Composite material thin shell dynamics prediction method based on isogeometry

Abstract

The invention discloses an isogeometry-based composite material thin shell dynamics prediction method, and belongs to the field of composite material thin shell dynamics behavior prediction. The implementation method comprises the steps that geometric modeling is conducted on the composite thin shell based on an isogeometric analysis method, unification of geometric modeling and numerical analysis is achieved through a non-uniform B spline (NURBS), and a composite thin shell geometric model is obtained; calculating a tensile stiffness matrix, a tensile-bending coupling stiffness matrix and a bending stiffness matrix of the composite material thin shell through the composite material parameters; establishing a kinetic model of the composite material thin shell unit through continuous medium mechanics, assembling the kinetic model to obtain an overall kinetic model of the composite material thin shell, and establishing a kinetic equation of the composite material thin shell based on the overall kinetic model of the composite material thin shell and the stiffness matrix; a kinetic equation is solved based on a generalized alpha implicit time integration algorithm, the kinetic behavior of the composite thin shell under the action of an external force F is predicted, and the stability and precision of thin shell kinetic behavior prediction are improved.

Description

Technical Field

[0001] The present invention relates to a method for predicting the dynamics of composite thin shells based on isogeometric analysis, belonging to the technical field of predicting the dynamic behavior of composite thin shells. Background Technique

[0002] In the aerospace field, in order to achieve lightweight design, composite thin shells are often used in deployable space membrane mechanisms, and their elastic potential energy stored by bending is used to drive the deployment. This design makes full use of the excellent mechanical properties and lightweight characteristics of composite thin shells, not only improving the structural efficiency but also significantly reducing the system weight. In addition to aerospace, composite thin shells are also widely used in other fields, such as the lightweight design of vehicle bodies in the automotive industry and high-performance structures in construction engineering. With the continuous expansion of engineering applications, composite thin shells have attracted increasing attention due to their outstanding specific strength, specific stiffness, and design flexibility. At the same time, in-depth research on the dynamic behavior of composite thin shells is of great significance for optimizing design, improving reliability, and meeting the requirements of complex working conditions.

[0003] In engineering structure analysis, the traditional finite element method (FEM) is a numerical analysis method widely used in various engineering problems. By dividing a complex structure into a series of simple elements, different shape functions are used to approximately describe the geometric shape and physical behavior of the structure. However, there is a certain disconnection between geometric modeling and physical analysis in the traditional finite element method. Usually, polynomial interpolation functions are used to approximate the geometric shape, which may lead to inconsistencies between the geometry and physical fields, thereby affecting the analysis accuracy.

[0004] Specifically, the geometric models in the traditional finite element method usually adopt low-order polynomials (such as linear or quadratic interpolation functions), which makes it easy to cause distortion when analyzing complex geometric shapes and large deformations. Especially in engineering applications with high-precision requirements, such as thin shell structure analysis, numerical locking and other issues often need to be considered specifically. At the same time, the traditional finite element method usually relies on node-based shape functions to describe the physical field and the displacement field of the structure. When dealing with high-order continuity modeling, especially when simulating thin shell problems, due to the requirement of high C1 continuity, the traditional finite element method is often difficult to handle accurately. Summary of the Invention

[0005] To solve the problems of insufficient accuracy, low computational efficiency, and poor adaptability to complex geometries and non-linear behaviors in the traditional finite element analysis method when dealing with the large deformation dynamic behavior of composite thin shells. The object of the present invention is to provide an isogeometric-based dynamic prediction method for composite thin shells. Geometric modeling of the composite thin shell is carried out based on the isogeometric analysis method, and the unity of geometric modeling and numerical analysis is achieved through non-uniform B-splines (NURBS) to obtain the geometric model of the composite thin shell; the tensile stiffness matrix, tension-bending coupling stiffness matrix, and bending stiffness matrix of the composite thin shell are calculated through composite material parameters; the dynamic model of the composite thin shell element is established through continuum mechanics. After assembling the dynamic models of the composite thin shell elements, the overall dynamic model of the composite thin shell is obtained. Based on the overall dynamic model of the composite thin shell and the stiffness matrix of the composite thin shell, the dynamic equation of the composite thin shell is established; the dynamic equation of the composite thin shell is solved based on the generalized α implicit time integration algorithm to predict the dynamic behavior of the composite thin shell under the action of the external force F, significantly improving the stability and accuracy of predicting the dynamic behavior of the composite thin shell. The present invention is particularly suitable for predicting the dynamic behavior of composite thin shells under complex loading conditions and large deformation situations.

[0006] The object of the present invention is achieved by the following technical solutions:

[0007] An isogeometric-based dynamic prediction method for composite thin shells disclosed by the present invention includes the following steps:

[0008] Step 1: Geometric modeling of the composite thin shell is carried out based on the isogeometric analysis method, and the unity of geometric modeling and numerical analysis is achieved through non-uniform B-splines (NUR-BS). It can not only accurately describe complex geometric shapes but also improve the accuracy of the geometric model of the composite thin shell through high-order continuity, avoiding geometric errors and numerical locking problems of the traditional finite element method, and obtaining a geometric model of the composite thin shell with unified geometric modeling and numerical analysis.

[0009] For the composite thin shell surface, a binary NURBS basis function of the composite thin shell surface is constructed by using the tensor product method of two B-spline basis functions. From the NURBS basis function combined with the control point coordinates q i,j to form the geometric model of the composite thin shell surface. A NURBS surface with p degrees in the ξ direction and q degrees in the η direction is expressed as:

[0010]

[0011] where: q i,j is the position vector of the control point, is the two-dimensional NURBS basis function, and N in the two-dimensional NURBS basis functioni,p (ξ), M j,q (η) are B-spline basis functions of single variables ξ and η, w is the weight coefficient corresponding to the basis function, p and q are the orders of the B-spline basis functions, and n and m are the numbers of B-spline basis functions in the ξ direction and η direction respectively.

[0012] According to formula (1), the position vector of any point on the middle surface of the thin shell element is written in the form of the product of the shape function constructed by the NURBS basis function and the coordinates of the corresponding control points.

[0013]

[0014] where is the shape function vector composed of NURBS basis functions, and its form is

[0015]

[0016] where is the element generalized coordinate matrix composed of the global position vectors of the corresponding control points as shown in the following formula

[0017]

[0018] According to formulas (1) and (2), the unification of geometric modeling and numerical analysis is realized through NURBS. It can not only accurately describe complex geometric shapes, but also improve the analysis accuracy through high-order continuity, avoiding the geometric error and numerical locking problems of the traditional finite element method.

[0019] Step 2: Construct the tensile stiffness matrix D0, the tension-bending coupling stiffness matrix D1, and the bending stiffness matrix D2 of the composite thin shell according to the composite material parameters.

[0020] The composite material parameters include Young's modulus E1, E2, shear modulus G 12 , Poisson's ratio v 12 , v 21 , ply angle θ, density ρ, and the thickness of each layer of composite material is h.

[0021] Based on the thin shell theory, the material matrix of the k-th layer of the composite material without considering the ply angle is

[0022]

[0023] where Q 11 , Q 12 , Q 22 , Q 66 are obtained from the Young's modulus, Poisson's ratio, and shear modulus of the composite material.

[0024] When the ply angle is φ, through the rotation matrix T, the material matrix Map it into the global coordinate system to obtain the material matrix

[0025]

[0026] Among them, the rotation matrix T is

[0027] For a composite material with a thickness of h, the stiffness matrix is obtained by integrating the material matrix along the thickness direction to obtain the tensile stiffness matrix D0, the tensile-bending coupling stiffness matrix D1, and the bending stiffness matrix D2:

[0028]

[0029] Step 3: Establish a dynamic model of the composite thin-shell element composed of the mass matrix M e , the internal force matrix P e , and the tangent stiffness matrix using continuum mechanics. After assembling the dynamic model of the composite thin-shell element, a global dynamic model of the composite thin-shell composed of the mass matrix M, the internal force matrix P, and the tangent stiffness matrix K t is obtained.

[0030] Based on the Kirchhoff-love thin-shell theory, the kinematic relationship between the current configuration and the initial configuration of the thin-shell element is

[0031] u = x - X (6)

[0032] where u is the deformation displacement vector, x is the position vector of any point P'(ξ, η, z) on the thin shell in the deformed current configuration, and X is the position vector of any point P'(ξ, η, z) on the thin shell in the undeformed initial configuration.

[0033] A in the initial configuration i and G i take i = 1, 2, 3. Among them, the vectors A1 and A2 describe the tangent vectors of the mid-surface of the shell in the ξ, η directions in the initial configuration. The unit direction vector A3 in the z direction in the initial configuration is obtained from the vectors A1 and A2: A3 = (A1 × A2) / |A1 × A2|. According to the straight normal criterion of the thin-shell theory, the tangent vector at any point on the shell is obtained from the corresponding tangent vector on the mid-surface G α = A α + zA3, G3 = A3, where α takes 1, 2.

[0034] a in the tangent vector of the current configuration i and g iLet \(i = 1, 2, 3\). Among them, the vectors \(\vec{a}_1\) and \(\vec{a}_2\) describe the tangent vectors of the shell mid-surface in the \(\xi\) and \(\eta\) directions in the current configuration. The unit direction vector \(\vec{a}_3\) in the \(z\) direction in the current configuration is also obtained from the vectors \(\vec{a}_1\) and \(\vec{a}_2\): \(\vec{a}_3=\frac{\vec{a}_1\times\vec{a}_2}{\vert\vec{a}_1\times\vec{a}_2\vert}\).

[0035] The position vector \(\vec{x}\) of any point \(P'(\xi,\eta,z)\) on the shell in the current configuration after deformation is

[0036] \(\vec{x}(\xi,\eta,z)=\vec{r}(\xi,\eta)+z\vec{a}_3\quad(7)\)

[0037] where \(\vec{r}(\xi,\eta)\) is the position vector of any point \(P(\xi,\eta)\) on the thin shell mid-surface in the current configuration. Based on the isogeometric description, the position vector \(\vec{r}(\xi,\eta)\) is obtained according to Equation (2).

[0038] The deformation gradient \(\mathbf{F}\) is obtained according to the theory of continuum mechanics as

[0039]

[0040] The Green-Lagrange strain tensor \(\mathbf{E}\) is obtained from the deformation gradient:

[0041]

[0042] \(\mathbf{I}\) is the identity tensor, and the identity tensor \(\mathbf{I}\) has the same dimension as the strain tensor \(\mathbf{E}\). Among them, the covariant components of the strain tensor \(\mathbf{E}\) are

[0043]

[0044] For thin shell elements, transverse shear is not considered, and only in-plane strain components are considered. The covariant components of the strain tensor \(\mathbf{E}\) are transformed as

[0045] \(\mathbf{E}\) αβ =\(\boldsymbol{\varepsilon}\) αβ +z\(\boldsymbol{\kappa}\) αβ \((11)\)

[0046] where \(\alpha,\beta = 1, 2\); for Equation (11), the left part describes the in-plane deformation of the thin shell element, and the other part describes the bending deformation of the thin shell element. \(\boldsymbol{\varepsilon}\) αβ is the tensile strain component of the thin shell mid-surface, and \(\boldsymbol{\kappa}\) αβ is the bending strain component of the thin shell.

[0047] In the local coordinate system, the relationship between the tensor components of the stress tensor \(\mathbf{S}\) and the strain tensor \(\mathbf{E}\) is

[0048]

[0049] where is the stiffness matrix of the composite thin shell obtained from Equation (5).

[0050] Integrate the obtained stress tensor along the thickness direction to obtain the internal force n and internal moment m of the thin shell element as shown in Equation (13), where α, β take 1, 2, and written in Voigt form as

[0051]

[0052]

[0053] Based on the principle of virtual displacement, the virtual work done by the internal force on the system is calculated as

[0054] δW int =∫ Ω (S:δE)dΩ=∫ A (n:δε+m:δκ)dA (15)

[0055] where S is the stress, E is the strain, n is the internal force, m is the internal moment, ε is the membrane strain, and κ is the curvature.

[0056] Take the partial derivative of the strain energy with respect to the generalized coordinate q of the control point r to obtain the generalized internal force vector of the thin shell element, expressed as

[0057]

[0058] Then take the partial derivative with respect to the generalized coordinate q s to obtain the tangent stiffness matrix of the thin shell element which is

[0059]

[0060] According to the density ρ of the material, the thickness h, and the NURBS basis function vector R, obtain the mass matrix M of the thin shell element e which is

[0061] M e =ρh∫ Ω R T RdΩ (18)

[0062] Assemble the matrices of the obtained thin shell element to obtain the overall dynamic model of the composite thin shell composed of the mass matrix M, the internal force matrix P, and the tangent stiffness matrix K t Step 4: Based on the overall dynamic model of the composite thin shell composed of the mass matrix M, the internal force matrix P, and the tangent stiffness matrix K obtained in Step 3, establish the dynamic equation of the composite thin shell; solve the dynamic equation of the composite thin shell based on the generalized α implicit time integration algorithm to predict the dynamic behavior of the composite thin shell under the action of the external force F.

[0063] Step 4: According to the overall dynamic model of the composite thin shell composed of the mass matrix M, the internal force matrix P, and the tangent stiffness matrix K t obtained in Step 3, establish the dynamic equation of the composite thin shell; solve the dynamic equation of the composite thin shell based on the generalized α implicit time integration algorithm to predict the dynamic behavior of the composite thin shell under the action of the external force F.

[0064] Step 4.1: Based on the overall dynamic model of the composite thin shell composed of the mass matrix M, internal force matrix P, and tangent stiffness matrix K obtained in Step 3, construct the dynamic equation of the composite thin shell under external forces as t

[0065]

[0066] where is the generalized acceleration, M is the mass matrix, P is the generalized internal force vector, and F ext is the generalized external force vector.

[0067] Step 4.2: Solve the dynamic equation of the composite thin shell based on the generalized α implicit time integration algorithm to predict the dynamic behavior of the composite thin shell under the action of the external force F.

[0068] Step 4.2.1: According to the dynamic equation (19), after time discretization, we get

[0069]

[0070] where q n+1 is the generalized coordinate at the (n + 1)-th step, is the generalized acceleration at the (n + 1)-th step.

[0071] Step 4.2.2: Predict the generalized coordinate and generalized acceleration at the (n + 1)-th time step according to Equation (21) through the generalized α implicit time integration algorithm

[0072]

[0073] The parameter selection method for Equation (21) is as follows:

[0074]

[0075] In the parameter selection method, ρ ∈ [0, 1] is the spectral radius of the generalized α implicit time integration algorithm, and α m and α f are both parameters of the generalized α implicit time integration algorithm.

[0076] Step 4.2.3: Set the convergence accuracy tol, and then use the Newton iteration method to solve Equation (23)

[0077]

[0078] where r n+1 is the residual force vector, J is the Jacobian matrix, and the parameters satisfy and ​It represents the result of setting 0s and 1s for the matrix after considering the boundary conditions, and Δq represents the increment of the system's generalized coordinates at the current moment.

[0079] Step 4.2.4: Calculate the norm ||r n+1 || of the residual vector obtained in Step 4.2.3. If ||r n+1 || > tol, it indicates that the Newton iteration does not converge, and continue the iteration until convergence. If ||r n+1 || < tol, it means the iteration converges, and update the generalized coordinates q n+1 .

[0080] q n+1 = q n + Δq (24)

[0081] Step 4.2.5: Iterate Steps 4.2.3 and 4.2.4 to solve the dynamic equation of the composite thin shell until the given dynamic calculation time ends, and obtain the predicted results of the dynamic behavior of the composite thin shell under the action of the external force F.

[0082] Step 4.2.6: Perform a visualization operation on the predicted results of the dynamic behavior obtained in Step 4.2.5 to display the visualized results of the dynamic behavior of the composite thin shell under the action of the external force F.

[0083] Step 5: According to the predicted results of the dynamic behavior of the composite thin shell in Step 4, accurately evaluate its mechanical response under complex working conditions, and provide reliable data support for engineering structure design. By deeply analyzing the dynamic behavior of the thin shell structure, optimize the composite thin shell structure to improve its mechanical properties and stability. At the same time, the predicted results contribute to the vibration control, structural health monitoring, and fault diagnosis of the composite thin shell, effectively solve related engineering problems, and promote the wide application of composite thin shells in the fields of aerospace, automotive engineering, etc.

[0084] Beneficial effects:

[0085] 1. A dynamic prediction method for composite thin shells based on isogeometric analysis disclosed in the present invention adopts the isogeometric analysis method, and establishes an accurate geometric model of the composite thin shell through non-uniform B-splines (NURBS), realizing the unity of geometric modeling and numerical analysis. Compared with the traditional finite element analysis method, it does not require complex and cumbersome mesh generation operations, and significantly improves the efficiency of predicting the dynamic behavior of composite thin shells.

[0086] 2. A method for predicting the dynamics of composite thin shells based on isogeometric analysis, which fully considers the characteristics of composite materials and constructs the tensile stiffness matrix, tension-bending coupling stiffness matrix, and bending stiffness matrix of composite thin shells through composite material parameters. It can better be applied to the prediction of the dynamic behavior of composite thin shells under complex loading conditions and large deformations, meet the requirements of composite materials in the applications of aerospace, automotive engineering, etc., and contribute to vibration control, structural health monitoring, and fault diagnosis in the corresponding fields.

[0087] 3. A method for predicting the dynamics of composite thin shells based on isogeometric analysis, which establishes the dynamic equation of composite thin shells based on the overall dynamic model of composite thin shells and the stiffness matrix of composite thin shells; and solves the dynamic equation of composite thin shells based on the generalized α implicit time integration algorithm to predict the dynamic behavior of composite thin shells under the action of external force F. This method can efficiently analyze the dynamic behavior of composite thin shells under large deformation conditions, not only significantly improve the calculation accuracy but also enhance the adaptability to complex nonlinear problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 Flowchart of a method for predicting the dynamics of composite thin shells based on isogeometric analysis of the present invention;

[0089] Figure 2 Schematic diagram of the current configuration and initial configuration of the shell element model based on the thin shell assumption in step 3 of the present invention;

[0090] Figure 3 Schematic diagram of the geometric model of an isogeometric-based composite circular thin shell in Example 1 of the present invention;

[0091] Figure 4 Dynamic response curve of the center of an isogeometric-based composite circular thin shell under the action of external force F within 0.5 s in Example 1 of the present invention;

[0092] Figure 5 Schematic diagram of the geometric model of a composite cylindrical thin shell surface patch based on isogeometric analysis in Example 2 of the present invention;

[0093] Figure 6 Schematic diagram of the dynamic behavior of an isogeometric-based composite cylindrical shell patch under the action of external force F within 5 ms in Example 2 of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0094] To better illustrate the purpose and advantages of the present invention, the following further describes the content of the invention in conjunction with the drawings and examples.

[0095] Example 1:

[0096] As Figure 1As shown in the figure, a method for predicting the dynamics of composite thin shells based on isogeometric analysis disclosed in this embodiment is specifically implemented as follows:

[0097] Step 1: Geometrically model the composite thin shell based on the isogeometric analysis method. Establish a circular thin shell surface with a geometric parameter of radius R = 300 mm through Equation (1), and divide it into 30 * 30 elements. The boundary condition is hinged on all sides, and an external force F = 20sin(10πt) N acts at the center position, as Figure 2 shown.

[0098] Step 2: According to the parameters of the composite material: Young's modulus E1 = 92000 Mpa, E2 = 7000 Mpa, shear modulus G 12 = 2700 Mpa, Poisson's ratio v 12 = 0.3 and v 21 = 0.0228, density = 1.8e - 6 kg / mm 3 , ply angle φ = [90 / 0 / 90], and the thickness of each layer of the composite material is h = 0.03 mm. Equation (5) can be expanded into Equation (25) to obtain the stiffness matrix of the composite thin shell.

[0099]

[0100] where the layer always parallel to the x - axis is set as the 0° ply, and D ki is the stiffness matrix of the i - th layer obtained through Equation (4).

[0101] Step 3: Establish a dynamic model of the composite thin shell element consisting of the mass matrix M e , internal force matrix P e , and tangent stiffness matrix through continuum mechanics. After assembling the dynamic model of the composite thin shell element, a global dynamic model of the composite thin shell consisting of the mass matrix M, internal force matrix P, and tangent stiffness matrix K t is obtained. For the ply angle φ = [90 / 0 / 90], the internal force n and internal moment m of the composite thin shell element are obtained through Equation (25) and Equation (26).

[0102]

[0103] where is the stress tensor component of the i - th layer. The letter S represents stress, E represents strain, and D represents the material matrix. For D0, D1, and D2, they are the overall tensile stiffness, tensile - bending coupling stiffness, and bending stiffness, respectively. Here, i and g take 1, 2, 3, as shown in Equation (25) and Equation (26). When taking 1, it represents the lowest layer, and the calculation is carried out from bottom to top, and so on.

[0104] Step 4: Based on the overall dynamic model of the composite thin shell composed of the mass matrix M, internal force matrix P, and tangent stiffness matrix K obtained in Step 3, establish the dynamic equation of the composite thin shell; solve the dynamic equation of the composite thin shell based on the generalized α implicit time integration algorithm to predict the dynamic behavior of the composite thin shell under the action of the external force F = 20sin(10πt) N. Through visualization operations, obtain the dynamic response of the center point of the composite circular thin shell within 0.5 s, as t shown below. Figure 4

[0105] Step 5: According to the results of the dynamic behavior of the composite thin shell predicted in Step 4, its mechanical response under complex working conditions can be accurately evaluated, providing reliable data support for engineering structure design. By deeply analyzing the dynamic behavior of the thin shell structure, the structure design can be optimized to improve its mechanical properties and stability.

[0106] Example 2:

[0107] As Figure 1 shown below, the specific implementation steps of a dynamic prediction method for composite thin shells based on isogeometric analysis disclosed in this example are as follows:

[0108] Step 1: Based on the isogeometric analysis method, perform geometric modeling on the composite thin shell, and establish a cylindrical thin shell surface patch with geometric parameters R = 12.5 mm, length L = 100 mm, and circumferential angle through Equation (1), and divide it into 15*60 elements, as Figure 5 shown below.

[0109] Step 2: According to the composite material parameters: Young's modulus E1 = 92000 Mpa, E2 = 7000 Mpa, shear modulus G 12 = 2700 Mpa, Poisson's ratio v 12 = 0.3 and v 21 = 0.0228, density = 1.8e-6 kg / mm 3 , ply angle φ = [90 / 0 / 90], and the thickness of each layer of composite material is h = 0.03 mm, obtain the stiffness matrix of the composite thin shell through Equation (25).

[0110] Step 3: Establish a dynamic model of the composite thin shell element composed of the mass matrix M e , internal force matrix P e , and tangent stiffness matrix through the theory of continuum mechanics. After assembling the dynamic model of the composite thin shell element, obtain the mass matrix M, internal force matrix P, and tangent stiffness matrix K t ​The overall dynamic model of the composite thin shell formed. Among them, for the ply angle φ = [90 / 0 / 90], the internal force n and internal moment m of the composite thin shell element are obtained through equations (25) and (26).

[0111] Step 4: Based on the overall dynamic model of the composite thin shell formed by the mass matrix M, internal force matrix P, and tangent stiffness matrix K obtained in Step 3 t The overall dynamic model of the composite thin shell is established, and the dynamic equation of the composite thin shell is established; based on the generalized α implicit time integration algorithm, the dynamic equation of the composite thin shell is solved to predict the dynamic behavior of the composite thin shell under the action of the external force F = 200t N. Through visualization operations, the deformation of the composite thin shell at different times within 5 ms is obtained, and Um is the maximum displacement of the composite thin shell, as Figure 6 shown.

[0112] Step 5: According to the results of the dynamic behavior of the composite thin shell predicted in Step 4, the mechanical response of the composite thin shell under complex working conditions can be accurately evaluated, providing reliable data support for engineering structure design. By deeply analyzing the dynamic behavior of the thin shell structure, the structure design can be optimized to improve its mechanical properties and stability.

[0113] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the dynamics of composite thin shells based on isogeometry, characterized by: The following steps are included: Step 1: Based on the isogeometric analysis method, geometric modeling of the composite thin shell is carried out, and the unification of geometric modeling and numerical analysis is achieved through non-uniform B-spline (NURBS), so as to obtain a unified composite thin shell geometric model of geometric modeling and numerical analysis; Step 2: Construct the tensile stiffness matrix D0, the tension-bending coupling stiffness matrix D1, and the bending stiffness matrix D2 of the composite thin shell according to the composite material parameters; The composite material parameters include Young's modulus E1, E2, shear modulus G 12 , Poisson's ratio v 12 、v 21 , ply angle θ, density ρ, thickness of each layer of composite material is h; Step 3: Use continuum mechanics to establish the mass matrix M e , the internal force matrix P e , the tangent stiffness matrix The dynamic model of the composite thin shell unit is composed of the mass matrix M, the internal force matrix P, and the tangent stiffness matrix K. t The overall dynamic model of the composite thin shell; Step 4: Based on the mass matrix M, internal force matrix P, and tangent stiffness matrix K obtained in step 3 t The overall dynamic model of the composite thin shell is constructed, and the dynamic equation of the composite thin shell is established; the dynamic equation of the composite thin shell is solved based on the generalized α implicit time integration algorithm, and the dynamic behavior of the composite thin shell under the action of external force F is predicted.

2. The method for predicting dynamics of composite thin shells based on isogeometry according to claim 1, characterized in that: The method also includes step 5: accurately evaluating the mechanical response of the composite thin shell under complex working conditions based on the dynamic behavior results of the composite thin shell predicted in step 4; optimizing the composite thin shell structure and improving its mechanical properties and stability through in-depth analysis of the dynamic behavior of the thin shell structure; at the same time, the prediction results are helpful for vibration control, structural health monitoring, and fault diagnosis of the composite thin shell.

3. A composite thin shell dynamics prediction method based on isogeometry as claimed in claim 1 or 2, characterized in that: Step 1 is implemented as follows: For the composite thin shell surface, the binary NURBS basis function of the composite thin shell surface is constructed by using the tensor product method of two B-spline basis functions. With the control point coordinates q i,j Combined to form a composite thin shell surface geometric model; a NURBS surface with p-order in the ξ direction and q-order in the η direction is expressed as: Among them: qi,j is the position vector of the control point, is a two-dimensional NURBS basis function. i,p (ξ), M j,q (η) is the B-spline basis function of the single variable ξ and η, w is the weight coefficient corresponding to the basis function, p and q are the orders of the B-spline basis function, n and m are the numbers of B-spline basis functions in the ξ direction and the η direction. According to formula (1), the position vector of any point on the surface of the shell element is written as the product of the shape function constructed by the NURBS basis function and the coordinates of the corresponding control point: in is the shape function vector composed of NURBS basis functions, and its form is in The unit generalized coordinate matrix composed of the global position vectors of the corresponding control points is shown as follows According to equations (1) and (2), the unification of geometric modeling and numerical analysis is achieved through NURBS, which can not only accurately describe complex geometric shapes, but also improve the analysis accuracy through high-order continuity, avoiding the geometric errors and numerical locking problems of traditional finite element methods.

4. The method for predicting dynamics of composite thin shells based on isogeometry according to claim 3, characterized in that: In step 2, Based on the thin shell theory, the material matrix of the kth layer of the composite material does not consider the ply angle for Where Q 11 , Q 12 , Q 22 , Q 66 It is obtained from Young's modulus, Poisson's ratio and shear modulus of the composite material; When the ply angle is φ, the material matrix is ​​rotated by the matrix T. Mapped to the global coordinate system, the material matrix is ​​obtained The rotation matrix T is For a composite material with a thickness of h, the stiffness matrix is ​​integrated along the thickness direction by the material matrix to obtain the tensile stiffness matrix D0, the tension-bending coupling stiffness matrix D1, and the bending stiffness matrix D2:

5. The method for predicting dynamics of composite thin shells based on isogeometry according to claim 4, characterized in that: Step 3 is implemented as follows: Based on the Kirchhoff-love thin shell theory, the kinematic relationship between the current configuration and the initial configuration of the thin shell element is obtained as follows: u=xX (6) Where u is the deformation displacement vector, x is the position vector of any point P′(ξ,η,z) on the thin shell in the current configuration after deformation, and X is the position vector of any point P′(ξ,η,z) on the thin shell in the initial configuration before deformation; A in the initial configuration i and G i where i is 1, 2, or 3; vectors A1 and A2 describe the tangent vectors of the shell midplane in the ξ and η directions under the initial configuration; the unit direction vector A3 in the z direction under the initial configuration is obtained through vectors A1 and A2: A3 = (A1×A2) / |A1×A2|; according to the straight normal criterion of thin shell theory, the tangent vector of any point on the shell is obtained through the tangent vector on the corresponding midplane G α =A α +zA3, G3 = A3, where α is 1 or 2; a in the tangent vector of the current configuration i and g i The i in the equation is 1, 2, or 3; the vectors a1 and a2 describe the tangent vectors of the shell mid-surface in the ξ and η directions in the current configuration; the unit direction vector a3 in the z direction in the current configuration is also obtained through the vectors a1 and a2: a3 = (a1×a2) / |a1×a2|; The position vector x of any point P′(ξ,η,z) on the shell in the current configuration after deformation is x(ξ,η,z)=r(ξ,η)+za3 (7) Where r(ξ,η) is the position vector of any point P(ξ,η) on the middle surface of the thin shell under the current configuration; Based on the isogeometric description, the position vector r(ξ,η) is obtained according to formula (2); According to the theory of continuum mechanics, the deformation gradient F is obtained as follows: According to the deformation gradient, the Green Lagrangian strain tensor E is obtained: I is the unit tensor, and the unit tensor I has the same dimension as the strain tensor E; the covariant component of the strain tensor E is For thin shell elements, transverse shear is not considered, only the in-plane strain component is considered, and the covariant component of the strain tensor E is transformed into E αβ =e αβ +zk αβ (11) Where α and β are 1 and 2 respectively. For equation (11), the left part describes the in-plane deformation of the shell element, and the other part describes the bending deformation of the shell element. αβ is the tensile strain component of the shell mid-surface, κ αβ is the bending strain component of the shell; In the local coordinate system, the tensor components of the stress tensor S and the strain tensor E are related by in is the stiffness matrix of the composite thin shell obtained by formula (5); The obtained stress tensor is integrated along the thickness direction to obtain the internal force n and internal moment m of the thin shell element as shown in formula (13), where α and β are 1 and 2, and written in Voigt form as Based on the principle of virtual displacement, the virtual work done by the internal force on the system is calculated as δW int =∫ Ω (S:δE)dΩ=∫ A (n:δε+m:δκ)dA (15) Where S is stress, E is strain, n is internal force, m is internal moment, ε is membrane strain, and κ is curvature; The strain energy is expressed as the generalized coordinates q of the control point r By taking partial derivatives, we can obtain the generalized internal force vector of the shell element, which is expressed as Then for the generalized coordinate q s Find the partial derivative and get the tangent stiffness matrix of the shell element for According to the material density ρ, thickness h and NURBS basis function vector R, the mass matrix M of the thin shell element is obtained e for M e =ρh∫ Ω R T RdΩ (18) The obtained matrix of the thin shell element is assembled to obtain the mass matrix M, internal force matrix P, tangent stiffness matrix K t The overall dynamic model of the composite thin shell.

6. The method for predicting dynamics of composite thin shells based on isogeometry according to claim 5, characterized in that: Step 4 is implemented as follows: Step 4.1: Based on the mass matrix M, internal force matrix P, and tangent stiffness matrix K obtained in step 3 t The overall dynamic model of the composite thin shell is constructed, and the dynamic equation of the composite thin shell under the action of external force is constructed as follows: in is the generalized acceleration, M is the mass matrix, P is the generalized internal force vector, F ext is the generalized external force vector; Step 4.2: Solve the dynamic equations of the composite thin shell based on the generalized α implicit time integration algorithm to predict the dynamic behavior of the composite thin shell under the action of external force F.

7. The method for predicting dynamics of composite thin shells based on isogeometry according to claim 6, characterized in that: Step 4.2 is implemented as follows: Step 4.2.1: According to the dynamic equation (19), after time discretization, we can obtain where q n+1 is the generalized coordinate of the n+1th step, is the generalized acceleration of the n+1th step; Step 4.2.2: Predict the generalized coordinates and generalized acceleration at the n+1th time step using the generalized α implicit time integration algorithm according to equation (21): The parameter selection method for formula (21) is as follows: ρ∈[0,1] in the parameter selection method is the spectral radius of the generalized α implicit time integration algorithm, α m and α f are the parameters of the generalized α implicit time integration algorithm; Step 4.2.3: Set the convergence precision tol, and then use the Newton iteration method to solve equation (23) where r n+1 is the residual force vector, J is the Jacobian matrix, and the parameters satisfy and It is the result of setting the matrix from 0 to 1 after considering the boundary conditions, and Δq is the increment of the generalized coordinates of the system at the current moment; Step 4.2.4: Calculate the modulus of the residual vector obtained in step 4.2.3 || r n+1 ||; if ||r n+1 ||>tol, indicating that the Newton iteration does not converge. Continue iterating until it converges. If ||r n+1 ||<tol indicates that the iteration converges, and the generalized coordinates q of the composite thin shell as a whole are updated by equation (24): n+1 ; q n+1 =q n +Δq (24) Step 4.2.5: Iterate steps 4.2.3 and 4.2.4 to solve the dynamic equation of the composite thin shell until the given dynamic calculation time is completed, and obtain the prediction result of the dynamic behavior of the composite thin shell under the action of the external force F.

8. The method for predicting dynamics of composite thin shells based on isogeometry according to claim 7, characterized in that: Step 4.2 also includes step 4.2.6: by visualizing the dynamic behavior prediction results obtained in step 4.2.5, the dynamic behavior visualization results of the composite material thin shell under the external force F are displayed.

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