Topological optimization method and device for continuous fiber periodic unit cell structure

Abstract

The invention discloses a topological optimization method and device for a continuous fiber periodic unit cell structure, and relates to the technical field of continuous fiber reinforced composite 3D printing. Determining the configuration of the selected periodic unit cell structure; constructing a feature component in a design domain of a periodic unit cell, performing projection on a fiber angle to calculate an elastic matrix, and determining a weight coefficient in an overlapping region based on a component level set function so as to solve an equivalent elastic matrix; solving the equivalent elastic property of the periodic unit cells of the fiber reinforced composite material; constructing a unit constitutive matrix in an interpolation format; constructing a periodic unit cell structure topological optimization model by taking the flexibility as a target function; calculating the derivative of the flexibility about the design variable formed by the artificial density of the alternative unit cell material, and carrying out sensitivity filtering treatment; optimization iterative analysis is carried out under different working conditions, and the convergence degree of an optimization result is evaluated by using an inequality relation. The problem of how to further improve the mechanical performance of the periodic unit cell structure is solved.

Description

Technical Field

[0001] This application relates to the technical field of 3D printing of continuous fiber reinforced composites, and particularly to a topology optimization method and device for continuous fiber periodic unit cell structures. Background Art

[0002] Periodic unit cell structures have excellent mechanical properties such as high specific stiffness, high specific strength, energy absorption and impact resistance, and have been increasingly widely used in engineering fields such as aerospace, power machinery, and medical devices. With the increasing maturity of additive manufacturing technology, it endows complex periodic unit cell structures with highly flexible design and forming degrees of freedom. With the emergence of 3D printing continuous fiber composite material technology, combining the excellent mechanical properties of composite materials and the geometric characteristics of periodic unit cell structures can further reduce the structural weight and improve the structural performance. Different from the optimization technology of periodic unit cell structures under isotropy, due to the introduction of continuous fibers, manufacturing constraints such as printing width and one-stroke printing need to be considered. Currently, the common types of continuous fiber periodic honeycomb structures are hexagons, rhombuses, rectangles, and circles, etc.

[0003] Since the current common filling configurations of continuous fiber periodic structures are single, mainly concentrated on several common types of geometric shapes, they cannot be combined with topology optimization. This limits the diversity of structural design and cannot meet the special requirements for structural performance in some special application scenarios.

[0004] Therefore, how to solve the problem of the single filling configuration of the current common continuous fiber periodic structures to further improve the mechanical properties of the periodic unit cell structures and expand their design diversity is an urgent problem to be solved currently. Summary of the Invention

[0005] In the embodiments of this application, by providing a topology optimization method for continuous fiber periodic unit cell structures, the problem of how to further improve the mechanical properties of periodic unit cell structures and expand their design diversity and innovation is solved.

[0006] In a first aspect, an embodiment of the present application provides a topology optimization method for a continuous fiber periodic unit cell structure, which determines the configuration of the selected periodic unit cell structure according to preset rules; constructs feature components in the design domain of the periodic unit cell through a feature-driven method, projects the fiber angle by using a fixed grid response to calculate the elastic matrix, and determines the weight coefficient based on the component level set function in the overlapping region to solve the equivalent elastic matrix; uses the energy homogenization method to solve the equivalent elastic properties of the selected fiber-reinforced composite periodic unit cell; uses the discrete unit optimization method to construct an interpolation-form unit constitutive matrix; constructs a topology optimization model of the periodic unit cell structure with compliance as the objective function; calculates the derivative of the compliance with respect to the design variables composed of the artificial density of the alternative unit cell materials, and performs sensitivity filtering; performs optimization iteration analysis under different working conditions, and evaluates the convergence degree of the optimization results by using inequality relations.

[0007] In a possible implementation, the preset rules include: setting the width of all edges in the periodic unit cell structure to a fixed fiber spacing or an even multiple thereof; designing the periodic unit cell structure to conform to the characteristics of an Euler graph, and the number of edges connected to any node in the periodic unit cell structure is even; after any periodic unit cells are combined, all nodes can be connected to each other.

[0008] In a possible implementation, the constructing feature components in the design domain of the periodic unit cell through a feature-driven method, projecting the fiber angle by using a fixed grid response to calculate the elastic matrix, and determining the weight coefficient based on the component level set function in the overlapping region to solve the equivalent elastic matrix includes: extracting a single feature component from the periodic unit cell structure, and describing the single feature component through a component level set function; the expression of the component level set function is: ; where is the component level set function value of the th feature component, is the distance from the point in the design domain of the periodic unit cell to the th feature component, is the radius of the th feature component, is the penalty coefficient; dividing fixed grid cells in the design domain of the periodic unit cell, and using the method of fixed grid response to judge the component level set function value of each feature component in each grid cell to determine whether there is a feature component in the grid cell; if the component level set function value is greater than a preset threshold, it is considered that there is a feature component in the grid cell; if the component level set function value is less than or equal to the preset threshold, it is considered that there is no feature component in the grid cell; for grid cells without an overlapping region, the elastic matrix is expressed as: ; where is the elastic matrix under the overall global coordinates, is the stress-strain relationship under the material coordinates, is the coordinate transformation matrix; the expression of the stress-strain relationship under the material coordinates is: wherein, is the longitudinal elastic modulus, is the transverse elastic modulus, is the transverse Poisson's ratio, is the longitudinal Poisson's ratio, is the in-plane shear modulus; the expression of the coordinate transformation matrix is: wherein, is the angle between the material coordinates of the fiber-reinforced composite material and the overall global coordinates, , is the abscissa of the position where the th characteristic component node is located, is the ordinate of the position where the th characteristic component node is located; for the grid cells with overlapping regions, the weight coefficients are determined according to the level set function values of each characteristic component in the overlapping regions; based on the weight coefficients, the equivalent elastic matrix of the grid cells in the overlapping regions under the material coordinates is calculated; the expression of the equivalent elastic matrix of the grid cells under the material coordinates is: wherein, is the equivalent elastic matrix of the grid cells in the overlapping regions under the material coordinates, is the weight coefficient of the th characteristic component in the overlapping regions, is the elastic matrix of the th characteristic component under the material coordinates.

[0009] In a possible implementation manner, the equivalent elastic properties of the selected periodic unit cell of the fiber-reinforced composite material are solved by using the energy homogenization method, including: within the linear elastic range of the fiber-reinforced composite material, the stress tensor and the strain tensor of the equivalent homogeneous body satisfy Hooke's law: wherein, is the average stress tensor of the periodic unit cell structure, , and are all components of the average stress tensor of the periodic unit cell structure, is the average strain tensor of the periodic unit cell structure, , and are all components of the average strain tensor of the periodic unit cell structure, , , , , and Elements in the equivalent elastic matrix of grid cells that are all overlapping regions in material coordinates, represent symmetric elements.

[0010] In a possible implementation, the discrete unit cell optimization method is used to construct the constitutive matrix of the unit in an interpolation format, including: The expression of the constitutive matrix of the unit in an interpolation format is: ; where, is the constitutive matrix of the unit in an interpolation format, is the artificial density of the th alternative unit cell material in the th grid cell, is the th alternative unit cell material in the th grid cell corresponding to the equivalent elastic matrix, is the number of alternative unit cell materials, penalty factor, is the index of the alternative unit cell material, is the weight function.

[0011] In a possible implementation, constructing a periodic unit cell structure topology optimization model with compliance as the objective function includes: determining design variables, defining the objective function, defining the equilibrium equation, the range of design variables, and defining the constraint function of the periodic unit cell structure; Determining the design variables is determined as: , ; where, is the design variable composed of the artificial density of alternative unit cell materials, is the artificial density of the th material distribution in the th periodic unit cell, is the total number of grid cells; Defining the objective function as: ; where, is the minimum compliance of the periodic unit cell structure, is the overall displacement matrix of the structure, is the nodal load vector, is the overall stiffness matrix of the structure, is the transpose of the overall displacement matrix of the structure; Defining the equilibrium equation as: ; The range of design variables is: ; where, is the minimum value of the design variable composed of the artificial density of alternative unit cell materials; When the filling rate of the periodic unit cell structure is used as a constraint, the constraint function is: ; where, is the filling rate of the periodic unit cell structure, is the volume of the fiber-reinforced composite material used, is the total volume of the design domain of the periodic unit cell, is the maximum packing ratio of the periodic unit cell structure; when the volume fraction of the periodic unit cell structure is used as a constraint, the constraint function is: ; where, is the overall structural volume fraction of the periodic unit cell structure, is the total volume of the structure, is the volume of the th alternative unit cell material, is the total volume of the design domain of the periodic unit cell; when the fiber length during printing is used as a constraint, the constraint function is: ; where, is the length of the fiber in the th periodic unit cell structure,

[0012] In a possible implementation, calculating the derivative of the compliance with respect to the design variables of the artificial density composition of the alternative unit cell materials and performing sensitivity filtering processing includes: The expression for the derivative of the compliance with respect to the design variables of the artificial density composition of the alternative unit cell materials is: ; where, is the compliance of the periodic unit cell structure, is the strain-displacement matrix, is the design domain of the periodic unit cell, is the integral over the design domain of the periodic unit cell, is an unknown term; the sensitivity result after sensitivity filtering processing is: ; where, is the artificial density of the th unit cell material in the grid cell , the convolution operator is the weight coefficient of the grid cell , , ; where, is the filtering radius, is the center distance between the grid cell and the grid cell ; if the packing ratio of the periodic unit cell structure is used as a constraint, the sensitivity of the volume occupied by the non-empty material in the periodic unit cell structure with respect to the artificial density is expressed as: ; where, is the volume occupied by the non-empty material in the periodic unit cell structure.

[0013] In a possible implementation, performing optimization iteration analysis under different working conditions and evaluating the convergence degree of the optimization result by using inequality relations includes: The inequality relation is: ; where is the weight function of all alternative configurations, is the convergence tolerance, and its value ranges from [0.95 to 0.99]; Define the overall structure convergence index as: ; where is the overall structure convergence index, is the total number of converged grid cells, is the total number of grid cells.

[0014] In a second aspect, an embodiment of the present application provides a topology optimization device for a continuous fiber periodic unit cell structure, including: a determination module, configured to determine the configuration of the selected periodic unit cell structure according to a preset rule; a feature component construction module, configured to construct feature components in the design domain of the periodic unit cell by a feature-driven method, calculate the elastic matrix by projecting the fiber angle using a fixed grid response, and determine the weight coefficient based on the component level set function in the overlapping region to solve the equivalent elastic matrix; a solution module, configured to solve the equivalent elastic properties of the selected fiber-reinforced composite periodic unit cell by using the energy homogenization method; a unit constitutive matrix construction module, configured to construct an interpolation-form unit constitutive matrix by using a discrete unit optimization method; a topology optimization model construction module, configured to construct a topology optimization model of the periodic unit cell structure with compliance as the objective function; a sensitivity filtering processing module, configured to calculate the derivative of compliance with respect to the design variables composed of the artificial density of the alternative unit cell materials and perform sensitivity filtering processing; an evaluation module, configured to perform optimization iteration analysis under different working conditions and evaluate the convergence degree of the optimization result by using inequality relations.

[0015] One or more technical solutions provided in the embodiments of the present application have at least the following technical effects: The embodiment of the present application provides a topology optimization method for continuous fiber periodic unit cell structures. According to preset rules, it can quickly and accurately determine the applicable periodic unit cell structure configurations, providing a solid foundation for subsequent composite material design and analysis. In the design domain of the periodic unit cell, feature components are flexibly constructed through a feature-driven method, improving the design freedom and customizability. The fiber angles are projected using a fixed grid response to effectively calculate the elastic matrix, ensuring the accuracy and stability of the calculation results. The weight coefficients of the overlapping regions are determined through the component level set function, and then the equivalent elastic matrix is solved. Using the energy homogenization method, the equivalent elastic properties of the selected fiber-reinforced composite periodic unit cell are accurately solved, providing a reliable basis for the performance evaluation of composite materials. The discrete unit cell optimization method is used to construct an interpolation format unit constitutive matrix, realizing the refined optimization of the periodic unit cell structure, improving the flexibility and accuracy of the optimization, and making the optimization results more in line with actual requirements. With compliance as the objective function, a topology optimization model of the periodic unit cell structure is constructed, providing a clear goal for seeking the optimal structure. By calculating the derivative of compliance with respect to the design variables of the artificial density composition of the alternative unit cell materials and performing sensitivity filtering, the efficiency and stability of the optimization process are improved. Optimization iteration analysis is carried out under different working conditions to ensure the general applicability and reliability of the optimization results. The convergence degree of the optimization results is evaluated using inequality relations, providing a clear basis for judging whether the optimization process is over. It solves the problem of how to solve the single filling configuration of the current common continuous fiber periodic structures, further improving the mechanical properties of the periodic unit cell structure and expanding its design diversity. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for the description in the embodiments of the present application or the prior art. Obviously, the drawings in the following description are some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0017] Figure 1 It is a flowchart of a topology optimization method for continuous fiber periodic unit cell structures provided by an embodiment of the present application; Figure 2 It is a schematic diagram of two common filling configurations of 3D printed continuous fibers provided by an embodiment of the present application as periodic unit cell structures; Figure 3 It is a schematic diagram of component features constructed using movable components provided by an embodiment of the present application; Figure 4 It is a schematic diagram of the boundary conditions for the optimization of the periodic unit cell structure provided by an embodiment of the present application; Figure 5 It is a schematic diagram of the implementation working conditions and dimensions provided by the embodiments of the present application; Figure 6 It is a schematic diagram of the result of the designed continuous fiber periodic unit cell structure provided by the embodiments of the present application; Figure 7 It is a schematic diagram of the 3D printed component optimized based on the continuous fiber periodic unit cell structure provided by the embodiments of the present application; Figure 8 It is a schematic diagram of a topology optimization device for a continuous fiber periodic unit cell structure provided by the embodiments of the present application; Figure 9 It is a schematic diagram of a topology optimization server for a continuous fiber periodic unit cell structure provided by the embodiments of the present application. Detailed implementation manners

[0018] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present application.

[0019] The following explanations are made for some technologies involved in the embodiments of the present application to facilitate understanding. It should be considered that they are only exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described here without departing from the scope and spirit of the present application. Similarly, for the sake of clarity and conciseness, some descriptions of well-known functions and structures are omitted in the following description.

[0020] The embodiments of the present application provide a topology optimization method for a continuous fiber periodic unit cell structure. As Figure 1 shown, this method includes steps S101 to S107. Among them, Figure 1 This is only an execution order shown in the embodiments of the present application and does not represent the only execution order of a topology optimization method for a continuous fiber periodic unit cell structure. In the case where the final result can be achieved, Figure 1 the steps shown can be executed in parallel or reversed.

[0021] S101: Determine the configuration of the selected periodic unit cell structure according to the preset rules.

[0022] The preset rules include: the widths of all edges in the periodic unit cell structure are set to a fixed fiber spacing or an even multiple thereof. The periodic unit cell structure is designed to conform to the properties of an Eulerian graph, and the number of edges connected to any node in the periodic unit cell structure is even. After any combination of periodic unit cells, all nodes can be interconnected.

[0023] Specifically, the periodic unit cell structure is the basic unit that can be repeatedly arranged to form a larger structure. The edges in the periodic unit cell structure refer to the line segments or interfaces connecting various parts of the unit cell structure. Check whether each periodic unit cell structure conforms to the properties of an Eulerian graph, that is, the number of edges connected to any node in the periodic unit cell structure is even. For this purpose, the periodic unit cell structure can be converted into a point-line graph according to the fiber spacing, number all the nodes in the structure, and construct an adjacency matrix between the nodes. By analyzing the adjacency matrix, determine whether the degree of each node is even, so as to confirm whether the periodic unit cell structure is an Eulerian graph. When selecting the periodic unit cell structure, it is necessary to fully ensure the connectivity between unit cells. Ensure that after any combination of periodic unit cells, all nodes can be interconnected, and the degrees of all nodes in the combined structure still remain even, so as to meet the condition that the overall structure can be manufactured in one stroke.

[0024] Figure 2 Schematic diagrams of two common filling configurations of 3D printed continuous fibers provided in the embodiments of the present application as periodic unit cell structures. Figure 2 in (a) and Figure 2 in (b) are both periodic unit cell structures that meet the preset rules.

[0025] S102: Construct feature components through a feature-driven method within the design domain of the periodic unit cell, calculate the elastic matrix by projecting the fiber angle using a fixed grid response, and determine the weight coefficient based on the component level set function in the overlapping region and then solve the equivalent elastic matrix.

[0026] Specifically, since the fiber-reinforced composite material is anisotropic, the overlapping region needs to be processed.

[0027] Constructing feature components through a feature-driven method within the design domain of the periodic unit cell, calculating the elastic matrix by projecting the fiber angle using a fixed grid response, and determining the weight coefficient based on the component level set function in the overlapping region and then solving the equivalent elastic matrix includes: Derive a single feature component from the periodic unit cell structure, and the single feature component is described by the component level set function. The expression of the component level set function is: . Wherein, is the component level set function value of the th feature component, and is the point within the design domain of the periodic unit cell The distance to the th feature component, is the radius of the th feature component, and [[[PENALTY_COEFFICIENT]]] is the penalty coefficient.

[0028] The penalty coefficient controls the slope of the component level set function at the structural boundary, that is, the rate of change of the component level set function value from the inside to the outside of the component. By adjusting the penalty coefficient, the sharpness or blurriness of the boundary can be changed.

[0029] Figure 3 FIG. [[[FIGURE_NUMBER]]] is a schematic diagram of component features constructed using movable components provided by an embodiment of the present application. Figure 3 The left figure in [[[FIGURE_NUMBER]]] is a periodic unit cell structure, Figure 3 and the right figure in [[[FIGURE_NUMBER]]] is the structure after adjusting the nodes by the movable component method. When analyzing the periodic unit cell structure, key node positions are identified from the complex unit cell structure through node extraction techniques. These nodes are the basis for constructing the feature components of the unit cell structure, and they determine the shape, position, and connection method of the feature components. The movable component method is used to construct these feature components. The movable component method is a flexible and effective structural design method that allows adjusting the position, shape, and size of the components during the design process. For a single component feature, a level set function is used for description. Figure 3 The arrow in [[[FIGURE_NUMBER]]] is the fiber printing direction.

[0030] In the design domain of the periodic unit cell, fixed grid cells are divided, and the method of fixed grid response is used to judge the component level set function value of each feature component in each grid cell to determine whether there is a feature component in the grid cell. If the component level set function value is greater than the preset threshold, it is considered that there is a feature component in the grid cell. If the component level set function value is less than or equal to the preset threshold, it is considered that there is no feature component in the grid cell. For grid cells without overlapping regions, the elastic matrix is expressed as: . Wherein, is the elastic matrix in the overall global coordinates, is the stress-strain relationship in the material coordinates, is the coordinate transformation matrix.

[0031] The expression of the stress-strain relationship in the material coordinates is: . Wherein, is the longitudinal elastic modulus, is the transverse elastic modulus, is the transverse Poisson's ratio, is the longitudinal Poisson's ratio, is the in-plane shear modulus.

[0032] The expression of the coordinate transformation matrix is as follows: . Among them, is the angle between the material coordinates of the fiber-reinforced composite material and the overall global coordinates, , is the abscissa of the position where the th characteristic component node is located, is the ordinate of the position where the th characteristic component node is located.

[0033] For the grid cells with overlapping regions, the weight coefficients are determined according to the level set function values of each characteristic component in the overlapping region.

[0034] Based on the weight coefficients, the equivalent elastic matrix of the grid cells in the overlapping region in the material coordinates is calculated.

[0035] The expression of the equivalent elastic matrix of the grid cells in the material coordinates is as follows: . Among them, is the equivalent elastic matrix of the grid cells in the overlapping region in the material coordinates, is the weight coefficient of the th characteristic component in the overlapping region, is the elastic matrix of the th characteristic component in the material coordinates.

[0036] S103: Solve the equivalent elastic properties of the selected periodic unit cell of the fiber-reinforced composite material by using the energy homogenization method.

[0037] Solving the equivalent elastic properties of the selected periodic unit cell of the fiber-reinforced composite material by using the energy homogenization method includes: Within the linear elastic range of the fiber-reinforced composite material, the stress tensor and strain tensor of the equivalent homogeneous body satisfy Hooke's law: . Among them, is the average stress tensor of the periodic unit cell structure, , and are all components of the average stress tensor of the periodic unit cell structure, is the average strain tensor of the periodic unit cell structure, , and are all components of the average strain tensor of the periodic unit cell structure, , , , , and are all elements in the equivalent elastic matrix of the grid cells in the overlapping region in the material coordinates, Represents symmetry elements.

[0038] Specifically, for two-dimensional orthotropic materials , its equivalent elastic matrix contains 4 independent terms. To solve for the equivalent elastic matrix of the grid cells in the material coordinates within the overlapping region, according to the principle of reciprocal elastic strain energy under uniform boundary load conditions, linearly independent test strain fields are applied to the periodic unit cell structure. By calculating the elastic strain energy per unit area corresponding to different working conditions, this energy information can be used to obtain the equivalent elastic matrix.

[0039] S104: Adopt the discrete unit cell optimization method to construct the constitutive matrix of the element in interpolation format.

[0040] Specifically, during the optimization process of the periodic unit cell structure, the goal is to select a suitable configuration of the unit cell structure within the grid cell to minimize the objective function. To achieve this goal, it is necessary to construct the constitutive matrix of the element in interpolation format.

[0041] Adopt the discrete unit cell optimization method to construct the constitutive matrix of the element in interpolation format, including: The expression of the constitutive matrix of the element in interpolation format is: . Wherein, is the constitutive matrix of the element in interpolation format, is the artificial density of the th alternative unit cell material in the th grid cell, is the equivalent elastic matrix corresponding to the th alternative unit cell material in the th grid cell, is the number of alternative unit cell materials, is the penalty factor, is the index of the alternative unit cell material, is the weight function.

[0042] Specifically, the penalty factor is used to adjust the influence degree of the artificial density on the constitutive matrix of the element.

[0043] S105: Construct a topology optimization model of the periodic unit cell structure with compliance as the objective function.

[0044] Construct a topology optimization model of the periodic unit cell structure with compliance as the objective function, including: Determine the design variables, define the objective function, define the equilibrium equation, the range of the design variables, and define the constraint function of the periodic unit cell structure.

[0045] Determine the design variables as: , . Wherein, is the design variable for the artificial density composition of the alternative unit cell materials. is the th artificial density of the material distribution in the

[0046] specifically, the design variable determines the parameters that can be adjusted during the optimization process, thereby affecting the final structural performance.

[0047] Define the objective function as: . Wherein, is the minimum compliance of the periodic unit cell structure, is the overall displacement matrix of the structure, is the nodal load vector, is the overall stiffness matrix of the structure, is the transpose of the overall displacement matrix of the structure.

[0048] Specifically, compliance is the ability of a structure to deform under the action of force. Minimizing compliance means increasing the stiffness of the structure, making it more resistant to deformation caused by external forces. When the structure is subjected to external forces, each node will undergo displacement, and these displacements form the overall displacement matrix of the structure.

[0049] Define the equilibrium equation as: .

[0050] The range of the design variable is: . Wherein, is the minimum value of the design variable for the artificial density composition of the alternative unit cell materials.

[0051] Specifically, the equilibrium equation ensures that the structure is in a state of equilibrium under the action of force. can be set to a non - negative decimal to ensure that there is no completely material - free state during the optimization process.

[0052] When the filling rate of the periodic unit cell structure is used as a constraint, the constraint function is: . Wherein, is the filling rate of the periodic unit cell structure, is the volume of the fiber - reinforced composite material used, is the total volume of the design domain of the periodic unit cell, is the maximum filling rate of the periodic unit cell structure.

[0053] When the volume fraction of the periodic unit cell structure is used as a constraint, the constraint function is: . Wherein, is the overall structural volume fraction of the periodic unit cell structure, is the total volume of the structure, is the volume of the th alternative unit cell material, and is the total volume of the design domain of the periodic unit cell.

[0054] When the fiber length during printing is used as a constraint, the constraint function is: . Among them, is the total length of all fibers, is the th fiber length in the periodic unit cell structure, and is the maximum fiber length.

[0055] S106: Calculate the derivative of the compliance with respect to the design variables of the artificial density composition of the alternative unit cell material, and perform sensitivity filtering.

[0056] Figure 4 is a schematic diagram of the boundary conditions for the optimization of the periodic unit cell structure provided by the embodiments of the present application. Figure 4 The external load in Figure 4 is the nodal load vector in the present application. Figure 4 The blue squares in Figure 4 represent different unit cell types.

[0057] Calculate the derivative of the compliance with respect to the design variables of the artificial density composition of the alternative unit cell material, and perform sensitivity filtering, including: The expression for the derivative of the compliance with respect to the design variables of the artificial density composition of the alternative unit cell material is: . Among them, is the compliance of the periodic unit cell structure, is the strain-displacement matrix, is the design domain of the periodic unit cell, is the integral over the design domain of the periodic unit cell, is the unknown term.

[0058] Specifically, the unknown term can be solved by a material interpolation format, such as the SIMP method.

[0059] The sensitivity result after performing sensitivity filtering is: . Among them, is the artificial density of the th unit cell material in the grid cell , the convolution operator is the weight coefficient of the grid cell , , . Among them, is the filtering radius, is the grid cell and the grid cell is the center distance between them.

[0060] When the filling rate of the periodic unit cell structure is used as a constraint, the sensitivity of the volume occupied by the non-empty material in the periodic unit cell structure with respect to the artificial density is expressed as: . Among them, is the volume occupied by the non-empty material in the periodic unit cell structure.

[0061] S107: Perform optimization iteration analysis under different working conditions, and evaluate the convergence degree of the optimization results using inequality relationships.

[0062] Perform optimization iteration analysis under different working conditions, and evaluate the convergence degree of the optimization results using inequality relationships, including: The inequality relationship is: . Among them, is the weight function of all alternative configurations, is the weight coefficient of the alternative unit cell material, is the convergence tolerance, and its value is [0.95 - 0.99].

[0063] Define the overall structure convergence index as: . Among them, is the overall structure convergence index, is the total number of converged grid cells, is the total number of grid cells.

[0064] Specifically, the present application selects a gradient optimization algorithm such as GCMMA as the solver to perform optimization analysis based on the sensitivity information obtained previously. The convergence rate of the grid cells using the gradient optimization algorithm is greater than 99%, meeting the requirements of the optimization analysis.

[0065] Figure 5 is a schematic diagram of the implementation working conditions and dimensions provided by the embodiment of the present application. Considering the symmetry of the design domain and boundary conditions, the right half of the MBB beam structure (a beam structure model) is selected for optimization. The structural dimensions of the MBB beam are 320mm × 80mm, the unit cell size is 4mm × 4mm, and the design domain is divided into 40 × 20 grids. Figure 5 The midpoint of the upper boundary of the design domain in [] is subjected to a vertical downward external load force, which is the node load vector in the present application, with a magnitude of 1 Newton. The structural target volume fraction is set to 50%. Figure 5 shows the design domain and loading form of the periodic unit cell structure optimization.

[0066] Figure 6 is a schematic diagram of the result of the designed continuous fiber periodic unit cell structure provided by the embodiment of the present application. Select the periodic unit cell structure shown in Figure 2 as the initial design for topology optimization. The optimization result is as shown in Figure 6 , showing the optimized material distribution.

[0067] Figure 7 This is a schematic diagram of a 3D printed component optimized based on a continuous fiber periodic unit cell structure provided by an embodiment of the present application. The optimized trajectory point information is converted into the G-code format (a programming language) and imported into a continuous fiber composite 3D printer for printing. The printing result is as Figure 7 shown, presenting the actually printed structure.

[0068] In the initial design stage of the present application, it is ingeniously ensured that the overall periodic unit cell structure can achieve one-stroke manufacturing by skillfully applying different unit cell configurations for topology optimization design under specific working conditions. This design strategy not only integrates the excellent mechanical properties of composite materials but also makes full use of the unique geometric characteristics of the periodic unit cell structure, providing strong support for further reducing the structural weight and improving the structural performance. The present application not only focuses on the optimization of macroscopic topological geometric structure features but also delves into the microscopic level and carefully selects the periodic unit cell configuration. This approach fully guarantees the continuity of fibers during the 3D printing process, perfectly meeting the requirements of the 3D printing process. In addition, the present invention also has high adaptability and flexibility, and can flexibly select appropriate constraint types according to different design requirements, such as fiber length during printing, filling rate of the periodic unit cell structure, volume fraction of the periodic unit cell structure, etc., so as to meet diverse design needs.

[0069] An embodiment of the present application also provides a topology optimization device 800 for a continuous fiber periodic unit cell structure, as Figure 8 shown. The device includes: a determination module 801, a feature component construction module 802, a solution module 803, a unit constitutive matrix construction module 804, a topology optimization model construction 805, a sensitivity filtering processing module 806, and an evaluation module 807.

[0070] The determination module 801 is used to determine the configuration of the selected periodic unit cell structure according to preset rules.

[0071] The feature component construction module 802 is used to construct feature components within the design domain of the periodic unit cell by a feature-driven method, calculate the elastic matrix by projecting the fiber angle using a fixed grid response, and determine the weight coefficient based on the component level set function in the overlapping region to solve the equivalent elastic matrix.

[0072] The solution module 803 is used to solve the equivalent elastic properties of the selected fiber-reinforced composite periodic unit cell by an energy homogenization method.

[0073] The unit constitutive matrix construction module 804 is used to construct an interpolation-format unit constitutive matrix by a discrete unit cell optimization method.

[0074] Build a topology optimization model 805 to build a topology optimization model of a periodic unit cell structure with compliance as the objective function.

[0075] The sensitivity filtering processing module 806 is used to calculate the derivative of compliance with respect to the design variables composed of the artificial density of the alternative unit cell materials, and perform sensitivity filtering processing.

[0076] The evaluation module 807 is used to perform optimization iteration analysis under different working conditions, and evaluate the convergence degree of the optimization results using inequality relationships.

[0077] Some modules in the device described in this application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc. that perform specific tasks or implement specific abstract data types. This application can also be practiced in a distributed computing environment, where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0078] The device or module illustrated in the above application embodiment can be specifically implemented by a computer chip or entity, or by a product with certain functions. For convenience of description, the above device is described by dividing it into various modules according to functions. When implementing the application embodiment, the functions of each module can be implemented in the same or multiple software and / or hardware. Of course, the module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0079] The methods, apparatuses or modules described in this application can be implemented in the form of computer-readable program code. The controller can be implemented in any suitable manner. For example, the controller can take the form of, for example, a microprocessor or a processor, and a computer-readable medium storing computer-readable program code (such as software or firmware) executable by the (micro)processor, logic gates, switches, application specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of the controller include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicone Labs C8051F320. The memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art also know that in addition to implementing the controller in the form of pure computer-readable program code, the method steps can be logically programmed to enable the controller to be implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, and embedded microcontrollers to achieve the same function. Therefore, such a controller can be considered a hardware component, and the devices included therein for implementing various functions can also be regarded as the structures within the hardware component. Or even, the devices for implementing various functions can be regarded as either software modules for implementing the method or structures within the hardware component.

[0080] As Figure 9 As shown, the embodiment of this application also provides a topology optimization server for a continuous fiber periodic unit cell structure, including a memory 901 and a processor 902; the memory 901 is used to store computer-executable instructions; the processor 902 is used to execute the computer-executable instructions to implement a topology optimization method for a continuous fiber periodic unit cell structure as described above in the embodiment of this application.

[0081] The embodiment of this application also provides a computer-readable storage medium, which stores executable instructions, and when the computer executes the executable instructions, it can implement a topology optimization method for a continuous fiber periodic unit cell structure as described above in the embodiment of this application.

[0082] As can be seen from the description of the above embodiments, those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary hardware. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product or can also be embodied in the implementation process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a mobile terminal, a server, or a network device, etc.) to execute the method described in the embodiments of the present application.

[0083] The various embodiments in this specification are described in a progressive manner. For the same or similar parts between the various embodiments, reference can be made to each other. The key point of each embodiment is to illustrate the differences from other embodiments. All or part of the present application can be used in many general or special computer system environments or configurations.

[0084] The above embodiments are only used to illustrate the technical solutions of the present application and do not limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present application.

Claims

1. A topology optimization method for continuous fiber periodic unit cell structure, characterized in that: include: Determine the configuration of the selected periodic unit cell structure according to preset rules; The feature components are constructed by feature-driven method in the design domain of periodic unit cells, and the elastic matrix is ​​calculated by projecting the fiber angle using fixed grid response. The weight coefficient of the overlapping area is determined based on the component level set function to solve the equivalent elastic matrix. The energy homogenization method is used to solve the equivalent elastic properties of the periodic unit cell of the selected fiber-reinforced composite material; The discrete unit cell optimization method is used to construct the unit constitutive matrix in interpolation format; A topology optimization model of periodic unit cell structure is constructed with compliance as the objective function; Calculate the derivative of the compliance with respect to the design variables composed of artificial density of the candidate unit cell materials and perform sensitivity filtering; Iterative optimization analysis is performed under different working conditions, and the convergence degree of the optimization results is evaluated using inequality relations.

2. The topology optimization method for continuous fiber periodic unit cell structure according to claim 1, characterized in that: The preset rules include: The widths of all edges in the periodic unit cell structure are set to a fixed fiber spacing or an even multiple thereof; The periodic unit cell structure is designed to conform to the characteristics of the Euler graph, so that the number of edges connected to any node in the periodic unit cell structure is an even number; After any periodic unit cell combination, all nodes can be connected to each other.

3. The topology optimization method for continuous fiber periodic unit cell structure according to claim 1, characterized in that: The method constructs a feature component by a feature-driven method in the design domain of a periodic unit cell, projects the fiber angle using a fixed grid response to calculate the elastic matrix, and determines the weight coefficient of the overlapping region based on the component level set function to solve the equivalent elastic matrix, including: A single characteristic component is derived from the periodic unit cell structure, and the single characteristic component is described by the component level set function; The expression of the component level set function is: ;in, For the The component level set function value of feature components, is a point in the design domain of the periodic unit cell To The distance between the characteristic components, For the The radius of the feature component, is the penalty coefficient; Fixed grid units are divided in the design domain of the periodic unit cell, and the component level set function value of each characteristic component in each grid unit is determined by using the fixed grid response method to determine whether there is a characteristic component in the grid unit; If the component level set function value is greater than the preset threshold, it is considered that there is a characteristic component in the grid cell; If the component level set function value is less than or equal to the preset threshold, it is considered that there is no feature component in the grid unit; For grid cells with no overlapping regions, the elasticity matrix is ​​expressed as: ;in, is the elastic matrix in the overall coordinates, is the stress-strain relationship in material coordinates, is the coordinate transformation matrix; The expression of stress-strain relationship in material coordinates is: ;in, is the longitudinal elastic modulus, is the transverse elastic modulus, is the transverse Poisson’s ratio, is the longitudinal Poisson’s ratio, is the in-plane shear modulus; The expression of the coordinate transformation matrix is: ;in, is the angle between the material coordinates of the fiber-reinforced composite material and the overall coordinates of the whole, , For the The horizontal coordinate of the location of the feature component node, For the The vertical coordinate of the location of the feature component node; For grid cells with overlapping areas, the weight coefficient is determined according to the level set function value of each feature component in the overlapping area; Based on the weight coefficient, the equivalent elastic matrix of the grid cells in the overlapping area in material coordinates is calculated; The expression of the equivalent elastic matrix of the mesh element in material coordinates is: ;in, is the equivalent elastic matrix of the mesh elements in the overlapping area in material coordinates, For the The weight coefficient of feature components in the overlapping area, For the The elastic matrix of the characteristic component in material coordinates.

4. The topology optimization method for continuous fiber periodic unit cell structure according to claim 3, characterized in that: The energy homogenization method is used to solve the equivalent elastic properties of the selected fiber reinforced composite periodic unit cell, including: In the linear elastic range of fiber reinforced composite materials, the stress tensor and strain tensor of the equivalent homogeneous body satisfy Hooke's law: ;in, is the average stress tensor of the periodic unit cell structure, , and are the components of the mean stress tensor of the periodic unit cell structure, is the average strain tensor of the periodic unit cell structure, , and are the components of the average strain tensor of the periodic unit cell structure, , , , , and are the elements of the equivalent elastic matrix of the grid cells in the overlapping area in material coordinates, Represents a symmetric element.

5. The topology optimization method for continuous fiber periodic unit cell structure according to claim 4, characterized in that: The discrete unit cell optimization method is used to construct a unit constitutive matrix in an interpolation format, including: The expression of the unit constitutive matrix in the interpolation format is: ;in, is the unit constitutive matrix in interpolation format, For the The first grid cell The artificial density of the candidate unit cell materials, For the The first grid cell The equivalent elastic matrix corresponding to the candidate unit cell material is: is the number of candidate unit cell materials, Penalty factor, is the index of the candidate unit cell material, is the weight function.

6. The topology optimization method for continuous fiber periodic unit cell structure according to claim 5, characterized in that: The periodic unit cell structure topology optimization model is constructed with compliance as the objective function, including: Determine the design variables, define the objective function, define the equilibrium equations, the range of the design variables and define the constraint functions of the periodic unit cell structure; The design variables are determined as: , ;in, is the design variable of artificial density composition of alternative unit cell materials, For the In a periodic unit cell The artificial density of the material distribution, is the total number of grid cells; The objective function is defined as: ;in, is the minimum compliance of the periodic unit cell structure, is the overall displacement matrix of the structure, is the node load vector, is the overall stiffness matrix of the structure, is the transpose of the overall displacement matrix of the structure; Define the equilibrium equation as: ; The ranges of the design variables are: ;in, is the minimum value of the design variable composed of artificial density of the alternative unit cell material; When the filling rate of the periodic unit cell structure is constrained, the constraint function is: ;in, is the filling rate of the periodic unit cell structure, is the volume of fiber reinforced composite material used, is the total volume of the design domain of the periodic unit cell, is the maximum filling rate of the periodic unit cell structure; When the volume fraction of the periodic unit cell structure is used as a constraint, the constraint function is: ;in, is the overall structural volume fraction of the periodic unit cell structure, is the total volume of the structure, For the The volume of the candidate unit cell material, is the total volume of the design domain of the periodic unit cell; When the fiber length during printing is used as a constraint, the constraint function is: ;in, is the total length of all fibers, For the The length of the fibers in a periodic unit cell structure, is the maximum length of the fiber.

7. The topology optimization method for continuous fiber periodic unit cell structure according to claim 6, characterized in that: The method of calculating the derivative of the compliance with respect to the design variable composed of the artificial density of the candidate unit cell material and performing sensitivity filtering processing includes: The expression of the derivative of the design variable of the artificial density composition of the alternative unit cell material is: ;in, is the flexibility of the periodic unit cell structure, is the strain-displacement matrix, is the design domain of the periodic unit cell, is the integral over the design domain of the periodic unit cell, is an unknown item; The sensitivity results after sensitivity filtering are: ;in, For grid cells The Artificial density of unit cell materials, convolution operator For grid cells The weight coefficient of , ;in, is the filter radius, For grid cells With grid cells The center distance between If the filling rate of the periodic unit cell structure is constrained, the sensitivity of the volume occupied by non-empty materials in the periodic unit cell structure to the artificial density is expressed as: ;in, is the volume occupied by the non-empty material in the periodic unit cell structure.

8. The topology optimization method for continuous fiber periodic unit cell structure according to claim 7, characterized in that: The optimization iterative analysis is performed under different working conditions, and the convergence degree of the optimization results is evaluated using inequality relationships, including: The inequality relationship is: ;in, is the weight function of all alternative configurations, is the weight coefficient of the candidate unit cell material, is the convergence tolerance, the value is [0.95~0.99]; The overall structural convergence index is defined as: ;in, is the overall structural convergence index, is the total number of converged mesh elements, is the total number of grid cells.

9. A topology optimization device for continuous fiber periodic unit cell structure, characterized in that: include: A determination module, used to determine the configuration of the selected periodic unit cell structure according to a preset rule; Construct a feature component module, which is used to construct feature components in the design domain of the periodic unit cell through the feature-driven method, project the fiber angle using a fixed grid response to calculate the elastic matrix, and determine the weight coefficient of the overlapping area based on the component level set function to solve the equivalent elastic matrix; A solution module for solving the equivalent elastic properties of the selected fiber-reinforced composite periodic unit cell using an energy homogenization method; The module for constructing unit constitutive matrix is ​​used to construct the unit constitutive matrix in interpolation format by using discrete unit cell optimization method; Construct a topology optimization model to construct a periodic unit cell structure topology optimization model with flexibility as the objective function; A sensitivity filtering processing module is used to calculate the derivative of the design variable of the flexibility with respect to the artificial density composition of the candidate unit cell material, and perform sensitivity filtering processing; The evaluation module is used to perform iterative optimization analysis under different working conditions and evaluate the convergence degree of the optimization results using inequality relationships.

Images