND2021）摘要集》, 7 May 2021 (2021-05-07), pages 266 * |
| 罗操群等: "《多刚体系统分离策略及释放动力学研究》", 《力学学报》, vol. 52, no. 2, 18 February 2020 (2020-02-18), pages 503 - 513 * |
| 陈修龙等: "《基于绝对节点坐标法的3-RRPaR空间并联机构刚柔耦合动力学建模》", 《农业机械学报》, vol. 52, no. 4, 9 March 2021 (2021-03-09), pages 392 - 401 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113919081A (en) * | 2021-11-15 | 2022-01-11 | 北京航空航天大学 | Flexible flight dynamics modeling and analyzing method considering inertial coupling |
| CN113919081B (en) * | 2021-11-15 | 2023-09-19 | 北京航空航天大学 | Flexible flight dynamics modeling and analysis method considering inertial coupling |
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