A method for optimizing fiber angles in carbon fiber reinforced composites

Abstract

The application discloses a carbon fiber reinforced composite material fiber angle optimization method, which comprises the following steps: step one, determining the parameter information of a carbon fiber reinforced composite material laminated plate to be optimized, and establishing a geometric model of the laminated plate; wherein the parameter information comprises the planar size, the layer number, the thickness and the initial fiber arrangement angle of the laminated plate; step two, dividing each layer in the geometric model into a plurality of design domains in the form of a grid, and each design domain corresponds to a fiber laying angle; step three, establishing an overall stiffness matrix of the laminated plate; step four, taking the fiber laying angle corresponding to each design domain as an optimization variable, taking the minimum flexibility of the laminated plate as an optimization target, and iteratively updating the fiber laying angle corresponding to each design domain until the set convergence precision is reached, so that the optimal fiber laying angle of each design domain is obtained; and step five, obtaining the optimal fiber curve distribution of each layer according to the optimal fiber laying angle of each design domain in the layer.

Description

Technical Field

[0001] This invention belongs to the field of automotive passive safety and lightweight technology, and specifically relates to a method for optimizing the fiber angle of carbon fiber reinforced composite materials. Background Technology

[0002] Carbon fiber reinforced polymer (CFRP) possesses advantages such as high specific modulus, high specific strength, and strong design flexibility, making it the most ideal lightweight material for automobiles. Initially used in interior parts or non-load-bearing components such as doors, it is increasingly being applied to automotive load-bearing components, directly impacting pedestrian and occupant safety. Therefore, researching the mechanical properties of carbon fiber composites under dynamic impact conditions is essential for promoting the application of CFRP in automotive structural components.

[0003] Currently, the conventional layup method for carbon fiber composite laminates involves laying fibers in a straight line within a single layer, and then bonding multiple single layers together to form a laminate. This conventional straight-line layup method is prone to in-plane instability; furthermore, the straight fiber layup method cannot avoid stress concentration caused by abrupt changes in geometry, leading to a reduction in structural strength; at the same time, the single layup angle within a single layer greatly limits the designability of carbon fiber. Curved fiber composite laminates, on the other hand, can be laid at any angle within permissible limits, greatly improving the designability of composite materials, achieving different stiffnesses in different areas of the entire panel, enabling the structure to achieve higher standards with the same amount of material, and simultaneously altering the stress distribution of the structure.

[0004] Currently, the main optimization methods for curved fiber paths include the function method, principal stress method, stress gradient method, and topology optimization method. Research at home and abroad shows that curved fiber laminates obtained through the function method can be manufactured using automated fiber placement machines. However, this method, due to the pre-defined form of the curve function and the modification of only certain parameters, significantly limits the freedom of fiber design and cannot fully utilize the anisotropy and designability of carbon fibers. Fiber angles obtained through methods such as the principal stress method and topology optimization are constrained by the finite element mesh, resulting in discrete angles without specific curve formulas, making them difficult to engineer for manufacturing. Furthermore, while research on curved fibers under tensile, compressive, buckling, and cantilever beam conditions is relatively in-depth both domestically and internationally, research on impact conditions is less common. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the fiber angle of carbon fiber reinforced composite materials. The method uses topology optimization to optimize the fiber angle, starting with a straight fiber laminate and finally optimizing it into a variable angle fiber laminate, thereby improving the performance of the fiber laminate.

[0006] The technical solution provided by this invention is as follows:

[0007] A method for optimizing the fiber angle of carbon fiber reinforced composite materials includes the following steps:

[0008] Step 1: Determine the parameter information of the carbon fiber reinforced composite laminate to be optimized, and establish the geometric model of the laminate;

[0009] The parameter information includes: the planar dimensions of the laminate, the number of layers, the thickness, and the initial fiber arrangement angle;

[0010] Step 2: Divide each layer in the geometric model into multiple design domains in the form of a grid, with each design domain corresponding to a fiber layup angle;

[0011] Step 3: Establish the overall stiffness matrix of the laminated plate;

[0012] Step 4: Using the fiber layup angle corresponding to each design domain as the optimization variable and the minimum flexibility of the laminate as the optimization objective, iteratively update the fiber layup angle corresponding to each design domain until the set convergence accuracy is reached, and obtain the optimal fiber layup angle for each design domain.

[0013] Step 5: Obtain the optimal fiber curve distribution for each layer based on the optimal fiber layup angle for each design domain described in each layer.

[0014] Preferably, the fiber layup angle corresponding to each design domain is expressed as:

[0015] θ = arctan(β / α);

[0016] And the parameters α and β are used as optimization variables;

[0017] Where α represents the coordinate value of the fiber angle vector component on the X-axis of the global coordinate system, and β represents the coordinate value of the fiber angle vector component on the Y-axis of the global coordinate system.

[0018] Preferably, in step four, the method for optimizing the fiber laying angle corresponding to each design domain is as follows:

[0019] Set the initial values ​​of variables α and β to 0, and the upper and lower limits of α and β to 1 and -1, respectively. Change the values ​​of variables α and β to perform iterative calculations. After each iteration, calculate the optimization target value and compare the results of the two optimizations until the preset convergence accuracy is reached.

[0020] Preferably, the optimization process for the corresponding fiber layup angle also includes determining the sensitivity of the laminate flexibility to the optimization variables; the sensitivity is based on the design variables α and β, and the mathematical expression for the sensitivity is:

[0021]

[0022] Where C(α, β) represents the flexibility of the laminate, K is the stiffness matrix of the laminate, T is the coordinate transformation matrix with angle, and U is the displacement vector.

[0023] Preferably, before step four, the following steps are also included:

[0024] The optimization variables are filtered using Helmholtz partial differential equations, and the filtered optimization variables are obtained implicitly through the following filtering variables;

[0025]

[0026] Where r is the length parameter, and These are the optimized variables after filtering.

[0027] Preferably, in step five, obtaining the optimal fiber curve distribution includes the following steps:

[0028] Step 1: Using a uniform density curve arrangement, arrange the starting points of the curves around the perimeter of the laminate, extending from the perimeter of the laminate inward along the fiber angle direction, and automatically generate curves in the central area according to the fiber angle; and use the second-order Runge-Kutta algorithm for engineering interpretation to obtain the curves after the first engineering interpretation.

[0029] Step 2: Perform engineering interpretation on the curve after the first engineering interpretation, set a function form similar to the discontinuous curve, and use the function to fit the shape of the curve to form a continuous curve.

[0030] Preferably, in step four, the convergence accuracy is set to 0.001.

[0031] The beneficial effects of this invention are:

[0032] (1) The fiber angle optimization method of carbon fiber reinforced composite material provided by the present invention is based on the impact condition and obtains the optimal force transmission path, i.e. fiber laying path, through topology optimization. The optimization model has high efficiency and good convergence.

[0033] (2) The fiber angle optimization method of carbon fiber reinforced composite material provided by the present invention adopts the second-order Runge-Kutta algorithm for engineering interpretation, and spreads the curve in the form of a function expression throughout the entire plate to obtain a continuous fiber curve, thereby getting rid of the constraint of finite element mesh on fiber angle and realizing engineering manufacturing.

[0034] (3) The fiber angle optimization method for carbon fiber reinforced composite materials provided by this invention expresses the fiber angle using a vector, solving the problem of discrepancies with reality or discontinuous value range caused by a single angle variable; it uses Serendipity elements for isoparametric projection transformation, avoiding the optimization from getting trapped in local optima. This improves the accuracy and effectiveness of the model.

[0035] (4) The optimization model established by the fiber angle optimization method of carbon fiber reinforced composite material provided by the present invention has universality and is not limited to the number of layers and size of the plate.

[0036] (5) The fiber angle optimization method for carbon fiber reinforced composite materials provided by the present invention uses filtering technology based on Helmholtz partial differential equation (PDE) to filter design variables, improve fiber continuity, and avoid stress concentration problems. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the discrete design domain and design variables described in this invention.

[0038] Figure 2 This is a schematic diagram of the material coordinate system setup described in this invention.

[0039] Figure 3 This is a schematic diagram of the vector representation of the fiber angle described in this invention.

[0040] Figure 4 This is a schematic diagram of coordinate transformation using the isoparametric projection method described in this invention.

[0041] Figure 5 This is a flowchart illustrating the fiber angle optimization process described in this invention.

[0042] Figure 6 This is a schematic diagram of the alternating intralayer and interlayer layups described in this invention.

[0043] Figure 7 This is a schematic diagram of the multilayer board model described in this invention.

[0044] Figure 8 The fiber angle arrangement is optimized for the sixteen-layer rectangular plate described in this invention.

[0045] Figure 9 This is the convergence curve of total elastic strain energy and center point displacement in an embodiment of the present invention.

[0046] Figure 10 This is a graph obtained after the first engineering interpretation in an embodiment of the present invention.

[0047] Figure 11This is a graph obtained after the second engineering interpretation in an embodiment of the present invention.

[0048] Figure 12 This represents the optimal curved fiber path distribution for each layer of rectangular plates in this embodiment of the invention.

[0049] Figure 13 The 11J impact load-displacement curves of the optimal straight line, optimal discrete, and optimal curve fiber laminate are given. Detailed Implementation

[0050] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0051] like Figure 1-5 As shown, this invention provides a method for optimizing fiber angles in carbon fiber reinforced composite materials. It combines topology optimization with a finite element model. First, a geometric model for fiber angle optimization is established. Then, the design domain and design variables are defined and processed. Next, the objective function value is calculated until a preset convergence accuracy is achieved, resulting in the optimal discrete fiber angle arrangement. The curved fiber is interpreted as the optimal curved path, thereby obtaining the optimal curved fiber laminate.

[0052] like Figure 5 As shown, the specific implementation process of the fiber angle optimization method for carbon fiber reinforced composite materials provided by the present invention is as follows:

[0053] I. Establish a geometric model for fiber angle optimization. This model defines the dimensions, number of layers, layer thickness, and initial fiber arrangement (straight line) angle of the CFRP laminate. Input the basic mechanical parameters of the CFRP laminate in different directions obtained through experiments. It is necessary to constrain the six degrees of freedom around the perimeter of the rectangular plate and apply a Z-axis load at the center of the plate.

[0054] II. Discrete design domain, establish the rotating coordinate system and global stiffness matrix of the discrete design domain;

[0055] (1) Discretization of the design domain. For example... Figure 1 As shown, the geometric model is divided into different design domains. The initial design domain is the entire CFRP laminate Ω. First, the continuous design domain is discretized, so that each discretized design domain Ω is... i (Finite element mesh) has independent design variables θ i .

[0056] (2) In order to convert the stiffness matrix of each discrete design domain to the global stiffness matrix, the global stiffness matrix is ​​used for subsequent calculations. The element rotation coordinate system is established to realize the transformation relationship between the material coordinate system and the global coordinate system. The global stiffness matrix is ​​characterized by the plane curve fiber stress-strain relationship.

[0057] A fiber angle rotation coordinate system is set up. The solid mechanics module is selected, and a single-layer plate optimization model is simulated using solid elements. Each element is assigned a rotation coordinate system. The element rotation coordinate system enables the transformation between the material coordinate system and the local coordinate system. A rotation system is used to define an orthogonal coordinate system relative to the reference coordinate system (global coordinate system). A 2D rotation is performed on the global coordinate system (in the spatial coordinate system, only rotation in the XY plane is considered, i.e., rotation around the Z-axis), and Euler angles are used to specify the in-plane rotation angle θ. The element material coordinate system (1O2) and the global coordinate system (XOY) are as follows: Figure 2 As shown, direction 1 is the fiber direction, the X direction is parallel to the long side of the rectangular plate, and the Y direction is parallel to the short side. The material coordinate system is rotated by an angle θ relative to the global coordinate system, so the fiber angle of the element in the global coordinate system is also θ.

[0058] Regarding the fiber orientation angle, assume the fiber angle of the element in the global coordinate system is oriented as (v... x v y If the orientation coordinates of the material coordinate system are (v1, v2), then:

[0059] v x =v1 cosθ - v2 sinθ (1)

[0060] v y =v2 cosθ + v1 sinθ (2)

[0061] Right now:

[0062]

[0063] (3) The stress-strain relationship of curved fiberboard under plane stress is proposed, and the overall stiffness matrix is ​​established. This invention proposes to optimize the fiber angle using a topology optimization method, which essentially changes the stress distribution of the laminate, thereby improving the stiffness of the laminate. The overall stiffness matrix of the laminate needs to be represented by a stress-strain relationship, so the stress-strain relationship of curved fiberboard under plane stress is proposed first.

[0064] In composite single-layer plates, the thickness direction (direction 3) is very small compared to the dimensions in other directions (directions 1 and 2), and can usually be ignored. Similarly, the stress and strain associated with direction 3 are also ignored, i.e., σ3 = 0, τ 23 =τ 31 =σ4=σ5=0, for carbon fiber composites, which are orthotropic materials, the stress-strain relationship in the principal direction of a straight fiber layup composite under plane stress should be as shown in Equation 4:

[0065]

[0066] Where 1, 2, and 3 represent different directions, σ is the normal stress, τ is the shear stress, ε is the normal strain, γ is the shear strain, and Q is a 3×3 positive modulus matrix, where the positive modulus at each position is represented by Q. ij express.

[0067] Because the in-plane fiber layup angle α of a linear fiber layup is a fixed value, the positive axial modulus Q is... ij It is also a fixed value, as follows:

[0068]

[0069]

[0070]

[0071] Q 66 =G 12

[0072] E is Young's modulus, G is shear modulus, and v is Poisson's ratio.

[0073] This invention studies curved fiber layups, where the fiber angles within a single layer are not fixed values ​​but vary with the unit coordinates. Therefore, it is necessary to transform the stress and strain in the global coordinate system through stress and strain axes to obtain the stress-strain relationship in any direction. The stress and strain axis formulas are as follows:

[0074] [σ x σ y τ xy ] T =T -1 [σ1 σ2 τ 12 ] T

[0075] [ε x ε y γ xy ] T =T -1 [ε1 ε2 γ 12 ] T

[0076] Where T is the coordinate transformation matrix, T -1 Given its inverse matrix, the expansion of the coordinate transformation matrix T is:

[0077]

[0078] From the above equation, the stress-strain relationship in any θ direction of a single-layer composite material can be obtained:

[0079] [σx σ y τ xy ] T =Q -1 [ε1 ε2 γ 12 ] T

[0080]

[0081] The overall matrix stiffness is

[0082]

[0083] III. Setting variables and their upper and lower limits for optimization. For fiber angle optimization, the design variable θ... i In general, existing research results indicate that using a single angle θ i As a variable, it cannot accurately describe the angle of the fiber, sometimes yielding results that contradict reality or have discontinuous value ranges. To solve this problem, such as... Figure 3 As shown, the fiber angle is represented as a vector and decomposed into coordinates, that is, the fiber angle θ is expressed by two parameters α and β (θ = arctan(β / α)), and the values ​​of the two parameters are both in the range of [-1, 1].

[0084] Figure 3 In the line segment (1) region shown, α and β can both represent a 0° fiber orientation (β = 0, α can be any value), and in the line segment (2) region, α and β can both represent a 45° fiber orientation (α = β). However, because their lengths are different, their proportions in the entire design domain are different, resulting in different probabilities of the fiber angle θ being 0° and 45°, which can easily lead to local optima. Therefore, isoparametric projection is performed using the Serendipity element, and the isoparametric shape function N is introduced to transform the two parameters α and β into a and b, as shown in the figure. Figure 4 As shown. The coordinate transformation formulas for isoparametric projection are shown in Equations 5 and 6:

[0085]

[0086]

[0087] Among them, v i =[a i b i ] T Let be the coordinates of the i-th node in the actual coordinate system, represent the vector components of the fiber angle in the actual sense, and define a ≠ 0; if a = 0, then θ = π / 2. [α] i ,β i] represents the coordinate values ​​in the natural coordinate system, and the values ​​of α and β both range from [-1, 1], which are the design variables during optimization. Where N i The expression for (α, β) is as follows:

[0088]

[0089] IV. Filtering Design Variables Based on the Helmholtz Equation. Fibers can exhibit continuity or discontinuity in the discrete design domain. Fiber discontinuity can lead to stress concentration, therefore, fiber continuity is crucial for avoiding stress concentration. This invention employs a filtering method to address fiber discontinuity. This invention utilizes the filtering technique of the Helmholtz Partial Differential Equation (PDE), controlling the fiber angle orientation of the control unit by controlling α and β. The filtered variables are implicitly defined as solutions to this equation:

[0090]

[0091] The homogeneous Neumann boundary conditions are as follows:

[0092]

[0093]

[0094] Where r is the length parameter, which controls the filtering range; the larger r is, the smoother the adjacent fibers are; α and β are design variables. and These are the filtered variables.

[0095] 5. Substitute the values ​​into the mathematical model to calculate the objective function value and obtain the optimal discrete fiber angle arrangement.

[0096] The optimized objective function value is calculated using the filtered design variables. The objective function values ​​of two consecutive optimizations are compared to determine whether the preset convergence accuracy has been reached. If the preset accuracy has been reached, the calculation is stopped, and the optimal discrete fiber laminate is obtained.

[0097] As a preferred embodiment, the convergence accuracy is set to 0.001.

[0098] Using the filtered angle parameters α and β as the design variables for optimization, and aiming to maximize the overall stiffness of the laminate, a four-sided fixed constraint is applied to the entire design domain Ω, and the range of values ​​for the design variables is constrained, meaning that arbitrary angles can be represented. The mathematical model for fiber angle optimization is as follows:

[0099] Find α = {α1, α2, ..., α} n} Tβ={β1,β2…β n} T

[0100] Min C(α, β)=F T U

[0101] st.KU=F

[0102] for i = 1, 2, 3, ..., N

[0103] α min ≤α i ≤α max

[0104] β min ≤β i ≤β max

[0105] Where C(α, β) is the optimization objective, representing the structural flexibility; a smaller value indicates greater stiffness. K is the overall stiffness matrix of the laminate. F is the overall load vector, representing the magnitude and direction of the external forces acting on the structure. U is the displacement vector. The fiber angle θ of the i-th element is obtained. i ;α min α max β min β max α i and β i The upper and lower limits are both -1 and 1; N is the number of design domains after discretization, i.e. the number of finite element meshes.

[0106] In the calculation process, the sensitivity value of the objective function to the design variables determines the direction of change of the design variables in the optimization process. Therefore, sensitivity analysis of the design variables is necessary. Through sensitivity calculation, the influence of the two design variables on the optimization objective is analyzed, thereby better controlling the optimization trend of the fiber angle. Below is the mathematical expression for the sensitivity of compliance C(α, β) based on design variables α and β:

[0107]

[0108]

[0109] Where K is the overall stiffness matrix of the laminate, T is the coordinate transformation matrix with angle, and Q is the stress-strain relationship, which is independent of angle and has the following relationship:

[0110]

[0111] The minimum compliance value is calculated based on the above model, and the target values ​​obtained from the two calculations are compared. If the calculations do not converge, the design variables are updated. This process is repeated until convergence is achieved, and the required design variables α and β are obtained.

[0112] After continuous calculation and iteration, the obtained model is the optimal discrete fiber model. The convergence curves of the total elastic strain energy, center point displacement, and maximum stress energy of the CFRP laminate before and after optimization are analyzed with the number of iterations. Fiber angle distribution diagrams before and after optimization under different initial fiber angles are obtained (see...). Figure 8 ).

[0113] The discrete fibers in each layer are interpreted as the optimal curved fiber path, thus obtaining the optimal curved fiber laminate.

[0114] VI. Based on the optimized fiber angle results, the discrete fibers of each layer are interpreted in an engineering manner to form a continuous curve, resulting in the optimal curve fiber laminate, thus achieving engineering manufacturing. This invention employs a second-order Runge-Kutta algorithm for the first engineering interpretation. By interpolating, the vector of the given vector field is found at these points, and the vector field is normalized. Integration is performed along the vector direction to find the next point pointed to by the vector. At the next point, the algorithm finds the vector value through interpolation and performs another integration. The results of the first interpretation are then interpreted a second time, with the curve represented by a function expression covering the entire board.

[0115] Example

[0116] Taking a specific laminate as an example, the steps are explained in detail and the results are verified. The CFRP laminate described in this embodiment is made of unidirectional T300 grade carbon fiber prepreg, with a single layer thickness of 0.15mm, a total of 16 layers, a flat cross-lay thickness of 2.4mm, and a planar dimension of 150mm×100mm.

[0117] I. Establish the geometric model. Model parameters: length, width, and thickness are 150mm, 100mm, and 2.4mm respectively, with a total of 16 layers. Solid element modeling is used, with a single layer thickness of 0.135mm within a single layer and 0.015mm between layers. Modeling alternates between intra-layer and inter-layer elements. Figure 6 As shown. The initial straight layup angle does not affect the fiber angle optimization result, so the initial fiber angle of the laminate can be arbitrarily set. The multilayer board model is as follows. Figure 7 As shown, the layers are connected using a shared node method. Six degrees of freedom (X, Y, Z, XY, XZ, YZ) are fixedly constrained around the perimeter, and a load perpendicular to the laminate is applied at the center point. Because the fiber angle optimization result is independent of the load magnitude, any load can be applied; here, a load of 1N is set.

[0118] II. Discrete design domain. For example... Figure 1 As shown, the entire 16-layer plate design domain is discretized. The discretized design domain corresponds one-to-one with the mesh in the finite element method (the target mesh size is 2mm). In a single layer, there are 75 meshes on the long side and 50 meshes on the short side, which are evenly distributed. Therefore, there are 3750 discrete design domains and 3750 independent fiber angles in a single layer. The 16-layer rectangular plate includes 16×3750=60000 design domains. The fiber angles of each discrete design domain are optimized separately without interference.

[0119] 3. Determine the design variables as α and β, with a lower limit of -1 and an upper limit of 1 for both.

[0120] IV. Filtering Design Variables Based on the Helmholtz Equation. Filtering is performed only within each layer, ensuring no inter-layer interference. The optimization objective is set to minimize flexibility (maximize stiffness). The optimization variables for the fiber angles of each layer are their corresponding α and β: α1 and β1 for the first layer, α2 and β2 for the second, α3 and β3 for the third, and so on. After filtering, the fibers are continuous, resulting in smoother transitions and avoiding stress concentration.

[0121] 5. Substitute the values ​​into the mathematical model for calculation, and rely on sensitivity to determine the optimization direction, using a convergence accuracy of (0.001) as the criterion for stopping the calculation. The initial straight ply angle does not affect the fiber angle optimization result; therefore, the initial angle is set to 90° for fiber angle optimization of the 16-layer rectangular plate. The fiber angle optimization results are as follows: Figure 8 As shown. Figure 8 The laminate shows a rounded rectangle with concentric circular fiber angles at the center, and a diverging shape around the perimeter; this is the optimal discrete fiber angle distribution model. The convergence curves of the total elastic strain energy and the center point displacement during the optimization process are shown below. Figure 9 As shown, the parameters remain basically unchanged after 100 iterations, and the optimization ends at the 319th iteration. The results converge, indicating that the optimization goal is achieved and the optimization efficiency is high with good convergence.

[0122] VI. The optimal curve fiber distribution is obtained by interpreting the discrete fiber angles. The optimized discrete fiber angle arrangement has a certain regularity, and the angle values ​​of adjacent units are small, which can be connected into a curve. A uniform density curve arrangement is adopted, and the starting point of the curve is arranged around the plate. The curve extends from the periphery of the plate to the inside along the fiber angle direction. The curve in the central area is automatically generated according to the fiber angle. The second-order Runge-Kutta algorithm is used for the first engineering interpretation. The vector of the given vector field is found at these points by interpolation, and the vector field is normalized. The points are integrated along the vector direction to find the next point pointed to by the vector. At the next point, the algorithm finds the vector value by interpolation and performs another integration. The integration stops when the following situations occur: (1) the preset number of integration steps is reached; (2) the endpoint is outside the plate; (3) the "stationary point" where the vector field is zero. The curve of the first engineering interpretation is obtained as follows. Figure 10 The curve obtained after the first engineering interpretation ( Figure 10 The resulting curves are numerous and discontinuous, making them unsuitable as final curves for engineering manufacturing. To reduce the number of curves and smooth them out, [further steps are needed]. Figure 10 A second engineering interpretation is performed, in which the curve is represented by a function expression and spread across the entire board.

[0123] The concentric circle region in the middle needs to be connected to the surrounding divergent regions to ensure that the overall strength of the plate is not too weak. The stress on the long side is relatively large, so the curve is designed to start from one long side and extend to the other. Observing the results of the first engineering interpretation, the discontinuous curve from top to bottom in this region is more in line with the shape of "W". Therefore, a sixth-order function is used for fitting in this embodiment. The divergent regions near the short side are symmetrical and are represented by elliptic curves, which contract from both ends of the plate towards the center. Therefore, an elliptic function is used for fitting in this embodiment.

[0124] The curve after secondary interpretation is as follows Figure 11 As shown. Figure 11 The curves in the plate shown are symmetrical along their long sides. Half of the rectangular plate contains five elliptic curves and four "W"-shaped curves. The ends of the elliptic and "W"-shaped curves represent the diverging regions around the perimeter of the rectangular plate, while the middle portion of the "W"-shaped curves represents the concentric circular region at the center of the rectangular plate. The elliptic curves are expressed in functional form as follows:

[0125]

[0126] The fitted expressions for the five elliptic curves are as follows:

[0127]

[0128] The "W"-shaped curve is fitted using a sixth-order function, and the general form of the fitted curve is as follows:

[0129]

[0130] The expressions for the four fitted "W"-shaped curves are as follows:

[0131]

[0132] After optimization, the sixteen-layer straight fiber laminate is as follows: Figure 8 As shown, due to its symmetrical layup, only 8 layers need to be fitted. The central areas and angles of the first, second, third, fourth, fifth, sixth, seventh, and eighth layers are almost identical. The interpreted fiber curves adopt a single form, and to unify the function expression, the curve forms in the four interpreted curve graphs are consistent, differing only in the coefficients of the expression. All curves are expressed using 5 elliptic curves and 4 "W"-shaped curves. The final curve form obtained by interpreting the fiber angle arrangement of each layer using the above method is shown in the figure. Figure 12 .

[0133] Effect Verification: Steps 1 to 6 have described the methods for fiber angle optimization and engineered manufacturing. To verify the effectiveness of the methods, based on the same initial model, the model was optimized using both the three-step optimization method and the method proposed in this invention. The three-step optimization method yielded the optimal straight fiber laminate, while the fiber angle optimization method proposed in this invention yielded the optimal discrete fiber laminate. Figure 8 The optimal curve fiber laminate was obtained using the fiber angle optimization method and engineering interpretation method proposed in this invention. Figure 11 This study compares the impact mechanical properties of three types of laminates, mainly including the maximum displacement, peak load, and final deformation during impact. The three-step optimization method includes free-size optimization, size optimization, and layup sequence optimization.

[0134] Static analysis and dynamic drop hammer impact simulation were conducted to obtain and compare the stiffness of the three types of plates under loading conditions, verifying the feasibility of the method. The mechanical response of the three laminates was studied using load-displacement curves. The two variable-angle fiber laminates showed relatively delayed load and displacement at the initial delamination stage of impact, exhibiting higher stiffness. The rebound and penetration conditions were analyzed separately to determine the maximum deformation u. max The ratio of the final deformation to the maximum deformation, u t / u max The relationship between stiffness and damage degree is also affected by the introduction of curves, which disperse the load and result in a higher peak load and stronger toughness.

[0135] Table 1 Static stiffness values ​​of three optimal laminated plates

[0136]

[0137] The stiffnesses of the optimal straight, discrete, and curved fiber laminates under central loading conditions, obtained from static analysis, are shown in Table 1. The table shows that the stiffness of the optimal discrete fiber laminate, the optimal curved fiber laminate, and the optimal straight fiber laminate decrease sequentially. Using the stiffness of the optimal straight fiber laminate as a benchmark, the stiffness of the two optimal variable-angle fiber laminates increases by 20.40% and 6.91%, respectively, significantly improving the laminate stiffness and demonstrating the effectiveness of fiber angle optimization and engineering interpretation. Furthermore, although the efficiency of stiffness improvement in the optimal curved fiber laminate is lower than that in the optimal discrete fiber laminate, it achieves engineered manufacturing, while the optimal discrete fiber laminate represents only an ideal state in the optimization process.

[0138] Dynamic drop hammer impact simulation was performed on the three optimal laminates with an impact energy of 11 J (rebound condition). The load-displacement curves are shown below. Figure 13 As shown. Figure 13 In the load-displacement curves, point A represents the delamination point of the straight fiber laminate. After point A, the stiffness of the straight fiber laminate decreases. The optimal curved fiber laminate, due to its optimized fiber force transmission path, only experiences delamination at point B. Both displacement and load at the time of delamination are relatively delayed. Therefore, in the rebound condition, the stiffness (K) of the laminate in the second optimized segment (0.3mm-0.7mm) is significantly higher than that of the straight fiber laminate. However, as the impact velocity increases, i.e., in the penetration condition, the difference in structural stiffness decreases, but still follows the stiffness ranking of "optimal discrete fiber laminate ≥ optimal curved fiber laminate ≥ straight fiber laminate". This shows that the optimal discrete fiber laminate has the highest bending stiffness, although engineering interpretation results in a loss of some material bending stiffness, it is still superior to the straight fiber laminate.

[0139] Table 2. u of the three types of laminates t / u max

[0140]

[0141] Note: u t It is the final deformation of the laminate after impact, u max It is the maximum deformation of the laminate.

[0142] For the rebound condition, the maximum deformation u of the laminate is... max The value of the optimal discrete fiber laminate is higher than that of the other two, indicating that the straight and optimal curved fiber laminates have higher resistance to deformation than the optimal discrete fiber laminate. This suggests that the optimal discrete fiber laminate is slightly weaker, but the difference between it and the other two laminates is small, at 3.8%. Furthermore, u t / u max The value of u is also an important indicator for evaluating the dynamic stiffness of laminates. tThe ratio of the final deformation of the laminate after impact can reflect, to some extent, the relationship between the energy consumed by the laminate due to fiber breakage, matrix cracking, delamination, etc., and the elastic deformation energy: an increase in the ratio indicates a greater degree of damage to the final laminate. The u values ​​of the three types of laminates... t / u max The values ​​are shown in Table 2. Due to the greater stiffness of the optimized variable angle laminate, it has a greater impact load limit under low-speed impact, resulting in the final damage of both variable angle fiber laminates being less than that of the straight fiber laminate. Since the interpreted curve is more coherent than the uninterpreted curve, it can directly transfer the impact load to the edge of the plate, thus minimizing the final deformation.

[0143] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method of carbon fiber reinforced composite fiber angle optimization, characterized by, The method comprises the following steps: Step 1: determining parameter information of a carbon fiber reinforced composite laminate to be optimized, and establishing a geometric model of the laminate; The parameter information comprises: planar size, number of layers, thickness, and initial fiber arrangement angle of the laminate; Step 2: dividing each layer in the geometric model into a plurality of design domains in the form of a grid, each design domain corresponding to a fiber laying angle; Step 3: establishing an overall stiffness matrix of the laminate; Step 4: taking the minimum flexibility of the laminate as an optimization objective, iteratively updating the fiber laying angle corresponding to each design domain until a set convergence precision is reached, and obtaining an optimal fiber laying angle of each design domain; Step 5: obtaining an optimal fiber curve distribution of each layer according to the optimal fiber laying angle of each design domain in the layer. Before the step 4, the method further comprises: expressing the fiber laying angle corresponding to each design domain as: θ=arctan(β / α); and taking the parameters α and β as optimization variables; wherein α represents a coordinate value of a fiber angle vector component on an X-axis of a global coordinate system, and β represents a coordinate value of the fiber angle vector component on a Y-axis of the global coordinate system; filtering the optimization variables by using a Helmholtz partial differential equation, and obtaining filtered optimization variables through the following filtering variable implicit expression: where r is a length parameter, and are filtered optimization variables.

2. The carbon fiber reinforced composite material fiber angle optimization method according to claim 1, characterized by, In the step 4, the method for optimizing the fiber laying angle corresponding to each design domain is as follows: setting initial values of the variables α and β as 0, setting upper and lower limits of the variables α and β as 1 and -1, respectively, changing values of the variables α and β for iterative calculation, calculating an optimization objective value after each iteration, comparing results after two optimizations, and until a preset convergence precision is reached.

3. The carbon fiber reinforced composite material fiber angle optimization method according to claim 2, characterized by, In the process of optimizing the fiber laying angle, the method further comprises determining a sensitivity of the flexibility of the laminate to the optimization variables; and a mathematical expression of the sensitivity is as follows: wherein C(α, β) represents the flexibility of the laminate, K represents a stiffness matrix of the laminate, T represents a coordinate conversion matrix with an angle, and U represents a displacement vector.

4. The carbon fiber reinforced composite fiber angle optimization method according to claim 2 or 3, characterized by, In the step 5, obtaining the optimal fiber curve distribution comprises the following steps: Step 1: arranging starting points of curves in a uniform density curve arrangement manner around the laminate, extending the starting points along a fiber angle direction from the periphery of the laminate to the interior, automatically generating curves in a center region according to the fiber angle, and performing engineering interpretation on the curves by using a second-order Runge-Kutta algorithm to obtain curves after first engineering interpretation; Step 2: performing engineering interpretation on the curves after the first engineering interpretation, setting a function form similar to a discontinuous curve, fitting a shape of the curve by using a function, and forming a continuous curve.

5. The carbon fiber reinforced composite material fiber angle optimization method according to claim 4, characterized by, In the step 4, the set convergence precision is 0.001.

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