Topological optimization method and equipment for continuous carbon fiber reinforced composite material

Abstract

The invention belongs to the related technical field of structural topological optimization, and discloses a topological optimization method and equipment for a continuous carbon fiber reinforced composite material, and the method comprises the steps: S1, predicting the mechanical properties of a material at a bending printing path based on a mesoscopic representative volume element, and building a mapping relation between the curvature of the printing path and the corresponding mechanical properties of the material; s2, introducing relative density and a material direction angle for each unit to obtain a structural flexibility function containing the two design variables, and calculating an equivalent elastic matrix; s3, calculating to obtain the material mechanical property corresponding to the current unit based on the mapping relation, and updating the material mechanical property of the current unit; and S4, constructing a topological optimization model, and carrying out topological optimization by adopting the topological optimization model to obtain an optimal topological configuration. According to the method, the curvature generated by fibers induced by a bending printing path is combined, parameters are dynamically adjusted and optimized by introducing fiber curvature constraints, and the mechanical property of a final structure is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the technical field of structural topology optimization, and more specifically, relates to a topology optimization method and apparatus for continuous carbon fiber reinforced composite materials. Background Technology

[0002] Topology optimization is a technique that uses mathematical methods to find the optimal material distribution within a given design domain, aiming to achieve the optimal solution for structural performance. Traditional topology optimization is mostly applied to homogeneous materials, generating lightweight and high-performance structural configurations through finite element analysis and iterative algorithms. With the development of additive manufacturing technology, the design freedom of topology optimization has been greatly improved, enabling the fabrication of complex geometries that are difficult to process using traditional methods, making it a hot topic in the field of structural optimization design.

[0003] Continuous carbon fiber reinforced composites, with their advantages of high specific strength and strong designability, are widely used in aerospace, bulletproof armor, and other fields. Their topology optimization requires simultaneous consideration of material anisotropy and manufacturing process constraints: on the one hand, fiber orientation and distribution directly affect the structural mechanical properties, necessitating optimization algorithms to coordinate global stiffness and local reinforcement requirements; on the other hand, additive manufacturing constraints such as printing path curvature and fiber continuity require optimization results to match actual molding capabilities. Current topology optimization for composite materials focuses on multi-scale optimization, such as the synergistic optimization of macroscopic topology and microscopic fiber arrangement, neglecting the impact of fiber curvature in the curved printing path during additive manufacturing on material mechanical properties, and consequently ignoring the influence of changes in material properties on topological configuration. Therefore, topology optimization of 3D-printed continuous fiber reinforced composites considering additive manufacturing constraints to achieve a balance between composite material performance and manufacturability is an indispensable issue in engineering design. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a topology optimization method and device for continuous carbon fiber reinforced composite materials, which aims to solve the problem that the existing methods do not consider the influence of the curvature of the printing path on the topology configuration.

[0005] To achieve the above objectives, according to one aspect of the present invention, a topology optimization method for continuous carbon fiber reinforced composite materials is provided, comprising the following steps: S1, A mesoscopic representative volume element with curved fibers in a continuous carbon fiber reinforced composite material is constructed using a homogenization method. Based on the mesoscopic representative volume element, the mechanical properties of the material at the curved printing path are predicted, and then a mapping relationship between the curvature of the printing path and its corresponding material mechanical properties is established in additive manufacturing. S2. After associating each element in the design domain of the continuous carbon fiber reinforced composite material with a continuous relative density variable using a penalized interpolation model, the displacement field is solved based on the current density and equivalent modulus of each element, and the structural compliance in the current design domain is calculated. Then, the sensitivity of the objective function compliance and constraint function to relative density is analyzed. Then, the relative density of all elements is updated based on the obtained sensitivity, and two design variables, relative density and material orientation angle, are introduced into each element to obtain the structural compliance function containing these two design variables. Next, based on the design variables relative density and material orientation angle, the equivalent elastic matrix of all elements in the global coordinate system is calculated using a penalized interpolation model. S3. After calculating the difference between the material orientation angles of each unit and its neighboring units based on the obtained material orientation angles, the printing path curvature of the current unit is calculated using geometric relationships. Then, the material mechanical properties corresponding to the current unit are calculated based on the mapping relationship. The material mechanical properties of the current unit are updated based on the obtained material mechanical properties, and the equivalent elastic matrix is ​​updated at the same time. S4. Based on the equivalent elastic matrix of all elements, construct a topology optimization model for carbon fiber reinforced composite materials that takes into account manufacturing constraints and aims to minimize structural flexibility. Then, use the carbon fiber reinforced composite material topology optimization model to perform topology optimization on continuous carbon fiber reinforced composite materials to obtain the optimal topology configuration.

[0006] Furthermore, based on the aforementioned microscopic representative volumetric elements, the mechanical properties of the material at the curved printing path are predicted using the following formula:

[0007] In the formula, and These represent the macroscopic average stress tensor and the macroscopic average strain tensor, respectively. and Represents the stress tensor and strain tensor as they vary with position y at the microscale. V RVE This represents the volume of a representative volume unit. For the macroscopic volume of the material (here) V Actually, there's no need to explain the meaning of what it represents, because V RVE It is a whole. V It is simply an abbreviation of the English word "volume" (meaning volume). The expression corresponding to the mapping relationship is: , In the formula, These represent the elastic parameters of fiber-reinforced composite materials in a two-dimensional plane, specifically... E1 represents the elastic modulus along the fiber direction. E 2 represents the elastic modulus parallel to the fiber direction. G 12 Let be the shear modulus in both directions. Indicates the curvature corresponding to the curved printing path, subscript i Indicates the first i 1 sample point.

[0008] Furthermore, all curved printing paths are discretized and simplified into several reference points. Then, several corresponding mesoscopic representative volumetric elements with different radii of curvature are established, and their macroscopic material properties are predicted.

[0009] Furthermore, for classic penalized isotropic solid materials, the optimization objective is expressed as: , in, ρ The density vector is represented by the density of all elements in the design domain. ρ e The components are: c represents the flexibility, with a smaller value indicating greater structural stiffness; F and U represent the load vector and displacement vector, respectively. and This represents the volume of the optimized structure and the initial volume of the design domain; F The volume fraction is the maximum material ratio set during optimization.

[0010] Furthermore, the expression for the interpolation model is: , In the formula, E e This represents the equivalent elastic modulus of element e. E 0 represents the elastic modulus of a solid material. E min It is a minimum value, approximately 0, and P is the penalty factor.

[0011] Furthermore, the displacement field is solved based on the density and equivalent modulus of each element, and the compliance c of the structure in the current design domain is calculated:

[0012] In the formula, This represents the global stiffness matrix.

[0013] Furthermore, by introducing two design variables, relative density and material orientation angle, into each element, a structural compliance function is obtained that incorporates these two design variables: .

[0014] Furthermore, the equivalent elasticity matrix is: , In the formula, D0 represents the stiffness matrix of the orthotropic material. This represents the coordinate transformation matrix.

[0015] The present invention also provides a topology optimization system for continuous carbon fiber reinforced composite materials. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the topology optimization method for continuous carbon fiber reinforced composite materials as described above.

[0016] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the topology optimization method for continuous carbon fiber reinforced composite materials as described above.

[0017] In summary, compared with the prior art, the topology optimization method and equipment for continuous carbon fiber reinforced composite materials provided by this invention have the following advantages: 1. Significantly Improved Mechanical Performance, Achieving a Dual Breakthrough in Load Capacity and Stiffness: This invention addresses the curvature induced in fibers by bending the printing path in real-world additive manufacturing. By actively introducing fiber curvature constraints to dynamically adjust and optimize parameters, it significantly improves the overall mechanical performance of the final structure. Compared to traditional optimization methods, the peak load and maximum stiffness of three-point bending beams and four-point bending beams designed and manufactured using this invention are both improved. This directly demonstrates the outstanding beneficial effects of this invention in enhancing structural load capacity and stiffness.

[0018] 2. This invention incorporates the crucial but long-neglected manufacturing process factor of printing path curvature into the framework of topology optimization theory. By establishing a correlation model between printing path curvature and the corresponding equivalent elastic properties of the material, this invention can accurately predict and compensate for material performance losses caused by curved printing paths. Particularly for stress concentration areas such as structural corners, this method achieves efficient convergence and optimization of material distribution, effectively enhancing corner strength. This transforms the overall structural performance from a passive situation determined by its weakest link to one where performance is maximized through proactive design.

[0019] 3. Discretize all possible curved printing paths, simplify the curved printing paths into several reference points, and then use the fitting method to restore the continuity of the curvature radius of the real printing path with discrete sample points, thereby establishing the mapping relationship between the elastic mechanical properties of the material at the curved printing path and the curvature of the printing path.

[0020] 4. This invention not only provides a theoretical explanation for existing experimental phenomena, but more importantly, it lays a new theoretical foundation and provides practical tools for developing next-generation high-performance continuous fiber composite material structures through "design-oriented manufacturing." This framework is universal and can generate a variety of novel topological configurations that are unattainable by traditional methods, opening up new avenues for innovative designs of lightweight, high-load-bearing structures in high-end fields such as aerospace and automotive. Attached Figure Description

[0021] Figure 1 This is a flowchart of a topology optimization method for continuous carbon fiber reinforced composite materials provided in an embodiment of the present invention; Figure 2 (a) and (b) in the embodiments of the present invention are schematic diagrams of the continuous carbon fiber reinforced composite material generating curved fibers in the printing path; Figure 3 These are schematic diagrams showing the applied loads and performance prediction results of the RVE model for several fibers with varying curvatures. These represent the elastic parameters of carbon fiber composites in different directions; Figure 4 This is a schematic diagram of the curvature update strategy corresponding to the curved path provided in an embodiment of the present invention; Figure 5 These are two cases and topology optimization results for MBB beams and four-point bending beams, with (a) and (b) corresponding to the design domains of the two cases, respectively. Figure 6 The diagram illustrates the convergence of element angles at structural corners in two cases (symmetric half-models) of MBB beams and four-point bending beams according to embodiments of the present invention. Figure 7 (a), (b), (c), and (d) in the figure are the comparison and verification results. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0023] This invention provides a topology optimization method for continuous carbon fiber reinforced composite materials. This method incorporates the changes in material elastic properties caused by variations in fiber curvature into classic composite material topology optimization methods. It maximizes the integration of additive manufacturing process constraints with composite material topology optimization algorithms, ultimately generating a topology that more closely matches actual performance. This method not only achieves superior convergence in material distribution at corners but also significantly improves the overall stiffness of the structure.

[0024] The topology optimization method mainly includes the following steps: S1. A microscopic representative volumetric unit with curved fibers in a continuous carbon fiber reinforced composite material is constructed using a homogenization method. Based on the microscopic representative volumetric unit, the mechanical properties of the material at the curved printing path are predicted, and then a mapping relationship between the curvature of the printing path and its corresponding material mechanical properties is established in additive manufacturing.

[0025] In additive manufacturing of carbon fiber composites, the mechanical properties of the material at the bending path are difficult to obtain through standard tensile testing. Therefore, homogenization theory is used to construct a microscopic representative volume element with bent fibers to predict the mechanical properties of the material at the bending path. The corresponding formula is:

[0026] In the formula, and These represent the macroscopic average stress tensor and the macroscopic average strain tensor, respectively. and Represents the stress tensor and strain tensor as they vary with position y at the microscale. V RVE This represents the volume of a representative volume unit. For the macroscopic volume of the material (here) V Actually, there's no need to explain the meaning of what it represents, because V RVE It is a whole. V It is an abbreviation for volume (the English word for volume).

[0027] Specifically, the steps for predicting the mechanical properties of materials at different curved printing paths using the aforementioned representative volume elements are as follows: First, discretize all possible curved printing paths and simplify them into several reference points (e.g., define the curvature radii of the curved printing paths as 0mm, 1mm, 2mm, 3mm, 4mm, and 5mm, respectively, to fully encompass all curvature radii of the curved printing paths in additive manufacturing). Then, establish several corresponding mesoscopic representative volume elements with different curvature radii and predict their macroscopic material properties.

[0028] For the material properties predicted by the above method under different radii of curvature, a quadratic function is used to fit the above sample points to obtain:

[0029] In the formula, X represents the design matrix. , is the vector of undetermined coefficients of a quadratic function. This represents the observation vector. The aim is to reconstruct the continuity of the radius of curvature of the printed path in reality using discrete sample points through a fitting method, thereby establishing a mapping relationship between the elastic mechanical properties of the material at curved printed paths and the curvature of the printed path.

[0030] S2. After associating each element in the design domain of the continuous carbon fiber reinforced composite material with a continuous relative density variable using a penalized interpolation model, the displacement field is solved based on the current density and equivalent modulus of each element, and the structural compliance in the current design domain is calculated. Then, the sensitivity of the objective function compliance and constraint function to relative density is analyzed. Then, the relative density of all elements is updated based on the obtained sensitivity, and two design variables, relative density and material orientation angle, are introduced for each element to obtain the structural compliance function containing these two design variables. Next, based on the design variables relative density and material orientation angle, the equivalent elastic matrix of all elements in the global coordinate system is calculated using a penalized interpolation model.

[0031] The specific steps are as follows: S2.1. Determine the design domain of the continuous carbon fiber reinforced composite material to be optimized, apply loads and constraints, and clarify the optimization objective. For the classic penalized solid isotropic material method, the optimization objective can be expressed as: , in, ρ The density vector is represented by the density of all elements in the design domain. ρ e The composition is as follows: c represents the flexibility, and a smaller value indicates greater structural stiffness. F and U represent the load vector and displacement vector, respectively. and This represents the volume of the optimized structure and the initial volume of the design domain. F The volume fraction is the maximum material ratio set during optimization.

[0032] S2.2. Using a penalized interpolation model, each element is associated with a continuous relative density variable, making intermediate densities mechanically inefficient, thereby forcing the optimization results to tend towards pure solids or pure voids. This interpolation model can be expressed as: , E eThis represents the equivalent elastic modulus of element e. E 0 represents the elastic modulus of a solid material. E min It is a minimum value, approximately 0, and P is the penalty factor.

[0033] S2.3. Solve for the displacement field based on the density and equivalent modulus of each element, and calculate the compliance c of the structure in the current design domain:

[0034] This represents the global stiffness matrix.

[0035] S2.4 Further, analyze the sensitivity of the objective function and constraint functions to each design variable:

[0036] u represents the sensitivity of the objective function's compliance to density. e Let k represent the displacement vector of element e, and k0 represent the element stiffness matrix composed of solid material.

[0037] S2.5. Systematically update the density of all cells using the OC optimization algorithm:

[0038] B e This represents the ratio in the update criteria, which normalizes the sensitivity information. For the Grandes multiplier, The damping factor is what makes the iterative process stable.

[0039] S2.6. For penalized solid anisotropic material methods, the essence lies in adding extra optimization for the material orientation, introducing two design variables for each element: relative density. ρ and material orientation angle θ The flexibility c is a function containing two variables:

[0040] S2.7, Based on the relative density of variables ρ and material orientation angle θ The equivalent elasticity matrix of the unit in the global coordinate system is calculated using the penalty model: , In the formula, D0 represents the stiffness matrix of the orthotropic material. This represents the coordinate transformation matrix. Thus, the directionality of penalized isotropic solid materials can be extended to anisotropic materials.

[0041] S3. After calculating the difference between the material orientation angles of each unit and its neighboring units based on the obtained material orientation angles, the printing path curvature of the current unit is calculated using geometric relationships. Then, the material mechanical properties corresponding to the current unit are calculated based on the mapping relationship. The material mechanical properties of the current unit are updated based on the obtained material mechanical properties, and the equivalent elastic matrix is ​​updated at the same time.

[0042] Specifically, iterate through all elements and read the material orientation angle of each element obtained by the above method. This material orientation angle The local orientation of the fibers in the optimized material was characterized.

[0043] Using the material orientation angle obtained above, the difference between the orientation angles of the material and its neighboring cells is calculated, and then the curvature of the printing path at the center of the cell is calculated through geometric relationships.

[0044] Based on the calculated curvature of the printing path of each unit, the corresponding material mechanical properties are calculated through the mapping relationship between the printing path curvature in S1 and its corresponding material mechanical properties, and the original material stiffness of the unit is updated to obtain a curvature-corrected material mechanical property. The corrected material mechanical property is fed back into S2.7, thereby obtaining a topology optimization model of carbon fiber reinforced composite material that takes into account manufacturing constraints.

[0045] S4. Based on the equivalent elastic matrix of all elements, construct a topology optimization model for carbon fiber reinforced composite materials that takes into account manufacturing constraints and aims to minimize structural flexibility. Then, use the carbon fiber reinforced composite material topology optimization model to perform topology optimization on continuous carbon fiber reinforced composite materials to obtain the optimal topology configuration.

[0046] In the iterative optimization solution using the carbon fiber reinforced composite material topology optimization model, the sensitivity of the objective function relative to the design variables is used to solve the problem. The density, angle, and curvature variables of each element in the design domain are iteratively updated until the convergence condition is met, and the optimized topology configuration is finally obtained.

[0047] The present invention will be further described in detail below with reference to specific embodiments.

[0048] This invention proposes a topology optimization method for continuous carbon fiber reinforced composite materials considering manufacturing constraints, the process of which is as follows: Figure 1 As shown, the specific implementation steps are as follows: (1) Analyze the path and geometric characteristics of continuous carbon fiber reinforced composites in additive manufacturing, simplify the path appropriately, and construct a mesoscopic representative volume element based on the homogenization method to predict the macroscopic mechanical properties of the material. The simplified model of the mesoscopic representative volume element is as follows: Figure 2 As shown.

[0049] (2) The mesoscopic representative unit volume of a single fiber based on homogenization theory is adopted. The geometric characteristics of a single fiber correspond to the macroscopic additive manufacturing printing path. The corresponding formula is: , In the formula, and These represent the macroscopic average stress tensor and the macroscopic average strain tensor, respectively. and Represents the stress tensor and strain tensor as they vary with position y at the microscale. V RVE This indicates the volume of a representative unit.

[0050] When using mesoscopic representative volume elements to predict the macroscopic mechanical properties of materials, periodic boundary conditions need to be applied to the mesoscopic representative volume elements. The corresponding formula is:

[0051] In the formula, L represents the microscopic displacement field, and is a periodic vector used to connect the relative boundaries of the microscopic representative volume elements. This represents the applied macroscopic average strain tensor.

[0052] Specifically, the steps for predicting the mechanical properties of materials at different bending paths using the aforementioned microscopic representative volume elements are as follows: First, discretize all possible bending printing paths and simplify them into several reference points (e.g., define the curvature radii of the bending printing paths as 0mm, 1mm, 2mm, 3mm, 4mm, and 5mm, respectively, to fully encompass all curvature radii of the bending printing paths in additive manufacturing). Then, establish several corresponding microscopic representative volume elements with different curvature radii and predict their macroscopic material properties.

[0053] For the material properties predicted by the above method under different radii of curvature, a quadratic function is used to fit the above sample points to obtain: , Where X represents the design matrix, It is the vector of undetermined coefficients of a quadratic function. This represents the observation vector. The aim is to reconstruct the continuity of the radius of curvature of the printed path in reality using discrete sample points through fitting, thereby establishing a mapping relationship between the elastic mechanical properties of the material at curved printed paths and the curvature of the printed path. , In the formula, These represent the elastic parameters of carbon fiber composites in different directions. ck This indicates the curvature of the printed path. A detailed mapping between curvature and material properties is shown below. Figure 3 As shown.

[0054] (3) Based on the classical penalized solid isotropic material unit directionality, the model is extended to anisotropic materials, specifically: First, define the design domain of the structure, apply loads and constraints, and set the optimization objective. For the classic penalized solid isotropic material method, the optimization objective can be expressed as: , in, ρ Represents the density vector. θ The element orientation is represented by the density of all elements in the design domain. ρ e and θ e Composition; c represents flexibility, the smaller the value, the greater the structural stiffness. F and U represent the load vector and displacement vector, respectively. and These represent the volume of the optimized structure and the initial volume of the design domain, respectively. F The volume fraction is the maximum material ratio set during optimization.

[0055] Using a penalized interpolation model, each element is associated with a continuous relative density variable, making intermediate densities mechanically inefficient. This forces the optimization results to tend towards pure solids or pure voids. This interpolation model can be expressed as: , E e This represents the equivalent elastic modulus of element e. E 0 represents the elastic modulus of a solid material. E min It is a minimum value, approximately 0, and P is the penalty factor.

[0056] The displacement field is solved based on the density and equivalent modulus of each element, and the compliance c of the structure in the current design domain is calculated:

[0057] The global stiffness matrix is ​​obtained by assembling the element stiffness matrices.

[0058] The element stiffness matrix can be calculated using the following formula:

[0059] In the formula, D represents the element stiffness matrix. e B is the constitutive matrix of the material, and S is the strain-displacement matrix. V e Let be the volume of the unit.

[0060] The constitutive matrix of a material can be obtained by applying a direction variable to the rotation matrix: , In the formula, D0 represents the stiffness matrix of the orthotropic material. This represents the coordinate transformation matrix. Thus, the penalized solid isotropic material method can be extended to anisotropic materials.

[0061] Analyze the sensitivity of the objective function and constraint functions to each design variable:

[0062] u represents the sensitivity of the objective function's compliance to density. e Let k represent the displacement vector of element e, and k0 represent the element stiffness matrix composed of solid material.

[0063] The density of all cells is systematically updated using the OC optimization algorithm:

[0064] In the formula, B e This represents the ratio in the update criteria, which normalizes the sensitivity information. For the Grandes multiplier, The damping factor is what makes the iterative process stable.

[0065] Furthermore, the sensitivity of the compliance objective function to element angles can be calculated using the following formula:

[0066] This indicates the sensitivity of the objective function's compliance to the element angle.

[0067] The angles of all elements are systematically updated using the Moving Progressive Approach (MMA) method:

[0068] In the formula, and Representing the moving asymptotes, these are the two most crucial parameters controlling the shape of the approximate function. and These are two non-negative coefficients that determine the gradient of the approximate function at the current position. c 0 is a constant offset term.

[0069] (4) Traverse all elements and read the material orientation angle of each element obtained by the above method. Material orientation angle The local orientation of the optimized material fibers is characterized. Using the obtained element angle field, the mean value of the angles of the surrounding elements can be calculated for each element.

[0070] In the formula, This represents the average angle of the cells surrounding a specific cell. i Indicates the traversal of the first... i There are several elements. Assuming the angle of this element is initially 0°, the average angles of a given element and its surrounding elements can form a specific geometric relationship:

[0071] In the formula, R is the radius of curvature, and the curvature is... ck The curvature is the reciprocal of the radius of curvature. Therefore, the curvature at the center of this element can be expressed as:

[0072] The geometric relationship between curvature and element angle is as follows: Figure 4 As shown.

[0073] Based on the calculated curvature of each element, the original material stiffness of the element is updated through the mapping relationship between curvature and material properties, resulting in a curvature-corrected material stiffness. This corrected material stiffness is then fed back into the element stiffness matrix, thereby obtaining a topology optimization model for carbon fiber reinforced composite materials that takes into account manufacturing constraints.

[0074] The following is combined Figure 5 The advantages of the method proposed in this invention are explained in detail using two specific examples: an MBB beam and a four-point bending beam. Figure 5 In the MBB beam example shown in Figure a, the method proposed in this embodiment of the invention reduces the structural flexibility by 13.2% compared to methods that do not consider manufacturing constraints. Figure 5In the four-point bending beam case shown in b, the topological flexibility of the structure obtained by the method proposed in this embodiment is 1.8169, while the structural flexibility of the method without considering manufacturing constraints is 1.9822. The structural flexibility of this method is reduced by 8%. Both of these results fully demonstrate the beneficial effect of considering manufacturing constraints on reducing structural flexibility and improving structural stiffness.

[0075] Figure 6 This paper presents two specific examples—an MBB beam and a four-point bending beam—showing the element distribution at structural corners to illustrate the superior convergence of the proposed method in this invention. For methods that do not consider manufacturing constraints, the angular distribution of elements at structural corners is chaotic, resulting in poor local convergence. The method proposed in this invention considers the bending path constraints of additive manufacturing, specifically correcting the element orientation at structural corners, effectively improving the convergence of elements at structural corners. Furthermore, both the MBB beam and four-point bending beam examples demonstrate the significant beneficial effect of considering manufacturing constraints on improving algorithm convergence.

[0076] Please see Figure 7 Experiments further verified the superiority of the proposed method in improving structural stiffness and load-bearing capacity. In both sets of experiments, the peak load of the MBB beam with manufacturing constraints increased by 31% and the maximum stiffness increased by 39% compared to the MBB beam without manufacturing constraints. The peak load and maximum stiffness of the four-point bending beam with manufacturing constraints increased by 38% and 27% respectively compared to the one without manufacturing constraints, fully demonstrating the beneficial effects of the proposed method in improving structural stiffness and load-bearing capacity.

[0077] The present invention also provides a topology optimization system for continuous carbon fiber reinforced composite materials. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the topology optimization method for continuous carbon fiber reinforced composite materials as described above.

[0078] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the topology optimization method for continuous carbon fiber reinforced composite materials as described above.

[0079] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of topology optimization of continuous carbon fiber reinforced composites, characterized by, The steps are: S1, a meso-representative volume element with curved fibers of a continuous carbon fiber reinforced composite material is constructed by using a homogenization method, the mechanical properties of the material at a curved printing path are predicted based on the meso-representative volume element, and a mapping relationship between the curvature of the printing path in additive manufacturing and the corresponding mechanical properties of the material is established; S2, after each element in the design domain of the continuous carbon fiber reinforced composite material is associated with a continuous relative density variable using a penalized interpolation model, the displacement field is solved based on the density and equivalent modulus of each element, the structural flexibility in the current design domain is calculated, and the sensitivity of the objective function flexibility and the constraint function to the relative density is analyzed; then, the relative density of all elements is updated based on the obtained sensitivity, and two design variables of relative density and material direction angle are introduced for each element, and a structural flexibility function of the structural flexibility containing the two design variables is obtained; then, the equivalent elastic matrix of all elements in the global coordinate system is calculated based on the design variables of relative density and material direction angle through the penalized interpolation model; S3, after the difference between the material direction angle of each element and the material direction angle of its neighborhood element is calculated based on the obtained material direction angle of each element, the printing path curvature of the current element is calculated by using geometric relationship, the mechanical properties of the material corresponding to the current element are calculated based on the mapping relationship, and the mechanical properties of the material of the current element are updated based on the obtained mechanical properties of the material, and the equivalent elastic matrix is also updated; S4, a carbon fiber reinforced composite material topology optimization model considering manufacturing constraints is constructed based on the equivalent elastic matrix of all elements, and the topology optimization model is used to perform topology optimization on the continuous carbon fiber reinforced composite material to obtain an optimal topology configuration.

2. The method of topology optimization of continuous carbon fiber reinforced composites according to claim 1, characterized in that: The corresponding formula for predicting the mechanical properties of the material at the curved printing path based on the meso-representative volume element is: wherein and respectively represent the macroscopic average stress tensor and the macroscopic average strain tensor, and represent the stress and strain tensors at the microscale as a function of position y, V RVE V represents the volume of a representative volume element, V is the macroscopic volume of the material; The expression of the mapping relationship is: ， wherein, respectively represent the elastic parameters of the fiber-reinforced composite material in a 2-dimensional plane, in particular E 1 represents the elastic modulus in the fiber direction, E 2 represents the elastic modulus parallel to the fiber direction, G 12 is the shear modulus in both directions, represents the curvature corresponding to the curved printing path, the subscript i represents the i th sample point.

3. The method of topology optimization of continuous carbon fiber reinforced composites according to claim 2, characterized in that: All curved printing paths are discretized, the curved printing path is simplified as a plurality of reference points, a plurality of meso-representative volume elements with different curvature radii are established corresponding to the reference points, and the macroscopic material properties are predicted.

4. The method of topology optimization of continuous carbon fiber reinforced composites of claim 2, wherein: For a classical solid isotropic material with a penalty, the optimization objective is expressed as: ， where, ρ denotes the density vector, which is the sum of the density of all elements in the design domain The expression of the interpolation model is: e composes the stiffness matrix, c is the compliance, the smaller the value, the greater the structural stiffness; F and U represent the load vector and displacement vector, respectively; and represent the volume of the optimized structure and the initial volume of the design domain; F is the volume fraction, which is the maximum material ratio set in the optimization.

5. The method of topology optimization of continuous carbon fiber reinforced composites of claim 4, wherein: The displacement field is solved based on the density and equivalent modulus of each element, and the flexibility of the structure in the current design domain is calculated: ， wherein E e Ee represents the equivalent elastic modulus of the unit e, E 0 represents the elastic modulus of the solid material, E min is a minimum value, approximately 0, and P is a penalty factor.

6. The method of topology optimization of continuous carbon fiber reinforced composites of claim 4, wherein: Two design variables of relative density and material direction angle are introduced for each element, and a structural flexibility function of the structural flexibility containing the two design variables is obtained: In the formula, denotes the global stiffness matrix.

7. The method of topology optimization of continuous carbon fiber reinforced composites of claim 6, wherein: The equivalent elastic matrix is: 。 8. The method of topology optimization of continuous carbon fiber reinforced composites of claim 7, wherein: The system includes a memory and a processor, the memory stores a computer program, and the processor executes the computer program to perform the topology optimization method of the continuous carbon fiber reinforced composite material according to any one of claims 1-8. ， In the formula, D0 represents a stiffness matrix of an orthotropic material, represents a coordinate transformation matrix.

9. A system for topology optimization of continuous carbon fiber reinforced composites, characterized by: ​ 10. A computer-readable storage medium, characterized in that: The computer readable storage medium stores machine executable instructions that, when invoked and executed by a processor, cause the processor to implement the method of topology optimization of a continuous carbon fiber reinforced composite material according to any one of claims 1-8.

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