Texture structure design space, design method and system of 3D printed flexible structure and flexible structure

Abstract

The invention discloses a texture structure design space, a design method and a design system of a flexible structure for 3D printing and the flexible structure. The design method comprises the steps of designing spiral texture structure units, constructing the texture structure design space, splicing the corresponding spiral texture structure units in a grid surface, adjusting local characteristics of the flexible structure and forming the final flexible structure. A spiral-based elastic structure unit is used as a basic construction block for texture synthesis to generate a self-adaptive texture structure, so that the whole working process from design to manufacturing is simplified, an interactive user interface is adopted, texture design, performance preview and G code generation are seamlessly integrated together, cross-platform conversion is not needed, cross-platform conversion is eliminated, and the working efficiency is improved. And the manufacturing efficiency is obviously improved. A data-driven prediction model is adopted, and key mechanical characteristics such as rigidity and ductility can be efficiently approximated. The prediction result is directly visualized on the design structure, visual feedback is provided, and seamless iterative design optimization can be achieved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of 3D printing, and particularly relates to a texture structure design space, a design method, a system and a flexible structure of 3D printing. BACKGROUND

[0002] Flexible fabrics are widely used in wearable devices, human-computer interaction interfaces, flexible electronics, robot skins and other fields. Although traditional textile technology is mature, it has certain limitations in realizing complex structure design, material performance customization and automated manufacturing, especially in terms of material waste, design complexity and production cycle.

[0003] In the prior art, there is a research direction of preparing flexible structures by 3D printing technology, such as a scheme of constructing flexible structure units based on hinge structures, wave structures and spiral structures and other geometric units. These methods can improve customizability, but generally face the following problems:

[0004] Lack of flexible structure design tools, relying on professional modeling knowledge;

[0005] Without real-time performance feedback mechanism;

[0006] Manufacturing processes are scattered among multiple platforms, and the operation is complex;

[0007] Limited control ability of stiffness and ductility in different regions.

[0008] Flexible fabrics are widely used in clothing, wearable devices and hardware interfaces, but traditional manufacturing methods have problems such as material waste, high cost and complex process. 3D printing provides a promising alternative solution for this field, but due to the complexity of the structure and the reliance on repeated trials, the design of flexible fabrics is still quite challenging.

[0009] 3D printing technology has been used for the fabrication of flexible textiles through two approaches: (1) printing on existing flexible materials; (2) printing the flexible textile itself. Printing on existing flexible materials. 3D printing has been used to create specialized textures or structures on flexible materials (e.g., cloth) to enable dynamic shape changes. For example, a structure was designed and printed on a garment to transform the cloth into a functional button, shape memory alloy was 3D printed on a garment and its deformation was adjusted by applying an electrical stimulus. In some methods, the structure is printed on a pre-stretched material so that when the stress is released, the material forms the designed shape. Many interactive tools have been developed to support the 3D printing of complex digital models. General-purpose slicing software, which can convert 3D models (e.g., STL, 3MF, OBJ formats) into G-code for printing. However, these tools do not facilitate the direct design of complex geometric models, and users need to rely on CAD software for modeling. This cross-platform workflow prolongs the development cycle of 3D printing. To address this issue, some research explores interactive tools that combine design and manufacturing. For example, allowing users to directly design complex models and generate G-code in Grasshopper through visual programming. There is currently no tool specifically for the manufacture of flexible textiles.

[0010] Designing 3D-printed flexible fabrics faces a major challenge: creating aesthetically pleasing and structurally sound infill patterns to achieve the desired properties (e.g., stiffness and elasticity) while conforming to a given fabric profile. Traditional methods require a complex multi-step workflow, forcing users to switch back and forth between computer-aided design (CAD), computer-aided engineering (CAE), and slicing tools. These processes are highly dependent on the user's expertise and repeated trials, which are both tedious and time-consuming. Therefore, a tool is needed to simplify the design process, automatically generate infill patterns, and provide real-time feedback on structural performance. SUMMARY

[0011] The technical problem solved by the present application is to provide a 3D-printed flexible structure texture design space, a design method, a system and a flexible structure, which solves the problem of diversified design demand of 3D-printed flexible structure in the prior art.

[0012] The present application solves the above technical problems by adopting the following technical solutions:

[0013] The texture design space includes four dimensions: grid type, grid density, spiral angle, and spiral arrangement. The grid type is used to control the flexibility and aesthetics of the flexible structure; the grid density determines the rigidity of the flexible structure; the spiral angle controls the ductility of the flexible structure; and the spiral arrangement determines the stretching direction of the flexible structure.

[0014] The grid type includes triangle, quadrilateral and polygon; the grid density is controlled by the grid side length; the spiral angle controls the curvature and ductility of the spiral line; the spiral arrangement mode includes two modes of corner point alignment and edge alignment.

[0015] The design method of the flexible structure of 3D printing comprises the following steps:

[0016] Step 1, design a spiral texture structure unit, each texture structure unit contains several concentric Archimedes spiral lines which can freely regulate the spiral angle;

[0017] Step 2, according to the flexible structure to be designed, determine the contour area, and divide the contour area into several grid surfaces; according to the texture structure design space of claim 1, paste the corresponding spiral texture structure unit in each grid surface;

[0018] Step 3, according to the local characteristics of the flexible structure, adjust the density and helicity of the spiral line in the grid surface by setting the reference point, connect the spiral line to give the overall structure elasticity, and form the final flexible structure.

[0019] In each spiral texture structure unit, the number of spiral lines corresponds to the number of edges of the grid surface.

[0020] It also includes applying a data-oriented CAE model to test the performance of the flexible structure.

[0021] The construction method of the data-oriented CAE model is as follows:

[0022] Firstly, based on the four dimensions of the design space, the grid type and the spiral arrangement mode are combined into several groups, and the input parameters of each group are helicity and density;

[0023] Secondly, based on the input parameters, a flexible structure is generated;

[0024] Then, the corresponding stiffness and ductility of the generated flexible structure are obtained through physical experiments, and a training data set is constructed;

[0025] Finally, based on the training data set, a flexible structure estimation model for estimating ductility and stiffness is trained, and the model is evaluated to verify its accuracy.

[0026] The flexible structure estimation model includes a regression model corresponding to a specific combination of network type and alignment configuration.

[0027] The 3D printing design system of flexible structure includes an interactive user interface, a structure design and generation module, a performance index module, a path planning and G code generation module. The interactive user interface includes a main canvas for user input and structure visualization, allowing users to freely draw any planar contour to define the overall shape of the flexible structure.

[0028] The structure design and generation module includes a structure design configuration panel, which includes a global texture structure configuration panel and a local structure regulation panel, for generating diversified texture structure patterns according to the design method of 3D printed flexible structure, and precisely controlling local flexibility and rigidity, ductility.

[0029] The performance index module is used to real-time feedback the mechanical response performance of the flexible structure.

[0030] The path planning and G code generation module includes a manufacturing configuration panel for directly setting 3D printing related parameters, automatically optimizing printing path and generating G code.

[0031] The performance index module is connected with a data-driven CAE model for real-time regression analysis of the mechanical performance of the flexible structure and feedback of the performance index parameters.

[0032] The flexible structure printed by the 3D printing design system of flexible structure includes a grid surface composed of spiral structure units arranged in a given contour, and each spiral structure unit contains a group of stretchable concentric Archimedes spirals, and the number of spirals in each spiral structure unit corresponds to the number of edges of the respective grid surface.

[0033] Compared with the prior art, the present application has the following beneficial effects:

[0034] 1. TexStructor is the first interactive tool that supports flexible textile design and 3D printing. It simplifies the entire workflow from design to manufacturing, with an interactive user interface that seamlessly integrates texture design, performance preview, and G code generation, eliminating the need for cross-platform conversion and significantly improving manufacturing efficiency.

[0035] 2. Compared with these methods that are usually costly, time-consuming and require professional skills and equipment, the system uses 3D printing technology for flexible textile design and manufacturing. This method can realize rapid production, provide customizable structures, promote material innovation, and better meet various design needs.

[0036] 3. Real-time performance evaluation employs a data-driven predictive model that can efficiently approximate key mechanical properties such as stiffness and ductility. The prediction results are directly visualized on the designed structure, providing intuitive feedback and facilitating seamless iterative design optimization.

[0037] 4. Based on the spiral elastic structural unit as the basic building block of texture synthesis, adaptive texture structure is generated, optimizing mechanical flexibility and geometric complexity, while ensuring the computational efficiency of real-time preview. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the flexible triangular spiral structure unit of the present invention.

[0039] Figure 2 This is a schematic diagram of the flexible quadrilateral spiral structure unit of the present invention.

[0040] Figure 3 This is a schematic diagram of the flexible polygonal spiral structure unit of the present invention.

[0041] Figure 4 This is a schematic diagram of the helical rotation direction of the flexible structure of the present invention.

[0042] Figure 5 This is a schematic diagram of the local structural control of the flexible structure of the present invention.

[0043] Figure 6 This is a schematic diagram of the performance test of the flexible structure of the present invention.

[0044] Figure 7 This is a schematic diagram of the test results of the flexible structure of the present invention.

[0045] Figure 8 This is a schematic diagram of the performance evaluation regression model of the flexible structure of the present invention trained under different conditions.

[0046] Figure 9 A schematic diagram of a fruit platter made using the flexible structure of this invention.

[0047] Figure 10 A schematic diagram of a sports vest made using the flexible structure of this invention.

[0048] Figure 11 A schematic diagram of an indoor sports shoe made using the flexible structure of this invention.

[0049] Figure 12 A flowchart illustrating the manufacturing process of the robot skin made from the flexible structure of this invention.

[0050] Figure 13 A schematic diagram of an electronic skin test fabricated using the flexible structure of this invention. Detailed Implementation

[0051] The structure and working process of the present invention will be further described below with reference to the accompanying drawings.

[0052] The purpose of this solution is to address the challenges of 3D printing flexible fabrics in existing technologies. This solution introduces an interactive 3D printing design system, named TexStructor, for designing and manufacturing flexible textiles with complex textures. This tool allows users to draw textile outlines to generate various structural patterns. Spiral-based elastic structural units are used to fill the outlines, enabling precise control over mechanical properties. To predict structural performance, a data-driven CAE method is integrated, training a regression model using physical experimental data from the system design. The system provides real-time feedback through color-coded visualization, displaying the predicted mechanical properties. Finally, G-code for 3D printing is automatically generated, simplifying the entire workflow from design to manufacturing, eliminating cross-platform conversions, and improving manufacturing efficiency.

[0053] The texture structure design space includes four dimensions: grid type, grid density, spiral angle, and spiral arrangement. Among them, grid type controls the flexibility and aesthetics of the flexible structure; grid density determines the rigidity of the flexible structure; spiral angle controls the extensibility of the flexible structure; and spiral arrangement determines the stretching direction of the flexible structure.

[0054] The grid types include triangles, quadrilaterals, and polygons; the grid density is controlled by the grid side length; the helix angle controls the curvature and extensibility of the helix; the helix arrangement includes two methods: corner alignment and edge alignment.

[0055] The design methodology for flexible structures in 3D printing includes the following steps:

[0056] Step 1: Design a spiral texture structure unit. Each texture structure unit contains several concentric Archimedean spirals whose spiral angles can be freely adjusted.

[0057] Step 2: Determine the contour area according to the required flexible structure, and divide the contour area into several grid surfaces; according to the texture structure design space described in claim 1, assemble the corresponding spiral texture structure unit in each grid surface;

[0058] Step 3: Based on the local characteristics of the flexible structure, adjust the density and helicity of the spiral lines in the grid surface by setting reference points, connect the spiral lines to give the overall structure elasticity, and form the final flexible structure.

[0059] Specific embodiments, such as Figures 1 to 13 As shown:

[0060] The design methodology for flexible structures in 3D printing includes the following steps:

[0061] I. Structural Design and Generation: First, the spiral structural unit is defined as the basic building block of the flexible structure. Then, a design space for generating textured structures is proposed, and the principles of structure generation are further introduced. Within a given contour, a network of spiral structural units is connected by texture splicing to construct a flexible fabric, forming a mesh. Here, the spiral structural unit is the basic building block of the flexible fabric. It is a geometric unit containing a set of stretchable concentric Archimedean spirals, defined by the following parametric functions:

[0062]

[0063] in Let the arc length be , The angle of the helix is ​​determined by the degree of helix curvature. The curvature of these helices can be dynamically adjusted according to the degree of helix, thereby achieving precise control over the extensibility of the unit. The number of helices in each unit corresponds to the number of sides of its respective mesh face. For example, a unit in a triangular mesh contains three helices, while a unit in a quadrilateral mesh has four helices. These curved helices are interconnected, like springs, giving the final flexible structure its elastic properties.

[0064] Design Space: Several factors influence the performance of flexible structures with the proposed structure: mesh type (triangles, quadrilaterals, and polygons) affects the flexibility and aesthetics of the flexible structure; mesh density, determined by side length, determines the rigidity of the flexible structure; helicity controls the ductility of the helix; and the arrangement of the helical units (corner-aligned or edge-aligned) determines the main tensile direction of the flexible structure. Based on these factors, we constructed a design space, providing an intuitive method for precisely controlling the mechanical properties of flexible structures.

[0065] Structure generation; the structure of the repairable textile is generated through two key steps: (1) generating a uniform triangular mesh to fill the fabric outline; (2) mapping predefined helical structural units onto each mesh surface by texture tiling. For example, structural units can be mapped by, but not limited to, methods that map each point on the helical structural unit using centroid coordinates. Place on the triangular face superior:

[0066]

[0067] in ,and Determined in the following ways:

[0068]

[0069] in yes A sub-triangle, in which and .

[0070] For polygonal meshes, the mesh is converted to a triangular mesh before using the above method.

[0071] Local structure control, in this system, allows the user to control the structure around one or more selected reference points. Interactively adjust local density and helicity to customize material properties in different regions. This can be achieved, for example, through a distance field or other alternatives. In this embodiment, a Gaussian distance field is applied to modify the local density and texture helicity of the structure, thereby affecting its mechanical properties. Specifically, for a generated mesh delineated by a given contour, the Gaussian distance value for each vertex is calculated as follows:

[0072]

[0073] in Indicates in The peak value at a given location affects the magnitude of the intensity, and this value can be adjusted interactively by the user. Standard deviation is used to determine The scope of the impact. When adjusting density, it's a vertex in the mesh; when adjusting texture helicity, it's a face center. Specifically, based on... The position of each vertex in the mesh is updated by the gradient of the Gaussian field. , for reference point Adjust the surrounding density:

[0074]

[0075] The spiral structure element has a spiral angle around a reference point in each mesh plane. Depend on Confirmed, among which The center of the corresponding grid surface:

[0076]

[0077] Here, the function Map the Gaussian distance value to an angle within the angle range [0, β], where β is the maximum helix angle specified by the user.

[0078] II. Data-driven CAE collects mechanical property data of textiles with proposed structures through physical experiments, altering key parameters in the design space. Using this data, a regression model is trained to estimate the ductility and stiffness of the designed textile. Unlike traditional CAE methods that rely on computationally intensive physical simulations, data-driven methods, while only applicable to materials tested in experiments, offer a more efficient solution. It enables real-time structural editing while maintaining high accuracy.

[0079] Experimental conditions: A series of flexible textile samples were 3D printed using a TPU-95A 3D printer. Design parameters were systematically varied to evaluate two key performance indicators: stiffness and ductility. For stiffness testing, 216 samples were fabricated (details in Table 1), and their bending resistance was measured under controlled conditions. For ductility testing, samples were evaluated in two tensile directions: triangular and polygonal meshes were tensile tested in the vertical and horizontal directions, respectively, while quadrilateral meshes were tensile tested in the vertical and 45° directions. This resulted in a total of 432 samples (216 in each direction). To prevent overfitting and ensure robust regression analysis, an additional 120 samples were printed, with parameters randomly selected for each performance indicator. All these samples provide a comprehensive basis for analyzing how texture structure affects stiffness and ductility. Test samples were fabricated under fixed 3D printing conditions using common settings: 0.4 mm linewidth, 0.2 mm layer height, and two layers.

[0080] Table 1

[0081]

[0082] To balance the integrity of the texture structure and functional flexibility during testing, two key parameters—density (controlled by edge length) and helix angle—were carefully calibrated to prepare the test samples.

[0083] Density constraints are applied, with side length directly determining the density of the structure. Experiments have shown that side lengths less than 2 mm cause adjacent mesh cells to merge, reducing flexibility due to an overly dense pattern. Conversely, side lengths greater than 8 mm weaken the material's strength due to an overly sparse structure. Therefore, we limit the side lengths to a validated range of 2 to 8 mm to maintain optimal flexibility and strength.

[0084] Helix angle constraint: The helix angle controls the ductility of the helical geometry. When the helix angle is 0 radians, the structure becomes a rigid line without ductility. Angles exceeding π radians cause the helical curves to overlap and merge during printing, thus affecting flexibility. Therefore, we limit the helix angle to a functional range of 0 to π radians to ensure ductility and avoid structural interference.

[0085] Test Procedure: In the experiment, two key properties, stiffness and ductility, were estimated using the following methods:

[0086] Stiffness (i.e., rigidity) was measured using the heart-ring test [4,24]. This method involves bending the sample into a heart shape and measuring the sag length (ring length) to quantify the deformation caused by gravity, thus characterizing the sample's stiffness. A shorter sag length indicates higher stiffness. Each sample was 16 cm × 2 cm in size to ensure sufficient length for bending and sag under gravity.

[0087] Extensibility is tested by stretching the sample to the point of fracture using a tensile testing machine and measuring its elongation. Elongation at break (i.e.) , The structural ductility is assessed by measuring the original length of the sample. In this test, each sample measures 2 cm × 1.6 cm, ensuring that it can be clamped and stretched to break within the effective range of the testing machine.

[0088] Regression analysis: Figure 7 Experimental results demonstrating stiffness and ductility are presented. Specifically, such as... Figure 7 As shown in (a), stiffness decreases with increasing mesh side length, with the quadrilateral mesh exhibiting the lowest stiffness. Experimental results also indicate that the torsional angle affects stiffness, although the degree of influence varies depending on the structural parameters. Figure 7 In (b), the extensibility increases with the increase of the helix angle. However, in corner-aligned structures, excessive helicity or small-scale structures can lead to structural fusion, thus significantly reducing extensibility. Based on experimental data, several methods, but not limited to the methods in the following examples, can support this process for effectively predicting structural performance. A training dataset containing a set of triples has been prepared. ,in, Representing the first The helix angle, side length (defining the mesh density), and experimental results (indicating stiffness or ductility) of each test sample were used. To establish a model relating these parameters and fabric properties, this example trained six independent cubic polynomial regression models, each corresponding to a specific combination of mesh type (triangular, quadrilateral, or polygonal) and alignment configuration (corner-aligned or edge-aligned). The model is formally defined as follows:

[0089]

[0090] Where Θ is the coefficient vector to be fitted. An n-dimensional vector, where each component represents the performance (i.e., stiffness or ductility) of a sample, where n represents the number of samples. It is an n×10 characteristic matrix. Each row of the matrix... , k∈n is an eigenvector of a cubic polynomial, defined as follows:

[0091]

[0092] in It is the helix angle. This is the side length of the training sample. Least squares error is used to minimize the prediction error. and training values :

[0093]

[0094] Figure 8 The results of the final regression models used to estimate the stiffness and extensibility of textiles under different conditions are presented.

[0095] It should be noted that this embodiment only uses six independent cubic polynomials to form a regression model and provides a detailed example of the scheme. It is not a limitation on the regression model. In specific applications, technicians can use various methods of representing the regression model, such as quadratic polynomials, quartic polynomials, etc. Any alternative that can achieve the function is acceptable.

[0096] III. Application Examples: Through multiple application examples, the potential value of TexStructor is demonstrated, including clothing, shoes, flexible electronic skin, and robotic skin.

[0097] 1. Apparel: This section showcases an example of applying TexStructor to functional apparel design to meet the growing demand for comfortable and stable sportswear driven by increasing female participation in sports. The prototype sports vest integrates two distinct structural areas: a high-stiffness, low-stretch underbust panel provides crucial support, while the chest area utilizes a softer, more flexible structure to enhance fit and provide gentle compression stability.

[0098] The manufacturing process includes three steps:

[0099] (1) Generate planar patterns from 3D human body models;

[0100] (2) According to the design requirements, generate texture structures with different densities and helicity using TexStructor;

[0101] (3) Assemble the 3D printed fabric into the final vest.

[0102] To enhance wearing comfort, the printed structure is bonded to traditional fabrics via thermal bonding. This example highlights TexStructor's ability to unify different mechanical properties within a single garment while maintaining practical manufacturability.

[0103] 2. Footwear: This section showcases the application of TexStructor in the design of indoor athletic shoes. The instep area of ​​the upper utilizes a highly flexible and stretchable structure to enhance coverage and reduce pressure. In contrast, a high-density structure is used around the perimeter of the upper to improve stability.

[0104] The production process includes three steps:

[0105] (1) Generate a planar pattern from a 3D shoe last model;

[0106] (2) Use TexStructor to design and fabricate textured uppers;

[0107] (3) Assemble the upper and sole to complete the production of indoor sports shoes.

[0108] 3. Flexible Electronic Skin: Traditional flexible electronic skin typically uses base materials such as TPU or silicone, with circuitry printed on their surface. However, due to the complex curvature and dynamic movements of the human body, these materials must possess tensile strength, which can lead to cracks in the conductive layer, thereby reducing circuit stability. To address this issue, this example shifts the focus from material flexibility to structural tensile strength. Conductive silver is first coated onto the designed structure, then encapsulated with silicone to protect the conductive layer and enhance fit to the human body. Tensile testing shows that it maintains more stable conductivity compared to circuitry printed directly on a flexible substrate.

[0109] 4. Robot Skin: This section explores a potential application of robot skin in the field of robotics. Traditional rigid shells provide structural protection but lack adaptability, limiting flexibility and complex movements. To address this issue, a prototype flexible skin is proposed to cover a rigid robot skeleton. This skin can conform to complex geometries and dynamic movements, while its structural characteristics can be customized to meet different functional requirements. For example, a stiffer area can be incorporated into the skeletal region to provide support, while a softer structure can be used near the mouth to enhance flexibility. Its manufacturing process includes:

[0110] (1) Design and print the textured skin structure;

[0111] (2) Install it on the mold and coat it with silicone until it is completely covered;

[0112] (3) Curing components to produce finished skin that can be attached to the robot frame.

[0113] This approach presents new opportunities for biomimetic, adaptive robotic overlays.

[0114] IV. Performance Evaluation: The system adopts a data-oriented approach, using regression to perform structural performance estimation analysis and achieve real-time evaluation. However, it has two key limitations: (1) Limited training data. Due to the complexity and time-consuming nature of data collection, the current training set is still relatively small. Expanding the dataset will improve the accuracy of the prediction model; (2) Material limitations. The traditional 1218 training data is limited to TPU-95A, which limits its application in other 3D printing materials. Incorporating a wider range of materials will improve the system's versatility and usability. Addressing these limitations will improve the system's predictive performance and enhance its adaptability in various manufacturing scenarios.

[0115] Contour Input: The system proposed in this paper allows users to draw any closed planar contour, including areas with holes. For more complex designs, such as generating textures on surfaces, designers must first flatten the surface and extract the contour as input. This operation can be performed in Rhino, Blender, or other CAD software. While this preprocessing step is not the focus of this research, its direct integration into the system in the future may improve the efficiency of complex design tasks.

[0116] 3D Printer Compatibility: This system allows users to adjust the size of the printing platform and generates G-code suitable for Marlin or Klipper styles, ensuring compatibility with most FDM 3D printers. Printers running Klipper firmware (such as Voron) support automatic platform leveling before printing. For other brands, such as Bambu X1C and Raise3D, Marlin-style G-code is compatible, but users need to manually level the platform before printing. In the future, this system plans to integrate automatic platform leveling support for more printer types.

[0117] In summary, TexStructor, an interactive 3D printing tool, simplifies the design and manufacturing process of textiles. Users can generate various structures based on helical structural units by drawing textile outlines and precisely control their mechanical properties. Data-driven predictive models provide real-time feedback on structural performance, while automated G-code generation seamlessly integrates with the manufacturing process. Quantitative experiments, expert case studies, and follow-up interviews demonstrate that TexStructor improves design efficiency, enhances accessibility, and reduces the need for iterative prototyping. This work highlights the potential of computational design tools in advancing the creation of flexible 3D printed textiles.

[0118] Evaluation: First, the accuracy of the regression model used for data-driven CAE is evaluated. Then, the effectiveness of TexStructor (the 3D printing design system) is validated through case studies with expert users and follow-up interviews. Finally, various applications are showcased to highlight the potential value of TexStructor.

[0119] Quantitative evaluation, as shown in Table 2, is the quantitative evaluation of the regression model used for scalability prediction.

[0120] Table 2

[0121]

[0122] Table 3 shows the quantitative evaluation of the regression model used to predict stiffness.

[0123] Table 3:

[0124]

[0125] The fit of the regression model was evaluated using 113 test data sets generated by randomly assigning structural parameters (grid type, alignment, helicity, and density), with the scalability samples ranging in size from 20 mm to 100 mm. Three evaluation metrics were used: (1) coefficient of determination (R², values ​​closer to 1 indicate better performance), (2) root mean square error (RMSE, lower values ​​are better), and (3) mean absolute error (MAE, lower values ​​are better). Table 2 shows that the model performed strongly in scalability prediction, with an overall R² of 0.8438, an RMSE of 0.0736, and a MAE of 0.0510. The edge-aligned triangle structure performed best in prediction (R² = 0.9522). For stiffness prediction (Table 3), the model performed well but with relatively low values, with an overall R² of 0.7504, a root mean square error (RMSE) of 0.2405, and an antonymous mean absolute error (MAE) of 0.1636. The prediction for polygonal edge-aligned structures was the most accurate (R² = 0.8306). These results validate the accuracy and robustness of the regression model.

[0126] Case Study: A case study demonstrates the usability of TexStructor, involving two expert users, "Industrial Designers E1 and E2," with over five years of experience in CAD modeling and manufacturing. Their task was to design a resilient textile for use as a fruit bowl, requiring adjustments to the local structure to create three areas with high ductility and low stiffness to accommodate the fruit.

[0127] Process: The study began with a 15-minute introduction to the system interface and operation. The focus was solely on explaining the features and usage of each function, without providing any guidance on the design of the fruit platter itself. Participants then had 15 minutes to independently explore the system. After becoming familiar with it, they began completing the design task, with their operation time recorded individually. Finally, a 30-minute post-study interview was conducted to gather subjective evaluations and feedback from experts. Key insights will be presented next, along with a discussion of representative expert opinions.

[0128] Research findings: It took the experts approximately 10 minutes to complete the design task. Figure 9 The results of the case study are presented. E1 was achieved through the use of... Figure 9 The outline shown in (a) divides the fruit platter into three distinct areas, each capable of stretching under the weight of the fruit and interconnected by a highly ductile structure. In contrast, E2 designed a larger plate. Figure 9 (b) This approach achieves both regional classification and greater storage capacity. Both experts optimized the local structure by adjusting the density and helicity around a selected reference point. This makes the fruit placement area more flexible under stress while maintaining the rigidity of the surrounding area. Throughout the process, they rapidly iterated and improved the design using real-time performance feedback from the system.

[0129] Interactive Structural Design: Both experts agreed that the interactive user interface was "user-friendly," "intuitive," and "easy to use." They specifically mentioned the significant benefits of the proposed interactive design space for creating flexible textile structures. E1 stated that it "makes design easier and more efficient," while E2 said, "I can easily create designs from scratch." Local Structural Adjustments: Both experts emphasized the practicality of local density and helicity adjustments, which allow for fine-grained control over structural characteristics. E2 particularly praised point-based local control, stating, "This feature allows for the merging of effects, thereby creating diverse local effects in different areas."

[0130] Structural performance evaluation: Experts also emphasized the importance of real-time performance evaluation and visualization. E1 commented, "This helps me intuitively understand the behavior of the texture structure." E2 called it a "cool feature" and added, "The visualization is intuitive and very helpful for iterative design."

[0131] To further facilitate user application, this solution also discloses a 3D printing design system for flexible structures, including an interactive user interface, a structural design and generation module, a performance index module, and a path planning and G-code generation module. The interactive user interface is implemented using the Human UI plugin on the Grasshopper platform, and includes a main canvas for user input and structural visualization. Users can freely draw arbitrary planar contours on the main canvas to define the overall shape of the flexible structure. Users can interactively outline contours to define the shape of the fabric, while the system dynamically visualizes the internal structure. Each edge is color-coded to represent its mechanical properties, providing intuitive real-time feedback for design optimization.

[0132] The structural design and generation module includes a structural design configuration panel, which comprises a global texture structure configuration panel and a local structure adjustment panel. This panel generates diverse texture structure styles for the design method of the 3D-printed flexible structure and allows for precise control over local flexibility, rigidity, and ductility. Users can select from different types of meshes (e.g., triangles, quadrilaterals, and polygons) with varying densities, and adjust the internal texture of the structure through helix angles and arrangement methods. In flexible fabrics, different areas typically require different structural properties to achieve specific functions. For example, wearable devices require higher ductility and lower stiffness at joints to ensure free movement. To meet these needs, the system can locally control mesh density and structural helix angle. Users can interactively place reference points on the canvas to adjust the mesh density and helix angle of the surrounding areas, thereby achieving precise control over the stiffness and ductility required for specific functional needs.

[0133] The performance index module provides real-time feedback on the mechanical response performance of the flexible structure. This index is a color-coded icon with a drop-down menu, allowing users to switch between two indices (stiffness and ductility). The index is directly connected to a data-driven CAE model, providing real-time performance feedback. Estimated performance values ​​are displayed on the edges of the fabric structure; for example, green indicates softness, while purple indicates stiffness.

[0134] The path planning and G-code generation module includes a manufacturing configuration panel for directly setting 3D printing parameters such as platform size, path width, and the number and height of layers. Once configured, the system automatically optimizes the printing path and generates G-code to drive the 3D printer. The generated G-code can be in Marlin or Klipper format, ensuring compatibility with common 3D printers.

[0135] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0136] It should be understood that this solution is not limited to the specific embodiments described above. Devices and structures not described in detail herein should be understood as being implemented in a manner common to the art. Any person skilled in the art can make many possible variations and modifications to this solution, or modify it into equivalent embodiments, without departing from the scope of this solution, using the methods and techniques disclosed above. This does not affect the substantive content of this solution. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of this solution, without departing from its scope, still fall within the protection scope of this solution.

Claims

1. Texture structure design space, characterized by: It includes four dimensions: grid type, grid density, helix angle, and helix arrangement. Among them, grid type is used to control the flexibility and aesthetics of the flexible structure; grid density determines the rigidity of the flexible structure; helix angle controls the ductility of the flexible structure; and helix arrangement determines the stretching direction of the flexible structure.

2. The texture structure design space according to claim 1, characterized in that: The grid types include triangles, quadrilaterals, and polygons; the grid density is controlled by the grid side length; the helix angle controls the curvature and extensibility of the helix; the helix arrangement includes two methods: corner alignment and edge alignment.

3. A design method for flexible structures in 3D printing, characterized by: Includes the following steps: Step 1: Design a spiral texture structure unit. Each texture structure unit contains several concentric Archimedean spirals whose spiral angles can be freely adjusted. Step 2: Determine the contour area according to the required flexible structure, and divide the contour area into several grid surfaces; according to the texture structure design space described in claim 1, assemble the corresponding spiral texture structure unit in each grid surface; Step 3: Based on the local characteristics of the flexible structure, adjust the density and helicity of the spiral lines in the grid surface by setting reference points, connect the spiral lines to give the overall structure elasticity, and form the final flexible structure.

4. The design method for 3D printed flexible structures according to claim 3, characterized in that: Within each spiral texture structure unit, the number of spiral lines corresponds to the number of edges on the mesh surface.

5. The design method for a flexible 3D printed structure according to claim 3, characterized in that: It also includes the application of data-driven CAE models to test the performance of flexible structures.

6. The design method for 3D printed flexible structures according to claim 5, characterized in that: The method for constructing the data-oriented CAE model is as follows: First, based on the four dimensions of the design space, the grid type and spiral arrangement are combined into several groups, and the input parameters for each group are the spiral degree and density; Secondly, flexible structures are generated based on input parameters; Then, the stiffness and elongation of the generated flexible structure are obtained through physical experiments, and a training dataset is constructed. Finally, based on the training dataset, a flexible structure estimation model for estimating ductility and stiffness is trained, and the model is evaluated to verify its accuracy.

7. The design method for a flexible 3D printed structure according to claim 6, characterized in that: The flexible structure estimation model includes a regression model that corresponds to a specific combination of network type and alignment configuration.

8. A 3D printing design system for flexible structures, characterized in that: It includes an interactive user interface, a structural design and generation module, a performance index module, and a path planning and G-code generation module; wherein, the interactive user interface includes a main canvas, which is used for user input and structural visualization, and arbitrary planar contours can be freely drawn on the main canvas to define the overall shape of the flexible structure; The structural design and generation module includes a structural design configuration panel, which includes a global texture structure configuration panel and a local structure control panel. It is used to generate diverse texture structure styles according to the design method of the 3D printed flexible structure, and to perform precise control of local flexibility, rigidity, and extensibility. The performance index module is used to provide real-time feedback on the mechanical response performance of flexible structures; The path planning and G-code generation module includes a manufacturing configuration panel for directly setting 3D printing-related parameters, automatically optimizing the printing path, and generating G-code.

9. The 3D printing design system for flexible structures according to claim 8, characterized in that: The performance index module is connected to a data-driven CAE model to perform real-time regression analysis on the mechanical properties of the flexible structure and to provide feedback on the performance index parameters.

10. A flexible structure printed using the 3D printing design system for the flexible structure described above, characterized in that: It includes a grid surface composed of helical structural units arranged within a given contour, each helical structural unit comprising a set of stretchable concentric Archimedean spirals, the number of spirals in each helical structural unit corresponding to the number of sides of its respective grid surface.

Images