A combined honeycomb design method capable of realizing planar boundary curvature matching

Abstract

This invention discloses a combined honeycomb design method that can achieve planar boundary curvature matching. The method mainly includes the following aspects: First, the boundary curvature of the target shape is used to divide the area; based on the area division results, appropriate honeycomb materials and honeycomb structures are selected. Simultaneously, deformation analysis is performed on the honeycomb structure to determine the relationship between the honeycomb angle, Poisson's ratio, and lateral displacement, obtaining the influence law of the honeycomb angle on deformation and Poisson's ratio, and establishing a mathematical model of the relationship between honeycomb angle, Poisson's ratio, and deformation. Further, based on the combined honeycomb boundary connection method, a suitable connection method is selected, and finally, honeycombs of different types and geometric parameters are filled into the corresponding areas. The design method of this invention is simple to operate, has a clear design mechanism, avoids a large amount of mechanical and mathematical calculations, and can quickly and accurately match complex planar states, possessing a wide range of applications and practical value.

Description

Technical Field

[0001] This invention relates to the field of mechanical metamaterials design, and in particular to a combined honeycomb design method that can achieve planar boundary curvature matching. Background Technology

[0002] The macroscopic material properties of cellular structures (such as complex deformation characteristics) are directly derived from their geometric design. A well-designed cellular structure can provide properties and functions not typically found in natural materials, such as negative Poisson's ratio, negative compressibility, elastic hysteresis, customizable elastic properties, and the ability to modify vibration damping and complex deformation capabilities through 3D design of metamaterials.

[0003] A novel goal of cellular structure design is to achieve predefined shapes through specific loading methods. Cellular structures capable of planar boundary curvature matching have enormous application potential, most notably in soft robotics and wearable (medical) devices. For example, planar boundary curvature matching cellular structures can be used to design soft grippers to hold objects with maximum surface contact and minimum contact force. Planar boundary curvature matching cellular structures have also found applications in exoskeletons, prostheses and orthotics, and adjustable mechanical storage. Therefore, establishing a combinatorial cellular design methodology capable of planar boundary curvature matching is of great significance.

[0004] Because cellular structures exhibit orthotropic anisotropy, their properties differ in the two principal directions, making the design of composite cellular structures with matching planar boundary curvature challenging. Various analytical models have been proposed to determine the elastic properties of cellular structures, but these models cannot accurately predict their shape transformation characteristics, especially for structures with complex shapes, making the design of corresponding composite cellular structures extremely difficult.

[0005] In summary, the design of composite cellular structures with matching planar boundary curvature faces a series of challenges and problems. To solve these problems, a new design method needs to be developed to design composite cellular structures with matching planar boundary curvature. Therefore, this invention proposes a design method for composite cellular structures with matching planar boundary curvature, providing theoretical and technical guidance for cellular structure designers. Summary of the Invention

[0006] This invention provides a combined honeycomb design method that enables planar boundary curvature matching, aiming to design combined honeycombs that achieve planar boundary curvature matching. It is particularly suitable for the fields of soft robotics and wearable medical devices. To achieve the above objective, this invention provides the following solutions: a method for region division of the target planar shape, a method for selecting honeycomb materials and combining honeycomb structures, a method for establishing mathematical models of honeycomb geometric parameters and deformation, and a method for connecting the boundaries of the combined honeycomb. The method for region division of the target planar shape partitions the target shape. The method for selecting honeycomb materials and combining honeycomb structures determines the honeycomb structure and materials. Combined with a mathematical model of geometric parameters and deformation relationships, the specific structure and geometric parameters of the filling honeycomb are determined. The method for connecting the boundaries of the combined honeycomb is then employed, selecting an appropriate honeycomb boundary connection method, ultimately establishing a combined honeycomb design method that enables planar boundary curvature matching. This method provides convenience for designers.

[0007] To achieve the above objectives, the present invention uses the following technical solution:

[0008] A combined honeycomb design method that enables planar boundary curvature matching includes the following steps:

[0009] Step 1: Divide the target planar shape into regions:

[0010] Using 3D modeling technology, a complex target shape plate is modeled in 3D. Based on the 3D modeling results, the target shape plate with multiple boundary curvatures is analyzed and the target shape plate is divided into multiple regions with different boundary curvatures.

[0011] Step Two: Selection of Cellular Materials and Assembly of Cellular Structures

[0012] Highly elastic materials with excellent deformation properties are used as the materials for manufacturing honeycomb structures to ensure that the selected materials have good strength and stability and can meet the deformation requirements. The finite element numerical simulation method is used to analyze the deformation behavior of different honeycomb structures under external tensile load, determine the type of boundary curvature of the honeycomb after tensile deformation, and fill the corresponding honeycomb cells in each region according to the boundary curvature type and region division results after honeycomb deformation.

[0013] Step 3: Establishing the cellular geometric parameters and deformation mathematical model:

[0014] The deformation process of the honeycomb under external load is recorded through finite element numerical simulation to obtain the corresponding deformation data. At the same time, the deformation behavior of the honeycomb is theoretically analyzed and modeled to obtain a mathematical model of the honeycomb angle θ and the lateral deformation. Finally, the deformation information of the honeycomb is mapped to the parameter representation of the honeycomb angle according to the mathematical model.

[0015] Step 4: Combined Cellular Boundary Connection Method: Analyze the geometry and boundary conditions of the cellular structure, and use geometric matching and performance coordination methods to determine the boundary connection requirements between different cellular structures; design corresponding connection structures and connection methods according to the boundary connection requirements to achieve good connection between different areas and improve the stability and strength of the combined cellular connection.

[0016] Furthermore, in step one, the boundary curvature is defined as the degree of curvature of the upper and lower boundary curves of the target shape plate.

[0017] Furthermore, step one specifically includes the following steps:

[0018] Using 3D modeling technology, a 3D model of the target shape plate is performed. Based on the modeling results, the target plate with multiple boundary curvatures is analyzed and geometric features are extracted. Based on the extraction results of the geometric features, the target shape plate is divided into N regions. For each region, the boundary curvature of the target plane is calculated according to Equation (1). Regions with ρ > 0 are divided into positive boundary curvature regions, regions with ρ = 0 are divided into zero boundary curvature regions, and regions with ρ < 0 are divided into negative boundary curvature regions. Each region is required to have the same boundary curvature type. If the boundary curvature types in a region are not the same, the number of partitions needs to be increased until each partition has only one boundary curvature type.

[0019]

[0020] In the formula, y represents the lateral coordinate of a point on the boundary of the target plane.

[0021] Furthermore, in step two, 95A-TPU material is selected as the base material for manufacturing the honeycomb structure.

[0022] Furthermore, in step two, the method for determining the honeycomb structure combination is as follows:

[0023] (1) Three types of honeycomb structures are defined by topological configuration. All three types of honeycomb structures are composed of six ribs on both sides and a ligament connecting the two pillars in the middle. Let the interior angle of the honeycomb adjacent to the ligament connecting the two pillars be θ. The three types of honeycomb structures are: a regular hexagonal honeycomb with θ > 100°, a concave hexagonal honeycomb with θ < 80°, and a rectangular honeycomb with θ = 90°.

[0024] (2) Using finite element numerical simulation and constitutive model of honeycomb material manufacturing, the deformation of different honeycombs under external tensile load is analyzed to determine the deformation boundary curvature corresponding to different honeycomb structures. From the honeycomb deformation, it can be seen that: the regular hexagonal honeycomb is a positive Poisson's ratio honeycomb, corresponding to the negative boundary curvature type in the filled division area; the rectangular honeycomb is a zero Poisson's ratio honeycomb, corresponding to the zero boundary curvature type in the filled division area; the concave hexagonal honeycomb is a negative Poisson's ratio honeycomb, corresponding to the positive boundary curvature type in the filled division area.

[0025] Furthermore, step three specifically includes the following steps:

[0026] (1) When designing the honeycomb structure, for the three types of honeycomb structures, the thickness t of the honeycomb unit cell is constant for regular hexagonal honeycomb, rectangular honeycomb and concave hexagonal honeycomb, and the honeycomb is only allowed to change in the longitudinal x direction while remaining constant in the transverse y direction. The number of transverse honeycomb unit cells is fixed to a constant value, and the three types of honeycomb structures have the same height h. The combined honeycomb that can achieve planar boundary curvature matching is named XNXZXP, where "X" represents the number of honeycomb unit cells in each region, and N, Z and P represent the positive boundary curvature region, the zero boundary curvature region and the negative boundary curvature region, respectively.

[0027] (2) By using the finite element numerical simulation method, the deformation process of the honeycomb under certain longitudinal strain conditions is recorded and the corresponding deformation data is obtained. The Poisson's ratio of the honeycomb is calculated according to formula (2). By fitting the Poisson's ratio corresponding to the honeycomb at different angles, formula (3) is obtained. Then, the specific geometric parameters of different Poisson's ratios can be obtained by formula (3).

[0028]

[0029] v = 0.025 × θ - 1.9 (3)

[0030] In the formula, ε y ε x v and v represent the strain in the y-direction, strain in the x-direction, and equivalent Poisson's ratio of the honeycomb, respectively;

[0031] (3) By using the finite element numerical simulation method, the deformation of honeycombs with different Poisson ratios under longitudinal strain conditions is captured, and the corresponding deformation data is obtained. The analytical relationship between the honeycomb Poisson ratio v and the transverse displacement is fitted by a cubic polynomial to obtain formula (4).

[0032] v = 0.35 + 8.1275u - 65.535u 3 (4)

[0033] (4) Combining formulas (3) and (4), we obtain the analytical relationship between the honeycomb angle θ and the lateral displacement, as shown in formula (5);

[0034] θ = 90 + 325.1u - 2621.4u 3 (5)

[0035] In the formula, u represents the lateral displacement of the honeycomb under longitudinal stretching due to the Poisson's ratio effect;

[0036] (5) After obtaining the analytical relationship between the honeycomb angle θ and the lateral displacement, it is necessary to obtain the lateral displacement distribution of the target plane, so as to determine the specific angle θ of the honeycomb. The continuous displacement of the target plane is discretized into the displacement of each column of unit cells in the partition. The required displacement must be calculated in the middle of each row of ligaments. According to formula (6), the boundary curve of the target plane is approximated by a three-term Fourier series, so as to obtain the specific displacement distribution of the target plane.

[0037] u=a1sin(ω(x-1))+a2sin(2ω(x-1))+a3sin(3ω(x-1))(6)

[0038]

[0039] Where p represents the number of unit cell columns, and a1, a2, and a3 specify shape parameters; for standardization, the y values ​​are normalized to the range [0,1].

[0040] (6) Discretize the x value into p points, and use the column number as the x value for the coordinates of each point to obtain the distribution of the lateral deformation u. Use u as the input target for the combined cellular design that can achieve planar boundary curvature matching, and then use formula (5) to obtain the specific angle θ of the cellular.

[0041] Furthermore, step four specifically includes the following:

[0042] First, we define geometric similarity and mechanical compatibility. The mathematical meaning of geometric similarity is the ratio of compatible binary elements to all entity elements on a shared boundary. The physical meaning of mechanical compatibility is the level of stress similarity on a shared boundary under a unit strain field. Defining geometric similarity and mechanical compatibility is to facilitate readers' understanding of the concepts, and there is no need to repeat the definitions during the operation of the method.

[0043] Step 1: Perform geometric similarity tests on the matching boundaries between the composite cellular structures. These tests ensure that the geometry of the connection points matches, guaranteeing a good connection between different cellular units. Simultaneously, mechanical compatibility tests ensure a smooth stress transition at the connection points, improving the stability and strength of the composite cellular structure connections. Finally, calculate the shape compatibility at the connection boundaries of the composite cellular structures to obtain specific values. The following formula represents the shape compatibility between adjacent cellular structures. Among them, l i and l jFor adjacent cell pairs numbered i and j, δ li (l i ,l j This indicates the degree of shape coordination between adjacent cells. Indicates the geometric compatibility between adjacent cells. Indicates the mechanical compatibility between adjacent cells;

[0044] Step 2: Based on the degree of shape coordination between the cellular structures, design corresponding connection structures and connection methods to achieve good connection between different areas.

[0045] The beneficial effects of this invention are as follows: By using the method of dividing the target planar shape into regions, the method of selecting honeycomb materials and combining honeycomb structures, the method of establishing honeycomb geometric parameters and deformation mathematical models, and the method of connecting the boundaries of the combined honeycomb, this invention can fill the corresponding honeycomb in each partition of the combined honeycomb structure. Based on the area of ​​the target shape, we select appropriate honeycomb size and the number of longitudinally arranged cells, and finally establish a combined honeycomb design method that can achieve planar boundary curvature matching. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. It is worth noting that the drawings described below are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0047] Figure 1 This invention provides a flowchart of the overall process for a combined honeycomb design that enables planar boundary curvature matching.

[0048] Figure 2 These are schematic diagrams of three honeycomb structures provided by the present invention: (a) a regular hexagonal honeycomb, (b) a rectangular honeycomb, and (c) a concave hexagonal honeycomb.

[0049] Figure 3 This is a flowchart of the region division of the target planar shape provided by the present invention;

[0050] Figure 4 This invention provides a method for target plane symmetry processing and coordinate system establishment.

[0051] Figure 5 This invention provides experimental equipment for obtaining the elastic constitutive structure of TPU material. (a) is a TPU test sample, and (b) is the overall experimental setup, including a DIC device, a tensile machine, and a sampling computer.

[0052] Figure 6These are schematic diagrams of the deformation of three honeycomb structures provided by the present invention under tensile load; (a) ρ < 0, (b) ρ = 0, (c) ρ > 0;

[0053] Figure 7 This is a schematic diagram of the honeycomb size and the division of the three regions provided by the present invention;

[0054] Figure 8 This is a schematic diagram of three types of honeycomb structure filling based on a target plane provided by the present invention;

[0055] Figure 9 This is a schematic diagram comparing the target plane and the actual deformation plane of the honeycomb provided by the present invention;

[0056] Figure 10 These are three schematic diagrams of a combined honeycomb structure that can achieve planar boundary curvature matching provided by the present invention. (a) is the first sample, (b) is the second sample, and (c) is the third sample. Detailed Implementation

[0057] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. It is worth noting that the described embodiments are only a part of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, those skilled in the art can obtain all other embodiments without creative effort, and these embodiments also fall within the protection scope of the present invention.

[0058] In the description of this invention, it should be understood that directional terms such as "front," "rear," "up," "down," "left," "right," "lateral," "vertical," "middle," "both sides," and "top," "bottom," etc., are generally based on the orientation or positional relationship shown in the accompanying drawings. These terms are only for the convenience of describing this invention and simplifying expression. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, these directional terms should not be construed as limiting the scope of protection of this invention. Furthermore, the directional terms "inner" and "outer" refer to the interior and exterior relative to the outline of each component itself.

[0059] To make the objectives, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] like Figures 1-10As shown: This embodiment provides a combined honeycomb design method that can achieve planar boundary curvature matching, including a target planar shape region division method, a honeycomb material selection and honeycomb structure combination method, a honeycomb geometric parameter and deformation mathematical model establishment method, and a combined honeycomb boundary connection method. First, the target planar shape region division method divides the target shape into partitions, and selects the corresponding honeycomb material and honeycomb structure according to the region division results. Next, using the honeycomb deformation and honeycomb geometric parameter mapping relationship, the honeycomb geometry and boundary curvature are mapped to each other. Based on the divided regions and their mathematical expressions, the specific structural form of the required honeycomb structure is determined. Finally, the combined honeycomb boundary connection method is used to determine the connection performance of adjacent honeycombs and select the connection method. Based on the area size of each region of the target shape, the number of longitudinal honeycombs is determined. Through these steps, a certain number of honeycombs can be filled in specific locations, thereby designing a combined honeycomb that can achieve planar boundary curvature matching.

[0061] like Figure 2 As shown, three honeycomb structures can be explained by a single topological configuration, all of which consist of six ribs on both sides and a ligament in the middle connecting the two pillars.

[0062] Step 1: The method for dividing the target planar shape into regions, such as... Figure 3 The flowchart for dividing the target planar shape into regions is shown below, and its specific steps are as follows:

[0063] Step 1: First, determine the target shape plate. Then, use computer-aided design software (Solidworks) to create a 3D model of the target plane. Use the measurement and curvature modules in Solidworks to obtain key geometric parameters such as the overall length, boundary curves, and area of ​​the target plane. Based on the distribution of the boundary curves of the target shape plate, divide the combined honeycomb structure into regions. The specific division method will be explained in Step 2.

[0064] Step 2: Example of this implementation Figure 4As shown, according to the region division method of the target plane shape, the boundary curvature features of the target plane are established and extracted. Furthermore, in order to reduce the amount of calculation, the target shape plate is symmetrically processed, and only half of the target shape plate model is analyzed. The boundary vertex of the target shape plate is taken as the origin to establish a plane rectangular coordinate system. Furthermore, the boundary curvature of the target plane is obtained according to formula (1), and the target plane is divided into three different curvature types using the sign of the obtained boundary curvature, namely positive boundary curvature ρ>0, zero boundary curvature ρ=0 and negative boundary curvature ρ<0. According to the dissimilarity of shape characteristics, the target shape plate is divided into three regions with separate mathematical characteristics. Furthermore, the boundary curvature type of each region must be the same. If the boundary curvature types are not the same, the number of partitions needs to be increased until each partition has only one boundary curvature type.

[0065]

[0066] In the formula, y represents the lateral coordinate of a point on the boundary of the target plane.

[0067] Step two, the method for selecting honeycomb materials and combining honeycomb structures, specifically includes the following steps:

[0068] Step 1: Based on the performance requirements and additive properties of the honeycomb structure, select the appropriate material, obtain the mechanical properties of the material, and establish a material constitutive model to prepare for the finite element analysis of the composite honeycomb structure.

[0069] Because the superelastic material TPU has high flexibility and can undergo large deformations, 95A-TPU was selected as the material for manufacturing the honeycomb in this embodiment. However, this invention is not limited to the use of 95A-TPU. Any material with similar properties and that meets the above requirements can be used to implement this invention. We obtained the superelastic constitutive model of 95A-TPU material through experiments. The specific experimental procedure is as follows: Figure 5 As shown, according to the size 1 in GB / T 528-2009 standard, 95A-TPU test specimens were prepared on a 3D fused deposition modeling (FDM) printer. Then, speckle patterns were sprayed onto the surface of the specimens, and tensile tests were performed using a WDW-1A tensile testing machine. During the test, the loading speed of the loading head was 5 mm / min, and the sampling frequency was 2 Hz. The nominal stress information of the test specimens was obtained by calculating formula (2). The nominal strain information of the test specimens was obtained using a non-contact strain measurement system DIC. Furthermore, the experimental data were imported into the uniaxial tensile module of the hyperelastic experimental data in ANSYS, and the data was fitted using the Mooney-Rivlin 5-parameter hyperelastic model. The fitted data are shown in Table 1.

[0070]

[0071] In the formula, σ represents stress, F represents force, and A represents the area of ​​force application.

[0072] Table 1. Fitting parameters of the Mooney-Rivlin 5-parameter constitutive model

[0073]

[0074] Step 2: Further, to establish the relationship between the honeycomb structure and the boundary curvature type, three honeycomb structures are first established based on the curvature type. Figure 2 As shown in (a), the main form is the regular hexagonal honeycomb (θ>100°) topology, which is obtained by changing the honeycomb angle parameters. Figure 2 The concave hexagonal honeycomb (θ < 80°) shown in (c) and Figure 2 The rectangular honeycomb (θ = 90°) shown in (b) is further analyzed using finite element numerical simulation to determine the three types of honeycomb boundary curvature under external tensile load. Furthermore, during the simulation, it is assumed that the three honeycomb structures have perfect, defect-free geometry, and solid elements are used to simulate the honeycomb. The constitutive model of 95A-TPU material is input into the finite element material property library as the material property of the honeycomb. Three-dimensional models of the three honeycombs are established using Solidworks and exported as .x_t format. The exported .x_t files of the three honeycombs are imported into the DM module of Ansys, meshed, and the mesh type is defined as solid element solid186. Boundary conditions are added to the three honeycomb structures, and loads are applied. One end of the honeycomb structure is fixed, and a tensile displacement load of 20% strain is applied to the other end. The large deformation switch is enabled, and the structure is solved and post-processed to obtain deformation cloud diagrams of different honeycomb structures, such as... Figure 6 As shown in the deformation cloud map, the regular hexagonal honeycomb is a positive Poisson's ratio honeycomb corresponding to the negative boundary curvature type, the rectangular honeycomb is a zero Poisson's ratio honeycomb corresponding to the zero boundary curvature type, and the concave hexagonal honeycomb is a negative Poisson's ratio honeycomb corresponding to the positive boundary curvature type.

[0075] Step 3, the method for establishing the cellular geometric parameters and deformation mathematical model, specifically includes the following steps:

[0076] Step 1: According to Figure 7As shown, any target shape can be divided into at most three curvature types: positive boundary curvature region, zero boundary curvature region, and negative boundary curvature region. The positive boundary curvature region needs to be filled with concave hexagonal honeycomb, the zero boundary curvature region needs to be filled with rectangular honeycomb, and the negative boundary curvature region needs to be filled with regular hexagonal honeycomb. When designing the combined honeycomb structure, for the three types of honeycomb, such as regular hexagonal, rectangular, and concave hexagonal, the wall thickness should be set to 1mm, and the honeycomb is only allowed to vary in the longitudinal direction (x direction) while remaining constant in the transverse direction (y direction). The number of transverse unit cells is fixed at 6, and the honeycomb structure has the same height h (18mm) under any angle parameter. Therefore, the total height of the sample is L = 18 * 6 = 108mm. The combined honeycomb is named XNXZXP, where "X" represents the number of unit cells in the longitudinal direction of each region, and N, Z, and P represent the positive boundary curvature region, the zero boundary curvature region, and the negative boundary curvature region.

[0077] According to the embodiments Figure 8 As shown, the target surface is divided into three regions according to the region division method of the target planar shape. Based on the relationship between the honeycomb and boundary curvature types, positive Poisson's ratio-regular hexagonal honeycomb, zero Poisson's ratio-rectangular honeycomb, and negative Poisson's ratio-concave hexagonal honeycomb are filled into the corresponding regions respectively. In the embodiment, the honeycombs filled from left to right are concave hexagonal honeycomb, regular hexagonal honeycomb, and rectangular honeycomb, and the combined honeycomb is named 6N8P10Z.

[0078] Step 2: Further, the deformation process of the honeycomb under 20% longitudinal strain condition is recorded by the finite element method, and the corresponding deformation data is obtained. The Poisson's ratio of the honeycomb is calculated according to formula (3). By linear fitting of the Poisson's ratio corresponding to the honeycomb at different angles, formula (4) is obtained. Further, the specific geometric parameters of different Poisson's ratios can be obtained by formula (4).

[0079]

[0080] v = 0.025 × θ - 1.9 (4)

[0081] In the formula, ε y ε x v and v represent the strain in the y-direction, strain in the x-direction, and equivalent Poisson's ratio of the honeycomb, respectively.

[0082] Step 3: Using the finite element numerical simulation method, the deformation of honeycombs with different Poisson ratios under 20% longitudinal strain conditions was recorded to obtain the corresponding deformation data. The analytical relationship between the honeycomb Poisson ratio (v) and lateral displacement was determined using a cubic polynomial fitting method in Matlab software, resulting in formula (5). Furthermore, using formulas (4) and (5), the analytical relationship between the honeycomb angle (θ) and lateral displacement was obtained, as shown in formula (6). Finally, based on the mathematical model, the deformation information of the honeycomb structure was mapped to the parameter representation of the honeycomb angle.

[0083] v = 0.35 + 8.1275u - 65.535u 3 (5)

[0084] θ = 90 + 325.1u - 2621.4u 3 (6)

[0085] In the formula, u represents the lateral displacement of the honeycomb under longitudinal stretching due to the Poisson's ratio effect.

[0086] Step 4: After obtaining the analytical relationship between the honeycomb angle (θ) and the lateral displacement, it is necessary to obtain the lateral displacement distribution of the target plane to determine the specific angle (θ) of the honeycomb. Further, the continuous displacement of the target plane is discretized into the displacement of each column of unit cells in the partition. Further, the required displacement must be calculated in the middle of each row of ligaments. According to formula (7), the boundary curve of the target plane is approximated by a three-term Fourier series to obtain the specific displacement distribution of the target plane.

[0087] u=a1sin(ω(x-1))+a2sin(2ω(x-1))+a3sin(3ω(x-1))(7)

[0088]

[0089] Where p represents the number of unit cell columns, and a1, a2, and a3 specify shape parameters. For standardization, the value of u is normalized to the range [0,1]. In this embodiment, for example... Figure 10 As shown in the first sample (a), the shape parameters used are a3=1, a1=a2=0. Further, the x value is discretized into p points, and the coordinates of each point are taken as the x value by the column number to obtain the distribution of the lateral deformation displacement u. u is used as the input parameter of the combined honeycomb that can realize the curvature matching of the plane boundary. Then, the specific angle (θ) of the honeycomb is obtained by using formula (6).

[0090] Step four, the combined cellular boundary connection method, specifically includes the following steps:

[0091] First, geometric similarity and mechanical compatibility are defined. Mathematically, geometric similarity can be interpreted as the ratio of compatible binary elements to all solid elements on a shared boundary. Physically, mechanical compatibility can be interpreted as the stress similarity level of a shared boundary under a unit strain field. The formula for the shape compatibility between adjacent honeycomb structures is shown below. Among them, l i and l j For adjacent cell pairs numbered i and j, δ li (l i ,l j This indicates the degree of shape coordination between adjacent cells. Indicates the geometric compatibility between adjacent cells. This indicates the mechanical compatibility between adjacent cells. Defining geometric similarity and mechanical compatibility is for the reader's convenience in understanding the concepts; they do not need to be redefined during the operation of the method.

[0092] Step 2: Perform geometric similarity tests on the matching between the combined cellular structures. These tests ensure that the geometry of the connection points matches, guaranteeing good connectivity between different cells. Simultaneously, mechanical compatibility tests ensure a smooth stress transition at the cell connection points. Finally, the boundary shape compatibility of adjacent cells is calculated to obtain specific numerical values ​​for the shape compatibility of the matching boundaries of the combined cellular structure.

[0093] Step 3: Based on the shape compatibility index values ​​between each honeycomb structure, design corresponding connection structures and methods to achieve good connections between different areas. Specifically, first, determine the connection method based on the shape compatibility index. If the shape compatibility index is greater than 0.8, a direct connection method is selected; if it is less than 0.8, a suitable connection method needs to be selected based on the shape and boundary conditions of the honeycomb, such as mortise and tenon joints or adding intermediate transition materials. In this embodiment, the shape compatibility index is greater than 0.8, therefore a direct connection method is used for honeycomb connection. After determining the specific geometric parameters of the honeycomb and achieving good connections, as follows... Figure 9 As shown in the example, the final deformation state of the combined honeycomb is consistent with the target plane, and the combined honeycomb design is completed;

[0094] By using the region division method of the target planar shape, the honeycomb material selection and honeycomb structure combination method, the honeycomb geometric parameters and deformation mathematical model establishment method, and the combined honeycomb boundary connection method, each partition of the combined honeycomb structure is filled with corresponding honeycombs. The appropriate honeycomb size and longitudinal arrangement number are selected according to the area of ​​the target shape, thereby realizing the combined honeycomb design with planar boundary curvature matching.

[0095] This specification uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of these examples are solely for the purpose of helping to understand the methods and core ideas of the present invention and are not intended to limit the invention. Those skilled in the art can make corresponding changes to the specific implementation methods and application scope based on their understanding of the inventive concept. Therefore, the content of this specification should not be considered as a limitation of the present invention.

Claims

1. A combined honeycomb design method capable of achieving planar boundary curvature matching, characterized in that: Includes the following steps: Step 1: Divide the target planar shape into regions: Using 3D modeling technology, a complex target shape plate is modeled in 3D. Based on the 3D modeling results, the target shape plate with multiple boundary curvatures is analyzed and the target shape plate is divided into multiple regions with different boundary curvatures. Step Two: Selection of Cellular Materials and Assembly of Cellular Structures Highly elastic materials with excellent deformation properties are used as the materials for manufacturing honeycomb structures to ensure that the selected materials have good strength and stability and can meet the deformation requirements. The finite element numerical simulation method is used to analyze the deformation behavior of different honeycomb structures under external tensile load, determine the type of boundary curvature of the honeycomb after tensile deformation, and fill the corresponding honeycomb cells in each region according to the boundary curvature type and region division results after honeycomb deformation. Step 3: Establishing the cellular geometric parameters and deformation mathematical model: Finite element numerical simulation was used to record the deformation process of a honeycomb structure under external load, obtaining corresponding deformation data. Simultaneously, theoretical analysis and modeling of the honeycomb deformation behavior were performed to obtain the honeycomb angle. Finally, based on the mathematical model of lateral deformation, the deformation information of the honeycomb is mapped to the parameter representation of the honeycomb angle. Step three specifically includes the following steps: (1) When designing the honeycomb structure, for the three types of honeycomb structures, the thickness t of the honeycomb unit cell is constant for regular hexagonal honeycomb, rectangular honeycomb and concave hexagonal honeycomb, and the honeycomb is only allowed to change in the longitudinal x direction while remaining constant in the transverse y direction. The number of transverse honeycomb unit cells is fixed to a constant value, and the three types of honeycomb structures have the same height h. The combined honeycomb that can achieve planar boundary curvature matching is named XNXZXP, where "X" represents the number of honeycomb unit cells in each region, and N, Z and P represent the positive boundary curvature region, the zero boundary curvature region and the negative boundary curvature region, respectively. (2) By using the finite element numerical simulation method, the deformation process of the honeycomb under certain longitudinal strain conditions is recorded and the corresponding deformation data is obtained. The Poisson's ratio of the honeycomb is calculated according to formula (2). By fitting the Poisson's ratio corresponding to the honeycomb at different angles, formula (3) is obtained. Then, the specific geometric parameters of different Poisson's ratios can be obtained by formula (3). (2) (3) In the formula, , , These represent the strain in the y-direction, the strain in the x-direction, and the equivalent Poisson's ratio of the honeycomb, respectively. (3) The deformation of honeycomb with different Poisson ratios under longitudinal strain conditions was captured by the finite element numerical simulation method, and the corresponding deformation data was obtained. The Poisson ratio of the honeycomb was fitted by a cubic polynomial. Based on the analytical relationship with the lateral displacement, we obtain formula (4); (4) (4) Combine formulas (3) and (4) to obtain the cell angle. The analytical relationship with the lateral displacement is shown in equation (5); (5) In the formula, This indicates the lateral displacement of the honeycomb under longitudinal stretching due to the Poisson's ratio effect. (5) Obtain the cell angle After determining the analytical relationship with the lateral displacement, it is necessary to obtain the lateral displacement distribution of the target plane in order to determine the specific angle of the honeycomb. The continuous displacement of the target plane is discretized into the displacement of each column of unit cells in the partition. The required displacement must be calculated in the middle of each row of ligaments. According to formula (6), the boundary curve of the target plane is approximated by a three-term Fourier series, so as to obtain the specific displacement distribution of the target plane. (6) Where p represents the number of unit cell columns, and a1, a2, and a3 specify shape parameters; for standardization, the y values ​​are normalized to the range [0,1]. (6) Discretize the x-value into p points, and use the column number as the x-value for the coordinates of each point to obtain the lateral deformation. The distribution will As the input target for the combined cellular design that can achieve planar boundary curvature matching, the specific angle of the cellular structure is then obtained using formula (5). ; Step 4: Combined Cellular Boundary Connection Method: Analyze the geometry and boundary conditions of the cellular structure, and use geometric matching and performance coordination methods to determine the boundary connection requirements between different cellular structures; design corresponding connection structures and connection methods according to the boundary connection requirements to achieve good connection between different areas and improve the stability and strength of the combined cellular connection.

2. The combined honeycomb design method for achieving planar boundary curvature matching according to claim 1, characterized in that, In step one, boundary curvature is defined as the degree of curvature of the upper and lower boundary curves of the target shape plate.

3. The combined honeycomb design method for achieving planar boundary curvature matching according to claim 1, characterized in that, Step one specifically includes the following steps: Using 3D modeling technology, a 3D model of the target-shaped plate is created. Based on the modeling results, the target plate with various boundary curvatures is analyzed, and geometric features are extracted. Based on the extraction results of the geometric features, the target-shaped plate is divided into N regions. For each region, the boundary curvature of the target plane is calculated according to equation (1). The region is divided into positive boundary curvature regions. The region is divided into a zero-boundary curvature region. The region is divided into negative boundary curvature regions. Each region is required to have the same boundary curvature type. If the boundary curvature types in a region are not the same, the number of partitions needs to be increased until each partition has only one boundary curvature type. （1） In the formula, y represents the lateral coordinate of a point on the boundary of the target plane.

4. The combined honeycomb design method for achieving planar boundary curvature matching according to claim 1, characterized in that, In step two, 95A-TPU material is selected as the base material for manufacturing honeycomb.

5. The combined honeycomb design method for achieving planar boundary curvature matching according to claim 1, characterized in that, Step two, the method for determining the honeycomb structure combination: (1) Three honeycomb structures are defined by topological configuration. All three honeycomb structures consist of six ribs on both sides and a ligament connecting the two pillars in the middle. Let the interior angle of the honeycomb adjacent to the ligament connecting the two pillars be denoted as . The three honeycomb structures are as follows: Regular hexagonal honeycomb Concave hexagonal honeycomb and Rectangular honeycomb; (2) Using finite element numerical simulation and constitutive model of honeycomb material manufacturing, the deformation of different honeycomb structures under external tensile load is analyzed to determine the deformation boundary curvature of different honeycomb structures. As can be seen from the honeycomb deformation, the regular hexagonal honeycomb is a positive Poisson's ratio honeycomb, corresponding to the negative boundary curvature type in the filled division region; Rectangular honeycombs are zero Poisson's ratio honeycombs, corresponding to zero boundary curvature type in the filled division region; The concave hexagonal honeycomb is a negative Poisson's ratio honeycomb, corresponding to the positive boundary curvature type in the filled region.

6. The combined honeycomb design method for achieving planar boundary curvature matching according to claim 1, characterized in that, Step four specifically includes the following: First, we define geometric similarity and mechanical compatibility. The mathematical meaning of geometric similarity is the ratio of compatible binary elements to all entity elements on a shared boundary. The physical meaning of mechanical compatibility is the level of stress similarity on a shared boundary under a unit strain field. Defining geometric similarity and mechanical compatibility is to facilitate readers' understanding of the concepts, and there is no need to repeat the definitions during the operation of the method. Step 1: Perform geometric similarity tests on the matching boundaries between the composite cellular structures. These tests ensure that the geometry of the connection points matches, guaranteeing a good connection between different cellular units. Simultaneously, mechanical compatibility tests ensure a smooth stress transition at the connection points, improving the stability and strength of the composite cellular structure connections. Finally, calculate the shape compatibility at the connection boundaries of the composite cellular structures to obtain specific values. The following formula represents the shape compatibility between adjacent cellular structures. ;in, and For adjacent cell pairs numbered i and j, Indicates the shape compatibility between adjacent cells. Indicates the geometric compatibility between adjacent cells. Indicates the mechanical compatibility between adjacent cells; Step 2: Based on the degree of shape coordination between the cellular structures, design corresponding connection structures and connection methods to achieve good connection between different areas.

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