Combined honeycomb design method capable of realizing specified space curved surface deformation

Abstract

The invention discloses a combined honeycomb design method capable of achieving specified space curved surface deformation, and belongs to the field of mechanical metamaterial design. In order to solve the technical problems that a traditional honeycomb structure is single in deformation mode and is difficult to spontaneously form a predetermined space curved surface under simple excitation, the invention provides a design method which comprises the following steps: firstly, performing curvature analysis and discretization on a target space curved surface; secondly, based on a database containing honeycomb units with different mechanical characteristics, establishing a mapping relation between local deformation and geometric characteristics of the honeycomb units; and finally, arranging various honeycomb units in a non-uniform manner according to the mapping relation to generate a combined honeycomb structure. The structure is made of a single material, can spontaneously and accurately deform into a preset complex curved surface under simple excitation of buckling compression and the like, and has excellent bearing capacity. Accurate programming of structural deformation is achieved, the driving mode is simplified, and an efficient design approach is provided for development of a high-performance deformable structure.

Description

Technical Field

[0001] This invention relates to the field of mechanical metamaterials design, and more specifically, to a systematic method for designing deformable structures, particularly a combined honeycomb design method that achieves precise deformation from an initial two-dimensional planar configuration to a predetermined three-dimensional spatial surface by combining and controlling the parameters of honeycomb microstructures. Background Technology

[0002] Honeycomb structures have been widely used in aerospace, transportation, and construction engineering due to their lightweight, high strength, high specific stiffness, and excellent energy absorption characteristics. However, traditional honeycomb structures, such as those composed of uniform hexagonal cells, typically exhibit orthotropic macroscopic mechanical behavior. Under load, their deformation modes are relatively simple and uniform, making it difficult to meet the demands of current cutting-edge technologies for complex morphological changes.

[0003] With the rapid development of technologies such as soft robotics, wearable medical devices, and deployable spatial structures, the market demand for novel structures capable of large-scale, programmable, and complex shape transformations is becoming increasingly urgent. Transforming an initial planar structure into a complex spatial surface with non-zero Gaussian curvature (e.g., a dome shape with positive Gaussian curvature or a saddle shape with negative Gaussian curvature) is a significant technological challenge. According to Gauss's theorem in differential geometry, to change the Gaussian curvature of a surface, its interior must undergo non-uniform stretching or compression, thereby altering its geometric metric.

[0004] To achieve such surface deformation, existing technologies mainly employ the following approaches: One method involves deformation through geometric manipulations (such as paper cutting / folding) or discrete unit assembly. While this approach offers a high degree of freedom in deformation, it typically relies on thin sheet materials or non-integrated connections, resulting in structures with poor load-bearing capacity, susceptible to external disturbances, and unsuitable for bearing actual loads in engineering applications. Another approach utilizes the non-uniform "growth" of active materials (such as hydrogels and liquid crystal elastomers) to drive deformation. However, this technology often uses soft materials, resulting in an inherent contradiction between deformation capacity and load-bearing capacity. The deformed structure lacks stiffness, and non-uniform expansion induces significant material strain, which is unacceptable in many engineering applications (such as flexible electronic devices).

[0005] In summary, existing technologies in this field generally face a core technical contradiction in achieving complex surface deformation: the difficulty in simultaneously achieving both deformation capacity and load-bearing capacity. Therefore, designing an integrated structure that can spontaneously and accurately form a predetermined spatial surface through simple excitation, while simultaneously possessing good load-bearing capacity, without relying on complex external molds or multi-point drive systems, is a pressing technical challenge in this field. SUMMARY

[0006] The present application aims to overcome the deficiencies of the prior art, and provide a combined honeycomb design method that can realize the deformation of a specified spatial curved surface, so as to solve the technical problems that the deformation mode of the traditional honeycomb structure is single, the predetermined spatial curved surface cannot be spontaneously formed under simple excitation, and the deformation ability and the bearing capacity of the deformable structure are difficult to be considered.

[0007] To achieve the above-mentioned purpose, the present application provides a combined honeycomb design method that can realize the deformation of a specified spatial curved surface, the core of which is to guide the programmed non-uniform deformation of the overall structure when subjected to uniform global excitation, and finally accurately fit the predetermined three-dimensional spatial curved surface, by heterogeneously combining honeycomb units with different mechanical response characteristics, and pre-setting non-uniform stiffness distribution and deformation mode in the structure.

[0008] The technical scheme of the present application is as follows:

[0009] A combined honeycomb design method that can realize the deformation of a specified spatial curved surface, the steps are as follows:

[0010] Step 1. Three-dimensional modeling of the target three-dimensional spatial curved surface

[0011] Obtain the digital information of the target three-dimensional spatial curved surface, which is point cloud data obtained by three-dimensional scanning, or a three-dimensional model generated by computer-aided design (CAD) software, or a mathematical function expression S(x,y,z).

[0012] Step 2. Curvature analysis and discretization

[0013] Differential geometry analysis is performed on the target three-dimensional spatial curved surface, and the Gaussian curvature K of each point on the surface is calculated, K is the product of the principal curvatures κ1 and κ2. According to the sign (positive, negative, zero) of the Gaussian curvature K, the target three-dimensional spatial curved surface is divided into regions with different geometric characteristics, and then the entire target three-dimensional spatial curved surface model is discretized into a grid composed of a plurality of small deformation units in the parameter domain.

[0014] Further, the Gaussian curvature K is the product of the two principal curvatures κ1 and κ2, and the specific formula is as follows:

[0015]

[0016] Where (E,F,G) is the first fundamental form of the surface, and (L,M,N) is the second fundamental form of the surface.

[0017] The two principal curvatures κ1 and κ2 are calculated simultaneously, and the calculation formula is shown in formula (3):

[0018]

[0019] where the coefficients of the first and second fundamental forms are calculated by the partial derivatives of the surface parameter equation

[0020]

[0021] where, denotes the partial derivative vector of the target surface parameter equation r(u,v) with respect to the parameters u,v. denotes the second-order partial derivative vector of the target surface parameter equation r(u,v) with respect to the parameters u,v.

[0022] And the unit normal vector n of the surface is calculated as shown in equation (5):

[0023]

[0024] So the final expression of the Gaussian curvature of the surface is shown in equation (6):

[0025]

[0026] Further, when the local curvature of the target three-dimensional space surface satisfies the condition K>0, the region is an ellipsoidal region; when the local curvature of the target three-dimensional space surface satisfies the condition K<0, the region is a saddle-shaped region; when the local curvature of the target three-dimensional space surface satisfies the condition K=0, the region is a cylindrical surface region.

[0027] Step 3. Construction of the honeycomb macro-mechanical response characteristic proxy model

[0028] Step 3.1, define the unit configuration: three basic topological configurations are defined: regular hexagonal honeycomb, rectangular honeycomb and concave hexagonal honeycomb. The geometric parameters of each configuration include: wall thickness t, unit width w, unit length l, internal angle θ and height h.

[0029] Step 3.2, obtain the material constitutive parameters through experiments;

[0030] Step 3.3, use the central composite design method to sample the geometric parameters of the honeycomb structure, and the honeycomb representative volume elements with their respective geometric parameters obtained after sampling constitute the data set for machine learning.

[0031] Step 3.4, using the honeycomb representative volume elements with their respective geometric parameters obtained in step 3.3 and the material constitutive parameters obtained in step 3.2, the macro-mechanical response characteristics corresponding to different honeycomb representative volume elements are obtained through numerical homogenization analysis.

[0032] ​Step 3.5, machine learning is performed by taking the honeycomb representative volume elements with respective geometric parameters obtained in step 3.3 as input and the macro-mechanical response characteristics of different honeycomb representative volume elements obtained in step 3.4 as output, to obtain a surrogate model capable of quickly predicting the macro-mechanical response characteristics of the honeycomb under any combination of geometric parameters. eff ,E eff ,…) of the honeycomb.

[0033] Step 4. Configuration mapping

[0034] Based on the honeycomb representative volume elements with respective geometric parameters obtained in step 3.3 and the corresponding macro-mechanical response characteristics obtained in step 3.4, a qualitative mapping relationship between the macro-mechanical response characteristics (ν eff ,E eff ,…) and the local Gaussian curvature of the target surface is obtained through finite element numerical simulation: the positive Gaussian curvature region with K>0 corresponds to the concave honeycomb filled with equivalent Poisson's ratio ν eff <0; the negative Gaussian curvature region with K<0 corresponds to the positive hexagonal honeycomb filled with equivalent Poisson's ratio ν eff >0; the zero Gaussian curvature region with K=0 corresponds to the rectangular honeycomb filled with equivalent Poisson's ratio ν eff =0.

[0035] Step 5. Parameter mapping

[0036] Step 5.1, the target principal curvature κ 目标 is set as the optimization target, the target principal curvature κ 目标 includes the principal curvatures κ1 and κ2; according to the plate and shell mechanics theory, the target principal curvature κ 目标 corresponding to the target macro-mechanical response characteristics y 目标 is obtained; the target performance y 目标 is a vector containing the macro-mechanical response characteristics such as the target equivalent Poisson's ratio ν 目标 and the target equivalent Young's modulus E 目标 , i.e. y 目标 ={ν 目标 ,E 目标 ,...}.

[0037] Step 5.2, the prediction performance f(x) of the surrogate model is a vector containing multiple prediction values, f(x)={f ν(x) ,f E(x) ,...}. Genetic algorithm or particle swarm optimization algorithm is adopted to minimize the weighted error between the performance f(x) predicted by the surrogate model and the target macro-mechanical response characteristics y 目标 , and thus obtain the optimal geometric parameters of the filled honeycomb. The objective function is:

[0038] min[w ν ‖f ν (x)-v 目标 ‖ 2 +w E ·‖f E (x)-E 目标 ‖ 2 +…] (7)

[0039] wherein: w v , w E are the weight coefficients of the corresponding equivalent Poisson's ratio, equivalent Young's modulus error term, used to adjust the importance of different mechanical response characteristics in the optimization process, the greater the weight, the smaller the error of the corresponding characteristics, the greater the impact on the optimization goal.f v (x) is the equivalent Poisson's ratio predicted by the surrogate model.f E (x) is the equivalent Young's modulus predicted by the surrogate model.v 目标 is the target equivalent Poisson's ratio expected to be achieved in design, E 目标 is the target equivalent Young's modulus expected to be achieved in design.x represents the geometric parameters of the filled honeycomb.

[0040] Compared with the prior art, the present application has achieved remarkable beneficial effects through the above technical solutions:

[0041] 1) Achieve precise controllable programmable deformation: the present application establishes a quantitative mapping relationship between the target curvature and the honeycomb microstructure, converts complex macroscopic deformation requirements into microstructure design, and thus realizes precise, programmable shape transformation from an initial two-dimensional plane to an arbitrary three-dimensional spatial surface.

[0042] 2) Simplify the drive and achieve preset deformation: the structure designed by the present application does not require complex external molds or multi-point driving systems, only a simple, globally unified excitation is needed to activate the preset deformation, greatly simplifying the driving and control system.

[0043] 3) Light weight and high bearing capacity: the present application realizes large deformation while completely inheriting the advantages of light weight and high strength of the honeycomb structure, and the deformed curved surface structure can stably exist and withstand considerable external load, successfully overcoming the technical contradiction between large deformation and high bearing capacity of traditional deformable structures. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a flowchart of a combined honeycomb design method for realizing specified spatial curved surface deformation according to the present application.

[0045] Figure 2are configuration diagrams of several typical honeycomb cells in the honeycomb cell database of the present application; wherein (a) is a regular hexagonal honeycomb, (b) is a rectangular honeycomb, and (c) is a concave hexagonal honeycomb.

[0046] Figure 3 are schematic diagrams of the global deformation and corresponding different sign Gaussian curvature of three kinds of honeycomb structures provided by the present application under global excitation load; wherein (a) is a regular hexagonal honeycomb deformed into a saddle shape corresponding to negative Gaussian curvature K<0, (b) is a concave hexagonal honeycomb deformed into an ellipsoid shape corresponding to positive Gaussian curvature K>0, and (c) is a rectangular honeycomb deformed into a cylindrical shape corresponding to positive Gaussian curvature K=0.

[0047] Figure 4 is a schematic diagram of the numerical homogenization method adopted by the present application to obtain the macroscopic mechanical properties of honeycomb, which shows six kinds of unit strain loads applied to the representative volume element (RVE).

[0048] Figure 5 is a schematic diagram of the experimental equipment for verifying the deformation state of the combined honeycomb structure of the present application.

[0049] Figure 6 is a design diagram and deformation effect diagram of embodiment one of the present application; wherein (a) is a planar combined honeycomb plate arrangement designed to realize the deformation of a complex combined surface similar to a dumbbell, and (b) is a schematic diagram of the state of the combined honeycomb plate spontaneously deformed into the target complex combined surface after being excited by buckling.

[0050] Figure 7 is a design diagram and deformation effect diagram of embodiment two of the present application; wherein (a) is a regular hexagonal honeycomb plate arrangement with wall thickness gradient designed to realize the deformation of a saddle surface, and (b) is a schematic diagram of the state of the honeycomb plate spontaneously deformed into the target saddle surface after being excited by buckling.

[0051] Figure 8 is a real object diagram of two combined honeycomb structure samples designed and manufactured by the method of the present application.

[0052] Figure 9 is a complete design process description of the generation of the target surface to the honeycomb arrangement in the embodiment of the present application. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. The embodiments are part of the embodiments of the present application, rather than all. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0054] As Figures 1 to 9As shown, the embodiment of the present application provides a combined honeycomb design method which can realize the deformation of a specified spatial curved surface. The method comprises a target curved surface input and analysis step, a honeycomb unit database establishment step, a deformation amount and unit mapping step, and a combined honeycomb generation and verification step. First, through the target curved surface input and analysis step, differential geometry analysis is performed on the three-dimensional target curved surface to be deformed, the Gaussian curvature and principal curvature distribution are calculated, and the target curved surface is discretized into a variable cell grid. Next, based on the pre-established honeycomb unit database containing different geometric configurations and parameters, the deformation amount and unit mapping method is used to map the local deformation amount required by each variable cell grid to a honeycomb unit with specific mechanical response. Finally, through the combined honeycomb generation and verification step, the grid is filled and arranged on the initial two-dimensional planar configuration, thereby designing a integrated combined honeycomb structure which can spontaneously deform into a target spatial curved surface under global unified excitation. As shown, Figure 1 As shown, the present application discloses a combined honeycomb design method which can realize the deformation of a specified spatial curved surface. The method aims to create a heterogeneous honeycomb structure which can spontaneously deform from an initial planar state to a predetermined three-dimensional curved surface through a reverse design process. The specific steps of the method are described in the summary section, and here they will be described in more detail through examples.

[0055] Step one, the target curved surface input and analysis step, the specific steps are as follows:

[0056] (1) Three-dimensional modeling of the target spatial curved surface: Use three-dimensional computer-aided design (CAD) software, such as SolidWorks 2022 version, to establish or import an accurate digital model of the target spatial curved surface. The model can be a parametric curved surface or a free curved surface fitted from point cloud data obtained through reverse engineering such as three-dimensional scanning. Further, by analyzing the curvature of the target spatial curved surface, the Gaussian curvature distribution of the target spatial curved surface is obtained, and the specific division method of Gaussian curvature is described in step 2;

[0057] (2) Curvature calculation: Import the established curved surface model into mathematical analysis software, such as MATLAB R2021b, and use its differential geometry toolbox to perform curvature analysis. According to the first fundamental form (E, F, G) and the second fundamental form (L, M, N) of the curved surface, the precise Gaussian curvature K and the average curvature H of each point on the curved surface are calculated. The calculation formulas are shown in equations (1) and (2):

[0058]

[0059] The two principal curvatures κ1 and κ2 are also calculated, and the calculation formula is shown in equation (3):

[0060]

[0061] where the coefficients of the first and second fundamental forms are calculated by the partial derivatives of the parametric equation of the surface

[0062]

[0063] and the unit normal vector of the surface is calculated as shown in equation (5):

[0064]

[0065] Therefore, the final expression of the Gaussian curvature of the surface is shown in equation (6):

[0066]

[0067] When the local curvature of the surface satisfies the condition K>0, according to the relationship between the Gaussian curvature and the type of points on the surface, it can be known that the type of points in the region is elliptic point, and the representative surface is shown in (a) of Figure 3 When the Gaussian curvature K of the region is equal to 0, the type of points in the region is hyperbolic point, and the representative surface is shown in (b) of Figure 3 Similarly, when K<0, the type of points in the region is parabolic point, and the representative surface is shown in (c) of Figure 3

[0068] (3) Region division and discretization: according to the sign of the Gaussian curvature K of the target surface, the surface is divided into regions. Specifically, the region with K>0 is defined as a positive curvature region, the region with K<0 is defined as a negative curvature region, and the region with K≈0 is defined as a zero curvature region. Subsequently, in order to facilitate subsequent cell mapping, the entire surface model is discretized into a P×Q quadrilateral variable cell grid on the parameter domain. It should be noted that the "grid" is a conceptual design partition, and the size is much larger than a single honeycomb cell. Each grid will be filled with multiple honeycomb cells. The designer can determine the number of grids (P×Q) according to the total size (such as total length L tatal , total width W total ) of the target surface and the required design accuracy, and then determine the reference size of a single honeycomb cell (for example, the cell length l≈L total / Q).

[0069] Step two: proxy model establishment: this step aims to establish a quantitative relationship library between the geometric information of the honeycomb cell and its mechanical response, which specifically includes:

[0070] (1) Cell configuration definition: as shown in Figure 2 , three basic topological configurations are defined: regular hexagonal honeycomb Figure 2 ​​(a) in FIG. 1, rectangular honeycomb Figure 2 (b) in FIG. 1, and concave hexagonal honeycomb Figure 2 (c) in FIG. 1. The geometric parameters of each configuration include: wall thickness t, cell width w, cell length l, internal angle θ, and height h.

[0071] (2) Material constitutive model acquisition:

[0072] (2.1) To ensure the accuracy of the finite element analysis, the precise constitutive model of the manufacturing material needs to be obtained. In this embodiment, a commercial thermoplastic polyurethane (TPU, Shore hardness 95A) material is selected. According to the GB / T 528-2009 standard, standard tensile specimens are printed by Fused Deposition Modeling (FDM) technology.

[0073] (2.2) Uniaxial tensile tests are performed on standard tensile specimens on a universal testing machine (e.g. Instron 5967) at a loading rate of 5 mm / min, while the non-contact digital image correlation (DIC) technique is used to measure the surface strain field in real time.

[0074] (2.3) The obtained "nominal stress-nominal strain" data is imported into the material module of the finite element software ANSYS Workbench2021R2, and the Mooney-Rivlin five-parameter hyperelastic model is selected for fitting, so as to obtain the material constitutive parameters required for subsequent simulation. In the embodiments of the present application, unless otherwise specified, the materials used are single homogeneous thermoplastic polyurethane (TPU, Shore hardness 95A). The structure is manufactured by Fused Deposition Modeling (FDM) 3D printing technology.

[0075] (3) Numerical homogenization analysis and performance prediction:

[0076] (3.1) The central composite design method is used to sample the geometric parameters of the honeycomb structure, and the honeycomb structures with their respective geometric parameters are used to form a data set for machine learning.

[0077] Specifically: in ANSYS software, under the condition of geometric parameter boundary conditions (such as l from 6mm to 12mm, t from 0.5mm to 1.6mm, θ from 60° to 130°, w from 8mm to 20mm, h from 1mm to 10mm), the central composite design method is used to construct different representative volume elements (RVE) of the honeycomb.

[0078] (3.2) Using the honeycomb structures with their respective geometric parameters obtained in step (3.1) and the material constitutive parameters obtained in step (2.3), the macroscopic mechanical response characteristics of different honeycomb structures are obtained through numerical homogenization analysis.

[0079] Specifically: asFigure 4 The complete macroscopic three-dimensional stiffness matrix of the honeycomb is calculated by applying six independent unit strains and periodic boundary conditions to a representative volume element (RVE) of the honeycomb using the strain energy equivalence principle, and then the macroscopic mechanical response characteristics are obtained.

[0080] Step 3.5, taking the honeycomb structure with respective geometric parameters obtained in step (3.1) as the input of machine learning, and taking the macroscopic mechanical response characteristics of different honeycomb structures obtained in step (3.2) as the output of machine learning, machine learning is performed to obtain a proxy model capable of quickly predicting the macroscopic mechanical response characteristics (ν eff ,E eff ,…) of the honeycomb under any combination of geometric parameters.

[0081] Specifically, machine learning is based on input and output data to train a multi-input and multi-output neural network, the target error is 1e-4, the learning rate is 0.01, the sigmoid and tanh functions are selected as the activation function, 80% is selected as the training set, and 20% is selected as the test data for training and testing. Through this process, a proxy model capable of quickly predicting the macroscopic mechanical response characteristics (ν eff ,E eff ,…) of the honeycomb under any combination of geometric parameters is finally established.

[0082] Step three: the method for establishing the deformation-unit mapping relationship specifically includes the following steps:

[0083] (1) Configuration mapping: the establishment of this mapping relationship is completed by finite element numerical simulation on the three basic honeycomb configurations shown in Figure 2 This is the core idea of the method, that is, to establish a direct mapping between the local Gaussian curvature of the target surface and the macroscopic mechanical response characteristics (ν eff ,E eff ,…) of the honeycomb; the qualitative mapping relationship between the macroscopic mechanical response characteristics (ν eff ,E eff ,…) and the local Gaussian curvature of the target surface is obtained by finite element numerical simulation; in the simulation, high-order solid elements SOLID186 are used to divide the model into meshes, the macroscopic mechanical response characteristics obtained above are assigned, global excitation load is applied, and the large deformation geometric nonlinear analysis switch is turned on, the structure is solved and post-processed, and the deformation cloud diagram of different honeycomb plates is obtained. From the simulation results of different honeycomb plates, the Gaussian curvature K distribution of the surface of the honeycomb plate is extracted, and the relationship is established; that is as in (b) of Figure 3 ; as in Figure 3 , as in Figure 3(c) in claim 1.

[0084] (2) Parameter mapping: To precisely control the magnitude of curvature, further mapping between principal curvature κ and honeycomb geometry parameters is needed, which is to embed the neural network surrogate model built in step two into the optimization algorithm framework as an efficient performance prediction tool, and determine the optimal geometry parameters through iterative optimization. The specific implementation is as follows:

[0085] (1) Set optimization goal: for each grid after discretization, the optimization goal comes from the target principal curvature κ determined in step one 目标 . The present application utilizes the principle that the honeycomb structure as a kind of orthotropic plate will occur out-of-plane buckling when subjected to global excitation. According to the theory of plate and shell mechanics, the stable three-dimensional curved surface morphology formed after the buckling of the orthotropic plate depends on the macroscopic mechanical response characteristics of the plate. Therefore, the purely geometric design goal (κ 目标 ) can be converted into the design requirement for physical performance, i.e. a set of target macroscopic mechanical response characteristics y 目标 .

[0086] (2) Construct objective function: the goal of optimization is to find a set of geometry parameters, so that the weighted error between the performance f(x) predicted by the neural network surrogate model and the target macroscopic mechanical response characteristics y 目标 is minimized. Here, the target performance y 目标 is a vector containing target equivalent Poisson's ratio ν 目标 and target equivalent Young's modulus E 目标 and other macroscopic mechanical response characteristics, i.e. y 目标 ={ν 目标 ,E 目标 ,...}. Correspondingly, the predicted performance f(x) of the neural network surrogate model is also a vector containing multiple predicted values, f(x)={f ν(x) ,f E(x) ,...}. Therefore, the weighted multi-objective function as shown in (7) is constructed:

[0087] min[w ν ·‖f ν (x)-ν 目标 ‖ 2 +w E ·‖f E (x)-E 目标 ‖ 2 +…] (7)

[0088] (3) Execution of the algorithm: Genetic algorithm or particle swarm optimization algorithm is used to solve the above objective function. In each iteration of the algorithm, the algorithm generates a set of candidate geometric parameters, and calls the trained neural network proxy model to get its predicted mechanical properties f(x) in an instant, and then calculates the error with the target macroscopic mechanical response characteristics (v 目标 ,E 目标 ,…) of the error.

[0089] (4) Obtain the optimal parameters: after multiple iterations, the optimization algorithm will converge and give a set of geometric parameters that minimize the objective function. This set of parameters is the optimal design parameter that can achieve the target curvature.

[0090] (5) Traverse and apply: by traversing all the grids and executing the above optimization process for each grid, the specific geometric parameters of the honeycomb unit that should be filled in each region on the entire plane can be obtained.

[0091] Step four: the combined honeycomb generation and verification method specifically comprises the following steps:

[0092] (1) Arrangement generation: based on the complete mapping relationship established in step three, an algorithm script (for example, using a Python script to drive the CAD software API) is written to automatically generate the initial configuration of the combined honeycomb on a two-dimensional plane. The script reads the discretized curvature data and matches the most suitable honeycomb configuration and geometric parameters for each grid. To prevent unintended deformation of the honeycomb structure during loading, thin plates are added to the upper and lower sides of the honeycomb thick plate. Finally, the STL or STEP file output can be used for 3D printing.

[0093] (2) Manufacturing and experimental verification: the finally determined model is manufactured by FDM 3D printer. As shown in Figure 5 , the finished product is placed on the testing machine to apply the predetermined global excitation, and the mark points are attached to the ends of the test piece. A high-precision handheld three-dimensional scanner (FreeScan UE Pro, precision 0.02mm, fine mode 0.01mm, scanning depth 510mm) is used for measurement. The scanner uses a high-resolution camera, combined with 26 cross-laser beams for global scanning, 7 parallel laser beams for detailed fine scanning, and 1 single-line laser beam for deep hole data acquisition, to accurately capture the deformation profile of the honeycomb structure. Each test piece is scanned from at least 11 angles, and the image registration is completed using the FreeScan software. After removing the noise points, the point cloud data is imported into the Geomagic Control X three-dimensional detection software for comparison and analysis.

[0094] Example one: design and implementation of a complex combined surface

[0095] This embodiment aims to design and manufacture a combined honeycomb structure that can spontaneously deform into a complex surface containing both positive and negative Gaussian curvature regions.

[0096] (1) Target surface definition and analysis: A dumbbell-like target surface is defined as the design goal of this embodiment. The total length of the surface is 281 mm, with two convex spherical cap regions at both ends, each with a length of 99 mm, and a concave saddle-shaped neck region in the middle, with a length of 83 mm. According to the curvature analysis method in step one, the target surface can be clearly divided into three regions: two convex spherical cap regions with positive Gaussian curvature (K > 0) at both ends, and a concave saddle-shaped region with negative Gaussian curvature (K < 0) in the middle.

[0097] (2) Honeycomb cell mapping and parametric design: To achieve reverse design from the target surface to the planar honeycomb arrangement, according to the configuration mapping rules in step three, the following operations are performed:

[0098] Cell configuration selection: Since the two convex spherical cap regions have positive Gaussian curvature, the concave hexagonal honeycomb shown in (c) of Figure 2 is selected for filling (with a base angle θ r = 70°); since the concave saddle-shaped region has negative Gaussian curvature, the convex hexagonal honeycomb shown in (a) of Figure 2 is selected for filling (with a base angle θ h = 120°).

[0099] Cell parameter determination: To accurately match the different curvature sizes of each point on the target surface, the geometric parameters of the honeycomb cells need to be gradient designed. In this embodiment, the cell height h is selected for regulation. For example, for the center point of the saddle-shaped neck region, the absolute value of the target principal curvature is the largest, and through the optimization algorithm described in step three (2) of the invention, it can be determined that the honeycomb cell height h at this position should take the minimum value of 1 mm. Correspondingly, for the regions with relatively flat curvature, the solved cell height h is larger, with a maximum of 5 mm. Other geometric parameters are set in this embodiment as follows: cell length l = 18 mm, wall thickness t = 1 mm.

[0100] (3) Combined honeycomb planar configuration generation and verification: The honeycomb cells with different configurations and gradient heights obtained by the above mapping are combined and arranged on the initial two-dimensional plane to generate a 281 mm x 108 mm planar combined honeycomb plate, and the final planar arrangement diagram is shown in (a) of Figure 6 . The entity is manufactured using TPU 95A material and FDM printer. It is placed on the testing machine to apply a 20% buckling strain. The experimental results show that the planar structure stably spontaneously deforms into the preset dumbbell-like three-dimensional surface, as shown in Figure 6The RMS error with the target model is less than 2.5% through three-dimensional scanning comparison, verifying the success of the design.

[0101] Example Two: Saddle Design with Gradient Wall Thickness

[0102] This example aims to elaborate the process of realizing a single type of non-uniformly sized negative Gaussian curvature surface through a relatively concise design.

[0103] (1) Target surface input and analysis: The target surface is a standard saddle with a size of 180 mm x 135 mm, with all points having a Gaussian curvature K < 0, and the absolute value of the curvature gradually increases from one side to the other.

[0104] (2) Honeycomb cell mapping and parametric design: Since only negative Gaussian curvature is included, all hexagonal honeycombs are selected. To match the gradient distribution of curvature size, only the wall thickness t needs to be designed with a gradient. The side with the smallest curvature corresponds to the thickest wall thickness t max = 1.2 mm; the side with the largest curvature corresponds to the thinnest wall thickness t min = 0.6 mm.

[0105] (3) Honeycomb arrangement generation and deformation: A 180 mm x 135 mm planar gradient honeycomb plate composed only of hexagonal honeycombs is generated, as shown in (a) of Figure 7 The wall thickness decreases linearly from one side to the other. The entity is manufactured using TPU 95A material and an FDM printer. As shown in (b) of Figure 7 After applying a 22% flexural strain, the structure accurately deforms into the preset saddle. This example demonstrates that through fine control of a single geometric parameter, the precise molding of a specific surface can be achieved.

[0106] As shown in Figure 8 are other embodiments of the present application, Figure 9 is a complete design process description from the target surface to the honeycomb arrangement generation.

[0107] In this specification, specific examples are applied to explain the principles and implementation methods of the present application. The description of the examples is only used to help understand the method and core idea of the present application, and is not a limitation of the present application. Based on the understanding of the idea of the present application, the skilled person can make corresponding changes in specific implementation methods and application ranges. Therefore, the content of this specification should not be regarded as a limitation of the present application.

Claims

1. A method of designing a combined honeycomb, which can realize a prescribed spatial surface deformation, characterized by, The steps are as follows: Step 1. Three-dimensional modeling of the target three-dimensional spatial surface; Step 2. Curvature analysis and discretization; Step 3. Construction of a honeycomb macroscopic mechanical response characteristic proxy model; Step 4. Configuration mapping; Step 5. Parameter mapping.

2. The method of claim 1, wherein, Said step 1 is specifically: obtaining digital information of the target three-dimensional spatial surface, wherein the digital information is point cloud data obtained by three-dimensional scanning, or a three-dimensional model generated by computer-aided design software, or a mathematical function expression S(x, y, z).

3. The method of claim 1, wherein the method is a method of designing a combined honeycomb that can achieve a prescribed spatial surface deformation. Said step 2 is specifically: performing differential geometry analysis on the target three-dimensional spatial surface, calculating the Gaussian curvature K of each point on the surface, wherein K is the product of the principal curvatures κ1 and κ2; dividing the target three-dimensional spatial surface into regions with different geometric characteristics according to the sign of the Gaussian curvature K, and then discretizing the entire target three-dimensional spatial surface model into a grid composed of a plurality of small deformation units in the parameter domain.

4. The method of claim 3, wherein the method is a method of designing a combined honeycomb that can achieve a prescribed spatial surface deformation. The Gaussian curvature K is the product of the two principal curvatures κ1 and κ2, and the specific formula is as follows: Where (E, F, G) is the first fundamental form of the surface, and (L, M, N) is the second fundamental form of the surface; The two principal curvatures κ1 and κ2 are calculated, and the calculation formula is as shown in formula (3): where the coefficients of the first and second fundamental forms are calculated from the partial derivatives of the parametric equation of the surface ​ wherein, denotes the partial derivative vector of the target surface parameter equation r(u,v) with respect to the parameters u, v; denotes the second-order partial derivative vector of the target surface parameter equation r(u,v) with respect to the parameters u, v; And the unit normal n of the surface is calculated, and the calculation formula is as shown in formula (5): Therefore, the final expression of the Gaussian curvature of the surface is as shown in formula (6): Further, when the local curvature of the target three-dimensional spatial surface satisfies the condition K>0, the region is an ellipsoidal region; when the local curvature of the target three-dimensional spatial surface satisfies the condition K<0, the region is a saddle-shaped region; and when the local curvature of the target three-dimensional spatial surface satisfies the condition K=0, the region is a cylindrical surface region.

5. The method of claim 1, wherein the method is a method of designing a combined honeycomb that can achieve a prescribed spatial surface deformation. Said step 3 is specifically: Step 3.1, define the unit configuration: three basic topological configurations are defined, namely, a regular hexagonal honeycomb, a rectangular honeycomb and an inwardly recessed hexagonal honeycomb; the geometric parameters of each configuration include: wall thickness t, unit width w, unit length l, internal angle θ and height h; Step 3.2, obtain the material constitutive parameters through experiments; Step 3.3, sample the geometric parameters of the honeycomb structure by using the central composite design method, and form a data set for machine learning by using the representative volume elements of the honeycomb with respective geometric parameters after sampling; Said step 5 is specifically: Step 3.

5. Take the honeycomb representative volume elements with respective geometric parameters obtained in step 3.3 as input and the macro-mechanical response characteristics of different honeycomb representative volume elements obtained in step 3.4 as output, and perform machine learning to obtain a surrogate model capable of quickly predicting the macro-mechanical response characteristics of the honeycomb under any combination of geometric parameters. eff ,E eff ,… 6. The method of claim 5, wherein the method is a method of designing a combined honeycomb that can achieve a prescribed spatial surface deformation. The step 4 is specifically: based on the honeycomb representative volume element with respective geometric parameters obtained in step 3.3, and the corresponding macro-mechanical response characteristics obtained in step 3.4, the qualitative mapping relationship between the macro-mechanical response characteristics (ν eff , E eff , …) and the local Gaussian curvature of the target surface is obtained through finite element numerical simulation: the positive Gaussian curvature region with K>0 corresponds to the concave honeycomb with the equivalent Poisson's ratio ν eff <0; the negative Gaussian curvature region with K<0 corresponds to the positive hexagonal honeycomb with the equivalent Poisson's ratio ν eff >0; the zero Gaussian curvature region with K=0 corresponds to the rectangular honeycomb with the equivalent Poisson's ratio ν eff =0.

7. The method of claim 1, wherein the method is a method of designing a combined honeycomb that can achieve a prescribed spatial surface deformation. The objective function is: Step 5.1, set the target principal curvatures κ 目标 as optimization objectives, the target principal curvatures κ 目标 include principal curvatures κ1and κ2; according to the theory of plate shell mechanics, the target principal curvatures κ 目标 corresponding to the target macro mechanical response characteristics y 目标 ; the target performance y 目标 is a vector, containing target equivalent Poisson's ratio ν 目标 and target equivalent Young's modulus E 目标 and other macro mechanical response characteristics, that is, y 目标 ={ν 目标 ,E 目标 ,...} Step 5.2, the prediction performance f(x) of the surrogate model is a vector containing multiple prediction values, f(x) = {f ν(x) ,f E(x) ,...}; a genetic algorithm or a particle swarm optimization algorithm is used to minimize the weighted error between the performance f(x) predicted by the surrogate model and the target macro-mechanical response characteristics y 目标 , and thus obtain the optimal geometric parameters of the filled honeycomb; wherein ​ min[w ν ·‖f ν (x)-ν 目标 ‖ 2 +w E ·‖f E (x)-E 目标 ‖ 2 +…] (7) wherein: w v , w E are the weight coefficients of the error terms of the equivalent Poisson's ratio, the equivalent Young's modulus, respectively, used to adjust the importance of different mechanical response characteristics in the optimization process, the greater the weight, the smaller the error of the corresponding characteristics, the greater the impact on the optimization objective; f v (x) is the equivalent Poisson's ratio predicted by the surrogate model; f E (x) is the equivalent Young's modulus predicted by the surrogate model; v 目标 is the target equivalent Poisson's ratio expected to be achieved in the design, E 目标 is the target equivalent Young's modulus expected to be achieved in the design; x represents the geometric parameters of the filled honeycomb.

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