Fiber orientation optimization method for dynamic smooth control based on Gaussian filtering

Abstract

The invention discloses a fiber orientation optimization method for dynamic smooth control based on Gaussian filtering. The method comprises the following steps: defining a model design domain and initializing a fiber angle design variable; establishing a unit elastic constitutive matrix according to the fiber angle design variable and the coordinate change matrix; constructing a fiber angle orientation optimization objective function according to the unit elastic constitutive matrix; solving the sensitivity of the fiber angle orientation optimization objective function to a fiber angle design variable; performing iterative optimization on the fiber angle direction field by using a gradient descent method according to the sensitivity information; smoothing the iterated fiber angle direction field by using a Gaussian filtering dynamic smoothing control method under a Cartesian coordinate system; and repeating the processes of matrix establishment, objective function construction, sensitivity solving, iterative optimization and smoothing until convergence conditions are met, thereby completing fiber orientation optimization. According to the method, the fiber angle optimization design of the fiber reinforced composite material is realized.

Description

Technical Field

[0001] This invention belongs to the field of fiber-reinforced composite material optimization design, and particularly relates to a fiber orientation optimization method based on Gaussian filtering and dynamic smooth control. Background Technology

[0002] Fiber-reinforced composites, with their superior specific strength, specific stiffness, and designability, demonstrate irreplaceable application value in aerospace, automotive manufacturing, and high-end equipment industries. Fiber orientation, as a core parameter determining the mechanical properties of composite materials, directly impacts the load-bearing capacity and fatigue resistance of structures through its optimized design. Therefore, optimizing the fiber orientation of composite materials is crucial for improving structural performance, additive manufacturing, and economic benefits. With the rapid development of additive manufacturing technologies, such as 3D printing, the "customized fiber orientation" manufacturing of composite components has become possible. Through 3D printing and fiber placement control, additive manufacturing technology can achieve spatially variable fiber orientation distributions that are difficult to achieve with traditional processes, providing a technological foundation for fully leveraging the anisotropic advantages of composite materials.

[0003] In space, the orientation angle of a fiber is determined by two angles: azimuth θ (the angle with the x-axis) and elevation φ (the angle with the fiber's projection plane). In the traditional spherical coordinate system, a mathematical singularity exists when the elevation φ approaches ±90°. When the fiber direction is perpendicular to the projection plane, any change in the azimuth θ will not alter the actual fiber direction, leading to non-convergence of the fiber direction in this extreme region. Furthermore, due to the non-convexity of the fiber orientation optimization problem, the material's fiber orientation field becomes irregular, with some fiber angles falling into local optima (the discrete fiber orientation angles clearly violate the principal stress directions of the material), increasing the difficulty of additive manufacturing. Meanwhile, traditional fiber angle smoothing techniques (such as density-based weighted averaging) generally use fixed parameters, which cannot adapt to the dynamic requirements of the optimization process. In the early stages of optimization, it is necessary to fully explore the globally optimal orientation; excessive smoothing can suppress the search capability of gradient descent. In the later stages of optimization, it is necessary to ensure the process feasibility of the orientation field; static smoothing intensity is difficult to balance "performance optimization" and "manufacturing constraints." Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a fiber orientation optimization method based on Gaussian filtering and dynamic smoothing control. This method solves the problems of fiber orientation optimization in extreme regions, discrete fiber orientation angles getting trapped in local optima, and traditional fiber angle smoothing methods failing to adapt to the dynamic requirements of the optimization process.

[0005] To achieve the above objectives, this invention provides a fiber orientation optimization method based on Gaussian filtering and dynamic smoothing control, comprising:

[0006] Define the model design domain and initialize the fiber angle design variables;

[0007] The unit elastic constitutive matrix is ​​established based on the fiber angle design variables and coordinate transformation matrix.

[0008] Construct a fiber angle orientation optimization objective function based on the unit elastic constitutive matrix;

[0009] Solve for the sensitivity of the fiber angle orientation optimization objective function to the fiber angle design variable;

[0010] Based on the sensitivity information, the gradient descent method is used to iteratively optimize the fiber angular orientation field;

[0011] The fiber angle direction field after iteration is smoothed using a Gaussian filter dynamic smoothing control method in Cartesian coordinates.

[0012] Repeat the above process of establishing the matrix, constructing the objective function, solving for sensitivity, iterative optimization, and smoothing until the convergence condition is met, thus completing the fiber orientation optimization.

[0013] Preferably, the process of defining the model design domain and initializing the fiber angle design variables includes:

[0014] Determine the boundaries of the design domain in three-dimensional space;

[0015] Discretize the cell mesh within the design domain;

[0016] Each unit is assigned an initial fiber azimuth angle θ and elevation angle φ as design variables.

[0017] Preferably, the process of establishing the unit elastic constitutive matrix based on the fiber angle design variables and coordinate transformation matrix includes:

[0018] Establish the elastic matrix of orthogonal anisotropic materials;

[0019] Construct a transformation matrix from the local coordinate system to the global coordinate system based on the fiber angle design variables;

[0020] Multiplying the elasticity matrix by the transformation matrix yields the unit elastic constitutive matrix.

[0021] Preferably, the process of constructing the fiber angle orientation optimization objective function based on the unit elastic constitutive matrix includes:

[0022] Calculation of element strain energy density based on element elastic constitutive matrix;

[0023] The objective function value is obtained by volume integral of the strain energy density of all elements in the design domain.

[0024] Preferably, the process of solving the sensitivity of the fiber angle orientation optimization objective function to the fiber angle design variable includes:

[0025] The sensitivity value is obtained by taking the first-order partial derivatives of the objective function with respect to the azimuth angle θ and the elevation angle φ.

[0026] Preferably, the process of iteratively optimizing the fiber angular orientation field using the gradient descent method based on sensitivity information includes:

[0027] Determine the angle update direction based on the sensitivity value obtained from the current iteration;

[0028] Adjust the azimuth angle θ and elevation angle φ of each unit along the update direction with a preset step size;

[0029] Use the updated angle as input for the next iteration.

[0030] Preferably, the process of smoothing the iterated fiber angular direction field using a Gaussian filter dynamic smoothing control method in Cartesian coordinates includes:

[0031] Convert the fiber angle variable of each unit into a direction vector;

[0032] Construct a Gaussian filtering weighting function based on the distance between the center points of the cells;

[0033] The direction vector is weighted and averaged using a dynamic smoothing control factor to obtain a smoothed direction vector.

[0034] Preferably, the dynamic smoothing control factor changes according to the number of iteration steps:

[0035] When the number of iterations t is less than the first threshold, the smoothing control factor is set to 0;

[0036] When the number of iterations t is between the first threshold and the second threshold, the smoothing control factor takes the first preset value;

[0037] When the number of iterations t is greater than or equal to the second threshold, the smoothing control factor takes the second preset value;

[0038] Wherein, the first preset value is less than the second preset value.

[0039] Preferably, the process of determining whether the convergence condition is met includes:

[0040] Determine if the maximum number of iterations has been reached;

[0041] If the maximum number of steps is reached, stop the optimization and output the current fiber angle orientation field;

[0042] If the maximum number of steps is not reached, the process of establishing the matrix, constructing the objective function, solving for sensitivity, iterative optimization, and smoothing is returned.

[0043] Preferably, the fiber angle orientation field is the input data for the continuous fiber layup path in additive manufacturing, used to guide the directional changes of the fiber in space.

[0044] Compared with the prior art, the present invention has the following advantages and technical effects:

[0045] (1) This invention constructs the constitutive matrix of the unit by means of fiber angle direction field and coordinate transformation, establishes the objective function, solves the sensitivity information, and realizes the fiber angle optimization design of fiber reinforced composite material;

[0046] (2) This invention solves the problem of fiber orientation optimization in the pole region by using Cartesian coordinate system direction vector driving;

[0047] (3) The present invention uses a Gaussian filtering dynamic smoothing control method to control the smoothness of the orientation angle, which solves the problems of discrete fiber orientation angle getting stuck in local optimum and traditional density filtering being unable to adapt to the dynamic requirements of the optimization process.

[0048] (4) This invention provides the formula derivation of the constitutive formula, objective function and apparent sensitivity of fiber reinforced composite materials. Attached Figure Description

[0049] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0050] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram of an optimized fiber-reinforced composite material structure for applying five loads to a plate according to an embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of the optimization design results of the dynamic smoothing control optimization method without Gaussian filtering according to an embodiment of the present invention;

[0053] Figure 4 This is a schematic diagram of the optimized design results of the fiber orientation optimization method with a Gaussian filtering dynamic smoothing control factor of 0.2 according to an embodiment of the present invention.

[0054] Figure 5 This is a schematic diagram of the optimized design results of the fiber orientation optimization method with a Gaussian filtering dynamic smoothing control factor of 0.4 according to an embodiment of the present invention.

[0055] Figure 6 This is a schematic diagram of the optimized design results of the fiber orientation optimization method with a Gaussian filtering dynamic smoothing control factor of 0.6 according to an embodiment of the present invention.

[0056] Figure 7 This is a schematic diagram of the optimization design results of the fiber orientation optimization method with a dynamic smoothing control factor of 1 for Gaussian filtering according to an embodiment of the present invention. Detailed Implementation

[0057] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0058] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0059] Example 1

[0060] like Figure 1-2 As shown, this embodiment provides a fiber orientation optimization method based on Gaussian filtering and dynamic smoothing control, including:

[0061] S1: Define the model design domain and initialize fiber angle design variables;

[0062] S2: Establish the unit elastic constitutive matrix based on fiber angle design variables and coordinate transformation matrix;

[0063] S3: Establish the objective function for fiber angle orientation optimization based on the unit elastic constitutive matrix;

[0064] S4: Solve the objective function for optimizing fiber angle orientation with respect to the fiber angle design variables θ and Sensitivity;

[0065] S5: Based on the sensitivity information, the gradient descent method is used to iteratively optimize and solve the fiber angular direction field;

[0066] S6: The smoothness of the fiber angle direction field after iteration is optimized by using a dynamic smoothing control method of Gaussian filtering in Cartesian coordinate system.

[0067] S7: Repeat steps S2 to S6 above until the objective function meets the convergence condition, reaches the maximum number of iterations, stops the optimization, and completes the fiber orientation optimization with dynamic smoothing control of Gaussian filtering.

[0068] Furthermore, the process of defining the model design domain and initializing the fiber angle design variables in S1 includes:

[0069] Determine the boundaries of the design domain in three-dimensional space;

[0070] Discretize the cell mesh within the design domain;

[0071] Each unit is assigned an initial fiber azimuth angle θ and elevation angle φ as design variables.

[0072] Furthermore, S2 establishes the elastic matrix of the orthogonal anisotropic material, and then designs variables based on fiber angles. The process of constructing the element elastic constitutive matrix from the coordinate transformation matrix includes:

[0073] Establish the elastic matrix of orthogonal anisotropic materials;

[0074] Construct a transformation matrix from the local coordinate system to the global coordinate system based on the fiber angle design variables;

[0075] Multiplying the elasticity matrix by the transformation matrix yields the element elastic constitutive matrix.

[0076] The specific formula is as follows:

[0077]

[0078]

[0079] Among them, superscript T is the transpose symbol; D is the elastic matrix of the orthotropic material, and T is the transpose symbol. θ (θ e )and For the coordinate transformation matrix related to the fiber angle design variable, s θ =sinθ,c θ =cosθ, It is the unit elastic constitutive matrix that includes fiber angle design variables.

[0080] Furthermore, the process of constructing the fiber angle orientation optimization objective function based on the element elastic constitutive matrix includes:

[0081] Calculation of element strain energy density based on element elastic constitutive matrix;

[0082] The objective function value is obtained by volume integral of the strain energy density of all elements in the design domain.

[0083] Specifically, the objective function J for fiber optimization in S3 is:

[0084]

[0085] Among them, E sed The strain energy density, that is ε represents strain, and Ω represents the design domain volume.

[0086] Furthermore, the process of determining the sensitivity of the fiber angle orientation optimization objective function to the fiber angle design variable includes:

[0087] The sensitivity value is obtained by taking the first-order partial derivatives of the objective function with respect to the azimuth angle θ and the elevation angle φ.

[0088] Specifically, by solving for the first derivative of the objective function with respect to the fiber angle design variable, the sensitivity information in S4 is obtained. and for:

[0089]

[0090] Furthermore, based on the sensitivity information, the process of iteratively optimizing the fiber angular orientation field using the gradient descent method includes:

[0091] Determine the angle update direction based on the sensitivity value obtained from the current iteration;

[0092] Adjust the azimuth angle θ and elevation angle φ of each unit along the update direction with a preset step size;

[0093] Use the updated angle as input for the next iteration.

[0094] Specifically, in S5, the gradient descent method is used to solve for the optimal angle of each unit in the current iteration based on the sensitivity information. and The formula is as follows:

[0095]

[0096] in, and To optimize the angle at step t of the iteration, and To optimize the angle at step t-1 of the iteration, η is the update step size, which controls the magnitude of the angle update decrease in each iteration.

[0097] Furthermore, the process of smoothing the iterated fiber angular direction field using the Gaussian filter dynamic smoothing control method in the Cartesian coordinate system includes:

[0098] Convert the fiber angle variable of each unit into a direction vector;

[0099] Construct a Gaussian filtering weighting function based on the distance between the center points of the cells;

[0100] The direction vector is weighted and averaged using a dynamic smoothing control factor to obtain a smoothed direction vector.

[0101] The dynamic smoothing control factor changes according to the number of iterations:

[0102] When the number of iterations t is less than the first threshold, the smoothing control factor is set to 0;

[0103] When the number of iterations t is between the first threshold and the second threshold, the smoothing control factor takes the first preset value;

[0104] When the number of iterations t is greater than or equal to the second threshold, the smoothing control factor takes the second preset value;

[0105] The first preset value is less than the second preset value.

[0106] Specifically, S6 uses a dynamic smoothing control method based on Gaussian filtering in Cartesian coordinates to first convert the fiber angle variable into a direction vector:

[0107]

[0108] Where dx, dy, and dz are vectors along the fiber direction.

[0109] Then, a Gaussian filter weighting function with direction vector driving is established, and the smoothed fiber angle direction vectors Sx, Sy, and Sz are solved:

[0110]

[0111] Where w is the distance between the centers of each unit, and ξ is a dynamic smoothing control factor with a value between 0 and 1. The smaller the value, the weaker the smoothing effect and the closer it is to the original angle; the larger the value, the better the smoothing effect. The smoothing value can be set according to the number of iterations, as follows:

[0112]

[0113] The iteration step number is set to t = 200. In the early stage (t < 50): ξ = 0 to maintain the original sensitivity update and make full use of gradient descent to explore the global optimum. In the middle stage (50 ≤ t < 150): moderate smoothing ξ = 0.3 is introduced to initially adjust the smoothness of fiber orientation. In the later stage (t ≥ 150): strong smoothing γ = 0.6 is applied to ensure the manufacturability of fiber orientation. The value of ξ can be set arbitrarily according to the actual situation. The smoothing factor ξ value given in the subsequent examples is the final set value.

[0114] Furthermore, the process of determining whether the convergence condition is met includes:

[0115] Determine if the maximum number of iterations has been reached;

[0116] If the maximum number of steps is reached, stop the optimization and output the current fiber angle orientation field;

[0117] If the maximum number of steps is not reached, the process of establishing the matrix, constructing the objective function, solving for sensitivity, iterative optimization, and smoothing is returned.

[0118] The fiber angular orientation field is the input data for the continuous fiber layup path in additive manufacturing, used to guide the directional changes of the fiber in space.

[0119] Specifically, the convergence condition in S7 is set to 200 iterations. If the condition is not met, steps S2 to S6 are repeated until the objective function meets the convergence condition, at which point the optimization stops, and the fiber orientation optimization with Gaussian filtering dynamic smoothing control is completed.

[0120] In one example of the invention, such as Figure 2 As shown, given a single-layer plate of 24m×1m×15m, five concentrated loads F=1500N are applied to it. The initial angle is set to 0 degrees, parallel to the y-axis. Optimization calculations are performed using both the method without smoothness optimization and the method of this invention. The method without smoothness optimization is as follows: Figure 3 As shown, this scheme sets the dynamic smoothing control factors to 0.2, 0.4, 0.6, and 1 respectively, and the calculated optimization results are as follows. Figure 4 , Figure 5 , Figure 6 and Figure 7 As shown in the figure, the white short lines represent discrete short fibers, and the black background represents the matrix.

[0121] In summary, the calculation results clearly demonstrate that the structure using this scheme exhibits significantly better mechanical properties and fiber continuity than the structure without smoothness optimization, indicating the effectiveness of the proposed scheme. It is worth noting that this method is not limited to the given examples and is applicable to optimization designs in other situations. Specifically, a smoothness factor of 1 provides the best fiber continuity smoothness but may result in the loss of structural details; therefore, it is necessary to find the most suitable smoothness value for the model.

[0122] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A fiber orientation optimization method based on Gaussian filtering and dynamic smoothing control, characterized in that, include: Define the model design domain and initialize the fiber angle design variables; The unit elastic constitutive matrix is ​​established based on the fiber angle design variables and coordinate transformation matrix. Construct a fiber angle orientation optimization objective function based on the unit elastic constitutive matrix; Solve for the sensitivity of the fiber angle orientation optimization objective function to the fiber angle design variable; Based on the sensitivity information, the gradient descent method is used to iteratively optimize the fiber angular orientation field; The fiber angle direction field after iteration is smoothed using a Gaussian filter dynamic smoothing control method in Cartesian coordinates. Repeat the above process of establishing the matrix, constructing the objective function, solving for sensitivity, iterative optimization, and smoothing until the convergence condition is met, thus completing the fiber orientation optimization.

2. The method according to claim 1, characterized in that, The process of defining the model design domain and initializing the fiber angle design variables includes: Determine the boundaries of the design domain in three-dimensional space; Discretize the cell mesh within the design domain; Each unit is assigned an initial fiber azimuth angle θ and elevation angle φ as design variables.

3. The method according to claim 1, characterized in that, The process of establishing the unit elastic constitutive matrix based on the fiber angle design variables and coordinate transformation matrix includes: Establish the elastic matrix of orthogonal anisotropic materials; Construct a transformation matrix from the local coordinate system to the global coordinate system based on the fiber angle design variables; Multiplying the elasticity matrix by the transformation matrix yields the unit elastic constitutive matrix.

4. The method according to claim 1, characterized in that, The process of constructing the fiber angle orientation optimization objective function based on the unit elastic constitutive matrix includes: Calculation of element strain energy density based on element elastic constitutive matrix; The objective function value is obtained by volume integral of the strain energy density of all elements in the design domain.

5. The method according to claim 1, characterized in that, The process of determining the sensitivity of the fiber angle orientation optimization objective function to the fiber angle design variable includes: The sensitivity value is obtained by taking the first-order partial derivatives of the objective function with respect to the azimuth angle θ and the elevation angle φ.

6. The method according to claim 1, characterized in that, Based on the sensitivity information, the process of iteratively optimizing the fiber angular orientation field using the gradient descent method includes: Determine the angle update direction based on the sensitivity value obtained from the current iteration; Adjust the azimuth angle θ and elevation angle φ of each unit along the update direction with a preset step size; Use the updated angle as input for the next iteration.

7. The method according to claim 1, characterized in that, The process of smoothing the fiber angular direction field after iteration using the Gaussian filter dynamic smoothing control method in Cartesian coordinates includes: Convert the fiber angle variable of each unit into a direction vector; Construct a Gaussian filtering weighting function based on the distance between the center points of the cells; The direction vector is weighted and averaged using a dynamic smoothing control factor to obtain a smoothed direction vector.

8. The method according to claim 7, characterized in that, The dynamic smoothing control factor changes according to the number of iterations: When the number of iterations t is less than the first threshold, the smoothing control factor is set to 0; When the number of iterations t is between the first threshold and the second threshold, the smoothing control factor takes the first preset value; When the number of iterations t is greater than or equal to the second threshold, the smoothing control factor takes the second preset value; Wherein, the first preset value is less than the second preset value.

9. The method according to claim 1, characterized in that, The process of determining whether the convergence condition is met includes: Determine if the maximum number of iterations has been reached; If the maximum number of steps is reached, stop the optimization and output the current fiber angle orientation field; If the maximum number of steps is not reached, the process of establishing the matrix, constructing the objective function, solving for sensitivity, iterative optimization, and smoothing is returned.

10. The method according to claim 9, characterized in that, The fiber angle orientation field is the input data for the continuous fiber layup path in additive manufacturing, used to guide the directional changes of the fiber in space.

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