Continuous fiber reinforced composite material additive manufacturing stiffened structure impact resistance design method

Abstract

The application provides a continuous fiber reinforced composite material additive manufacturing stiffened structure impact resistance design method, B-spline parameterization characterization is performed on a macroscopic topological distribution pseudo-density field and a microscopic fiber orientation fiber direction field, and B-spline control parameters are used as optimization design variables; impact resistance topology optimization based on an equivalent static load method is adopted, dynamic nonlinear analysis is performed through external circulation, and the stiffened topology and the fiber direction are cooperatively optimized under the equivalent static load through internal circulation, so that the stiffened structure topology distribution and the fiber direction distribution are obtained; then, the B-spline parameter field is mapped to a physical space reconstruction grid, and the topological and fiber direction representation of the physical space is obtained; finally, a continuous path planning algorithm based on a vector field is used to generate a one-stroke continuous printing path. The application solves the problem that the existing method is difficult to consider dynamic impact response modeling, fiber path continuity control and additive manufacturing process constraints, and cooperatively improves the impact resistance performance and manufacturability.

Description

Technical Field

[0001] This invention relates to the field of fiber-reinforced composite additive manufacturing technology, and specifically to an impact-resistant design method for reinforced structures manufactured from continuous fiber-reinforced composite additives. Background Technology

[0002] Continuous fiber reinforced composites have garnered widespread attention in high-end equipment fields such as aerospace, rail transportation, and new energy due to their excellent specific stiffness, specific strength, and designability. The development of additive manufacturing technology has further expanded the application potential of these materials in the forming of complex structures, especially stiffened panel structures. Because of their combination of lightweight and high load-bearing efficiency, they have been identified as one of the six major development directions for low-cost structural technologies in the future aerospace field. Additive manufacturing of continuous fiber reinforced composites enables precise control of the fiber path during the forming process, thus providing new design freedom for the directional regulation of structural performance.

[0003] In actual service, reinforced structures often face dynamic loads such as low-velocity impacts. Compared to static conditions, low-velocity impact loads are characterized by their instantaneous nature, high amplitude, and localized energy concentration, easily leading to irreversible damage such as fiber breakage, interlaminar debonding, and interfacial peeling, severely impacting the safety and service life of the structure. However, current optimization design methods for continuous fiber reinforced composites are mostly based on static load assumptions, making it difficult to accurately capture the structural response behavior under dynamic impacts. Although some studies have attempted to introduce topology optimization into composite structure design, their optimization objectives are often limited to maximizing stiffness or reducing weight, failing to fully consider the complex response characteristics such as geometric nonlinearity and contact effects caused by dynamic loads. This results in composite structures prone to stress concentration and localized failure when subjected to instantaneous high-amplitude impacts, affecting their engineering applications in critical components such as aircraft skin and load-bearing stiffening plates.

[0004] To address dynamic optimization problems, the equivalent static load method has been proposed and applied to structural dynamics optimization. By transforming the displacement field at the peak of the transient response into an equivalent static load, the nonlinear dynamic optimization problem is approximated as a series of linear static optimization subproblems, thus achieving approximate modeling of the dynamic response while ensuring computational efficiency. Existing patents (such as CN109726506A) have successfully applied this method to the dimensional optimization of isotropic structures such as automotive bumpers. However, the application of this method in continuous fiber-reinforced composite structures still faces challenges: on the one hand, the anisotropic nature of composite materials makes the fiber orientation have a significant impact on local stiffness and failure modes, and the equivalent static load method has not yet effectively integrated the optimization of the material orientation field; on the other hand, additive manufacturing has extremely high requirements for the continuity of fiber paths, and drastic changes or abrupt changes in fiber orientation will lead to fiber accumulation, breakage, or forming defects during the printing process, restricting the manufacturability of the optimization results.

[0005] Furthermore, existing structural optimization methods for additive manufacturing of continuous fiber-reinforced composites often employ filtering techniques (such as convolution filtering and Helmholtz-type filtering) to post-process and smooth the fiber orientation, thereby improving its continuity. However, these methods often require storing local gradient information in each iteration, leading to high computational resource consumption and memory usage, and making it difficult to establish global constraints on fiber continuity during the optimization process. Simultaneously, existing design methods rarely consider physical constraints in the additive manufacturing process, such as fiber tension, minimum forming radius, and overhang angle thresholds. This results in problems such as fiber bridging, path interruptions, or poor interface bonding in actual printing, limiting their engineering application in complex reinforced structures.

[0006] In summary, current technologies have not yet developed a comprehensive design methodology for continuous fiber reinforced composite additive manufacturing stiffened structures that can simultaneously address dynamic impact response modeling, fiber path continuity control, and additive manufacturing process constraints. There is an urgent need to develop a design theory that can synergistically consider dynamic load response, fiber orientation optimization, and manufacturability constraints to support the manufacturing and application of high-performance continuous fiber reinforced composite structures under complex working conditions. Summary of the Invention

[0007] To address the technical problems existing in the prior art, this invention proposes an impact-resistant design method for reinforced structures manufactured using additive manufacturing of continuous fiber reinforced composite materials. This method fully considers the influence mechanism of dynamic impact loads on the response of the reinforced structure, overcoming the problem that traditional continuous fiber design and manufacturing methods based on static loads are difficult to apply to dynamic working conditions. Furthermore, it employs a B-spline parameter field to parametrically characterize the design variables, and based on the filtering characteristics of the B-spline field itself, efficiently obtains smooth and continuous fiber distribution results. In addition, it conducts collaborative constraints on the fixed dimensions and sag angles of the reinforced structure based on the characteristics of the structural skeleton line, and further smooths the fiber direction based on the geometric characteristics of the skeleton line, effectively improving the manufacturability of the reinforced structure.

[0008] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0009] A method for impact-resistant design of additively manufactured reinforced structures using continuous fiber reinforced composite materials includes the following steps:

[0010] Step S1: Divide the physical design domain in the three-dimensional model of the additive manufacturing reinforced structure of continuous fiber reinforced composite material. And map the physical design domain to the B-spline parameter space. Define design variables that reflect the macroscopic topological distribution and microscopic fiber orientation of continuous fiber reinforced composite materials, and characterize the design variables using B-spline parameterization.

[0011] Define pseudo-density field Representing the macroscopic topological distribution of the material, defining the fiber orientation field. To represent the micro-fiber orientation, the B-spline control parameters used to characterize the pseudo-density field and fiber orientation field are used as the final optimization design variable matrix. Design variables To characterize the pseudo-density field The B-spline control parameter matrix of the distribution, design variables To characterize the fiber orientation field The B-spline control parameter matrix of the distribution;

[0012] Step S2: Conduct impact optimization design based on the equivalent static load method for the additive manufacturing stiffened structure of continuous fiber reinforced composite material to obtain the final topology distribution and fiber orientation distribution of the stiffened structure: the equivalent solution of dynamic characteristics is achieved by alternately executing the inner and outer loops. The outer loop performs dynamic nonlinear dynamic analysis to extract the structural displacement response, the inner loop constructs the equivalent static load, and the topology and fiber orientation of the stiffened structure are optimized and the design variables are updated under the equivalent static load.

[0013] Step S3: For the physical design domain A reconstructed mesh is generated for continuous path planning, based on the coordinates of the reconstructed mesh center point in the physical design domain and the B-spline parameter space. The mapping relationship of the coordinate system will design variables. and Mapping this onto the reconstructed mesh yields the final representation of the stiffened structure's topological distribution and fiber orientation in the actual physical space.

[0014] Step S4: Based on the representation of the topological distribution of the stiffened structure and the fiber orientation distribution in the actual physical space obtained in Step S3, a continuous path generation algorithm based on vector field is used to generate a continuous path in one stroke.

[0015] A further preferred solution, the specific steps of step S1 are as follows:

[0016] Step S1-1: Divide the physical design domain in the solid structure. , physical design domain Mapping to B-spline parameter space ;

[0017] Step S1-2, in the B-spline parameter space Inside, along and Construct B-spline basis functions for each direction;

[0018] Steps S1-3: Establish the pseudo-density and fiber orientation B-spline parameter field based on the B-spline basis function to obtain the optimization design variable matrix. .

[0019] Further preferred solutions, in steps S1-2, The recursive formula for the B-spline basis functions in the direction is:

[0020]

[0021] in For along The direction of the first 0th-order B-spline basis functions for each node To characterize the B-spline parameter space along Direction parameter variable, , , and Along The first direction is uniformly distributed , , and The coordinates of each node. For B-spline parameter space Middle The number of nodes that are uniformly distributed in the direction. , Along The direction of the first Each node order and B-order spline basis functions, For along The direction of the first Each node B-order spline basis functions, express The order of the B-spline basis functions in the direction;

[0022] The recursive formula for the B-spline basis functions in the direction is:

[0023]

[0024] in For along The direction of the first 0th-order B-spline basis functions for each node To characterize the B-spline parameter space along Direction parameter variable, , , and Along The first direction is uniformly distributed , , and The coordinates of each node. For B-spline parameter space Middle The number of nodes that are uniformly distributed in the direction. , Along The direction of the first Each node order and B-order spline basis functions, For along The direction of the first Each node B-order spline basis functions, express The order of the B-spline basis functions in the direction.

[0025] In a further optimized approach, in steps S1-3, the formula for the B-spline parameter field is:

[0026]

[0027] in For pseudo-density field exist The pseudo density value at that location, For fiber orientation field exist The fiber orientation value at that location, and For B-spline parameter space middle The pseudo-density control parameters at that location, For B-spline parameter space middle Fiber orientation control parameters at the location; by Pseudo-density control parameters The matrix formed by the arrangement represents the pseudo-density field. B-spline control parameter matrix of distribution ,Depend on fiber orientation control parameters The matrix formed by the arrangement represents the fiber orientation field. B-spline control parameter matrix of distribution .

[0028] A further preferred solution, the specific steps of step S2 are as follows:

[0029] Step S2-1: Initialize the design variable matrix And set the target body ratio ;

[0030] Step S2-2: Physical design domain Perform finite element mesh generation and assign design variables and From the B-spline parameter space Mapping to the physical design domain In the physical design domain Design variables are represented as and ;

[0031] Step S2-3, in the physical design domain In this study, the finite element method was used to conduct dynamic nonlinear dynamic analysis on the additive manufacturing of reinforced structures from continuous fiber reinforced composite materials.

[0032] Step S2-4: Calculate the equivalent static load based on the dynamic analysis results obtained in step S2-3;

[0033] Step S2-5: Physical design domain Extract the structural skeleton lines;

[0034] Steps S2-6: Based on the structural skeleton lines, introduce cylindrical regions with diameter R and height H at each skeleton line point, where the height direction of the cylinder coincides with the normal direction of the plane containing the skeleton line, thereby obtaining the target stiffened region. ;

[0035] Step S2-7: Design the domain based on the physical design The design variables in the model are calculated using the SOMP material interpolation model to determine the physical design domain. The element elasticity matrix and element stiffness matrix of all finite element meshes are obtained and assembled to obtain the overall stiffness matrix of the structure;

[0036] Step S2-8: Based on the equivalent static load obtained in step S2-4 and the overall structural stiffness matrix obtained in step S2-7, perform finite element analysis of the structure to obtain the structural displacement response and structural compliance under the corresponding equivalent static load conditions.

[0037] Step S2-9: Based on the multi-condition analysis results, construct a multi-condition optimization model;

[0038] Step S2-10: Solve the multi-condition optimization model using the MMA optimization algorithm and update the design variables; determine whether the optimization meets the inner loop convergence condition. If not, return to step S2-4 to continue iterative optimization; if it does, end the inner loop and proceed to the next step.

[0039] Step S2-11: Design domain based on physical design The design variables in the model are reconstructed using piecewise functions to remove the portion of pseudo-density less than the reconstruction threshold in the additive manufacturing of reinforced structures of continuous fiber reinforced composite materials.

[0040] Step S2-12: Determine whether the optimization meets the outer loop convergence condition. If not, return to step S2-2. If it does, stop the iteration and obtain the final stiffened structure topology distribution and fiber direction distribution data according to the corresponding design variables.

[0041] A further preferred approach involves performing dynamic nonlinear dynamic analysis in step S2-3, which includes solving the governing equations:

[0042]

[0043] in This is the matrix of design variables mapped from the B-spline parameter space to the physical design domain; , and These represent the mass matrix, damping matrix, and stiffness matrix of the reinforced structure manufactured by additive manufacturing of continuous fiber reinforced composite materials. , and They are respectively The acceleration vector, velocity vector, and displacement vector of the continuously fiber-reinforced composite additive manufacturing stiffened structure at any given time; for Dynamic loads that constantly act on additively manufactured stiffened structures of continuous fiber-reinforced composite materials; This represents the number of analysis steps in the kinetic analysis; the subscript D indicates that the corresponding parameter is a result of the kinetic analysis. For the time steps corresponding to the dynamic analysis, a total of That moment.

[0044] A further preferred solution, in steps S2-4, is based on the formula...

[0045]

[0046] exist Uniformly spaced extraction in each dynamic analysis step Calculation of displacement field at each time step and equivalent static load ;in The linear stiffness matrix for additively manufactured stiffened structures from continuous fiber-reinforced composite materials, where the subscript L indicates linear static analysis. This indicates the extract from the results of the dynamic analysis. Displacement vector of continuously fiber-reinforced composite additive manufacturing reinforced structure at any time; The selected moment for calculating the equivalent static load.

[0047] Further optimization, in steps S2-9, involves constructing a multi-condition optimization model as follows:

[0048]

[0049] in, To optimize for multiple operating conditions, Let be the structural compliance under the s-th equivalent static load condition; The weights under the s-th equivalent static load condition of Power; for abbreviation, For linear analysis of the displacement field, for Abbreviation; Volumetric reinforcement structure for additive manufacturing of continuous fiber reinforced composite materials Design the domain volume for physics; , and This is the set minimum value; For local fiber orientation constraint This represents the fiber orientation angle at the y-th finite element mesh. This represents the tangent direction angle of the skeleton line closest to the y-th finite element mesh; and All are dimensional constraints, among which For the first The pseudo-density value at each finite element mesh, For the first The pseudo-density value at each finite element mesh, The finite element mesh index represents the material growth region. The finite element mesh index represents the material removal region. This is a pseudo-density lower limit value; and The sets of element indices for material growth and removal regions are represented as follows:

[0050]

[0051] in For the l-th finite element mesh region, Let K be the pseudo-density value at the l-th finite element mesh, and K be the physical design domain. The number of finite element meshes in the data. Reinforce the target area; The set pseudo-density threshold for material growth, The pseudo-density in the domain is less than The cell index will be added to the cell index set of the material growth region. ; To remove the pseudo-density threshold set for the material, The pseudo-density outside the domain is greater than or equal to The cell index will be added to the material removal area cell index set. ; This is the lower limit value of the pseudo-density control parameter. For B-spline parameter space middle The pseudo-density control parameters at that location, For B-spline parameter space middle Fiber orientation control parameters at the location.

[0052] A further preferred solution, the specific process of step S3 is as follows:

[0053] Step S3-1, for the physical design domain Divide the grid into a reconstructed mesh for continuous path planning;

[0054] Step S3-2: Based on the mapping relationship between the coordinates of the reconstructed mesh center point in the physical design domain and the coordinates in the B-spline parameter space, adjust the B-spline control parameters. and Mapping this onto the reconstructed mesh yields a representation of the final stiffened structure's topological distribution and fiber orientation in actual physical space. and ,in This is pseudo-density data. This is fiber orientation data.

[0055] A further preferred solution, the specific process of step S4 is as follows:

[0056] Step S4-1: Based on the pre-defined fiber stacking direction vector field G, solve the Poisson equation. Obtain scalar field ,in For the Laplace operator, For divergence operators;

[0057] Step S4-2: Based on the fiber orientation data obtained through optimization Perform a cross product operation with the fiber stacking direction vector field G to obtain the generating vector direction. By solving the Poisson equation Obtain scalar field ;

[0058] Step S4-3: Scalar field obtained from steps S4-1 and S4-2 and The intersection of the scalar field contour lines is obtained as multiple continuous fiber paths;

[0059] Step S4-4: For the multiple continuous paths obtained in step S4-3, use Eulerian graphs to perform continuous path planning, which will be used as the final printing path.

[0060] Step S4-5: Calculate the local curvature of the obtained printing path, where the first printing speed is set for paths with curvature above the curvature threshold, and the second printing speed is set for the remaining paths, where the second printing speed is higher than the first printing speed.

[0061] Beneficial effects:

[0062] The present invention has the following beneficial effects:

[0063] 1. This invention constructs an equivalent static load model for dynamic impact loads, enabling efficient modeling and optimization of the impact response of continuously fiber-reinforced composite additive manufacturing reinforced structures. It solves the problems in existing designs for continuously fiber-reinforced composite additive manufacturing reinforced structures, particularly in handling material anisotropy caused by fiber orientation and the dynamic response introduced by impact load conditions. This provides an effective technical means for designing continuously fiber-reinforced composite additive manufacturing reinforced structures under dynamic conditions.

[0064] 2. By introducing B-spline functions to perform unified parameterized modeling of the pseudo-density field of macroscopic topological distribution and the microscopic fiber orientation field, the number of design variables is effectively reduced, and automatic smoothing and continuous control of the parameter field are achieved. This avoids post-processing operations such as convolution filtering on fiber orientation in traditional methods, and significantly improves the computational efficiency and stability of large-scale structures in the optimization process.

[0065] 3. The structural skeleton line is extracted by structural erosion and center refinement algorithm. Combined with the stiffening stacking direction and target size features, the target size and droop angle constraints are introduced. The local tangent direction of the skeleton line is analyzed to further smooth the fiber direction and generate a fiber direction field that adapts to the stiffening topological boundary and stiffening forming direction.

[0066] 4. This invention maps the B-spline parameter field to the reconstructed mesh to achieve a continuous expression of the structural topology and fiber orientation in physical space. Combined with a vector field-driven path planning algorithm, it forms a strategy for connecting contour lines and Euler graph paths of multiple paths, ensuring that the fiber path is continuous and printable in physical space and guaranteeing the feasibility of structural manufacturing.

[0067] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0068] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0069] Figure 1 This is a flowchart illustrating the method of an embodiment of this application;

[0070] Figure 2 This is a schematic diagram of the physical design domain, loads, and boundary conditions of the cantilever beam structure in the embodiments of this application;

[0071] Figure 3 The following are the optimization results of pseudo density and fiber orientation angle design variables in the B-spline parameter space in the embodiments of this application; (a) optimization result of pseudo density in the B-spline parameter space, (b) optimization result of fiber orientation angle in the B-spline parameter space;

[0072] Figure 4 This represents the final optimization result of the embodiments of this application in the actual physical domain;

[0073] Figure 5 This is a schematic diagram of the continuous printing path and printing speed of an embodiment of this application. (a) is the printing path of the wall panel, and (b) is the printing path of the reinforced structure. Detailed Implementation

[0074] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0075] The impact-resistant design method for additive manufacturing reinforced structures of continuous fiber reinforced composite materials provided in this embodiment solves the problem that traditional continuous fiber design methods based on static loads are difficult to apply due to the complex nonlinear dynamic response caused by low-speed impact loads. It realizes the impact-resistant optimization design and manufacturing of additive manufacturing reinforced structures of continuous fiber reinforced composite materials.

[0076] This embodiment uses a multi-point support structure as an example. The overall length, width, and height of the reinforced wall panel structure are 120mm × 120mm × 8mm. The four bottom corners are fixed, and a dynamic load is applied to the center of the bottom to simulate complex dynamic loads. The wall panels are outside the design domain and are 1mm thick, laid in a symmetrical ply direction. The upper part of the panel is reinforced with 7mm of stiffener. A robotic arm-based additive manufacturing system is used to form the continuous fiber-reinforced structure on the panel.

[0077] like Figure 1 As shown, the impact-resistant design method for the additive manufacturing of reinforced structures using continuous fiber reinforced composite materials includes the following steps:

[0078] Step S1: Divide the physical design domain in the three-dimensional model of the additive manufacturing reinforced structure of continuous fiber reinforced composite material. And map the physical design domain to the B-spline parameter space. Define design variables that reflect the macroscopic topological distribution and microscopic fiber orientation of continuous fiber reinforced composite materials, and characterize these design variables using B-spline parameterization; wherein a pseudo-density field is defined. Representing the macroscopic topological distribution of a material, the angle between the fiber direction and the specified principal direction is defined, i.e., the fiber direction field. Representing the microfiber orientation, the combined representation of the two types of design variables is as follows: The B-spline control parameters, which characterize the distribution of the two types of variable fields, are used as the final design variable matrix for optimization. ,in To characterize the pseudo-density field The B-spline control parameter matrix of the distribution. To characterize the fiber orientation field The B-spline control parameter matrix of the distribution.

[0079] The specific process of step S1 is as follows:

[0080] Step S1-1: Divide the physical design domain in the three-dimensional model of the additive manufacturing reinforced structure of continuous fiber reinforced composite material according to the design requirements. ,like Figure 2 As shown. The physical design domain is mapped to the B-spline parameter space according to the size range of the physical design domain. This process is existing technology in this field.

[0081] Step S1-2, in the B-spline parameter space Inside, along and Construct B-spline basis functions for each direction;

[0082] in The recursive formula for the B-spline basis functions in the direction is:

[0083] (1)

[0084] in For along The direction of the first 0th-order B-spline basis functions for each node To characterize the B-spline parameter space along Direction parameter variable, , , and Along The first direction is uniformly distributed , , and The coordinates of each node. For B-spline parameter space Middle The number of nodes that are uniformly distributed in the direction. , Along The direction of the first Each node order and B-order spline basis functions, For along The direction of the first Each node B-order spline basis functions, express The order of the B-spline basis functions in the direction.

[0085] The recursive formula for the B-spline basis functions in the direction is:

[0086] (2)

[0087] in For along The direction of the first 0th-order B-spline basis functions for each node To characterize the B-spline parameter space along Direction parameter variable, , , and Along The first direction is uniformly distributed , , and The coordinates of each node. For B-spline parameter space Middle The number of nodes that are uniformly distributed in the direction. , Along The direction of the first Each node order and B-order spline basis functions, For along The direction of the first Each node B-order spline basis functions, express The order of the B-spline basis functions in the direction.

[0088] Steps S1-3: Establish the pseudo-density and fiber orientation B-spline parameter field based on the B-spline basis function to obtain the optimization design variable matrix. The formulas can be expressed as follows:

[0089] (3)

[0090] in For pseudo-density field exist The pseudo density value at that location, For fiber orientation field exist The fiber orientation value at that location, and For B-spline parameter space middle The pseudo-density control parameters at that location, For B-spline parameter space middle The fiber orientation control parameters at that location. (From...) Pseudo-density control parameters The matrix formed by the arrangement represents the pseudo-density field. B-spline control parameter matrix of distribution ,Depend on fiber orientation control parameters The matrix formed by the arrangement represents the fiber orientation field. B-spline control parameter matrix of distribution .

[0091] Step S2: Conduct impact optimization design based on the equivalent static load method for the additive manufacturing of reinforced structures of continuous fiber reinforced composite materials to obtain the final topological distribution and fiber orientation distribution of the reinforced structure.

[0092] The core of the equivalent static load method is to transform the transient dynamic response into a series of equivalent static optimization problems. The equivalent solution of dynamic characteristics is achieved by alternately executing the inner and outer loops. The outer loop performs dynamic nonlinear dynamic analysis to extract the structural displacement response, while the inner loop constructs the equivalent static load and optimizes the topology and fiber orientation of the stiffened structure and updates the design variables under the equivalent static load. After the two-layer loop iteration converges, the coordinated optimization of the topology and fiber orientation of the stiffened structure under impact load can be achieved.

[0093] In this embodiment, an impact-resistant optimization design based on the equivalent static load method is carried out on the wall panel stiffening structure to obtain the final distribution of the stiffening structure topology and fiber direction in the B-spline parameter space.

[0094] In this embodiment, the specific process of step S2 is as follows:

[0095] Step S2-1: Initialize the design variable matrix , To characterize the pseudo-density field The B-spline control parameter matrix of the distribution. To characterize the fiber orientation field The B-spline control parameter matrix of the distribution is set, and the target volume ratio is defined. It is 0.3.

[0096] Step S2-2: Physical design domain Perform finite element mesh generation and assign design variables and From the B-spline parameter space Mapping to the physical design domain Used for numerical calculations in the physical design domain The corresponding design variables are represented as follows: and .

[0097] Next, the load condition for optimization is calculated through steps S2-3 and S2-4, which is represented by the equivalent static load:

[0098] Step S2-3, in the physical design domain In this study, the finite element method was used to conduct dynamic nonlinear dynamic analysis on a reinforced wall panel structure. The governing equations for the solution are as follows:

[0099] (4)

[0100] in This is the matrix of design variables mapped from the B-spline parameter space to the physical design domain; , and These are the mass matrix, damping matrix, and stiffness matrix of the reinforced wall panel structure, respectively. , and They are respectively The acceleration vector, velocity vector, and displacement vector of the stiffened wall panel structure at any given moment; for Dynamic loads that constantly act on the wall panel stiffening structure; This represents the number of analysis steps in the kinetic analysis; the subscript D indicates that the corresponding parameter is a result of the kinetic analysis. For the time steps corresponding to the dynamic analysis, a total of That moment.

[0101] Step S2-4: Based on the kinetic analysis results obtained in step S2-3, in Uniformly spaced extraction in each dynamic analysis step Calculation of displacement field at each time step and equivalent static load :

[0102] (5)

[0103] in This is the linear stiffness matrix of the panel-reinforced structure. The subscript L indicates linear static analysis. This indicates the extract from the results of the dynamic analysis. The displacement vector of the stiffened wall panel structure at any given moment; For the selected time moment used to calculate the equivalent static load, a total of That moment.

[0104] Then, the optimization constraint range is determined through steps S2-5 and S2-6:

[0105] Step S2-5: Physical design domain The structural skeleton lines are extracted using a structural erosion and center refinement algorithm and used as a reference for structural stiffening dimension constraints. This process is existing technology in this field.

[0106] Step S2-6: Based on the structural skeleton lines, introduce cylindrical regions with diameter R and height H at each skeleton line point, where the height direction of the cylinder coincides with the normal direction of the plane containing the skeleton line, thereby obtaining the target stiffening region of the wall panel stiffening structure. , represented as:

[0107] (6)

[0108] in Let K be the l-th finite element mesh region, and K be the physical design domain. The number of finite element meshes in the data; Using skeleton lines and points A cylindrical region with center R, diameter R, and height H. For structural skeleton lines, To extract the area of ​​the structural skeleton line, express The union of .

[0109] The target reinforced region is the material growth region during the optimization process, while the remaining physical design domains are material removal regions.

[0110] Step S2-7: Based on design variables The physical design domain is calculated using the SOMP material interpolation model. The element elasticity matrix and element stiffness matrix of all finite element meshes are obtained, and then assembled to obtain the overall stiffness matrix of the wall panel stiffened structure. This process is existing technology in this field.

[0111] Step S2-8: Based on the equivalent static load obtained in step S2-4 and the overall structural stiffness matrix obtained in step S2-7, perform finite element analysis of the structure to obtain the structural displacement response under the corresponding equivalent static load condition. And structural flexibility.

[0112] Step S2-9: Based on the multi-condition analysis results, construct a multi-condition optimization model, which is expressed as follows:

[0113] (7)

[0114] in, To optimize for multiple operating conditions, To determine the structural compliance under the s-th equivalent static load condition extracted based on the analysis results of steps S2-8, a logarithm is taken here to reduce the impact of the difference between the objective function and constraint values ​​on the optimization results. The weights under the s-th equivalent static load condition of This embodiment uses proportional weights, with the weighting index being... Take 2; Linear stiffness matrix of a wall panel reinforced structure abbreviation, For linear analysis of the displacement field, Equivalent static load Abbreviation; For the volume of the reinforced wall panel structure, Design the domain volume for physics; , and The minimum value is set to relax the constraints and ensure the convergence of the optimization. In this embodiment, it is set to 0.0001. For local fiber orientation constraint This represents the fiber orientation angle at the y-th finite element mesh. This represents the tangent direction angle of the skeleton line closest to the y-th finite element mesh. This value is calculated based on the skeleton line point coordinate sequence of the structural skeleton line obtained in step S2-5. and All of these are dimensional constraints used to control the growth and removal of local structural regions within the structure. For the first The pseudo-density value at each finite element mesh, For the first The pseudo-density value at each finite element mesh, The finite element mesh index represents the material growth region. The finite element mesh index represents the material removal region. This is a pseudo-density lower limit value; and The sets of element indices for material growth and removal regions are represented as follows:

[0115] (8)

[0116] in For the l-th finite element mesh region, Let K be the pseudo-density value at the l-th finite element mesh, and K be the physical design domain. The number of finite element meshes in the data. The target reinforced area obtained in step S2-6; The set pseudo-density threshold for material growth, i.e. The pseudo-density in the domain is less than The cell index will be added to the cell index set of the material growth region. ; Remove the pseudo-density threshold set for the material, i.e. The pseudo-density outside the domain is greater than or equal to The cell index will be added to the material removal area cell index set. ; The lower limit value for the pseudo-density control parameter is 0.001 in this embodiment. For B-spline parameter space middle The pseudo-density control parameters at that location, For B-spline parameter space middle Fiber orientation control parameters at the location.

[0117] Step S2-10: Solve the multi-condition optimization model using the MMA optimization algorithm and update the design variables; determine whether the optimization meets the inner loop convergence condition, that is, whether the set maximum inner loop iteration step has been reached. In this work, the maximum inner loop iteration step is set to 6; if it does not meet the condition, return to step S2-4 to continue iterative optimization; if it does meet the condition, end the inner loop and proceed to the next step.

[0118] Step S2-11: Design the domain based on the physical design The design variables in the model are reconstructed using piecewise functions to remove the portion of the stiffened wall panel structure where the pseudo-density is less than the reconstruction threshold; the piecewise function is:

[0119] (9)

[0120] in In this embodiment, the reconstruction threshold is set to 0.3. The pseudo-density variable is the reconstructed value, and K is the physical design domain. The number of finite element meshes in the model.

[0121] Step S2-12: Determine whether the optimization satisfies the outer loop convergence condition. In this invention, the design variable matrix obtained from two adjacent outer loop steps is taken. In this process, the proportion of design variables with differences greater than the set value to the total number of design variables is used as the judgment criterion. If the proportion is less than the set criterion, it is considered to have converged, the iteration stops, and the final topological distribution and fiber direction distribution data of the stiffened structure are obtained according to the corresponding design variables; otherwise, the process returns to step S2-2.

[0122] Step S3: For the physical design domain Divide the mesh for continuous path planning, such as a triangular mesh (two-dimensional problem) or a tetrahedral mesh (three-dimensional problem). It should be noted that the reconstructed mesh here is different from the finite element mesh used for numerical calculation in step S2.

[0123] Based on the reconstructed mesh center point in the physical design domain Coordinates in B-spline parameter space The mapping relationship of the coordinate system will design variables. and Mapping this onto the reconstructed mesh yields a representation of the final stiffened structure's topological distribution and fiber orientation in actual physical space; where the pseudo-density data is an M-row, 1-column vector. The fiber orientation data is an M-row, 1-column vector. M represents the number of reconstructed meshes, which corresponds one-to-one with the reconstructed mesh cell numbers; the final topology is as follows: Figure 4 As shown.

[0124] Then, during the manufacturing process, a continuous path is obtained through step S4.

[0125] Step S4: Based on the representation of the stiffened structure topology and fiber orientation distribution in actual physical space obtained in Step S3, a continuous path generation algorithm based on vector fields is used to generate a continuous path in one stroke. The generated continuous path is as follows: Figure 5 As shown.

[0126] Step S4 is as follows:

[0127] Step S4-1: Define the direction perpendicular to the plane containing the stiffened structure as the fiber stacking direction vector field G, and obtain the scalar field by solving the Poisson equation. The Poisson equation is: , For the Laplace operator, For divergence operators;

[0128] Step S4-2: Based on the fiber orientation data obtained through optimization Perform a cross product operation with the fiber stacking direction vector field G to obtain the generating vector direction. And its scalar field is obtained by solving the Poisson equation. The Poisson equation is: ;

[0129] Step S4-3: Scalar field obtained from steps S4-1 and S4-2 and The intersection of the contour lines of the scalar field is obtained, which is the multi-segment continuous fiber path;

[0130] Step S4-4: For the multiple continuous fiber paths obtained in step S4-3, use Euler graphs to plan continuous paths, which will then serve as the final printing paths.

[0131] Step S4-5: Calculate the local curvature of the obtained printing path. Set a lower printing speed of 2 mm / min for paths with curvature above the curvature threshold of 0.1, and set a higher printing speed of 6 mm / min for the remaining paths.

[0132] Based on the optimized design and the resulting continuous printing path, a robotic arm-based additive manufacturing system was used to continuously reinforce the wall panel with fiber, ultimately forming the component. Testing showed that this structure exhibited approximately 30% better impact resistance under low-speed impact loads compared to traditional design methods, with a continuous and uninterrupted fiber path and excellent surface quality, validating the effectiveness and feasibility of this method.

[0133] In summary, this invention employs an equivalent static load method based on B-spline parameterization for impact topology optimization of continuous fiber additive manufacturing composite structures. It fully considers the influence mechanism of dynamic impact loads on structural response, overcoming the problem that traditional continuous fiber design and manufacturing methods based on static loads are difficult to apply to dynamic conditions. Furthermore, by using B-spline parameter fields to parameterize the design variables, smooth and continuous fiber distribution results are efficiently obtained, improving the manufacturability of the formed prototypes. Ultimately, this achieves an improvement in the impact resistance of continuous fiber reinforced composite structures.

[0134] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for impact-resistant design of additively manufactured reinforced structures using continuous fiber reinforced composite materials, characterized in that: Includes the following steps: Step S1: Divide the physical design domain in the three-dimensional model of the additive manufacturing reinforced structure of continuous fiber reinforced composite material. And map the physical design domain to the B-spline parameter space. Define design variables that reflect the macroscopic topological distribution and microscopic fiber orientation of continuous fiber reinforced composite materials, and characterize the design variables using B-spline parameterization. Define pseudo-density field Representing the macroscopic topological distribution of the material, defining the fiber orientation field. To represent the micro-fiber orientation, the B-spline control parameters used to characterize the pseudo-density field and fiber orientation field are used as the final optimization design variable matrix. Design variables To characterize the pseudo-density field The B-spline control parameter matrix of the distribution, design variables To characterize the fiber orientation field The B-spline control parameter matrix of the distribution; Step S2: Conduct impact optimization design based on the equivalent static load method for the additive manufacturing stiffened structure of continuous fiber reinforced composite material to obtain the final topology distribution and fiber orientation distribution of the stiffened structure. Equivalent solutions to dynamic characteristics are achieved by alternately executing inner and outer loops. The outer loop performs dynamic nonlinear dynamic analysis to extract the structural displacement response, while the inner loop constructs the equivalent static load and optimizes the topology and fiber orientation of the stiffened structure and updates the design variables under the equivalent static load. The constructed multi-condition optimization model is as follows: To optimize for multiple operating conditions, Let be the structural compliance under the s-th equivalent static load condition; The weights under the s-th equivalent static load condition of Power; for abbreviation, For linear analysis of the displacement field, for Abbreviation; Volumetric reinforcement structure for additive manufacturing of continuous fiber reinforced composite materials Design the domain volume for physics; , and This is the set minimum value; For local fiber orientation constraint This represents the fiber orientation angle at the y-th finite element mesh. This represents the tangent direction angle of the skeleton line closest to the y-th finite element mesh; and All are dimensional constraints, among which For the first The pseudo-density value at each finite element mesh, For the first The pseudo-density value at each finite element mesh, The finite element mesh index represents the material growth region. The finite element mesh index represents the material removal region. This is a pseudo-density lower limit value; and These represent the sets of cell indices for the material growth and removal regions, respectively. Step S3: For the physical design domain A reconstructed mesh is generated for continuous path planning, based on the coordinates of the reconstructed mesh center point in the physical design domain and the B-spline parameter space. The mapping relationship of the coordinate system will design variables. and Mapping this onto the reconstructed mesh yields the final representation of the stiffened structure's topological distribution and fiber orientation in actual physical space. Step S4: Based on the representation of the topological distribution of the stiffened structure and the fiber orientation distribution in the actual physical space obtained in Step S3, a continuous path generation algorithm based on vector field is used to generate a continuous path in one stroke.

2. The impact-resistant design method for a reinforced structure manufactured using additive manufacturing of continuous fiber reinforced composite materials according to claim 1, characterized in that: The specific process of step S1 is as follows: Step S1-1: Divide the physical design domain in the solid structure. , physical design domain Mapping to B-spline parameter space ; Step S1-2, in the B-spline parameter space Inside, along and Construct B-spline basis functions for each direction; Steps S1-3: Establish the pseudo-density and fiber orientation B-spline parameter field based on the B-spline basis function to obtain the optimization design variable matrix. .

3. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 2, characterized in that: In step S1-2, The recursive formula for the B-spline basis functions in the direction is: in For along The direction of the first 0th-order B-spline basis functions for each node To characterize the B-spline parameter space along Direction parameter variable, , , and Along The first direction is uniformly distributed , , and The coordinates of each node. For B-spline parameter space Middle The number of nodes that are uniformly distributed in the direction. , Along The direction of the first Each node order and B-order spline basis functions, For along The direction of the first Each node B-order spline basis functions, express The order of the B-spline basis functions in the direction; The recursive formula for the B-spline basis functions in the direction is: in For along The direction of the first 0th-order B-spline basis functions for each node To characterize the B-spline parameter space along Direction parameter variable, , , and Along The first direction is uniformly distributed , , and The coordinates of each node. For B-spline parameter space Middle The number of nodes that are uniformly distributed in the direction. , Along The direction of the first Each node order and B-order spline basis functions, For along The direction of the first Each node B-order spline basis functions, express The order of the B-spline basis functions in the direction.

4. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 3, characterized in that: In steps S1-3, the formula for the B-spline parameter field is: in For pseudo-density field exist The pseudo density value at that location, For fiber orientation field exist The fiber orientation value at that location, and For B-spline parameter space middle The pseudo-density control parameters at that location, For B-spline parameter space middle Fiber orientation control parameters at the location; by Pseudo-density control parameters The matrix formed by the arrangement represents the pseudo-density field. B-spline control parameter matrix of distribution ,Depend on fiber orientation control parameters The matrix formed by the arrangement represents the fiber orientation field. B-spline control parameter matrix of distribution .

5. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 1, characterized in that: The specific process of step S2 is as follows: Step S2-1: Initialize the design variable matrix And set the target body ratio ; Step S2-2: Physical design domain Perform finite element mesh generation and assign design variables and From the B-spline parameter space Mapping to the physical design domain In the physical design domain Design variables are represented as and ; Step S2-3, in the physical design domain In this study, the finite element method was used to conduct dynamic nonlinear dynamic analysis on the additive manufacturing of reinforced structures from continuous fiber reinforced composite materials. Step S2-4: Calculate the equivalent static load based on the dynamic analysis results obtained in step S2-3; Step S2-5: Physical design domain Extract the structural skeleton lines; Steps S2-6: Based on the structural skeleton lines, introduce cylindrical regions with diameter R and height H at each skeleton line point, where the height direction of the cylinder coincides with the normal direction of the plane containing the skeleton line, thereby obtaining the target stiffened region. ; Step S2-7: Design the domain based on the physical design The design variables in the model are calculated using the SOMP material interpolation model to determine the physical design domain. The element elasticity matrix and element stiffness matrix of all finite element meshes are obtained and assembled to obtain the overall stiffness matrix of the structure; Step S2-8: Based on the equivalent static load obtained in step S2-4 and the overall structural stiffness matrix obtained in step S2-7, perform finite element analysis of the structure to obtain the structural displacement response and structural compliance under the corresponding equivalent static load conditions. Step S2-9: Based on the multi-condition analysis results, construct a multi-condition optimization model; Step S2-10: Solve the multi-condition optimization model using the MMA optimization algorithm and update the design variables; determine whether the optimization meets the inner loop convergence condition. If not, return to step S2-4 to continue iterative optimization; if it does, end the inner loop and proceed to the next step. Step S2-11: Design domain based on physical design The design variables in the model are reconstructed to remove the part of pseudo-density less than the reconstruction threshold in the additive manufacturing of stiffened structures of continuous fiber reinforced composite materials. Step S2-12: Determine whether the optimization meets the outer loop convergence condition. If not, return to step S2-2. If it does, stop the iteration and obtain the final stiffened structure topology distribution and fiber direction distribution data according to the corresponding design variables.

6. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 5, characterized in that: Step S2-3 involves dynamic nonlinear analysis, specifically solving the governing equations: in This is the matrix of design variables mapped from the B-spline parameter space to the physical design domain; , and These represent the mass matrix, damping matrix, and stiffness matrix of the reinforced structure manufactured by additive manufacturing of continuous fiber reinforced composite materials. , and They are respectively The acceleration vector, velocity vector, and displacement vector of the continuously fiber-reinforced composite additive manufacturing stiffened structure at any given time; for Dynamic loads that constantly act on additively manufactured stiffened structures of continuous fiber-reinforced composite materials; This represents the number of analysis steps in the kinetic analysis. The subscript D indicates that the corresponding parameter is a result of dynamic analysis; For the time steps corresponding to the dynamic analysis, a total of That moment.

7. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 6, characterized in that: In step S2-4, according to the formula exist Uniformly spaced extraction in each dynamic analysis step Calculation of displacement field at each time step and equivalent static load ;in The linear stiffness matrix for additively manufactured stiffened structures from continuous fiber-reinforced composite materials, where the subscript L indicates linear static analysis. This indicates the extract from the results of the dynamic analysis. Displacement vector of continuously fiber-reinforced composite additive manufacturing reinforced structure at any time; The selected moment for calculating the equivalent static load.

8. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 7, characterized in that: In the constructed multi-condition optimization model, and Represented as: in For the l-th finite element mesh region, Let K be the pseudo-density value at the l-th finite element mesh, and K be the physical design domain. The number of finite element meshes in the data. Reinforce the target area; The set pseudo-density threshold for material growth, The pseudo-density in the domain is less than The cell index will be added to the cell index set of the material growth region. ; To remove the pseudo-density threshold set for the material, The pseudo-density outside the domain is greater than or equal to The cell index will be added to the material removal area cell index set. ; This is the lower limit value of the pseudo-density control parameter. For B-spline parameter space middle The pseudo-density control parameters at that location, For B-spline parameter space middle Fiber orientation control parameters at the location.

9. The impact-resistant design method for a reinforced structure manufactured by additive manufacturing of continuous fiber reinforced composite materials according to claim 1, characterized in that: The specific process of step S3 is as follows: Step S3-1, for the physical design domain Divide the grid into a reconstructed mesh for continuous path planning; Step S3-2: Based on the mapping relationship between the coordinates of the reconstructed mesh center point in the physical design domain and the coordinates in the B-spline parameter space, adjust the B-spline control parameters. and Mapping this onto the reconstructed mesh yields a representation of the final stiffened structure's topological distribution and fiber orientation in actual physical space. and ,in This is pseudo-density data. This is fiber orientation data.

10. The impact-resistant design method for a continuous fiber reinforced composite additive manufacturing reinforced structure according to claim 9, characterized in that: The specific process of step S4 is as follows: Step S4-1: Based on the pre-defined fiber stacking direction vector field G, solve the Poisson equation. Obtain scalar field ,in For the Laplace operator, For divergence operators; Step S4-2: Based on the fiber orientation data obtained through optimization Perform a cross product operation with the fiber stacking direction vector field G to obtain the generating vector direction. By solving the Poisson equation Obtain scalar field ; Step S4-3: Scalar field obtained from steps S4-1 and S4-2 and The intersection of the scalar field contour lines is obtained as multiple continuous fiber paths; Step S4-4: For the multiple continuous paths obtained in step S4-3, use Eulerian graphs to perform continuous path planning, which will be used as the final printing path. Step S4-5: Calculate the local curvature of the obtained printing path, where the first printing speed is set for paths with curvature above the curvature threshold, and the second printing speed is set for the remaining paths, where the second printing speed is higher than the first printing speed.

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