Skinning-gradient lattice stiffening modeling design method for complex surface and related equipment

Abstract

The application discloses a skin-gradient lattice rib modeling design method for a complex surface and related equipment, and is based on a continuous scalar field, interpolates the topological form of the microstructure in different regions of an initial grid model, generates a continuous intermediate transition form, performs smooth Boolean operation on the implicit field, continuously geometrically fuses the microstructure and the main body boundary, eliminates geometric mutation at the connection, converts the fused overall structure into a solid model and outputs, realizes continuous smooth transition of the topological form of the microstructure and continuous transition connection between the microstructure and the main body boundary in geometry and mechanics, avoids stress concentration caused by topological mutation and boundary connection cracks, has high modeling efficiency and good structure continuity, and the design result can be directly used for engineering simulation and additive manufacturing.

Description

Technical Field

[0001] This invention relates to the field of model structure design technology, specifically to a skin-gradient lattice stiffening modeling design method and related equipment for complex curved surfaces. Background Technology

[0002] The development of additive manufacturing (AM) technology has enabled the widespread application of lightweight lattice structures in aerospace, automotive manufacturing, energy equipment, and biomedicine. A lattice structure is a spatial network structure composed of periodic or aperiodic units. By macroscopically controlling the topology, density, and size distribution of individual cells, it achieves lightweight, designable, and multifunctional characteristics.

[0003] Lattice structures exhibit significantly high specific strength, high specific stiffness, and excellent energy absorption characteristics. By adjusting the geometry and distribution density of the unit cells, the mechanical, thermal, and damping properties within the structure can be optimized in a targeted manner. For example, in aerospace components, lattice core materials can be used to reduce weight and improve the overall stiffness of the structure; in biomedical implants, tissue growth characteristics can be adjusted by controlling the lattice pore size and gradient distribution.

[0004] However, with the development of additive manufacturing and implicit geometry design methods, traditional CAD modeling technology faces multiple bottlenecks in the design of lattice surfaces on complex curved surfaces:

[0005] 1. Insufficient adaptability to complex curved surfaces. Existing CAD systems typically rely on explicit geometric boundary definitions (such as STL or NURBS patches), making it difficult to achieve continuous mapping and arrangement of lattice structures on complex curved surfaces. When the surface has complex geometric shapes such as capped cones, hyperboloids, or solids of revolution, lattice elements often exhibit distortion, overlap, or discontinuity, resulting in discontinuous structures or making them unmanufacturable.

[0006] 2. Limited gradient control methods. Traditional periodic lattices typically only support global parameter control, making it difficult to achieve gradual material distribution design in space. Although some studies have proposed multi-level lattice models based on Voronoi, BCC, or TPMS, their gradient changes are mostly achieved through discrete piecewise methods, lacking a unified field-driven or function-driven control mechanism, and thus unable to precisely control thickness and topological gradients along radial, axial, or arbitrary directions.

[0007] 3. Discontinuous topological transitions. In complex structures, different regions often require different types of lattice elements (such as BCC, Cubic, Gyroid, etc.). Traditional modeling methods often rely on manual Boolean operations or finite element preprocessing tools for splicing, resulting in geometrical abrupt changes and stress concentrations at the interfaces between lattices, making it difficult to achieve a smooth transition with continuous topology.

[0008] 4. In enclosed or highly curved shells (such as cylinders, fairings, and wing skins), the connection between the outer skin and the internal lattice often requires complex manual trimming or local transition design. Traditional Boolean operations often result in sharp edges or geometric cracks at the connection points, making it difficult to guarantee stress continuity and manufacturing feasibility.

[0009] 5. When the lattice size is large, explicit geometric modeling will cause a sharp increase in computational load. Boolean operations between different lattices require a lot of manual adjustment and lack parameterized control and process traceability, which is not conducive to engineering automation and CAE coupled analysis.

[0010] In recent years, researchers have attempted to introduce implicit geometric modeling and parametric field control methods to improve the above problems. For example, reference 1: "Zhang, C., &Li, Z. (2022). A Review of Lightweight Design for Space Mirror Core Structure: Tradition and Future. Machines, 10(11), 1066." evaluates the modeling capabilities of Voronoi and spherical BCC structures on multi-curvature surfaces in the study of lightweight lattice structures for space optical mirrors. This paper proposes a multi-level structural optimization framework to achieve a trade-off between high stiffness and lightweight. However, its work still focuses on the macroscopic structural level and lacks a systematic modeling process for the detailed processing of complex unit cells such as BCC-Z under large-area surface mapping, especially in terms of unit cell continuity and deformation control at curvature abrupt changes. For example, reference 2: "Li, H., Yang, W., Ma, Q., Qian, Z., &Yang, L. (2022). Specific Sensitivity Analysis and Imitative Full Stress Method for Optimal BCCZ Lattice Structure by Additive Manufacturing. Crystals, 12(12), 1844." Based on a simulated stress optimization strategy, parameter sensitivity analysis was conducted on the BCC-Z lattice structure, and experimental verification was achieved under complex geometry using additive manufacturing. This paper proposes a full stress method to optimize lattice thickness and layout, and verifies the improvement in mechanical properties under static compression. However, the modeling process of this method highly depends on finite element preprocessing, and its efficiency and scalability are still insufficient for highly complex heterogeneous curved surface skin structures. However, these studies mainly focus on the macroscopic optimization of single topological structures and have failed to systematically solve the problems of continuous transition, gradient control, and fillet connection of lattice elements under complex curved surface conditions. Summary of the Invention

[0011] Based on the problems raised in the background technology above, the purpose of this invention is to provide a skin-gradient lattice stiffening modeling and design method and related equipment for complex curved surfaces. It utilizes the spatial distribution and interpolation characteristics of a continuous scalar field to control the gradual change of the microstructure, and utilizes the smooth Boolean operation characteristics of the implicit field to achieve seamless fusion of geometric boundaries. This enables the continuous and smooth gradual change of the geometric parameters and topological morphology of the microstructure in space, as well as the continuous geometric and mechanical transition connection between the microstructure and the main body boundary.

[0012] This invention is achieved through the following technical solution:

[0013] The first aspect of this invention provides a skin-gradient lattice stiffening modeling and design method for complex curved surfaces, comprising the following steps:

[0014] Based on the implicit geometric definition of the 3D design domain, a complex surface composed of meshes is generated, and a stiffened lattice structure is generated on the complex surface to complete the initial assembly of the lattice and skin.

[0015] Based on the stiffened lattice structure, gradient-controllable lattice units are constructed to form parameterized gradient distribution rules, and the parameterized gradient distribution rules are mapped to the complex surface.

[0016] Based on the parameterized gradient distribution rule, a topological transition of the stiffened lattice structure is achieved between different regions using a continuous scalar field, and an intermediate transition shape is generated by an interpolation algorithm.

[0017] Based on the stiffened lattice structure after topological transition, a rounded corner connection structure is generated between the lattice and the complex curved surface skin, and geometric continuity is achieved through smooth Boolean operations of implicit fields.

[0018] The optimized overall structure is converted into a solid model and output in a mesh data format that can be used for numerical simulation or manufacturing.

[0019] In the above technical solution, the smooth and gradual change of the microstructure topology in different regions is achieved by continuous scalar field interpolation, which avoids stress concentration caused by topological abrupt changes. At the same time, the geometric cracks at the connection between the microstructure and the main body boundary are eliminated by the smooth Boolean operation of the implicit field, thus realizing the geometric and mechanical continuity of the overall structure.

[0020] In one alternative embodiment, the initial assembly of the dot matrix and the skin includes:

[0021] The geometric boundary of the target surface is defined based on implicit functions;

[0022] The moving cube algorithm is used to extract the isosurface of implicit functions and generate an initial triangular mesh surface;

[0023] The initial triangular mesh surface is reconstructed into a quadrilateral mesh to form a uniform and continuous quadrilateral mesh surface;

[0024] Sine or cosine stiffened lattice structures are generated using parametric equations;

[0025] The skin and the reinforced lattice structure are Boolean fused along the normal direction of the curved surface to assemble them into an integrated lattice-skin composite structure.

[0026] In one optional embodiment, the moving cube algorithm is used to extract the isosurface of the implicit function, including:

[0027] Divide the 3D design domain into uniform cubic mesh elements, traverse each mesh element and determine its vertex symbol:

[0028] If the vertex symbol of a mesh cell has both positive and negative signs, then a predefined triangular facet template is matched according to the vertex symbol, and the intersection of the isosurface and the edge is obtained by interpolation on the edge of the mesh cell. All intersections are connected to form a triangular facet.

[0029] The set of triangular faces of the mesh unit is extracted as the isosurface of the implicit function.

[0030] In one optional embodiment, generating a sinusoidal or cosine-type stiffened lattice structure via parametric equations includes:

[0031] Based on the parametric coordinates of the quadrilateral mesh surface Construct the stiffening path parametric equations:

[0032] Sinusoidal path parametric equations: ;

[0033] Cosine-type path parametric equations: ;

[0034] in, The amplitude is used to control the stiffening height; The period is used to control the spacing of the reinforcement. This is the phase angle, used to control path offset;

[0035] The stiffening path parametric equations are mapped to the quadrilateral mesh surface to generate sine or cosine stiffening paths distributed along the surface, and then stretched along the sine or cosine stiffening paths to form a sine or cosine stiffened lattice structure.

[0036] In one alternative embodiment, gradient-controllable lattice units are constructed to form parameterized gradient distribution rules, thereby achieving gradient control through at least one of the following methods:

[0037] Cloud-based scalar fields utilize two-dimensional or three-dimensional scalar data to control the geometric parameters of lattice units;

[0038] Point cloud field, a continuous parameter distribution is constructed by interpolating spatial point clouds;

[0039] Gradient fields, superimposed with multiple functions or contour signals, enable multi-dimensional, multi-objective optimization control;

[0040] Function field control achieves continuous variation of local lattice thickness, rod diameter, and topology through continuously differentiable functions along the radial, axial, or arbitrary directions. Its expression is:

[0041]

[0042] in, It is a continuously differentiable function. These are gradient control parameters used to define spatial variation.

[0043] In one alternative embodiment, a topological transition of the stiffened lattice structure is achieved between different regions using a continuous scalar field, including:

[0044] Set the geometric or topological parameters of the lattice elements in different regions;

[0045] By constructing a continuous weighting function, the geometric or topological parameters of adjacent regions are interpolated to obtain continuous intermediate states, thereby controlling the geometric deformation and topological changes of the lattice units in space.

[0046] In one alternative embodiment, geometric continuity is achieved through smooth Boolean operations on implicit fields, including:

[0047] ;

[0048] ;

[0049] in, This is a smoothing control factor used to determine the fillet radius; This is a numerical restriction function used to restrict variables; For transition weights; Let the coordinate vector of a point in the design domain be denoted by . The implicit field of the model after Boolean union operation; For the implicit field of the skin model; This is the implicit field of the gradient lattice model.

[0050] The second aspect of this invention provides a skin-gradient lattice stiffening modeling and design system for complex curved surfaces, comprising:

[0051] The Complex Surface and Initial Lattice Construction Module is used to generate complex surfaces composed of meshes based on the implicit geometric definition of the 3D design domain; and to generate stiffened lattice structures on the complex surfaces to complete the initial assembly of the lattice and skin.

[0052] The gradient lattice unit parametric design module is used to construct gradient-controllable lattice units on the basis of the stiffened lattice structure to form a parametric gradient distribution rule, and to map the parametric gradient distribution rule to the complex surface.

[0053] A cross-regional topology smooth transition module is used to realize the topological transition of the stiffened lattice structure between different regions based on the parameterized gradient distribution rules and using a continuous scalar field, and to generate intermediate transition forms through an interpolation algorithm.

[0054] The geometric continuity optimization module is used to generate a rounded corner connection structure between the lattice and the complex curved surface skin based on the stiffened lattice structure after topological transition, and to achieve geometric continuity through smooth Boolean operations of implicit fields.

[0055] The solid model and data output module is used to convert the optimized overall structure into a solid model and output a mesh data format that can be used for numerical simulation or manufacturing.

[0056] A third aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a skin-gradient lattice stiffening modeling and design method for complex curved surfaces.

[0057] The fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a skin-gradient lattice stiffening modeling and design method for complex curved surfaces.

[0058] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0059] 1. By introducing a continuous scalar field to interpolate the microstructure topology, and interpolating the microstructure parameters of adjacent regions based on a continuous weighting function, a continuous intermediate state is generated, enabling the microstructure to achieve a smooth transition between different topological types, thus avoiding the problems of topological abrupt changes and interface stress concentration caused by traditional splicing methods.

[0060] 2. By performing smooth Boolean operations on the implicit field, the microstructure and the main body boundary are continuously geometrically fused. Boolean union operations are performed based on the smooth control coefficients. Using the implicit field fusion formula that includes mixed variables and numerical constraint functions, a continuous and smooth transition zone is generated between the microstructure and the main body boundary. This eliminates the sharp edges or geometric cracks generated by traditional Boolean operations, ensuring the stress continuity and manufacturing feasibility of the overall structure.

[0061] 3. By driving the geometric parameter distribution of microstructures through continuous scalar fields, it supports the definition of function fields, cloud scalar fields or point cloud data, and can construct composite gradient fields through weighted superposition of multiple fields. This enables continuous and differentiable control of parameters such as the size and thickness of microstructures within the same topology, breaking through the limitation of traditional periodic lattices that only support global or discrete parameter control, and meeting the needs of multi-dimensional and multi-objective optimization design. Attached Figure Description

[0062] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0063] Figure 1 This is a flowchart illustrating the skin-gradient lattice stiffening modeling and design method for complex curved surfaces provided in Embodiment 1 of the present invention.

[0064] Figure 2 This is a schematic diagram of the three-dimensional design domain and initial mesh model defined by implicit geometry provided in Embodiment 1 of the present invention;

[0065] Figure 3 This is a schematic diagram of the microstructure topology interpolation transition and gradient control effect provided in Embodiment 1 of the present invention;

[0066] Figure 4 This is a schematic diagram illustrating the continuous geometric fusion effect of the microstructure and the main body boundary provided in Embodiment 1 of the present invention;

[0067] Figure 5 This is a schematic diagram of the solid mesh model output by the transformation provided in Embodiment 1 of the present invention;

[0068] Figure 6 This is a schematic diagram of the structure of an electronic device provided in Embodiment 3 of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0070] Example 1

[0071] Figure 1 This is a flowchart illustrating the skin-gradient lattice stiffening modeling and design method for complex curved surfaces provided in Embodiment 1 of the present invention, as shown below. Figure 1 As shown, the skin-gradient lattice stiffening modeling and design method for complex curved surfaces includes the following steps:

[0072] Based on the implicit geometric definition of the 3D design domain, a complex surface composed of meshes is generated, and a stiffened lattice structure is generated on the complex surface to complete the initial assembly of the lattice and skin.

[0073] Based on the stiffened lattice structure, gradient-controllable lattice units are constructed to form parameterized gradient distribution rules, and the parameterized gradient distribution rules are mapped to the complex surface.

[0074] Based on the parameterized gradient distribution rule, a topological transition of the stiffened lattice structure is achieved between different regions using a continuous scalar field, and an intermediate transition shape is generated by an interpolation algorithm.

[0075] Based on the stiffened lattice structure after topological transition, a rounded corner connection structure is generated between the lattice and the complex curved surface skin, and geometric continuity is achieved through smooth Boolean operations of implicit fields.

[0076] The optimized overall structure is converted into a solid model and output in a mesh data format that can be used for numerical simulation or manufacturing.

[0077] It should be noted that implicit geometry refers to defining the boundaries of the target geometry through implicit functions, rather than explicitly describing the topological connections of the boundaries. Complex surfaces refer to surfaces with complex geometric shapes composed of meshes in a 3D design domain, such as skins of revolution and hyperboloids. Sine or cosine stiffened lattice structures refer to periodically stiffened microstructures generated through parametric equations, with member distribution following a sine or cosine pattern, capable of withstanding loads in specific directions while maintaining lightweight characteristics. The initial assembly of the lattice and skin refers to Boolean fusion of the stiffened lattice structure with the skin along the surface normal direction, forming the initial form of an integrated lattice-skin composite structure.

[0078] Gradient-controllable lattice elements refer to lattice elements whose geometric parameters can be continuously and differently varied in space, rather than fixed-parameter elements with discrete piecewise assignments. Parameterized gradient distribution rules refer to defining the spatial distribution of lattice element parameters by mapping spatial coordinates to continuous parameter values ​​through a continuous scalar field.

[0079] A continuous scalar field refers to a scalar function field with continuous distribution characteristics in a three-dimensional design domain. Its values ​​at each point in space are continuously differentiable, rather than discrete piecewise step functions. Topological transition of a lattice structure refers to the process where different topological lattice structures are required to be arranged between different regions due to differences in load-bearing requirements or functions. This is achieved by mapping spatial coordinates to continuous weight values ​​using a continuous scalar field, and then interpolating the lattice parameters of different regions using these weight values, thereby generating a continuous intermediate transition form in space. Traditional modeling methods typically involve directly splicing lattice structures of different topological types in different regions. This discrete piecewise splicing method produces geometrical abrupt changes and topological discontinuities at the interface, failing to achieve a smooth transition and leading to stress concentration and structural discontinuity. This embodiment, however, eliminates the interface stress concentration caused by topological abrupt changes through an interpolation transition mechanism based on a continuous scalar field, achieving a continuous and smooth transition of the lattice structure's topological form in space.

[0080] Rounded corner connection refers to a smooth transition zone generated at the boundary between the lattice structure and the complex curved skin, rather than sharp edges or geometric cracks caused by simple hard truncation. Implicit field smooth Boolean operation refers to generating a smooth transition fusion zone at the boundary between the implicit field of the lattice structure and the implicit field of the complex curved skin through specific mathematical operators and control coefficients. Traditional hard Boolean operation, when splicing lattice structures and skin, directly generates sharp edges or geometric cracks at the connection point due to the lack of transition zone control. This geometric abrupt change not only disrupts the geometric continuity of the structure but also causes severe stress concentration mechanically. This embodiment introduces implicit field smooth Boolean operation, the core of which lies in nonlinearly smoothing the traditional hard Boolean operation through smoothing control coefficients. Mathematically, this ensures the continuity of the implicit function gradient in the fusion region, and geometrically, it manifests as a smooth transition from the lattice structure to the skin at the connection point, completely eliminating sharp edges and cracks. It should be understood that smooth Boolean operation is not limited to union operations; in other implementations requiring subtractive or intersection fusion, a smooth control mechanism can also be introduced to achieve a continuous transition.

[0081] After gradient modulation, topological transition, and geometric fusion, the overall structure possesses a complete and continuous geometric description in the implicit field space. To transform this implicit geometric description into a data format usable for engineering simulation and additive manufacturing, it needs to be converted into a solid model and output. This conversion process typically involves extracting the isosurfaces of implicit functions, discretizing the continuous implicit field into a mesh model. The output solid model format can be flexibly selected according to downstream application requirements; for example, it could be a mesh format for finite element analysis or a standardized 3D model format for additive manufacturing.

[0082] The above steps achieve the synergistic effect of two core operations: scalar field interpolation transition and implicit field Boolean fusion. The reason why existing technologies cannot solve the problem of the overall continuity between the lattice structure and the skin is that they treat topological gradation and boundary connection separately and rely on hard splicing, a discrete "either / or" operation.

[0083] The reason why the scheme in this embodiment can achieve overall continuity lies in the following microscopic mechanism: continuous scalar field interpolation ensures the continuous differentiability of the spatial distribution of the lattice structure at the topological level, eliminating topological abrupt changes; while implicit field smoothing Boolean operations ensure the continuity of the implicit function gradient at the boundary level, eliminating geometric cracks. Both achieve mathematical mechanism unification within the implicit field framework, thereby establishing a continuous stress transfer path from the microscopic topology to the macroscopic boundary at the physical level, producing unexpected overall continuity and strength enhancement effects.

[0084] In one alternative embodiment, the initial assembly of the dot matrix and the skin includes:

[0085] The geometric boundary of the target surface is defined based on implicit functions;

[0086] The moving cube algorithm is used to extract the isosurface of implicit functions and generate an initial triangular mesh surface;

[0087] The initial triangular mesh surface is reconstructed into a quadrilateral mesh to form a uniform and continuous quadrilateral mesh surface;

[0088] Sine or cosine stiffened lattice structures are generated using parametric equations;

[0089] The skin and the reinforced lattice structure are Boolean fused along the normal direction of the curved surface to assemble them into an integrated lattice-skin composite structure.

[0090] Specifically, based on the implicit function definition of the geometric boundary of the target surface, a three-dimensional implicit function is selected. As a basis for boundary definition, this embodiment takes a typical complex surface as an example, and its three-dimensional implicit function is as follows:

[0091]

[0092] in, Used to control the size of the basic ellipsoid. Used to control the amplitude and frequency of surface ripples For the design domain length; via Define the interior region of the surface. Define the external region to achieve a precise mathematical description of the geometric boundaries.

[0093] In one optional embodiment, the moving cube algorithm is used to extract the isosurface of the implicit function, including:

[0094] Divide the 3D design domain into uniform cubic mesh elements, traverse each mesh element and determine its vertex symbol:

[0095] If the vertex symbol of a mesh cell has both positive and negative signs, then a predefined triangular facet template is matched according to the vertex symbol, and the intersection of the isosurface and the edge is obtained by interpolation on the edge of the mesh cell. All intersections are connected to form a triangular facet.

[0096] The set of triangular faces of the mesh unit is extracted as the isosurface of the implicit function.

[0097] After defining the implicit geometric design domain, it needs to be transformed into an initial mesh model that can be used for subsequent microstructure mapping and parameter control. This transformation process is achieved by extracting the isosurfaces of implicit functions.

[0098] The mechanism of isosurface extraction lies in searching for regions in three-dimensional discrete space where the implicit function values ​​undergo sign changes, accurately locating the spatial coordinates of zero-value points through interpolation, and then connecting these points into patches to form a mesh model. Since the implicit field itself is continuous, the isosurface extraction algorithm can ensure that the generated mesh patches share vertices and edges at their boundaries, thus maintaining the geometric continuity inherited from the implicit field.

[0099] like Figure 2 As shown, a schematic diagram of the 3D design domain defined by implicit geometry and the initial mesh model generated therefrom is presented. Within this design domain, both the macroscopic boundary contours of the main body (such as the skin of a solid of revolution) and the microscopic stiffened regions of the microstructure are described within the same continuous implicit field framework. The solid of revolution surface and the stiffened structures distributed on its outer surface shown on the left are generated based on the continuous design domain defined by implicit functions; the magnified view on the right clearly shows the details of the initial mesh model, with blue triangular meshes covering the gray solid surface, demonstrating the well-geometrically continuous mesh generation generated after isosurface extraction. This implicit geometry-based starting point definition provides a consistent underlying mathematical support for the subsequent implicit field smooth Boolean fusion, ensuring a continuous closed loop throughout the entire process from start to finish.

[0100] Furthermore, the triangular mesh is reconstructed into a quadrilateral mesh. Through parametric mapping, tangent field guidance, or remeshing algorithms, a quadrilateral mesh surface with high regularity and good topological consistency is obtained, providing a stable foundation for subsequent lattice element mapping.

[0101] In one optional embodiment, generating a sinusoidal or cosine-type stiffened lattice structure via parametric equations includes:

[0102] Based on the parametric coordinates of the quadrilateral mesh surface Construct the stiffening path parametric equations:

[0103] Sinusoidal path parametric equations: ;

[0104] Cosine-type path parametric equations: ;

[0105] in, The amplitude is used to control the stiffening height; The period is used to control the spacing of the reinforcement. This is the phase angle, used to control path offset;

[0106] The stiffening path parametric equations are mapped to the quadrilateral mesh surface to generate sine or cosine stiffening paths distributed along the surface, and then stretched along the sine or cosine stiffening paths to form a sine or cosine stiffened lattice structure.

[0107] The construction of sinusoidal / cosine stiffening paths is controlled by parametric equations, where amplitude, phase angle, and period can be adjusted as design variables to adapt to different structural requirements.

[0108] Furthermore, the skin and stiffening lattice are assembled. Using the obtained quadrilateral mesh surface as the skin substrate, the generated stiffening lattice structure is Boolean-fused with the skin along the surface normal direction, assembling into an integrated lattice-skin composite structure. This ensures a continuous geometric connection between the stiffening lattice and the skin, providing a complete basic model for subsequent gradient control and topological transition.

[0109] In one alternative embodiment, gradient-controllable lattice units are constructed to form parameterized gradient distribution rules, thereby achieving gradient control through at least one of the following methods:

[0110] Cloud-based scalar fields utilize two-dimensional or three-dimensional scalar data to control the geometric parameters of lattice units;

[0111] Point cloud field, a continuous parameter distribution is constructed by interpolating spatial point clouds;

[0112] Gradient fields, superimposed with multiple functions or contour signals, enable multi-dimensional, multi-objective optimization control;

[0113] Function field control achieves continuous variation of local lattice thickness, rod diameter, and topology through continuously differentiable functions along the radial, axial, or arbitrary directions. Its expression is:

[0114]

[0115] in, It is a continuously differentiable function. These are gradient control parameters used to define spatial variation.

[0116] After generating the skin-lattice stiffened mesh model, the geometric parameters of the lattice elements are controlled by a function field or a cloud-based quantitative field to achieve structural gradient adjustment.

[0117] Spatial variations include spatial variations in local material thickness, unit cell size, or topological type.

[0118] In this context, the continuously differentiable function in the function field control can be configured with a specific function form according to different engineering requirements, for example:

[0119] (a) Linear functions: , used for uniform linear gradients;

[0120] (b) , used for localized enhancement of areas;

[0121] (c) Periodic function: It is used for periodic structural changes.

[0122] Explained in conjunction with gradient effects, such as Figure 3 As shown, while maintaining the same topological configuration, the microstructure exhibits a continuous and smooth gradient in geometric parameters such as rod thickness from top to bottom. From a microscopic perspective, the continuous scalar field drives the spatial distribution of geometric parameters from the traditional "discrete step assignment" to a "continuously differentiable function distribution." Discrete step assignment inevitably triggers abrupt changes in material distribution at step transition points, leading to local stress concentration. In contrast, the continuously differentiable function distribution ensures the finiteness and smoothness of the material distribution gradient, allowing stress flow to be smoothly transmitted without abrupt changes within the microstructure. This achieves lightweight material distribution while maintaining balanced and continuous strength.

[0123] In one alternative embodiment, a topological transition of the stiffened lattice structure is achieved between different regions using a continuous scalar field, including:

[0124] Set the geometric or topological parameters of the lattice elements in different regions;

[0125] By constructing a continuous weighting function, the geometric or topological parameters of adjacent regions are interpolated to obtain continuous intermediate states, thereby controlling the geometric deformation and topological changes of the lattice units in space.

[0126] To achieve a continuous transition between different types of lattice elements, this embodiment employs a parametric interpolation algorithm to control the lattice topology gradient. Parameter sets are defined in adjacent regions. and And construct a continuous weight function in the transition interval. Establish interpolation relationships:

[0127] ;

[0128] in, The spatial weighting function can be linear, spline, or implicit field interpolation. By adjusting the gradient and spatial distribution, the transition width and smoothness are controlled, thus achieving a gradual transformation from one lattice topology to another while maintaining structural continuity. This process can be widely applied to topology fusion between lattice types such as BCC and Gyroid, Cubic and TPMS.

[0129] In one alternative embodiment, geometric continuity is achieved through smooth Boolean operations on implicit fields, including:

[0130] ;

[0131] ;

[0132] in, This is a smoothing control factor used to determine the fillet radius; This is a numerical restriction function used to restrict variables; For transition weights; Let the coordinate vector of a point in the design domain be denoted by . The implicit field of the model after Boolean union operation; For the implicit field of the skin model; This is the implicit field of the gradient lattice model.

[0133] After completing the matrix construction and topology transition, implicit geometric smoothing Boolean operations are used to achieve rounded corner connections between the matrix and the skin.

[0134] The `clamp` function is a numerical constraint function commonly used in geometric modeling, computer graphics, and implicit function design to restrict a variable to a specified minimum and maximum value. In this embodiment, its functions include preventing numerical instability; ensuring the blending transition zone only functions near the boundary; and guaranteeing that the fillet radius and transition thickness are within a reasonable range. It ensures a smooth transition and stress continuity at the junction of the geometric model and the lattice skin, effectively avoiding sharp edges or geometric cracks caused by traditional CAD Boolean operations.

[0135] It should be explained that in implicit geometric modeling algorithms, the term "rounded corner" can be understood as a Boolean merge operation between two geometric objects.

[0136] Combination Figure 4 Explain the effects of fusion, such as Figure 4As shown, a continuous and smooth geometric fusion is achieved between the microstructure and the main body boundary, completely eliminating sharp edges and cracks at the connection. From a microscopic mechanism perspective, smooth Boolean operations, through the continuous allocation of the mixed variable h and the curvature adjustment of the nonlinear correction term, achieve a smooth transition from the microstructure to the main body boundary at the implicit field gradient level. This mathematical gradient continuity directly maps to the smooth transmission of stress flow at the physical level, avoiding the stress peaks caused by the forced sharp turns of stress flow at sharp edges due to hard Boolean splicing. Thus, while ensuring geometric continuity, it fundamentally improves the mechanical performance and manufacturing feasibility of the structure.

[0137] The geometric model, after function modulation, interpolation transition, and fillet blending, is uniformly expressed as an implicit field form. A triangular mesh model (STL or OBJ format) is generated using implicit geometry extraction algorithms (such as Marching Cubes), and beam or shell element formats can be further derived for finite element analysis. The output mesh possesses high topological consistency and geometric accuracy, and can be directly applied to structural simulation, additive manufacturing, and performance optimization design.

[0138] It should be noted that the method proposed in this embodiment uses implicit geometric algorithms and mesh generation to quickly achieve parametric modeling of skin lattice stiffened structures. The configuration of the lattice structure can be arbitrarily set. The overall structure of the finite element discretization of the lattice structure with uniform size on the macro scale has a clear size ratio with the lattice structure on the micro scale. The skin thickness and width can be customized. The generated mesh model can ensure the connectivity of the lattice structure on the micro scale on the macro scale. The designed topological structure configuration can be directly used for processing and manufacturing.

[0139] Furthermore, there is a need for mesh models to be directly used for finite element performance simulation.

[0140] Example 2

[0141] Based on Example 1, Example 2 of the present invention provides a skin-gradient lattice stiffening modeling and design system for complex curved surfaces, including:

[0142] The Complex Surface and Initial Lattice Construction Module is used to generate complex surfaces composed of meshes based on the implicit geometric definition of the 3D design domain; and to generate stiffened lattice structures on the complex surfaces to complete the initial assembly of the lattice and skin.

[0143] The gradient lattice unit parametric design module is used to construct gradient-controllable lattice units on the basis of the stiffened lattice structure to form a parametric gradient distribution rule, and to map the parametric gradient distribution rule to the complex surface.

[0144] A cross-regional topology smooth transition module is used to realize the topological transition of the stiffened lattice structure between different regions based on the parameterized gradient distribution rules and using a continuous scalar field, and to generate intermediate transition forms through an interpolation algorithm.

[0145] The geometric continuity optimization module is used to generate a rounded corner connection structure between the lattice and the complex curved surface skin based on the stiffened lattice structure after topological transition, and to achieve geometric continuity through smooth Boolean operations of implicit fields.

[0146] The solid model and data output module is used to convert the optimized overall structure into a solid model and output a mesh data format that can be used for numerical simulation or manufacturing.

[0147] Example 3

[0148] Figure 6 This is a schematic diagram of the structure of an electronic device provided in Embodiment 3 of the present invention, as shown below. Figure 6 As shown, the electronic device includes a processor 21, a memory 22, an input device 23, and an output device 24; the number of processors 21 in the computer device can be one or more. Figure 6 Taking a processor 21 as an example; the processor 21, memory 22, input device 23, and output device 24 in an electronic device can be connected via a bus or other means. Figure 6 Taking the example of a connection between China and Israel via a bus.

[0149] The memory 22, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules. The processor 21 executes various functional applications and data processing of the electronic device by running the software programs, instructions, and modules stored in the memory 22, thereby realizing the complex surface skin-gradient lattice stiffening modeling and design method of Embodiment 1.

[0150] The memory 22 may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function; the data storage area may store data created based on terminal usage. Furthermore, the memory 22 may include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory, or other non-volatile solid-state storage device. In some instances, the memory 22 may further include memory remotely located relative to the processor 21, which can be connected to the electronic device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0151] Input device 23 can be used to receive user input such as ID and password. Output device 24 is used to output the network configuration page.

[0152] Example 4

[0153] Embodiment 4 of the present invention also provides a computer-readable storage medium, wherein the computer-executable instructions, when executed by a computer processor, are used to implement the skin-gradient lattice stiffening modeling and design method for complex curved surfaces as provided in Embodiment 1.

[0154] The storage medium containing computer-executable instructions provided in the embodiments of the present invention is not limited to the method operation provided in Embodiment 1, but can also perform related operations in the complex surface skin-gradient lattice stiffening modeling and design method provided in any embodiment of the present invention.

[0155] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A skin-gradient lattice stiffening modeling and design method for complex curved surfaces, characterized in that, Includes the following steps: Based on the implicit geometric definition of the 3D design domain, a complex surface composed of meshes is generated, and a stiffened lattice structure is generated on the complex surface to complete the initial assembly of the lattice and skin. Based on the stiffened lattice structure, gradient-controllable lattice units are constructed to form parameterized gradient distribution rules, and the parameterized gradient distribution rules are mapped to the complex surface. Based on the parameterized gradient distribution rule, a topological transition of the stiffened lattice structure is achieved between different regions using a continuous scalar field, and an intermediate transition shape is generated by an interpolation algorithm. Based on the stiffened lattice structure after topological transition, a rounded corner connection structure is generated between the lattice and the complex curved surface skin, and geometric continuity is achieved through smooth Boolean operations of implicit fields. The optimized overall structure is converted into a solid model and output in a mesh data format that can be used for numerical simulation or manufacturing.

2. The skin-gradient lattice stiffening modeling and design method for complex curved surfaces according to claim 1, characterized in that, The initial assembly of the dot matrix and skin includes: The geometric boundary of the target surface is defined based on implicit functions; The moving cube algorithm is used to extract the isosurface of implicit functions and generate an initial triangular mesh surface; The initial triangular mesh surface is reconstructed into a quadrilateral mesh to form a uniform and continuous quadrilateral mesh surface; Sine or cosine stiffened lattice structures are generated using parametric equations; The skin and the reinforced lattice structure are Boolean fused along the normal direction of the curved surface to assemble them into an integrated lattice-skin composite structure.

3. The skin-gradient lattice stiffening modeling and design method for complex curved surfaces according to claim 2, characterized in that, The moving cube algorithm is used to extract the isosurfaces of implicit functions, including: Divide the 3D design domain into uniform cubic mesh elements, traverse each mesh element and determine its vertex symbol: If the vertex symbol of a mesh cell has both positive and negative signs, then a predefined triangular facet template is matched according to the vertex symbol, and the intersection of the isosurface and the edge is obtained by interpolation on the edge of the mesh cell. All intersections are connected to form a triangular facet. The set of triangular faces of the mesh unit is extracted as the isosurface of the implicit function.

4. The skin-gradient lattice stiffening modeling and design method for complex curved surfaces according to claim 3, characterized in that, Generating sinusoidal or cosine-type stiffened lattice structures through parametric equations includes: Based on the parametric coordinates of the quadrilateral mesh surface Construct the stiffening path parametric equations: Sinusoidal path parametric equations: ; Cosine-type path parametric equations: ; in, The amplitude is used to control the stiffening height; The period is used to control the spacing of the reinforcement. This is the phase angle, used to control path offset; The stiffening path parametric equations are mapped to the quadrilateral mesh surface to generate sine or cosine stiffening paths distributed along the surface, and then stretched along the sine or cosine stiffening paths to form a sine or cosine stiffened lattice structure.

5. The skin-gradient lattice stiffening modeling and design method for complex curved surfaces according to claim 1, characterized in that, Gradient controllable lattice units are constructed to form parameterized gradient distribution rules. Gradient control is achieved through at least one of the following methods: Cloud-based scalar fields utilize two-dimensional or three-dimensional scalar data to control the geometric parameters of lattice units; Point cloud field, a continuous parameter distribution is constructed by interpolating spatial point clouds; Gradient fields, superimposed with multiple functions or contour signals, enable multi-dimensional, multi-objective optimization control; Function field control achieves continuous variation of local lattice thickness, rod diameter, and topology through continuously differentiable functions along the radial, axial, or arbitrary directions. Its expression is: ； in, It is a continuously differentiable function. These are gradient control parameters used to define spatial variation.

6. The skin-gradient lattice stiffening modeling and design method for complex curved surfaces according to claim 1, characterized in that, Achieving topological transitions of stiffened lattice structures between different regions using continuous scalar fields includes: Set the geometric or topological parameters of the lattice elements in different regions; By constructing a continuous weighting function, the geometric or topological parameters of adjacent regions are interpolated to obtain continuous intermediate states, thereby controlling the geometric deformation and topological changes of the lattice units in space.

7. The skin-gradient lattice stiffening modeling and design method for complex curved surfaces according to claim 1, characterized in that, Achieving geometric continuity through smooth Boolean operations on implicit fields includes: ； ； in, This is a smoothing control factor used to determine the fillet radius; This is a numerical restriction function used to restrict variables; For transition weights; Let the coordinate vector of a point in the design domain be denoted by . The implicit field of the model after Boolean union operation; For the implicit field of the skin model; This is the implicit field of the gradient lattice model.

8. A skin-gradient lattice stiffening modeling and design system for complex curved surfaces, used to implement the skin-gradient lattice stiffening modeling and design method for complex curved surfaces as described in any one of claims 1 to 7, characterized in that, include: The Complex Surface and Initial Lattice Construction Module is used to generate complex surfaces composed of meshes based on implicitly defined 3D design domains. A stiffened lattice structure is generated on this complex curved surface to complete the initial assembly of the lattice and the skin. The gradient lattice unit parametric design module is used to construct gradient-controllable lattice units on the basis of the stiffened lattice structure to form a parametric gradient distribution rule, and to map the parametric gradient distribution rule to the complex surface. A cross-regional topology smooth transition module is used to realize the topological transition of the stiffened lattice structure between different regions based on the parameterized gradient distribution rules and using a continuous scalar field, and to generate intermediate transition forms through an interpolation algorithm. The geometric continuity optimization module is used to generate a rounded corner connection structure between the lattice and the complex curved surface skin based on the stiffened lattice structure after topological transition, and to achieve geometric continuity through smooth Boolean operations of implicit fields. The solid model and data output module is used to convert the optimized overall structure into a solid model and output a mesh data format that can be used for numerical simulation or manufacturing.

9. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the skin-gradient lattice stiffening modeling and design method for complex surfaces as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the skin-gradient lattice stiffening modeling and design method for complex surfaces as described in any one of claims 1 to 7.

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