Space-time discrete integral variation method for dynamic simulation of flexible large-deformation beam model based on ANCF full gradient

Abstract

The invention discloses a space-time discrete integral variation method for dynamic simulation of a flexible large-deformation beam model based on ANCF full gradient, and relates to the field of dynamic simulation of flexible structures. The problem that in the prior art, a numerical modeling method cannot completely meet the requirement for long-time dynamic simulation analysis based on a large-deformation ANCF full-gradient beam model is solved. The method comprises the following steps: carrying out time-space synchronous discretization on a flexible large deformation beam model; through space-time synchronous discretization, a position vector in each space-time discretization unit and an expression of the gradient of the position vector are obtained. And kinetic energy, elastic potential energy and external force work in [tn-1, tn + 1] are calculated. And substituting the expression into a Hamilton formula to obtain a dynamic equation set of the units, and integrating all the units to obtain a nonlinear algebraic dynamic equation set of the beam system. And solving the nonlinear algebraic equation set by adopting a Newton iteration method to obtain a position vector on the discrete node and a gradient vector of the position vector. The method is suitable for long-time history momentum-preserving and pungent-preserving simulation of the ANCF full-gradient model of the large-deformation beam.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible structure dynamics simulation, and in particular to a time-space discrete integral variational method for dynamics simulation of a flexible large deformation beam model based on ANCF full gradient. Background Art

[0002] In the field of flexible structure dynamics simulation, the structure will undergo significant shape and position changes under the action of external loads or its own inertial force, making the traditional small deformation assumption no longer applicable. As an emerging flexible body modeling method, the absolute node coordinate method ANCF has received widespread attention in the field of flexible structure dynamics simulation. This method can more accurately describe the geometric shape and deformation behavior of the flexible body by introducing the node position vector and the cross-sectional gradient field as unknown quantities. Compared with the traditional floating coordinate system method, ANCF exhibits higher calculation accuracy and better numerical stability. By considering the position vector at the cross-sectional node and the gradient field on the cross-sectional surface, including the three directions of x, y, and z as unknown quantities, it can accurately describe the large deformation behavior of the flexible beam, which is particularly suitable for the modeling and analysis of flexible large deformation beams. However, in this modeling method, the final differential algebraic equations need to be solved by independent integrators such as the Newmark method, the generalized α method, the BDF method, and the Runge-Kutta method. These integrators generally have the characteristics of numerical dissipation, resulting in energy dissipation and momentum non-conservation in long-term simulations. The simulation results have a large deviation from the actual situation, which ultimately leads to incorrect results.

[0003] Therefore, the current numerical modeling methods cannot fully meet the needs of long-term dynamic simulation analysis based on the large deformation ANCF full-gradient beam model. Summary of the invention

[0004] The present invention aims to solve the problem that the numerical modeling methods in the prior art cannot fully meet the needs of long-term dynamic simulation analysis based on the large deformation ANCF full gradient beam model. To solve the above technical problems, the present invention is implemented through the following technical solutions:

[0005] Solution 1: The present invention proposes a time-space discrete integral variational method for dynamic simulation of a flexible large deformation beam model based on ANCF full gradient, the method comprising the following steps:

[0006] S1. Discretize the flexible large deformation beam model in time and space. For the spatial coordinate x, let x k is the arc length coordinate of the kth spatial node, L is the total length of the beam; for the time coordinate t, let t n is the time size of the nth time node, and T is the total simulation time. Consider the space-time discrete unit area [xk ,x k+1 ]×[t n-1 ,t n+1 ],in and

[0007] S2. Define the generalized coordinates and interpolation function of the space-time discrete unit, let where r is the position vector of any point on the beam centerline, is the tangent vector to the center line, r y and r z are two basis vectors on the beam cross section. Then Indicates that q is in x k and t n The value of express exist and t n The value of and where h = t n+1 -t n =t n -t n-1 , l is the length of discrete space, t is the length of discrete time; r uses cubic Hermite interpolation in space, r y and r z Quadratic Lagrange interpolation is used in space, and quadratic Lagrange interpolation is used in time for all variables to obtain the expression of the position vector and its gradient in each space-time discrete unit;

[0008] S3, based on the expressions of the position vector and its gradient in each space-time discrete unit obtained in S2, calculate [t n-1 ,t n+1 ]Calculate the kinetic energy, elastic potential energy and work done by external forces in the interval and find the variation;

[0009] S4, substituting the kinetic energy, elastic potential energy and work done by external force obtained in S3 into Hamilton variational formula to obtain the dynamic equations of space-time discrete units, and integrating all space-time discrete units to obtain the nonlinear algebraic dynamic equations of the beam system;

[0010] S5. Use Newton's iteration method to solve the nonlinear algebraic equations to obtain the position vector and its gradient vector on the discrete node.

[0011] Furthermore, a preferred embodiment is provided, in which the region for time-space discretization of the flexible large deformation beam in S1 is [0, L]×[0, T].

[0012] Furthermore, a preferred implementation is provided, wherein S2 also includes a step of defining a Hermite variational interpolation function.

[0013] Further, a preferred implementation is provided, wherein the method for defining the Hermite variational interpolation function is:

[0014] H1=1-3ξ 2 +2ξ 3 ,H2=l(ξ-2ξ 2 +ξ 3 ),H3=3ξ 2 -2ξ 3 ,H4=l(ξ 3 -ξ 2 ).

[0015] Further, a preferred implementation is provided, in which the method for obtaining the position vector in each space-time discrete unit in S2 is:

[0016]

[0017] Among them, s = [H1 H2 0000H3 H4 00], Q represents the permutation and combination of generalized coordinates of each space-time discrete unit, and S and N are shape functions.

[0018] Further, a preferred implementation is provided, in which S3 calculates [t n-1 ,t n+1 The method of varying the kinetic energy, elastic potential energy and work done by external force in the interval is:

[0019]

[0020] in, Represents the time derivative of displacement at any point P, i.e. velocity, ρ A is the line density, and the stiffness coefficient matrix associated with the external forces, is the elastic force term of the unit, F α is the unit external force term.

[0021] Further, a preferred implementation is provided, in S4, by integrating all time-space discrete units, the nonlinear algebraic dynamic equations of the beam system are obtained as follows:

[0022]

[0023] in, Yes n The combination of generalized coordinates of all unit nodes at the moment, and They are tn-1 and t n+1 The combination of all generalized coordinates of the moment; Yes n The elastic force combination of all units at the moment, and They are t n-1 and t n+1 The combination of all unit elastic forces at the moment; F n Yes n The external force combination of all units at the moment, F n-1 and F n+1 They are t n-1 and t n+1 The combination of all unit external forces at the moment; M 11 are the generalized coordinate vectors in M ​​and at both ends and The corresponding mass matrix components are , where M is the total mass matrix of the integration.

[0024] Furthermore, a preferred embodiment is provided, wherein S4 also includes the step of confirming the nonlinear algebraic equation group of the unconstrained beam system and the nonlinear algebraic equation group of the constrained beam system.

[0025] Solution three: A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes any one of the methods described in Solution one.

[0026] Solution 4: A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method described in any one of Solution 1.

[0027] The present invention is beneficial in that:

[0028] The space-time discrete integral variation method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in the present invention introduces the integral variation principle and space-time simultaneous discretization technology into the dynamic simulation of flexible structure. Its integral variation principle provides a modeling method based on symmetric momentum conservation, while the space-time discretization technology converts the continuous system into a discrete system by reasonably dividing the time step and space grid, which is convenient for numerical calculation. Its application not only provides new ideas and methods for modeling and analysis of flexible beams, but also makes the numerical simulation results over a long period of time closer to the actual situation, providing engineers with more reliable dynamic analysis data.

[0029] The method described in the present invention adopts the ANCF full gradient modeling method based on considering the position vector at the cross-section node and the gradients in the three directions of x, y, and z on the cross-section as unknown quantities, and combines a variety of advanced theories and technical means such as Hamiltonian principle, space-time discretization technology and integral variation principle, aiming to develop an efficient and accurate numerical simulation method to meet the needs of dynamic analysis in complex engineering fields such as spacecraft.

[0030] The present invention adopts an ANCF unit different from the prior art. The present invention adopts a full-gradient ANCF unit. The full-gradient ANCF unit has a wider application range and can describe deformation more accurately.

[0031] The method described in the present invention has the characteristics of preserving symplectic structure, momentum and approximately energy, ensuring the preservation of symplectic structure and momentum during the simulation process, achieving the approximate preservation of system energy, and thus improving the stability and reliability of the simulation results.

[0032] The present invention is also applicable to the field of long-time momentum preservation and symmetric simulation of the ANCF full-gradient model of a large deformation beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flow chart of the time-space discrete integral variational method for dynamic simulation of a flexible large deformation beam model based on ANCF full gradient as described in Implementation Example 1.

[0034] Figure 2 Schematic diagram comparing the dynamic trajectory and displacement results of a large deformation flexible simple pendulum using the variational integration method and the generalized α method described in Implementation Example 11.

[0035] Figure 2 In the figure, (a) is a schematic diagram of the dynamic trajectory and displacement results of a large deformation flexible simple pendulum using the variational integration method described in the present invention, and (b) is a schematic diagram of the dynamic trajectory and displacement results of a large deformation flexible simple pendulum using the generalized α method.

[0036] Figure 3 Schematic diagram of the comparison of the dynamic energy of a large deformation flexible simple pendulum using the variational integration method and the generalized α method described in Implementation Example 11.

[0037] Figure 3 In the figure, (a) is a schematic diagram of the dynamic energy results of a large deformation flexible simple pendulum using the variational integration method described in the present invention, and (b) is a schematic diagram of the dynamic energy results of a large deformation flexible simple pendulum using the generalized α method.

[0038] Figure 4 Schematic diagram of momentum change calculated by the variational integration method described in Implementation eleven.

[0039] Figure 4In the figure, (a) is a momentum change diagram calculated by the variational integration method described in the present invention, and (b) is a momentum change diagram calculated by the generalized α method. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the implementation methods of the present application clearer, the technical solutions in the implementation methods of the present application will be clearly and completely described below in conjunction with the drawings in the implementation methods of the present application. Obviously, the described implementation methods are only part of the implementation methods of the present application, not all of the implementation methods.

[0041] Embodiment 1: This embodiment provides a time-space discrete integral variational method for dynamic simulation of a flexible large deformation beam model based on ANCF full gradient, the method comprising the following steps:

[0042] S1. Discretize the flexible large deformation beam model in time and space. For the spatial coordinate x, let x k is the arc length coordinate of the kth spatial node, L is the total length of the beam; for the time coordinate t, let t n is the time size of the nth time node, and T is the total simulation time. Consider the space-time discrete unit area [x k ,x k+1 ]×[t n-1 ,t n+1 ],in and

[0043] S2. Define the generalized coordinates and interpolation function of the space-time discrete unit, let where r is the position vector of any point on the beam centerline, is the tangent vector to the center line, r y and r z are two basis vectors on the beam cross section. Then Indicates that q is in x k and t n The value of express exist and t n The value of and where h = t n+1 -t n =t n -t n-1 , l is the length of discrete space, t is the length of discrete time; r uses cubic Hermite interpolation in space, r y and r zQuadratic Lagrange interpolation is used in space, and quadratic Lagrange interpolation is used in time for all variables to obtain the expression of the position vector and its gradient in each space-time discrete unit;

[0044] S3, based on the expressions of the position vector and its gradient in each space-time discrete unit obtained in S2, calculate [t n-1 ,t n+1 ]Calculate the kinetic energy, elastic potential energy and work done by external forces in the interval and find the variation;

[0045] S4, substituting the kinetic energy, elastic potential energy and work done by external force obtained in S3 into Hamilton variational formula to obtain the dynamic equations of space-time discrete units, and integrating all space-time discrete units to obtain the nonlinear algebraic dynamic equations of the beam system;

[0046] S5. Use Newton's iteration method to solve the nonlinear algebraic equations to obtain the position vector and its gradient vector on the discrete node.

[0047] Implementation method 2: This implementation method further limits the space-time discrete integral variation method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in implementation method 1. The area for space-time discretization of the flexible large deformation beam in S1 is [0, L] × [0, T].

[0048] Implementation method three: This implementation method further limits the spatiotemporal discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in implementation method one, and S2 also includes the step of defining Hermite variational interpolation function.

[0049] Embodiment 4: This embodiment further defines the spatiotemporal discrete integral variational method for dynamic simulation of a flexible large deformation beam model based on ANCF full gradient described in Embodiment 3. The method for defining the Hermite variational interpolation function is:

[0050] H1=1-3ξ 2 +2ξ 3 ,H2=l(ξ-2ξ 2 +ξ 3 ),H3=3ξ 2 -2ξ 3 ,H4=l(ξ 3 -ξ 2 ).

[0051] Embodiment 5: This embodiment further limits the spatiotemporal discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in embodiment 1. The method for obtaining the position vector in each spatiotemporal discrete unit in S2 is:

[0052]

[0053] Among them, s = [H1 H2 0 0 0 0 H3 H4 0 0], Q represents the permutation and combination of generalized coordinates of each space-time discrete unit, and S and N are shape functions.

[0054] Embodiment 6: This embodiment further defines the spatiotemporal discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in Embodiment 1. In S3, [t n-1 ,t n+1 The method of varying the kinetic energy, elastic potential energy and work done by external force in the interval is:

[0055]

[0056] in, Represents the time derivative of displacement at any point P, i.e. velocity, ρ A is the line density, and the stiffness coefficient matrix associated with the external forces, is the elastic force term of the unit, F α is the unit external force term.

[0057] Embodiment 7: This embodiment further defines the space-time discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in embodiment 1. In S4, by integrating all space-time discrete units, the nonlinear algebraic dynamic equations of the beam system are obtained as follows:

[0058]

[0059] in, Yes n The combination of generalized coordinates of all unit nodes at the moment, and They are t n-1 and t n+1 The combination of all generalized coordinates of the moment; Yes n The elastic force combination of all units at the moment, and They are t n-1 and t n+1 The combination of all unit elastic forces at the moment; F n Yes n The external force combination of all units at the moment, F n-1 and F n+1 They are t n-1 and t n+1The combination of all unit external forces at the moment; M 11 are the generalized coordinate vectors in M ​​and at both ends and The corresponding mass matrix components are , where M is the total mass matrix of the integration.

[0060] Implementation method eight. Implementation method is a further limitation of the space-time discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient described in implementation method seven. S4 also includes the step of confirming the nonlinear algebraic equation group of the unconstrained beam system and the nonlinear algebraic equation group of the constrained beam system.

[0061] Embodiment 9. This embodiment proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in any one of embodiments 1 to 8.

[0062] Embodiment 10: This embodiment proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method described in any one of Embodiments 1 to 8 are implemented.

[0063] Implementation eleven: This implementation provides an example, which is used to explain the above implementations one to eight. The specific example is as follows:

[0064] See also Figures 1 to 4 To illustrate this embodiment, the method described in this embodiment includes the following steps:

[0065] Step 1: Discretize the region [0,L]×[0,T] in time and space. For the spatial coordinate x, let For the time coordinate t, let Consider the discrete unit area [x k ,x k+1 ]×[t n-1 ,t n+1 ],in and

[0066] Step 2: Define unit generalized coordinates and interpolation function: Let Indicates that q is in x k and t n The value of express exist and t n The value of . Definition and where h = t n+1 -t n =t n -t n-1 . r uses cubic Hermite interpolation in space, r y and r z Quadratic Lagrange interpolation is used in space, and quadratic Lagrange interpolation is used in time for all variables. The Hermite interpolation function is defined as

[0067] H1=1-3ξ 2 +2ξ 3 ,H2=l k (ξ-2ξ 2 +ξ 3 ),H3=3ξ 2 -2ξ 3 ,H4=l k (ξ 3 -ξ 2 )

[0068] And define the quadratic Lagrange interpolation function as:

[0069]

[0070] N1=1-3η+2η 2 ,N2=4η(1-η),N3=η(2η-1)

[0071] Let the shape function:

[0072] s=[H1 H2 0 0 0 0 H3 H4 0 0]

[0073]

[0074]

[0075] N=[N1 N2 N3]

[0076] Then the position vector and its derivatives with respect to x and y can be expressed as:

[0077]

[0078] Among them, the permutation and combination of generalized coordinates of each unit is Q. Therefore, the expression of the position vector of any point on the flexible beam is

[0079] r P =r+yr y +zr z

[0080] Step 3: Calculate [tn-1 ,t n+1 ] The integral variation of the kinetic energy of the interval, that is,

[0081]

[0082] Using the conditions δq at the two end points n+1 =δq n-1 = 0, substitute the above unit discrete expression into the above formula to obtain the discrete result of variation

[0083]

[0084] in,

[0085]

[0086] In order to obtain the integral variation of elastic potential energy, it is necessary to obtain the expressions of stress and strain. In the unit discretization, the discretized strain component is

[0087]

[0088] in,

[0089]

[0090] In discrete units, the coefficient vector related to curvature is:

[0091]

[0092] in,

[0093]

[0094] Therefore, in [t n-1 ,t n+1 ]The integral of the elastic potential energy in the interval is:

[0095]

[0096] in,

[0097]

[0098] in,

[0099] C A =∫ A CdA,C yy =∫ A y 2 CdA,C yz =∫ A Yj Y

[0100] C zz =∫ A z 2 CdA,C y =∫ A YC z =∫ A ZlUT

[0101] and

[0102]

[0103] Taking the variation of the elastic potential energy, we can get

[0104]

[0105] Calculate [t n-1 ,t n+1 ] The integral variation of the work done by the external force in the interval is

[0106]

[0107] in, Represents the time derivative of displacement at any point P, i.e. velocity, ρ A is the line density, and the stiffness coefficient matrix associated with the external forces, is the elastic force term of the unit, F α is the unit external force term;

[0108] in:

[0109] Step 4: Substitute the above formulas (1), (2), and (3) into the Hamilton principle. get

[0110] Integrate the beam elements to obtain the dynamic equations for the assembled beams:

[0111]

[0112] in, Yes n The combination of generalized coordinates of all unit nodes at the moment, and They are t n-1 and t n+1 The combination of all generalized coordinates of the moment; Yes n The elastic force combination of all units at the moment, and They are t n-1 and tn+1 The combination of all unit elastic forces at the moment; F n Yes n The external force combination of all units at the moment, F n-1 and F n+1 They are t n-1 and t n+1 The combination of all unit external forces at the moment; M 11 are the generalized coordinate vectors in M ​​and at both ends and The corresponding mass matrix components are , where M is the total mass matrix of the integration.

[0113] Using boundary conditions get:

[0114]

[0115] Considering The arbitrariness of , we can obtain the nonlinear algebraic equations for the unconstrained beam system:

[0116]

[0117] For a beam system with constraint Φ = 0, the constrained Hamilton principle can be used, that is,

[0118]

[0119] Since the constraint equation must be satisfied at each discrete time point, we can combine the midpoint integration criterion to obtain

[0120]

[0121] Therefore, considering δλ n+1 The arbitrariness of , we can obtain the nonlinear algebraic equations of the constrained beam system:

[0122]

[0123] The Newton iteration method can be used to obtain the position vectors of all nodes at time n+1 and their gradient vectors and Lagrange multipliers.

[0124] In the specific implementation, the shape functions S, G, and P are first given, and their time derivatives are calculated and spatial derivatives, and then calculate the unit mass matrix m αβ , stiffness coefficient matrix and the integral constants related to the external forces, and then assemble the overall mass matrix M, the elastic force F e and external force F, and assemble the overall Jacobian matrix, and finally select the second set of equations to solve. Figure 2As shown, for the problem of large deformation flexible simple pendulum, the time-varying trends of momentum and energy calculated by the space-time discrete variational method and the generalized α method of the ANCF full gradient beam unit in the present invention are given here. From the comparison results, it can be seen that the variational method of the present invention can ensure good momentum conservation properties and approximate energy retention characteristics.

[0125] The effectiveness and advantages of the modeling and calculation method of the present invention can be verified for the problem of large deformation flexible single pendulum. Since the first-order difference is used to calculate the velocity from the displacement, the energy oscillation amplitude of the result calculated by the present invention is relatively large. When a higher-order difference is used to calculate the velocity, the energy amplitude calculated by the present invention will decrease. Figure 3 It can be seen that the attenuation is not obvious; in contrast, the energy attenuation of the generalized α method is significant.

[0126] Figure 1 Any process or method description in the flowchart described in or otherwise described herein can be understood as representing a module, fragment or portion of a code including one or more executable instructions for implementing the steps of a custom logic function or process, and the scope of the preferred embodiment of the present invention includes other implementations, in which the functions may be performed in a substantially simultaneous manner or in a reverse order according to the functions involved, which should be understood by a person skilled in the art of the present invention. The logic and / or steps represented in the flowchart or otherwise described herein illustrate the possible implementation architecture, functions and operations of the apparatus and methods according to various embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, a program segment, or a part of a code, and the above-mentioned module, program segment, or a part of a code contains one or more executable instructions for implementing the specified logic function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It is also noted that each block in the block diagram or flowchart, and combinations of blocks in the block diagram or flowchart, may be implemented by a dedicated hardware-based system that performs the specified functions or operations, or may be implemented by a combination of dedicated hardware and computer instructions. For example, what may be considered as an ordered list of executable instructions for implementing a logical function may be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can fetch instructions from and execute instructions in an instruction execution system, apparatus, or device).

[0127] Those skilled in the art will appreciate that the above are only preferred embodiments of the present invention, and the various embodiments of the present disclosure and / or the features described in the claims may be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the present disclosure. It is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments, or perform equivalent substitutions on some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

[0128] Although preferred embodiments of the present invention have been described, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A space-time discrete integral variational method for dynamic simulation of a flexible large deformation beam model based on ANCF full gradient, characterized by: The method comprises the following steps: S1. Discretize the flexible large deformation beam model in time and space. For the spatial coordinate x, let x k is the arc length coordinate of the kth spatial node, L is the total length of the beam; for the time coordinate t, let t n is the time size of the nth time node, t f is the total simulation time; considering the space-time discrete unit area [x k ,x k+1 ]×[t n-1 ,t n+1 ],in and S2. Define the generalized coordinates and interpolation function of the space-time discrete unit, let where r is the position vector of any point on the beam centerline, is the tangent vector to the center line, r y and r z are two basis vectors on the beam cross section; then Indicates that q is in x k and t n The value of express exist and t n The value of and where h = t n+1 -t n =t n -t n-1 , l is the length of discrete space, t is the length of discrete time; r uses cubic Hermite interpolation in space, r y and r z Quadratic Lagrange interpolation is used in space, and quadratic Lagrange interpolation is used in time for all variables to obtain the expression of the position vector and its gradient in each space-time discrete unit; S3, based on the expressions of the position vector and its gradient in each space-time discrete unit obtained in S2, calculate [t n-1 ,t n+1 ]Calculate the kinetic energy, elastic potential energy and work done by external forces in the interval and find the variation; S4, substituting the kinetic energy, elastic potential energy and work done by external force obtained in S3 into Hamilton variational formula to obtain the dynamic equations of space-time discrete units, and integrating all space-time discrete units to obtain the nonlinear algebraic dynamic equations of the beam system; S5. Use Newton's iteration method to solve the nonlinear algebraic equations to obtain the position vector and its gradient vector on the discrete node.

2. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 1 is characterized in that: The region for time-space discretization of the flexible large deformation beam in S1 is [0,L]×[0,t f ].

3. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 1 is characterized in that: S2 also includes the step of defining the Hermite variational interpolation function.

4. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 3 is characterized in that: The method for defining the Hermite variational interpolation function is: H1=1-3ξ 2 +2x 3 ,H2=l(ξ-2ξ 2 +ξ 3 ),H3=3ξ 2 -2x 3 ,H4=l(ξ 3 -x 2 )。 5. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 1 is characterized in that: The method for obtaining the position vector in each space-time discrete unit in S2 is: Among them, s = [H1 H2 0 0 0 0 H3 H4 0 0], Q represents the permutation and combination of generalized coordinates of each space-time discrete unit, and S and N are shape functions.

6. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 1 is characterized in that: In S3, [t n-1 ,t n+1 The method of varying the kinetic energy T, elastic potential energy U and work W done by the external force f in the interval is: in, Represents the time derivative of displacement at any point P, i.e. velocity, ρ A is the line density, and the stiffness coefficient matrix associated with the external forces, is the elastic force term of the unit, F α is the unit external force term.

7. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 1 is characterized in that: In S4, by integrating all time-space discrete units, the nonlinear algebraic dynamic equations of the beam system are obtained as follows: in, Yes n The combination of generalized coordinates of all unit nodes at the moment, and They are t n-1 and t n+1 The combination of all generalized coordinates of the moment; Yes n The elastic force combination of all units at the moment, and They are t n-1 and t n+1 The combination of all unit elastic forces at the moment; F n Yes n The external force combination of all units at the moment, F n-1 and F n+1 They are t n-1 and t n+1 The combination of all unit external forces at the moment; M 11 are the generalized coordinate vectors in M ​​and at both ends and The corresponding mass matrix components are , where M is the total mass matrix of the integration.

8. The time-space discrete integral variational method for dynamic simulation of flexible large deformation beam model based on ANCF full gradient according to claim 7 is characterized in that: S4 also includes the step of confirming the nonlinear algebraic equation group of the unconstrained beam system and the nonlinear algebraic equation group of the constrained beam system.

9. A computer device comprising a memory and a processor, characterized in that A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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