A method and device for modeling and simulation of structural dynamics of an aerial cable tow system

Abstract

The application discloses a structural dynamics modeling simulation method and device of an aerial towed cable system, and the method comprises the following steps: constructing an ANCF curved beam element; using a plurality of ANCF curved beam elements to perform finite element discrete modeling of a towed cable, and generating a corresponding curved beam of the towed cable; unifying the curved beam and a rigid body through motion degrees of freedom in an absolute coordinate system, and establishing a dynamics equation; the rigid body comprises a towing aircraft and a towed aircraft; constructing a fixed support constraint relationship between the curved beam and the rigid body; and establishing a multi-body dynamics model of the aerial towed cable system according to the dynamics equation and the fixed support constraint relationship. In this way, the problem of invalid constraint between a towing rigid body torsional motion and a towed cable can be solved, the roll divergence phenomenon of the towing rigid body in simulation calculation is eliminated, and high-precision physical modeling and numerical simulation can be performed on the release and recovery process of the aerial towed cable system in a real engineering.

Description

Technical Field

[0001] This invention relates to the field of modeling and simulation, and in particular to a method, apparatus, equipment, and storage medium for structural dynamics modeling and simulation of an aviation soft cable towing system. Background Technology

[0002] An aerial tethered system refers to an assembly in which an aircraft uses a tethered cable to tow an object during flight. Its applications include hose-and-drogue aerial refueling systems, towed aerial recovery systems, aerial decoys, airborne towed antennas, and towed aerial launch systems. Typical towed objects include refueling drogues, aerial docking drogues, decoy aircraft, and towed aircraft. With the development of autonomous aerial refueling and recovery technologies for unmanned aerial vehicles (UAVs), the engineering application prospects of aerial tethered systems are becoming increasingly broad. Research on the mechanical theory and engineering development of this system has become a hot topic in emerging aviation technologies.

[0003] Flexible cables have a high slenderness ratio and low bending stiffness. When their end-fixed components (generally treated as rigid bodies) are subjected to external loads, their structural response exhibits nonlinear dynamic characteristics such as large deformation and large rotation. The fluid-structure interaction mechanical properties of towed flexible cable-rigid body systems are an important prerequisite for evaluating the flight characteristics of towed systems and a key factor in determining the success rate of aerial refueling and docking.

[0004] Currently, dynamic modeling methods for flexible cables can be categorized into three types based on their development history: continuous cable partial differential equation method, piecewise rigid discretization method, and finite element method. Among these, the continuous cable partial differential equation method, based on theoretical models, is difficult to model real engineering structures. The piecewise rigid model discretizes the flexible cable into several rigid mass segments, deviating from the true continuous flexible cable characteristics; it can only approximate the cable's motion configuration and cannot obtain its internal stress and strain. While the finite element method can simulate real engineering structures while preserving continuous flexible characteristics, for aerospace cable towing devices, the cable-rigid structure is subject to aircraft maneuvering traction, transient aerodynamic loads, and docking forces from other aircraft, making it prone to large deformations and rotations. When using the finite element method based on small deformations to model and simulate this flexible cable, a large number of cable-beam finite element elements need to be discretized, increasing the computational demands on structural dynamics.

[0005] Therefore, how to address the shortcomings of the aforementioned dynamic modeling methods in the dynamic calculation of cable-stayed structures is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a structural dynamics modeling and simulation method and apparatus for aircraft cable-towed systems, which can perform high-precision physical modeling and numerical simulation of the release and retrieval process of aircraft cable-towed systems in real engineering. The specific solution is as follows:

[0007] A structural dynamics modeling and simulation method for an aircraft-mounted cable-stayed system includes:

[0008] Construct ANCF curved beam elements;

[0009] Finite element discretization modeling of the towed cable is performed using multiple ANCF curved beam elements to generate the curved beam corresponding to the towed cable;

[0010] The degrees of freedom of motion of the curved beam and the rigid body in the absolute coordinate system are unified to establish dynamic equations; the rigid body includes the towed aircraft and the towed aircraft.

[0011] Establish the fixed support constraint relationship between the curved beam and the rigid body;

[0012] Based on the dynamic equations and the fixed support constraint relationship, a multibody dynamic model of the aviation soft cable towing system is established.

[0013] Preferably, in the structural dynamics modeling and simulation method for the aviation soft cable towing system provided in the embodiments of the present invention, the ANCF curved beam element includes a first node and a second node located at both ends of the boundary, and the generalized coordinate expression of the ANCF curved beam element is:

[0014] e=[e1 e2]=[r(0) θ(0) r′(0) r(L) θ(L) r′(L)]

[0015] Where e is the generalized coordinate of the ANCF curved beam element, e1 is the generalized coordinate of the first node, e2 is the generalized coordinate of the second node, r(0), θ(0), and r′(0) are the position vector, torsion angle, and tangential vector of the first node in the absolute coordinate system, respectively, and r(L), θ(L), and r′(L) are the position vector, torsion angle, and tangential vector of the second node in the absolute coordinate system, respectively, and L is the material coordinate length.

[0016] Preferably, in the structural dynamics modeling and simulation method for the aviation soft cable towing system provided in the embodiments of the present invention, the position coordinates of the midpoint of the ANCF curved beam element axis are obtained by interpolation of the generalized coordinates of the ANCF curved beam element.

[0017] Preferably, in the structural dynamics modeling and simulation method for the aerospace cable-stayed system provided in the embodiments of the present invention, the material length L of the ANCF curved beam element is... eThe variation with time t follows the following pattern:

[0018]

[0019] Where v1 is the mass inflow velocity set at the first node, v2 is the mass outflow velocity set at the second node, and L e,0 The material length of the ANCF curved beam element at the initial moment is given.

[0020] Preferably, in the structural dynamics modeling and simulation method for the aviation soft cable towing system provided in the embodiments of the present invention, the dynamic equation is:

[0021]

[0022] Where E represents the system of differential dynamic equations, and C represents the system of constraint equations. In this context, q represents the generalized coordinates of the dynamical system, and M represents the coordinates of the system. r M b These are the mass matrices of the rigid body and the curved beam, respectively. Q represents the generalized coordinates of the rigid body and the curved beam, respectively; e Let Q be the elastic force term of the curved beam. v Let Q be the inertial force term of the rigid body. f,,r and Q f,,b The external force terms correspond to the rigid body and the curved beam, respectively, and λ is the Lagrange multiplier of the constraint equation.

[0023] Preferably, in the structural dynamics modeling and simulation method for the aviation soft cable towing system provided in the embodiments of the present invention, the constraint equation set corresponding to the fixed support constraint relationship between the curved beam and the rigid body is as follows:

[0024]

[0025] Where, r o Let r be the coordinate vector of the center of mass of the rigid body in the absolute coordinate system, c be the vector from the center of mass of the rigid body to the constraint node of the curved beam in the absolute coordinate system, and r be the coordinate vector of the center of mass of the rigid body. N Let r′ be the position coordinates of the curved beam constraint node N1 in the absolute coordinate system, r′ be the generalized coordinate vector of the tangential slope of the curved beam at point N1, a and b be two orthogonal unit coordinate vectors in the local coordinate system of the rigid body at point N1, and n be a coordinate axis vector of the material coordinate system within the cross-section of the curved beam at point N1. 1,2,3 The position of the curved beam node is constrained, C4 and C5 constrain the direction of the tangential slope at the constraint point of the curved beam, and C6 constrains the rotation of the cross section at the constraint point of the curved beam.

[0026] Preferably, in the structural dynamics modeling and simulation method for the aircraft cable-towed system provided in the embodiments of the present invention, the Jacobi iterative equations of the multibody dynamics model of the aircraft cable-towed system are as follows:

[0027]

[0028] Among them, E q Let C be the Jacobian matrix of the system of dynamic equations with respect to the generalized coordinate q. q Let be the Jacobian matrix of the constraint equation system with respect to the generalized coordinate q, where δq is the increment of the generalized coordinate to be solved, and δλ is the increment of the Lagrange multiplier to be solved.

[0029] This invention also provides a structural dynamics modeling and simulation device for an aircraft cable-stayed towing system, comprising:

[0030] The curved beam element construction module is used to construct ANCF curved beam elements;

[0031] The cable model generation module is used to perform finite element discretization modeling of the towed cable using multiple ANCF curved beam elements, and generate the curved beam corresponding to the towed cable.

[0032] The dynamic equation establishment module is used to unify the degrees of freedom of motion of the curved beam and the rigid body in the absolute coordinate system and establish dynamic equations; the rigid body includes the towed aircraft and the towed aircraft.

[0033] The constraint relationship construction module is used to construct the fixed support constraint relationship between the curved beam and the rigid body;

[0034] The system model building module is used to build a multibody dynamics model of the aviation soft cable towing system based on the dynamic equations and the fixed support constraint relationship.

[0035] This invention also provides an electronic device, including a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the structural dynamics modeling and simulation method for the aviation soft cable towing system provided in this invention.

[0036] This invention also provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the structural dynamics modeling and simulation method for the aviation soft cable towing system described above in this invention.

[0037] As can be seen from the above technical solution, the structural dynamics modeling and simulation method for an aviation cable-towing system provided by the present invention includes: constructing ANCF curved beam elements; using multiple ANCF curved beam elements to perform finite element discretization modeling of the towing cable, generating the curved beam corresponding to the towing cable; unifying the curved beam and rigid body through the degrees of freedom of motion in the absolute coordinate system to establish dynamic equations; the rigid body includes the towing aircraft and the towed aircraft; constructing the fixed support constraint relationship between the curved beam and the rigid body; and establishing a multibody dynamics model of the aviation cable-towing system based on the dynamic equations and the fixed support constraint relationship.

[0038] The structural dynamics modeling and simulation method for the aforementioned aviation tethered towing system provided by this invention constructs ANCF curved beam elements and uses multiple ANCF curved beam elements for finite element discretization modeling of the towing cable. This method can accurately handle the large deformation problem of the cable-beam while significantly reducing the discrete degrees of freedom. The generated large deformation curved beam can simultaneously withstand bending and torsional loads. Combined with the established curved beam-rigid body dynamic equations and the curved beam-rigid body fixed support constraint relationship, it can solve the problem of invalid constraints between the torsional motion of the towing rigid body and the cable, eliminate the roll divergence phenomenon of the towing rigid body in the simulation calculation, and thus perform high-precision physical modeling and numerical simulation of the release and recovery process of the aviation tethered towing system in real engineering. This structural dynamics modeling and simulation method can provide technical support for the development and research of aviation towing systems such as flexible aerial refueling, aerial docking and recovery in my country.

[0039] Furthermore, this invention also provides corresponding devices, equipment, and computer-readable storage media for structural dynamics modeling and simulation methods of aviation soft cable towing systems, further making the above methods more practical. These devices, equipment, and computer-readable storage media have corresponding advantages. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0041] Figure 1 Flowchart of the structural dynamics modeling and simulation method for an aviation soft cable towing system provided in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram illustrating the deformation and motion of a curved beam section with absolute nodal coordinates, provided in an embodiment of the present invention.

[0043] Figure 3 This is a schematic diagram of a curved beam element with variable mass and length and absolute node coordinates provided in an embodiment of the present invention.

[0044] Figure 4 A schematic diagram of aeronautical towed multibody dynamics modeling using curved beam elements provided in an embodiment of the present invention;

[0045] Figure 5 This is a schematic diagram of the curved beam-rigid body fixed support constraint relationship provided in an embodiment of the present invention;

[0046] Figure 6 This is a schematic diagram illustrating the comparison and verification of bending deformation displacement of the ANCF curved beam unit provided in an embodiment of the present invention.

[0047] Figure 7 This is a schematic diagram illustrating an example of torsional load verification of an ANCF curved beam element provided in an embodiment of the present invention.

[0048] Figure 8 A graph showing the variation of the torsional angle of the curved beam end node over time, provided for an embodiment of the present invention;

[0049] Figure 9 A schematic diagram illustrating a dynamic verification example of the aerial refueling hose-cone sleeve release process using ANCF curved beam modeling provided in an embodiment of the present invention.

[0050] Figures 10a to 10f These are schematic diagrams showing the process at different simulation times during the mass release of a flexible conical sleeve modeled as a curved beam element under complex loads according to embodiments of the present invention.

[0051] Figure 11 This is a curve showing the displacement versus time during the release process of the conical sleeve, provided in an embodiment of the present invention.

[0052] Figure 12 This is a graph showing the change of Euler angle of rotation over time during the release process of the conical sleeve, provided in an embodiment of the present invention.

[0053] Figure 13 A schematic diagram of the structural dynamics modeling and simulation device for an aviation soft cable towing system provided in an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] This invention provides a structural dynamics modeling and simulation method for an aircraft soft cable towing system, such as... Figure 1 As shown, it includes the following steps:

[0056] S101, Construct ANCF curved beam elements;

[0057] It should be noted that beam elements described by ANCF (Absolute Nodal Coordinate Formula) based on the Euler-Bernoulli assumption can avoid numerical problems such as Poisson lock-up in elastic energy calculations, and are suitable for simulating the deformation and motion problems of elements with large slenderness ratios. In this invention, ANCF curved beam elements with variable boundary mass can be constructed based on a unified rigid-flexible multibody dynamics calculation framework. This can accurately handle large deformation problems of cable-stayed beams while significantly reducing discrete degrees of freedom, and easily form a unified solution method for flexible-rigid multibody dynamics constraint systems.

[0058] S102. Use multiple ANCF curved beam elements to perform finite element discretization modeling of the towed cable and generate the curved beam corresponding to the towed cable.

[0059] In practical applications, aviation cable towing systems generally involve release and recovery processes, so it is necessary to model long curved beam structures that include mass inflow / outflow at both ends.

[0060] S103. Unify the degrees of freedom of motion of curved beams and rigid bodies in the absolute coordinate system and establish dynamic equations; rigid bodies include towed aircraft and towed aircraft.

[0061] Specifically, based on the absolute node coordinate method, the dynamic equations of the towed aircraft, the towed aircraft, and the towed cable are established by unifying the degrees of freedom of motion in the absolute coordinate system.

[0062] S104. Establish the fixed support constraint relationship between the curved beam and the rigid body;

[0063] It should be noted that, since the ANCF curved beam element can withstand the torsional moment within the cross section, in order to realize the torsional constraint between the towing cable and the towing body in a real aerospace towing system, a curved beam-rigid body fixed support constraint relationship was constructed.

[0064] S105. Based on the dynamic equations and the fixed support constraint relationship, establish a multibody dynamic model of the aviation soft cable towing system.

[0065] In the structural dynamics modeling and simulation method for the aforementioned aerospace cable-towing system provided in this invention embodiment, ANCF curved beam elements are constructed, and multiple ANCF curved beam elements are used for finite element discretization modeling of the towing cable. This method can accurately handle the large deformation problem of the cable-beam while significantly reducing the discrete degrees of freedom. The generated large deformation curved beam can simultaneously withstand bending and torsional loads. Combined with the established curved beam-rigid body dynamic equations and the curved beam-rigid body fixed support constraint relationship, the problem of invalid constraints between the torsional motion of the towing rigid body and the cable can be solved, and the rolling divergence phenomenon of the towing rigid body in the simulation calculation can be eliminated. This allows for high-precision physical modeling and numerical simulation of the release and recovery process of the aerospace cable-towing system in real engineering. This structural dynamics modeling and simulation method can provide technical support for the development and research of aerospace towing systems such as flexible aerial refueling, aerial docking, and recovery in my country.

[0066] Figure 2 The deformation and motion of a cross-section at any point within an ANCF curved beam element are described. The central axis of the curved beam intersects with a cross-section perpendicular to it at point c. A local cross-sectional coordinate system is defined with c as its origin: t is the local tangential vector along the central axis, m and n are the orthogonal coordinate axes within the cross-section, and [tmn] constitutes the local material coordinate system at point c. p is any point within the cross-section, R... c Let r be the vector from point c to point p within the cross section. Consider the coordinate vector r of point p in the global computational coordinate system O-xyz. p :

[0067] r p =r+Θ·R c

[0068] Where Θ = [tmn] is the transformation matrix between the cross-sectional orthogonal coordinate system and the global calculation coordinate system, and r is the position coordinate of any point on the axis.

[0069] In practical implementation, the ANCF curved beam element includes a first node and a second node located at both ends of the boundary. Figure 3 The description and definition of an ANCF curved beam element with variable mass and length are shown. Each ANCF curved beam element contains two nodes, the first being the left node and the second the right node, for a total of 14 degrees of freedom. Material coordinates x... e Defined as a curved beam element with a length L in material coordinates, starting from one end along the axis.

[0070] The generalized coordinate expression for the ANCF curved beam element is:

[0071] e=[e1 e2]=[r(0) θ(0) r′(0) r(L) θ(L) r′(L)]

[0072] Where e is the generalized coordinate of the ANCF curved beam element, e1 is the generalized coordinate of the first node, e2 is the generalized coordinate of the second node, r(0), θ(0), and r′(0) are the position vector, torsion angle, and tangential vector of the first node in the absolute coordinate system, respectively, and r(L), θ(L), and r′(L) are the position vector, torsion angle, and tangential vector of the second node in the absolute coordinate system, respectively, and L is the material coordinate length.

[0073] In practical implementation, the position coordinates of the midpoint of the ANCF curved beam element axis can be obtained by interpolation using the generalized coordinates of the ANCF curved beam element. The specific formula is as follows:

[0074] r(x e )=S(x e )·e

[0075] Where S(x) e ) is the Hermite interpolation function.

[0076] In addition, the strain energy of the ANCF curved beam element includes the tensile, compressive, torsional, and bending strain energies of the beam element, as shown in the following formula:

[0077]

[0078] Where U is the element strain energy, E is the Young's modulus of the curved beam element material, A is the cross-sectional area of ​​the curved beam, ε0 is the tensile strain at a point within the element, G is the shear modulus of the curved beam element material, and J... T Let J be the torsional moment of inertia of the element section, κ1 be the torsional strain of the element section, and J be the moment of inertia of the element section. yy Let J be the bending moment of inertia in the y-direction of the element section, κ2 be the bending curvature in the y-direction of the element section, and J be the bending moment of inertia in the y-direction of the element section. zz κ3 is the bending moment of inertia in the z-direction of the element cross section, κ3 is the bending curvature in the z-direction of the element cross section, and x is the integral variable along the length of the element material.

[0079] The kinetic energy expression for the ANCF curved beam element is:

[0080]

[0081] Where T is the kinetic energy of the curved beam element. Let M be the time derivative of the generalized coordinates of the element, and M be the mass matrix of the curved beam element.

[0082] The mass matrix expression for the ANCF curved beam element is:

[0083]

[0084] Where ρ is the density of the curved beam material, S t J is the interpolation shape function for the curved beam element. zzJ is the bending moment of inertia in the z-direction of the element section. yy Let be the bending moment of inertia in the y-direction of the element section, and e be the generalized coordinate of the element.

[0085] In specific implementation, in the structural dynamics modeling and simulation method for the above-mentioned aviation soft cable towing system provided in the embodiments of the present invention, Figure 3 Set the mass inflow / outflow velocities v1(t) and v2(t) at the two boundary nodes of the ANCF curved beam element, respectively; the material length L of the ANCF curved beam element. e The variation with time t follows the following pattern:

[0086]

[0087] Where v1 is the mass inflow velocity set at the first node, v2 is the mass outflow velocity set at the second node, and L e,0 The initial length of the curved beam element is denoted as .

[0088] It should be noted that the two endpoints exhibit the characteristics of Eulerian nodes at the instant of calculation, and are not rigidly connected to any material points. However, when using Eulerian nodes for intra-element point velocity interpolation, the influence of transport velocity must be considered. In the time-varying element dynamics equations, a generalized transport force caused by changes in element mass is added to the element load force term:

[0089]

[0090] Among them, F v Let N be the generalized transport capacity of the element, N be the interpolation shape function within the element, N1 be the first to third columns of the shape function N, N3 be the first to third columns of the shape function N, t1 be the tangent vector at the first node of the element, and t2 be the tangent vector at the second node within the element.

[0091] When the transport velocities on both sides are zero, the time-varying element degenerates into a constant-mass element. As matter continuously flows in and out, the length of the boundary element will become excessively large or approach zero, which will lead to computational instability or deterioration of solution accuracy. Therefore, it is necessary to dynamically reconstruct the boundary element and its neighboring elements under appropriate conditions, performing a meshing operation on excessively long elements and a merging operation on excessively short elements.

[0092] Furthermore, considering the potential single-aircraft towing processes in aerospace engineering, it is necessary to establish, for example... Figure 4The diagram shows a multibody dynamics model of an aircraft cable-towed system. In a specific implementation, the structural dynamics modeling and simulation method for the aircraft cable-towed system provided in this embodiment of the invention, based on the absolute nodal coordinate method, allows the towing aircraft, the towed aircraft (rigid body or multi-rigid body constrained combination), and the towed cable (modeled based on ANCF long curved beam) to establish dynamic equations within a unified framework of motion degrees of freedom in the absolute coordinate system. These dynamic equations are as follows:

[0093]

[0094] Where E represents the system of differential dynamic equations, and C represents the system of constraint equations. In this context, q represents the generalized coordinates of the multibody dynamics system. Writing E in block form gives:

[0095]

[0096] Among them, M r M b Let be the mass matrices of the rigid body and the curved beam, respectively, where the mass matrix of the curved beam element is a constant. Let Q be the generalized coordinates of the rigid body and the curved beam, respectively; e For the elastic force term of the curved beam, Q v Q is the inertial force term for a rigid body. f,,r and Q f,,b The external force terms (including distributed load, concentrated load, damping force, etc.) correspond to those of rigid bodies and curved beams, respectively, and λ is the Lagrange multiplier of the constraint equations.

[0097] In specific implementation, in the structural dynamics modeling and simulation method for the above-mentioned aviation soft cable towing system provided in the embodiments of the present invention, Figure 5 The rigid support constraint relationship between the curved beam and the rigid body is shown. The constraint equation set corresponding to this rigid support constraint relationship includes 6 constraint equations:

[0098]

[0099] Where, r o Let be the coordinate vector of the center of mass of the rigid body o in the absolute coordinate system, c be the vector from the center of mass of the rigid body to the constraint node of the curved beam in the absolute coordinate system, and r be the coordinate vector of the center of mass of the rigid body o in the absolute coordinate system. N Let be the position coordinates of the curved beam constraint node N1 in the absolute coordinate system, r′ be the generalized coordinate vector of the tangential slope of the curved beam at point N1, a and b be two orthogonal unit coordinate vectors of the local coordinate system of the rigid body o at point N1, and n be a coordinate axis vector of the material coordinate system within the cross-section of the curved beam at point N1; C 1,2,3 The position of the curved beam node is constrained, C4 and C5 constrain the direction of the tangential slope at the constraint point of the curved beam, and C6 constrains the rotation of the cross section at the constraint point of the curved beam.

[0100] In practical implementation, in the structural dynamics modeling and simulation method for the aviation soft cable towing system provided in the embodiments of the present invention, the dynamic equations and constraint equations are combined to obtain a unified set of multibody dynamic differential-algebraic equations (DAEs) for the rigid-flexible coupled constraint system:

[0101]

[0102] The DAE equations were transformed into the Jacobi iterative equations using the Newton iterative method for solution.

[0103]

[0104] Among them, E q C is the Jacobian matrix of the system of dynamic equations with respect to the generalized coordinate q. q Let δq be the Jacobian matrix of the constraint equations with respect to the generalized coordinate q, and let δλ be the increment of the generalized coordinates to be solved. Let δλ be the increment of the Lagrange multipliers to be solved.

[0105] The following specific example verifies the static deformation structural response of the ANCF curved beam element under a given load:

[0106] First, the following is a verification example of the bending deformation of the ANCF curved beam element:

[0107] The initial configuration of the cable-stayed beam is a quarter circle, with its lower end fixed to the ground (in the x-axis direction), and its slope parallel to the ground. The radius of the cable-stayed beam is 2m, the cross-section is a circle with a diameter of 0.02m, and the elastic modulus E = 2.0 × e 11 Pa, density ρ = 7800 kg / m³ 3 Discretization is performed using 15 ANCF cable elements (2 nodes, 12 degrees of freedom) or 15 ANCF curved beam elements, and the convergent static configuration under a given load (Fx = -8N, Fy = 2N) is calculated using the dynamic relaxation method.

[0108] Depend on Figure 6 As shown, the steady-state convergent configurations obtained by the two methods are consistent, indicating that the bending deformation calculation results of the curved beam element have been verified.

[0109] Secondly, the verification example of torsional deformation of ANCF curved beam element is as follows:

[0110] like Figure 7As shown, the initial configuration of the curved beam is a straight line along the x-axis. Its left end is fixed to the ground using a cable-ground fixed support constraint, and its constraint degrees of freedom include three translational degrees of freedom and three rotational degrees of freedom (including torsional degrees of freedom). Its right end is fixed to the center of mass of a rigid body, and the constraint relationship is a soft cable-rigid body fixed support constraint (6 constraint degrees of freedom, including torsional degrees of freedom).

[0111] The curved beam has a total length of L = πm, is discretized from 15 ANCF curved beam elements, has a circular cross-section with a diameter of 0.02m, and an elastic modulus E = 2.0 × e 11 Pa, with a density of ρ = 7800 kg / m³, has a torsional stiffness per unit length of its cross-section of GI. p =1.5708×10 3 N·m 2 A torque load of M = 100 N·m is applied to a rigid body fixed at the end of the curved beam. From the rotation angle formula:

[0112]

[0113] It can be seen that, since the center of mass of the rigid body at the right end of the curved beam is in the same position as the rightmost node of the curved beam and its six relative degrees of freedom are fixed, the formula for calculating the true rotation angle of the rigid body at the right end is:

[0114]

[0115] The calculated value is θ = 0.2 rad, which is the theoretical solution for the rigid body's torsional angle. Through multibody dynamics numerical calculations of the ANCF curved beam, the variation of the rigid body's torsional angle with time can be obtained, such as... Figure 8 As shown, the total calculation time is 1 second. It can be seen that the rigid body rotates back and forth periodically under the action of torque. The maximum amplitude of its rotation is 0.4 rad, which remains constant. It can be seen that under the presence of resistance, the equilibrium position of the rigid body torsion is located at θ = 0.2 rad. This result is consistent with the theoretical calculation result. The dynamic response of this ANCF curved beam element under the action of torsional torque has been verified through this example.

[0116] Next, in order to examine the modeling and simulation capability of the absolute ANCF curved beam element for the dynamics of the hose-cone sleeve structure in a real aerial refueling project, a curved beam-six-degree-of-freedom rigid body constrained dynamic model of the hose-cone sleeve release process was established, and the dynamic simulation capability of the variable mass ANCF curved beam element under bending, shear and torsional loads was evaluated.

[0117] The dynamic model of the soft aerial refueling device is as follows: Figure 9As shown, the refueling hose is discretized by several curved beam elements. The first node of the left curved beam is fixed to the ground, which constrains the three translational degrees of freedom and three rotational degrees of freedom of the first node of the curved beam. The right end of the curved beam is connected to the refueling cone sleeve through the curved beam element-rigid body fixed constraint. This constraint class also has six similar constraint equations.

[0118] The oiling cone sleeve is a six-degree-of-freedom rigid body with a mass of m = 40 kg and a moment of inertia J in the principal axis inertial frame. xx =1.0 kg·m 2 J yy =1.0 kg·m 2 J zz =1.0 kg·m 2 It is subjected to external loads including gravity G in the -y direction (gravitational acceleration 9.8 m / s²). 2 x-direction resistance F x =1500N, lateral force F in the z direction z =10N, x-direction torque M torque =100 N·m.

[0119] The hose is initially horizontal, 1m long, and has an initial number of discrete elements of 2 (each element L). ele =0.5m), the hose release speed is v = 2m / s, the hose linear density is ρ = 3kg / m, and the elastic modulus is E = 2.0 × 10⁻⁶. 10 Pa, shear modulus G = 7.6923 × 10 9 Pa, cross-sectional area A = 2.5761 × 10 -3 m 2 The bending moment of inertia of the cross section I c =2.19742×10 -6 m 4 Torsional moment of inertia I of cross section p =4.39484×10 -6 m 4 The structural damping coefficient is 0.

[0120] The total simulation time was T = 6.23 s. The configurational changes of the hose-cone sleeve during the mass release process were as follows: Figures 10a to 10f As shown; where Figure 10a The simulation time is 0 seconds. Figure 10b The simulation time was 0.999816 s. Figure 10c The simulation time was 1.999816 s. Figure 10d The simulation time was 3.999816 s. Figure 10e The simulation time was 4.999816 s. Figure 10f The simulation time was 5.999816 s. The curves showing the changes in x, y, and z displacements over time during the cone sleeve release process are as follows: Figure 11 As shown, the curve of its rotational Euler angle changing with time is as follows: Figure 12 As shown.

[0121] Calculation results show that the fixed constraints between the conical sleeve and the ground and rigid body remain throughout the release process. Under the action of gravity and external loads in the x-direction, the conical sleeve's sinking gradually increases due to the increasing length of the hose. Under the action of relatively small lateral forces and torsional moments, the conical sleeve oscillates slightly in the lateral and torsional directions. The six-component torque and force loads on the conical sleeve are completely transferred to the curved beam element through the constraints.

[0122] Based on the same inventive concept, this invention also provides a structural dynamics modeling and simulation device for an aircraft soft cable towing system. Since the principle of this device in solving the problem is similar to the aforementioned structural dynamics modeling and simulation method for an aircraft soft cable towing system, the implementation of this device can refer to the implementation of the structural dynamics modeling and simulation method for an aircraft soft cable towing system, and the repeated parts will not be described again.

[0123] In specific implementation, the structural dynamics modeling and simulation device for the aviation soft cable towing system provided in this embodiment of the invention, such as... Figure 13 As shown, it specifically includes:

[0124] Curved beam element construction module 11 is used to construct ANCF curved beam elements;

[0125] The cable model generation module 12 is used to perform finite element discretization modeling of the towed cable using multiple ANCF curved beam elements, and generate the curved beam corresponding to the towed cable.

[0126] The dynamic equation establishment module 13 is used to unify the degrees of freedom of motion of the curved beam and the rigid body in the absolute coordinate system and establish dynamic equations; the rigid body includes the towed aircraft and the towed aircraft.

[0127] The constraint relationship construction module 14 is used to construct the fixed support constraint relationship between the curved beam and the rigid body;

[0128] System model building module 15 is used to build a multibody dynamic model of the aviation soft cable towing system based on the dynamic equations and the fixed support constraint relationship.

[0129] In the structural dynamics modeling and simulation device for the aviation soft cable towing system provided in the embodiments of the present invention, the large deformation problem of the cable beam can be accurately handled through the interaction of the above five modules while significantly reducing the discrete degrees of freedom. The generated large deformation curved beam can simultaneously withstand bending and torsional loads, solving the problem of invalid constraints between the torsional motion of the towing rigid body and the soft cable, eliminating the rolling divergence phenomenon of the towing rigid body in the simulation calculation, and thus performing high-precision physical modeling and numerical simulation of the release and recovery process of the aviation soft cable towing system in real engineering, providing technical support for the development and research of aviation towing systems such as soft aerial refueling, aerial docking and recovery in my country.

[0130] For more detailed information on the working process of each of the above modules, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0131] Accordingly, embodiments of the present invention also disclose an electronic device, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the structural dynamics modeling and simulation method for the aviation soft cable towing system disclosed in the foregoing embodiments.

[0132] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0133] Furthermore, the present invention also discloses a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, it implements the aforementioned disclosed method for structural dynamics modeling and simulation of an aerospace cable-towing system.

[0134] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0135] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatuses, devices, and storage media disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0136] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0137] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0138] In summary, the structural dynamics modeling and simulation method for an airborne cable-towing system provided by this invention includes: constructing ANCF curved beam elements; using multiple ANCF curved beam elements to perform finite element discretization modeling of the towing cable, generating the curved beam corresponding to the towing cable; unifying the degrees of freedom of motion of the curved beam and the rigid body in the absolute coordinate system to establish dynamic equations; the rigid body includes the towing aircraft and the towed aircraft; constructing the fixed support constraint relationship between the curved beam and the rigid body; and establishing a multibody dynamics model of the airborne cable-towing system based on the dynamic equations and the fixed support constraint relationship. Constructing ANCF curved beam elements in this way, and using multiple ANCF curved beam elements for finite element discretization modeling of the towed cable, can accurately handle the large deformation problem of the cable-beam while significantly reducing the discrete degrees of freedom. The generated large deformation curved beam can simultaneously withstand bending and torsional loads. Combined with the established curved beam-rigid body dynamic equations and the curved beam-rigid body fixed support constraint relationship, the problem of invalid constraints between the torsional motion of the towed rigid body and the cable can be solved, eliminating the roll divergence phenomenon of the towed rigid body in the simulation calculation. This allows for high-precision physical modeling and numerical simulation of the release and recovery process of the aviation cable towing system in real engineering. The above method can provide technical support for the development and research of aviation towing systems such as flexible aerial refueling, aerial docking and recovery in my country. In addition, this invention also provides corresponding devices, equipment and computer-readable storage media for the above method, further making the method more practical. The devices, equipment and computer-readable storage media have corresponding advantages.

[0139] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0140] The structural dynamics modeling and simulation method and device for the aviation soft cable towing system provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A structural dynamics modeling and simulation method for an aircraft-mounted cable-stayed system, characterized in that, include: Construct ANCF curved beam elements; The ANCF curved beam element includes a first node and a second node located at both ends of the boundary. The generalized coordinate expression of the ANCF curved beam element is: ； in, e The generalized coordinates of the ANCF curved beam element are... e 1 represents the generalized coordinate of the first node. e 2 represents the generalized coordinate of the second node. , , These represent the position vector, twist angle, and tangential vector of the first node in the absolute coordinate system, respectively. , , These represent the position vector, twist angle, and tangential vector of the second node in the absolute coordinate system, respectively. L The length of the material coordinates; Finite element discretization modeling of the towed cable is performed using multiple ANCF curved beam elements to generate the curved beam corresponding to the towed cable; the position coordinates of the midpoint of the axis of the ANCF curved beam element are obtained by interpolation of the generalized coordinates of the ANCF curved beam element. The degrees of freedom of motion of the curved beam and the rigid body in the absolute coordinate system are unified to establish dynamic equations; the rigid body includes the towed aircraft and the towed aircraft. The fixed-support constraint relationship between the curved beam and the rigid body is established; the constraint equation set corresponding to the fixed-support constraint relationship between the curved beam and the rigid body is as follows: ； in, r o Let be the coordinate vector of the center of mass of the rigid body in the absolute coordinate system. c This is the vector in the absolute coordinate system from the center of mass of the rigid body to the constraint node of the curved beam. r N The curved beam constraint nodes in the absolute coordinate system N The position coordinates of 1 for N The generalized coordinate vector of the tangential slope of the curved beam at point 1, a and b The rigid body is respectively in N Two orthogonal unit coordinate vectors in the local coordinate system of point 1. n for N One coordinate axis vector of the material coordinate system within the cross-section of the curved beam mentioned in point 1. C 1,2,3 The location of the curved beam joints was constrained. C 4 and C 5. The direction of the tangential slope at the constraint point of the curved beam is constrained. C 6. The rotation of the cross section at the constraint point of the curved beam is constrained; Based on the dynamic equations and the fixed support constraint relationship, a multibody dynamic model of the aviation soft cable towing system is established.

2. The structural dynamics modeling and simulation method for an aircraft soft cable towing system according to claim 1, characterized in that, Material length of the ANCF curved beam element Over time t The pattern of change is as follows: ； in, v 1 represents the mass inflow velocity set at the first node. v 2 represents the mass outflow velocity set at the second node. The material length of the ANCF curved beam element at the initial moment.

3. The structural dynamics modeling and simulation method for an aircraft soft cable towing system according to claim 1, characterized in that, The dynamic equation is: ； in, E This is a system of differential dynamic equations. C For the constraint equation system, In q For the generalized coordinates of the dynamic system, M r , M b These are the mass matrices of the rigid body and the curved beam, respectively. r , b These are the generalized coordinates of the rigid body and the curved beam, respectively; Q e The elastic force term of the curved beam is... Q v The inertial force term of the rigid body is... Q f,r and Q f,b These correspond to the external force terms of the rigid body and the curved beam, respectively. is the Lagrange multiplier for the constraint equations.

4. The structural dynamics modeling and simulation method for an aircraft soft cable towing system according to claim 3, characterized in that, The Jacobi iterative equations of the multibody dynamics model of the airborne cable-stayed towing system are as follows: ； in, For the system of dynamic equations with respect to generalized coordinates q Jacobian matrix, For the constraint equations of the system of generalized coordinates q Jacobian matrix, The increment of the generalized coordinates to be solved. This represents the increment of the Lagrange multipliers to be solved.

5. A structural dynamics modeling and simulation device for an aircraft soft cable towing system, characterized in that, include: The curved beam element construction module is used to construct ANCF curved beam elements; The ANCF curved beam element includes a first node and a second node located at both ends of the boundary. The generalized coordinate expression of the ANCF curved beam element is: ； in, e The generalized coordinates of the ANCF curved beam element are... e 1 represents the generalized coordinate of the first node. e 2 represents the generalized coordinate of the second node. , , These represent the position vector, twist angle, and tangential vector of the first node in the absolute coordinate system, respectively. , , These represent the position vector, twist angle, and tangential vector of the second node in the absolute coordinate system, respectively. L The length of the material coordinates; The cable model generation module is used to perform finite element discrete modeling of the towed cable using multiple ANCF curved beam elements, and generate the curved beam corresponding to the towed cable; the position coordinates of the midpoint of the axis of the ANCF curved beam element are obtained by interpolation through the generalized coordinates of the ANCF curved beam element. The dynamic equation establishment module is used to unify the degrees of freedom of motion of the curved beam and the rigid body in the absolute coordinate system and establish dynamic equations; the rigid body includes the towed aircraft and the towed aircraft. The constraint relationship construction module is used to construct the fixed-support constraint relationship between the curved beam and the rigid body; the constraint equation set corresponding to the fixed-support constraint relationship between the curved beam and the rigid body is as follows: ； in, r o Let be the coordinate vector of the center of mass of the rigid body in the absolute coordinate system. c Let be the vector in the absolute coordinate system from the center of mass of the rigid body to the constraint node of the curved beam. r N The curved beam constraint nodes in the absolute coordinate system N The position coordinates of 1, for N The generalized coordinate vector of the tangential slope of the curved beam at point 1, a and b The rigid body is respectively in N Two orthogonal unit coordinate vectors in the local coordinate system of point 1. n for N One coordinate axis vector of the material coordinate system within the cross-section of the curved beam mentioned in point 1. C 1,2,3 The location of the curved beam joints was constrained. C 4 and C 5. The direction of the tangential slope at the constraint point of the curved beam is constrained. C 6. The rotation of the cross section at the constraint point of the curved beam is constrained; The system model building module is used to build a multibody dynamics model of the aviation soft cable towing system based on the dynamic equations and the fixed support constraint relationship.

6. An electronic device, characterized in that, It includes a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the structural dynamics modeling and simulation method for an aerospace soft cable towing system as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, Used to store computer programs, wherein the computer programs, when executed by a processor, implement the structural dynamics modeling and simulation method for an aerospace cable-towing system as described in any one of claims 1 to 4.

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