Three-period minimal curved surface circumferential fusion structure

Abstract

The invention discloses a three-period minimal curved surface circumferential fusion structure, and relates to the technical field of porous materials, the fusion structure comprises a parameter definition module used for defining a TPMS primitive mathematical model, a fusion region geometric parameter and a weight regulation parameter, a fusion calculation module used for realizing TPMS primitive space nonlinear fusion based on a weighting algorithm, and a fusion calculation module used for realizing TPMS primitive space nonlinear fusion. And dynamically calculating the weight distribution of each primitive in the fusion region. Specifically, parameters such as spatial distance and curvature distribution are introduced into a fusion process through an inverse distance weighting method and a dynamic weight regulation and control module, specifically, a weighting function is generated by calculating the Euclidean distance from a scalar field to an interpolation center point, local curvature is measured, and distance power parameters are dynamically adjusted. The spatial nonlinear positioning fusion mechanism breaks through a traditional linear superposition uniform mixing mode, element layout of'distribution as required 'is realized, the energy absorption efficiency of the porous structure under dynamic load is improved by more than one, and meanwhile, the material consumption is reduced.

Description

Technical Field

[0001] This invention relates to the field of porous structure technology, specifically to a three-period minimal surface circumferential fusion structure. Background Technology

[0002] With the increasing demand for lightweight and high-performance materials in industrial development, the need for advanced structures that can effectively absorb energy under dynamic load conditions in engineering applications is also growing. Lightweight and high-performance materials are widely used in aerospace, railway, automotive, and marine engineering. Novel structures with light weight and excellent mechanical properties are a research direction in industrial manufacturing. In recent years, the need to improve impact resistance has prompted the incorporation of porous materials into the design of energy absorption structures, such as improved honeycomb, truss lattice, and porous structures based on triple periodic minimum surfaces (TPMS). TPMS are surfaces with zero mean curvature. They can divide space into two non-intersecting regions, have a symmetrical topology, and have a minimum surface area under specific boundary conditions. TPMS have the characteristics of continuous zero mean curvature and three-dimensional periodicity, smooth surface, and no stress concentration problem due to the high connection of pores.

[0003] Innovations in TPMS lattice research include the development of hybrid structures that combine different types of TPMS lattices to optimize their mechanical properties. Hybrid TPMS structures aim to leverage the advantages of each type to achieve superior energy absorption and shock resistance. In the past, most fused structures were linear fusions of multiple TPMS structures without achieving spatial nonlinear localization fusion. Moreover, most fused structures are linear fusions, lacking spatial nonlinear localization fusion, making it difficult to dynamically control the mixing ratio of elementary elements. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a three-period minimal surface circumferential fusion structure, which solves the problems mentioned in the background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: the fusion structure includes: Parameter definition module: used to define the TPMS primitive mathematical model, the geometric parameters of the fusion region, and the weight adjustment parameters; Fusion Computation Module: Based on a weighted algorithm, this module achieves spatial nonlinear fusion of TPMS primitives and dynamically calculates the weight distribution of each primitive within the fusion region. The dynamic weight adjustment module is used to dynamically adjust the local curvature of the fusion surface of the weight distribution, thereby achieving dynamic adjustment of the curvature value. The fusion region geometry module divides the single flat cylindrical fusion region into multiple sub-regions, and each sub-region independently sets the primitive type, interpolation points, and weight parameters. Surface processing module: used to extract isosurfaces that conform to TPMS characteristics from the fused scalar field and generate a closed geometric model; Output application module: Used to export the fused structure as an STL file usable for additive manufacturing, and integrate process optimization parameters; Pre-fusion simulation module: used to pre-calculate the stress contribution of each element through finite element simulation before inverse distance weighted fusion of porous structures, and dynamically adjust the initial value of the weight.

[0006] Preferably, the parameter definition module includes a TPMS primitive library, which stores implicit function equations of typical TPMS. It selects four TPMS—Gyroid, Schwarz, Diamond, and Neovius—for circumferential fusion, and the specific fusion expression is as follows: The TPMS primitive library supports user-defined extensions.

[0007] Preferably, the Matlab mathematical expressions for the four TPMS types—Gyroid, Schwarz, Diamond, and Neovius—are as follows: in, , , , , and They are , and A constant related to the TPMS cell size in the direction; In this mathematical formula, take .

[0008] Preferably, the fusion region generation of the parameter definition module supports flat cylinders, spheres, and multi-segment geometric shapes with variable cross-sections, and the parameters include radius, height, body center coordinates, and number of segments; The weight parameters in the parameter definition module are configured as follows: interpolation center point coordinate matrix, distance power parameter. Orientation weighting factor and adaptive curvature parameter.

[0009] Preferably, the weighting algorithm of the fusion calculation module is specifically the inverse distance weighting method, and the specific calculation method of the inverse distance weighting method is as follows: Euclidean distance calculation: in, For scalar field coordinates, For the first The coordinates of the interpolation center point of each primitive; Composite weighting function: in, For polar coordinate direction weights, To prevent division by zero, It can be adaptively adjusted to a curvature function; Nonlinear fusion: in, For the first The scalar field value of each element is dynamically adjusted in terms of mixing ratio through weighting.

[0010] Preferably, the specific processing steps of the surface processing module are as follows: S1. Use the isosurface function to extract surfaces with zero average curvature and obtain surface data. and vertex data ; S2. Then, the isocaps function is used to generate a closed isosurface volume, and the closed surface data is obtained. and vertex data ; S3. Finally, merge the open and closed surface data: ; .

[0011] Preferably, the STL file export of the output application module generates a structured mesh file that supports multi-region stitching. This allows for the automatic generation of gradient mixing layers at the primitive boundaries, adapting to the SLM layer-by-layer printing process, reducing interface defects, and enabling the export and application of parametric model files.

[0012] Preferably, the curvature value is dynamically adjusted in the weight dynamic control module as follows: For a three-period minimum surface, its mean curvature is always zero; for a scalar field... The mean curvature of a defined surface can be calculated using the following formula: in, For the mean curvature, For divergence operators, The gradient of the standard field; Expanding the above formula, we get: Therefore, in this fusion structure, since each TPMS primitive is a minimal surface, the fused surface still approximately satisfies the characteristics of a minimal surface. Thus, the Laplacian operator can be used as a relative measure of local curvature, where the larger the absolute value, the more drastic the curvature change.

[0013] Preferably, the weight dynamic adjustment module is based on the circumferential angle. The directional weighting coefficients are assigned as follows: in, The circumferential angle of the target point. For the first The principal direction angle of each element. These are the directional weighting coefficients, which enable asymmetric circumferential fusion of weights.

[0014] The fusion region geometry module fuses Gyroid and Diamond in the upper segment of TPMS and Schwarz and Neovius in the lower segment, and then concatenates them into a whole structure through Boolean operations. The specific calculation is as follows: The union algorithm is used to stitch together the fused surfaces of multiple sub-regions into a single structure, ensuring that the sub-regions are seamlessly connected and do not overlap in space. Each sub-region generates independent surface data through the isosurface function. The surface data includes: Vertex data: a three-dimensional coordinate matrix. ; Face data: Triangle facet index matrix, ; in, Indicates the origin of the vertex , , The triangle formed has vertices in different sub-regions located in different spatial positions. By unifying the coordinates to the global coordinate system through coordinate offset, the geometric points and surfaces of the merged region can be completed.

[0015] Preferably, the pre-fusion simulation module simulates the impact load on the initial fused structure by calling the finite element toolkit in Matlab, and corrects the interpolation center point coordinates or weighting coefficients according to the stress cloud diagram. The specific finite element simulation iteration formula is as follows: in, To correct the step size, Using the basic element stress value, finite element simulation is used to reduce the trial and error cost of porous structure production and generate load-adaptive porous structures.

[0016] This invention provides a three-period minimal surface circumferential fusion structure. It possesses the following beneficial effects: (1) By using the inverse distance weighting method and dynamic weight control module, parameters such as spatial distance and curvature distribution are introduced into the fusion process. Specifically, the weight function is generated by calculating the Euclidean distance from the scalar field to the interpolation center point, and the local curvature is measured. The distance power parameter is dynamically adjusted. At the same time, the introduction of the polar coordinate direction weight factor enables the basic element distribution to be oriented and controlled along the circumferential angle. This spatial nonlinear positioning fusion mechanism breaks through the traditional linear superposition uniform mixing mode and realizes the basic element layout of "distribution on demand". This improves the energy absorption efficiency of the porous structure under dynamic load by more than 100% while reducing the amount of material used.

[0017] (2) By integrating the geometric modules of the region, it supports the design of various shapes such as flat cylinders, spheres, and multi-segment bodies with variable cross sections. The region is divided into dumbbell-shaped structures of upper and lower segments. After being spliced ​​by Boolean operations, gradient function integration is achieved. At the same time, the functional combination strategy of primitives breaks through the limitation of single mechanical performance. The multi-scale nested module can embed micro-scale TPMS structures in the macro-scale primitive pores to simulate the grading characteristics of bones, taking into account both lightweight and fatigue resistance, and significantly improving the adaptability of porous structures in aerospace, transportation, marine engineering and other fields.

[0018] (3) Through the finite element pre-fusion simulation module, the impact load is simulated by finite element simulation in the porous structure design stage. The initial weight value is dynamically corrected according to the stress cloud diagram, forming a closed loop of "design-simulation-iteration" for porous structure manufacturing, reducing the number of physical sample trials. At the same time, the additive manufacturing process adaptation module automatically generates a 100-200μm gradient mixing layer at the junction of the basic elements, avoiding the geometric abrupt change problem during SLM printing. Process verification shows that the interface defect rate can be reduced, realizing one-time molding of complex structures, significantly improving manufacturing accuracy and production efficiency. Attached Figure Description

[0019] Figure 1 The diagram shows four TPMS structures: Gyroid, Schwarz, Diamond, and Neovius, representing a three-period minimal surface circumferential fusion structure according to the present invention. Figure 2 This invention provides a three-period minimal surface circumferential fusion structure, including the Gyroid, Diamond, and Neovius circumferential fusion structures and their internal structures. Figure 3This invention provides a three-period minimal surface circumferential fusion structure, including Gyroid, Schwarz, Diamond, and Neovius circumferential fusion structures and their internal structures. Figure 4 The diagrams show (a) Gyroid, Schwarz and Neovius circumferential fusion structures and (b) Gyroid and Neovius circumferential fusion structures of a three-period minimal surface fusion structure according to the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Example Please see Figures 1-4 This invention provides a three-period minimal surface circumferential fusion structure. To achieve the above objectives, this invention utilizes the following technical solution: The fusion structure includes: Parameter definition module: used to define the TPMS primitive mathematical model, the geometric parameters of the fusion region, and the weight adjustment parameters; Fusion Computation Module: Based on a weighted algorithm, this module achieves spatial nonlinear fusion of TPMS primitives and dynamically calculates the weight distribution of each primitive within the fusion region. The dynamic weight adjustment module is used to dynamically adjust the local curvature of the fusion surface of the weight distribution, thereby achieving dynamic adjustment of the curvature value. The fusion region geometry module divides the single flat cylindrical fusion region into multiple sub-regions, and each sub-region independently sets the primitive type, interpolation points, and weight parameters. Surface processing module: used to extract isosurfaces that conform to TPMS characteristics from the fused scalar field and generate a closed geometric model; Output Application Module: Used to export the fused structure as an STL file usable for additive manufacturing and integrate process optimization parameters; Pre-fusion Simulation Module: Used to pre-calculate the stress contribution of each element through finite element simulation before inverse distance weighted fusion of porous structures, and dynamically adjust the initial weight values.

[0022] Design examples of porous structures, Example 1: Three TPMSs, Gyroid, Diamond, and Neovius, were selected for fusion. The fusion region was a cylindrical region with a bottom radius of 20 mm and a height of 10 mm, and its body center coordinates were (0,0,0). The interpolation center point coordinates of Gyroid type TPMS are selected as (0,10,0), Diamond type TPMS are selected as (-8.7,-5,0), Neovius type TPMS are selected as (8.7,-5,0), and the power parameter ρ of the distance is set to 6. After calculating the distance weight function, through The circumferential fusion was performed, and the fused structure and its internal structure are shown in the attached figure. Figure 2 As shown, the internal structure of the fusion was analyzed, and the transition between different TPMS was smooth, indicating a good fusion effect.

[0023] Design examples of porous structures, Example 2: Four TPMSs, Gyroid, Schwarz, Diamond, and Neovius, were selected for circumferential fusion. The fusion region was a cylindrical region with a bottom radius of 20 mm and a height of 10 mm, and its body center coordinates were (0,0,0). The interpolation center point coordinates of the Gyroid type TPMS are selected as (0,5,0), the Schwarz type TPMS are selected as (5,0,0), the Diamond type TPMS are selected as (0,-5,0), and the Neovius type TPMS are selected as (-5,0,0). The power parameter ρ of the distance is set to 6. After calculating the distance weight function, through The circumferential fusion was performed, and the fused structure and its internal structure are shown in the attached figure. Figure 3 As shown, the internal structure of the fusion was analyzed, and the transition between different TPMS was smooth, indicating a good fusion effect.

[0024] If the Diamond-type TPMS is changed to the Neovius-type, while the interpolation center point remains unchanged, the circumferential fusion structure is as follows: Figure 4 As shown in (a), if the Schwarz-type TPMS is changed to the Neovius-type, the interpolation center point remains unchanged, and the circumferential fusion structure is as follows: Figure 4 As shown in (b).

[0025] Specifically, a simple and easy-to-understand implicit functional equation expression is widely used, represented as: in, It is the amplitude. Pk is the periodicity factor, and Pk is the phase of the function; This paper selects typical TPMS lattices of Primitive (P), Gyroid (G), and Diamond (D) for research and design. In Matlab, the selected TPMS to be fused are expressed mathematically using implicit function equations. Interpolation centers are selected for each TPMS, and the Euclidean distance from the scalar field of the TPMS to the corresponding interpolation center is calculated. .

[0026] The programming code is as follows: ; in , and TPMS scalar field three-dimensional coordinate data , and The three-dimensional coordinates of the interpolation center point corresponding to this TPM scalar field; Calculate the weight function based on distance. The expression is: , To prevent small values ​​from being divided by zero, the size is... In the formula, ρ is a power parameter of the distance, taking positive integer values. The programming code is: ; Then, inverse distance weighted fusion is performed, and the nonlinear fusion formula is as follows:

[0027] in Let be the scalar field value of the i-th TPMS primitive. It is its corresponding weight function.

[0028] Taking the fusion of two TPMS using the inverse distance weighting method as an example, the programming code is as follows: To ensure that the average curvature of the three-period minimum surface is zero at any point on the surface, the isosurface function is used to extract the isosurface. The programming code is: isovalue=0; Where F is the face data and V is the vertex data; Use the isocaps function to generate the face and vertex data of a closed isosurface. The programming code is as follows: ; Where FC is the closed face data and VC is the closed vertex data; This leads to the merging of all face and vertex data; The programming code is as follows: ; Export STL files directly using vertex and face data; The programming code is as follows: .

[0029] The parameter definition module includes a TPMS primitive library, which stores the implicit function equations of typical TPMS. It selects four TPMS—Gyroid, Schwarz, Diamond, and Neovius—for circumferential fusion, and the specific fusion expression is as follows: Gyroid: Composed of a spiral surface formed by the intersection of sine and cosine functions, it has excellent energy absorption capabilities; Schwarz: A planar curved surface formed by the superposition of cosine functions in three orthogonal directions, resulting in high structural stiffness; Diamond: Generates complex wrinkled surfaces by combining the product of sine and cosine functions, exhibiting outstanding shear resistance; Neovius: Contains cubic and fourth cosine function terms, forming a complex curved surface with sharp peaks, exhibiting excellent torsional resistance; The TPMS primitive library supports user-defined extensions. The four primitives achieve spatial mixing through weighted fusion expressions. For example, Gyroid and Schwarz can dominate in different circumferential regions of a cylinder, achieving a smooth transition through weighted gradients.

[0030] The Matlab mathematical expressions for the four TPMS types, Gyroid, Schwarz, Diamond, and Neovius, are as follows: in, , , , , and They are , and A constant related to the TPMS cell size in the direction; In this mathematical formula, take .

[0031] The parameter definition module supports the generation of fusion regions for flat cylinders, spheres, and multi-segment geometric shapes with variable cross-sections. Parameters include radius, height, body center coordinates, and number of segments. Specifically, the fusion region geometry module supports three typical forms: Flat cylinder: Suitable for axially symmetrical load scenarios (such as bearing support structures), it can be divided into upper and lower sections or circumferential partitions. The upper section is set to Gyroid+Diamond fusion, and the lower section is set to Schwarz+Neovius fusion. Spherical: Suitable for isotropic force scenarios (such as aerospace buffer structures), omnidirectional fusion is achieved through the sphere's center interpolation point; Variable cross-section multi-segment body: suitable for complex shape requirements (such as bionic skeleton), each segment can be configured with an independent primitive type.

[0032] The weight parameters in the parameter definition module are configured as follows: interpolation center point coordinate matrix, distance power parameter. Orientation weighting factor and adaptive curvature parameter; Specifically, the interpolation center point coordinate matrix defines the "influence center" of each primitive in space. For example, the center point of Gyroid is located in the positive Y-axis direction of the cylinder, and the center point of Schwarz is located in the positive X-axis direction.

[0033] Distance power parameter : Controls the rate at which the weights decay with distance. The larger ρ is, the more concentrated the weights are in the near-field region.

[0034] Directional weighting factor: Weights are assigned based on the circumferential angle differences. When the main direction of the primitive is the Y-axis, the area near the Y-axis has a higher weight.

[0035] The weighting algorithm for the fusion computing module is specifically the inverse distance weighting method, and the specific calculation method of the inverse distance weighting method is as follows: Euclidean distance calculation: in, For scalar field coordinates, For the first The coordinates of the interpolation center point of each primitive; Composite weighting function: in, For polar coordinate direction weights, To prevent division by zero, It can be adaptively adjusted to a curvature function; Nonlinear fusion: in, For the first The scalar field value of each element is dynamically adjusted in terms of mixing ratio through weighting.

[0036] The specific processing steps of the surface processing module are as follows: S1. Use the isosurface function to extract surfaces with zero average curvature and obtain surface data. and vertex data ; S2. Then, the isocaps function is used to generate a closed isosurface volume, and the closed surface data is obtained. and vertex data ; S3. Finally, merge the open and closed surface data: ; .

[0037] Specifically, the surface processing module generates a closed geometric model in three steps: Extracting isosurfaces: The isosurface function is used to extract surfaces with zero mean curvature from the fused scalar field, resulting in surface data (triangle patch indices) and vertex data (3D coordinates).

[0038] Generate closed surfaces: The isocaps function is used to add top and bottom surfaces to open isosurfaces to form closed three-dimensional bodies, avoiding mechanical performance defects caused by structural openings.

[0039] Data merging: Merge the vertex and patch indices of open and closed surfaces to ensure mesh continuity, generate a complete model that can be used for additive manufacturing, and realize surface processing of the structure.

[0040] The STL file export of the output application module generates a structured mesh file that supports multi-region stitching. This allows for the automatic generation of gradient blending layers at primitive boundaries, adapting to the SLM layer-by-layer printing process, reducing interface defects, and enabling the export and application of parametric model files.

[0041] Specifically, the output application module generates STL files using structured mesh technology: The meshes of each sub-region are automatically aligned at the boundaries to avoid misalignment or overlap. At the same time, a gradient transition layer is generated at the boundaries of different primitives to reduce thermal stress concentration and interface defects during additive manufacturing. SLM process parameters are embedded in the file to directly guide the printing equipment to deposit materials layer by layer, ensuring the accuracy of structural forming and enabling more convenient design and manufacturing of fused materials.

[0042] The curvature value is dynamically adjusted in the weight dynamic control module as follows: For a three-period minimum surface, its mean curvature is always zero; for a scalar field... The mean curvature of a defined surface can be calculated using the following formula: in, For the mean curvature, For divergence operators, The gradient of the standard field; Expanding the above formula, we get: Therefore, in this fusion structure, since each TPMS primitive is a minimal surface, the fused surface still approximately satisfies the characteristics of a minimal surface. Thus, the Laplacian operator can be used as a relative measure of local curvature, where the larger the absolute value, the more drastic the curvature change.

[0043] The weight dynamic adjustment module is based on the circumferential angle. The directional weighting coefficients are assigned as follows: in, The circumferential angle of the target point. For the first The principal direction angle of each element. These are the directional weighting coefficients, which enable asymmetric circumferential fusion of weights.

[0044] The fusion region geometry module merges the upper region of TPMS with Gyroid and Diamond, and the lower region with Schwarz and Neovius, and then concatenates them into a whole structure through Boolean operations. The specific calculation is as follows: The union algorithm is used to stitch together the fused surfaces of multiple sub-regions into a single structure, ensuring that the sub-regions are seamlessly connected and do not overlap in space. Each sub-region generates independent surface data through the isosurface function. The surface data includes: Vertex data: a three-dimensional coordinate matrix. ; Face data: Triangle facet index matrix, ; in, Indicates the origin of the vertex , , The triangle formed has vertices in different sub-regions located in different spatial positions. By unifying the coordinates to the global coordinate system through coordinate offset, the geometric points and surfaces of the merged region can be completed.

[0045] The pre-fusion simulation module simulates the impact load on the initial fused structure by calling the finite element toolkit in Matlab. It corrects the interpolation center point coordinates or weighting coefficients based on the stress contour plot. The specific finite element simulation iteration formula is as follows: in, To correct the step size, Using the basic element stress value, finite element simulation is used to reduce the trial and error cost of porous structure production and generate load-adaptive porous structures.

[0046] In this embodiment, the fusion steps of the fusion system with the integrated porous structure are as follows: Choose a flat cylinder, sphere, or variable cross-section multi-segment body with a base radius of 20mm and a height of 10mm. Set parameters such as body center coordinates and number of segments. Then divide the fusion region into multiple sub-regions (such as upper segment, lower segment, or circumferential partition). Set the primitive type, interpolation point position, and weight parameters independently for each sub-region. Select the required primitive from four typical three-period minimal surfaces: Gyroid, Schwarz, Diamond, and Neovius (user-defined extensions are supported). When fusion with four primitives, select Gyroid, Schwarz, Diamond, and Neovius for different sub-regions. The domain is defined, and the coordinates of the interpolation center points are set. The Gyroid center point is (0,5,0), and the Schwarz center point is (5,0,0). The distance power parameter (default value is 6), the direction weight factor (based on the difference between the circumferential angle and the principal direction of the primitives), and the adaptive curvature parameter are determined. For any coordinate point within the fusion region, the Euclidean distance from it to the interpolation center point of each primitive is calculated. The closer the distance, the higher the weight. The weights are generated by combining the distance and direction factors: the closer the distance, the higher the weight. At the same time, the direction weights are adjusted according to the difference between the circumferential angle and the principal direction of the primitives. For example, primitives whose principal direction is the Y-axis have a higher weight in the area near the Y-axis. Then, the weights are mixed according to the weight ratio. By combining the scalar field values ​​of each primitive element, spatial nonlinear fusion is achieved, enabling different primitive elements to dynamically transition according to their weights within the fusion region. The specialized software function `isosurface` extracts isosurfaces conforming to the characteristics of a three-period minimum surface from the fused scalar field, obtaining surface and vertex data. The software function `isocaps` adds closed surfaces to the isosurfaces, ensuring the generation of a complete 3D closed structure and avoiding opening defects. The data of open and closed surfaces are merged to form a unified vertex and facet index matrix, constructing a complete geometric model. The finite element toolkit is then called within the software to apply simulated conditions such as impact loads to the initial fused structure, generating stress cloud maps. The system identifies stress concentration areas and iteratively corrects the interpolation center point coordinates or weight coefficients based on the stress cloud map results: it reduces the weight of corresponding primitives in high-stress areas or increases the weight of impact-resistant primitives until the stress distribution is uniform. The final fused model is exported as an STL format file usable for additive manufacturing, generating a structured mesh and automatically adding gradient mixing layers at primitive boundaries to adapt to layer-by-layer printing processes. Process parameters are embedded in the exported file to reduce interface defects during printing and improve the quality of structural forming. The output STL file can be directly used in additive manufacturing equipment to manufacture porous structures with multi-primary fusion characteristics through processes such as layer printing and material melting.

[0047] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention.

Claims

1. A three-period minimal surface circumferential fusion structure, characterized in that: The fusion structure includes: Parameter definition module: used to define the TPMS primitive mathematical model, the geometric parameters of the fusion region, and the weight adjustment parameters; Fusion Computation Module: Based on a weighted algorithm, this module achieves spatial nonlinear fusion of TPMS primitives and dynamically calculates the weight distribution of each primitive within the fusion region. The dynamic weight adjustment module is used to dynamically adjust the local curvature of the fusion surface of the weight distribution, thereby achieving dynamic adjustment of the curvature value. The fusion region geometry module divides the single flat cylindrical fusion region into multiple sub-regions, and each sub-region independently sets the primitive type, interpolation points, and weight parameters. Surface processing module: used to extract isosurfaces that conform to TPMS characteristics from the fused scalar field and generate a closed geometric model; Output application module: Used to export the fused structure as an STL file usable for additive manufacturing, and integrate process optimization parameters; Pre-fusion simulation module: used to pre-calculate the stress contribution of each element through finite element simulation before inverse distance weighted fusion of porous structures, and dynamically adjust the initial value of the weight.

2. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The parameter definition module includes a TPMS primitive library, which stores implicit function equations for typical TPMS. It selects four TPMS—Gyroid, Schwarz, Diamond, and Neovius—for circumferential fusion, and the specific fusion expression is as follows: The TPMS primitive library supports user-defined extensions.

3. The three-period minimal surface circumferential fusion structure according to claim 2, characterized in that: The Matlab mathematical expressions for the four TPMS methods, Gyroid, Schwarz, Diamond, and Neovius, are as follows: in, , , , , and They are , and A constant related to the TPMS cell size in the direction; In this mathematical formula, take .

4. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The parameter definition module generates a fusion region that supports flat cylinders, spheres, and multi-segment geometric shapes with variable cross-sections. The parameters include radius, height, body center coordinates, and number of segments. The weight parameters in the parameter definition module are configured as follows: interpolation center point coordinate matrix, distance power parameter. Orientation weighting factor and adaptive curvature parameter.

5. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The weighting algorithm of the fusion computing module is specifically the inverse distance weighting method, and the specific calculation method of the inverse distance weighting method is as follows: Euclidean distance calculation: in, For scalar field coordinates, For the first The coordinates of the interpolation center point of each primitive; Composite weighting function: in, For polar coordinate direction weights, To prevent division by zero, It can be adaptively adjusted to a curvature function; Nonlinear fusion: in, For the first The scalar field value of each element is dynamically adjusted in terms of mixing ratio through weighting.

6. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The specific processing steps of the surface processing module are as follows: S1. Use the isosurface function to extract surfaces with zero average curvature and obtain surface data. and vertex data ; S2. Then, the isocaps function is used to generate a closed isosurface volume, and the closed surface data is obtained. and vertex data ; S3. Finally, merge the open and closed surface data: ; .

7. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The STL file export of the output application module generates a structured mesh file, supports multi-region stitching, and can automatically generate gradient mixing layers at the primitive boundaries, adapting to the SLM layer-by-layer printing process, reducing interface defects, and realizing the export and application of parametric model files.

8. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The curvature value is dynamically adjusted in the weight dynamic control module as follows: For a three-period minimum surface, its mean curvature is always zero; for a scalar field... The mean curvature of a defined surface can be calculated using the following formula: in, For the mean curvature, For divergence operators, The gradient of the standard field; Expanding the above formula, we get: Therefore, in this fusion structure, since each TPMS primitive is a minimal surface, the fused surface still approximately satisfies the characteristics of a minimal surface. Thus, the Laplacian operator can be used as a relative measure of local curvature, where the larger the absolute value, the more drastic the curvature change.

9. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The weight dynamic adjustment module is based on the circumferential angle. The directional weighting coefficients are assigned as follows: in, The circumferential angle of the target point. For the first The principal direction angle of each element. These are the directional weighting coefficients, thereby achieving asymmetric circumferential fusion of weights; The fusion region geometry module fuses Gyroid and Diamond in the upper segment of TPMS and Schwarz and Neovius in the lower segment, and then concatenates them into a whole structure through Boolean operations. The specific calculation is as follows: The union algorithm is used to stitch together the fused surfaces of multiple sub-regions into a single structure, ensuring that the sub-regions are seamlessly connected and do not overlap in space. Each sub-region generates independent surface data through the isosurface function. The surface data includes: Vertex data: a three-dimensional coordinate matrix. ; Face data: Triangle facet index matrix, ; in, Indicates the origin of the vertex , , The triangle formed has vertices in different sub-regions located in different spatial positions. By unifying the coordinates to the global coordinate system through coordinate offset, the geometric points and surfaces of the merged region can be completed.

10. The three-period minimal surface circumferential fusion structure according to claim 1, characterized in that: The pre-fusion simulation module simulates the impact load on the initial fused structure by calling the finite element toolkit in Matlab, and corrects the interpolation center point coordinates or weighting coefficients based on the stress cloud diagram. The specific finite element simulation iteration formula is as follows: in, To correct the step size, Using the basic element stress value, finite element simulation is used to reduce the trial and error cost of porous structure production and generate load-adaptive porous structures.

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