Modeling and designing method for curved-surface thin-wall multi-scale structure

Abstract

The invention relates to the technical field of multi-dimensional multi-scale structure modeling and design, in particular to a modeling and design method for a curved-surface thin-wall multi-scale structure. And an implicit modeling method is adopted to calculate a meso-structure symbolic distance function. And calculating a curved surface two-dimensional parameter domain based on a conformal mapping method. On the basis of the periodicity characteristic of a multi-scale structure, Fourier transform is adopted in a two-dimensional parameter domain, and the irregular two-dimensional multi-scale structure meeting the specified design parameter requirement is calculated according to the relative density, the relative angle and the mesostructure size parameter of the multi-scale structure. And performing interpolation calculation on the single-layer grid model of the three-dimensional curved surface multi-scale structure, and providing a multi-scale structure thickening method combining a normal vector offset method and an interpolation method to obtain a curved surface thin-wall multi-scale structure geometric model. The method is suitable for a complex microstructure expressed by a two-dimensional symbol distance function, the irregular multi-scale structure meets specified relative density, relative angle and microstructure size parameters, the method is suitable for a complex curved surface design domain, and connectivity of the microstructure is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-dimensional and multi-scale structure modeling and design, and in particular to a modeling and design method for a curved thin-walled multi-scale structure. Background Art

[0002] Curved, thin-walled, multi-scale structures are widely present in major aerospace equipment and often serve as primary load-bearing components, such as rocket engines, spacecraft fuel tanks, and aircraft wings. These load-bearing components often must meet comprehensive requirements, including lightweight design, high load-bearing capacity, and adaptability to complex curved surfaces. Adding multi-scale structures that conform to the curved surface to thin-walled structures is an important design approach.

[0003] Curved, thin-walled multiscale structures are structures formed by periodic or near-periodic arrangements of multiscale structures on a thin curved surface. By manipulating parameters such as the relative density, relative angles, and microscopic structural dimensions of the multiscale structures, these structures can achieve superior performance compared to conventional curved, thin-walled structures of the same weight. Therefore, curved, thin-walled multiscale structures hold significant research and engineering application value.

[0004] Modeling thin-walled multiscale structures on curved surfaces requires smooth, continuous structures that conform to the surface, and the model information must be usable for additive manufacturing. However, common two-dimensional multiscale structure modeling methods are not applicable to curved surfaces. For example, coordinate translation and rotation transformations are only applicable to simple cylindrical surfaces, while mesh-based isoparametric transformation interpolation methods cannot guarantee smooth connections among multiscale structures, making it difficult to fit them to curved surfaces.

[0005] The multi-scale structure on the curved thin wall can be regarded as a rib structure. In order to ensure the smooth continuity and fit of the curved thin-walled rib structure, some researchers have used mesh deformation technology to realize the modeling of curved thin-walled structures. Invention patent CN115238392A defines control points, establishes a mapping relationship between control points and the node coordinates of the finite element model of the plane rib structure before deformation, makes the rib structure fit the curved surface through the free deformation method, and calculates the coordinates of the control points after deformation to obtain the finite element node coordinates. Invention patent CN111027250A uses a machine learning method to establish the control relationship between the curved surface background grid and the target grid point set, and deforms the simple curved surface grid into a special-shaped curved surface grid. This method can solve problems such as uneven model grid division and rough transition. In order to simplify the modeling of curved thin-walled structures, some researchers have combined the modeling method of the surface parameterization method. Invention patent CN114741782A discloses a modeling method for conical shell structures, which directly derives the parameter domain analytical formula through the conical surface analytical formula, and performs rib structure modeling and optimization design in the parameter domain. Invention patent CN114492114A uses the ARAP (As Rigid As Possible) method to calculate the parameter domain, employs a B-spline parameterization method to represent the rib structure, and defines a twist function to evaluate the accuracy of the B-spline parameterization method. Invention patent CN115630542A uses a conformal mapping method to calculate the parameter domain of the surface, and uses explicit geometric parameters to construct and describe the component-type stiffener in the parameter domain. The established model can be used for the optimized design of curved thin-walled structures.

[0006] The curved, thin-walled, multi-scale structure proposed in this invention differs from the aforementioned curved, thin-walled, ribbed structure in that it contains a large number of microstructures formed by a near-periodic arrangement, exhibiting typical multi-scale characteristics. Currently, methods for generating geometric models of curved, thin-walled, ribbed structures have been studied and applied. However, existing methods still have shortcomings when it comes to curved, thin-walled, multi-scale structures, including:

[0007] 1) In terms of mesostructure modeling of multi-scale structures, the current scheme mainly adopts the cross-shaped, hexahedral and other mesostructure configurations, which are single and difficult to design the mesostructure configuration and geometric parameters.

[0008] 2) In terms of modeling of irregular multi-scale structures, existing modeling methods usually only consider a single variable design parameter among relative density, angle and spacing. When considering multiple variable design parameters at the same time, it is difficult to ensure the connectivity of the microstructure, which limits the freedom of design of irregular multi-scale structures.

[0009] 3) In terms of geometric model generation of curved thin-walled multi-scale structures, existing methods are mainly used for modeling regular structures with simple thin-walled shapes such as planes and cylinders, and lack geometric modeling methods for irregular multi-scale structures with complex surfaces.

[0010] In summary, it is necessary to propose a modeling and design method for curved thin-walled multi-scale structures, which can establish microstructures with complex configurations, realize the modeling of irregular multi-scale structures considering multiple design parameters such as relative density, angle and spacing, and generate complex curved thin-walled irregular multi-scale structure geometric models that can be used for additive manufacturing. Summary of the Invention

[0011] The present invention provides a modeling and design method for a curved surface thin-walled multi-scale structure, which can realize the generation of a geometric model of the curved surface thin-walled multi-scale structure.

[0012] The technical solution of the present invention is as follows: a modeling and design method for curved thin-walled multi-scale structures, wherein the mesostructure is implicitly modeled based on the topological information of the mesostructure to obtain a signed distance function of the mesostructure; a conformal mapping method is used to calculate the two-dimensional parameter domain of the surface design domain;

[0013] Based on Fourier transform, irregular two-dimensional multi-scale structure modeling is carried out, and the relative angle and microscopic structure size parameters of irregular two-dimensional multi-scale structures are established to obtain the signed distance function of irregular two-dimensional multi-scale structure. The relative density function of irregular two-dimensional multi-scale structure is used as the projection function, and the irregular two-dimensional multi-scale structure voxel model is obtained based on the signed distance function of irregular two-dimensional multi-scale structure. Based on the two-dimensional parameter domain and the voxel model of irregular two-dimensional multi-scale structure, the single-layer grid model of irregular three-dimensional multi-scale structure and the three-dimensional multi-scale structure model are obtained, and then the irregular three-dimensional curved thin-wall multi-scale structure geometric model with specified curved thin wall and multi-scale structure thickness is established.

[0014] The implicit modeling of the mesostructure is specifically as follows: characteristic edges are used to represent the topological information of the mesostructure; and the signed distance function of the mesostructure is calculated according to the topological information of the mesostructure.

[0015] The specific steps of the implicit modeling of the mesostructure are:

[0016] 1) Establish characteristic edges representing microscopic structural topology information:

[0017] Establishing a local coordinate system , in the local coordinate system In the example, the two endpoints of the feature edge are and The endpoint coordinates are and , the design domain range is specified as ; A point on the local coordinate plane Relative Distance of feature edges The calculation formula is:

[0018] (1)

[0019] in, is the number of the feature edge, and Represents the two endpoints of the feature edge and The angle between the connecting line and the feature edge, point The coordinates satisfy ;

[0020] 2) Calculate the signed distance function of the microstructure ;

[0021] Signed distance function of microstructure Calculated by formula (2):

[0022] (2)

[0023] in, Used to indicate the Feature edges, is the number of characteristic edges.

[0024] The irregular two-dimensional multi-scale structure modeling based on Fourier transform is specifically as follows: according to the periodic characteristics of regular two-dimensional multi-scale structures, the geometric information of the mesoscopic structure is decomposed into a complex exponential function by using the Fourier transform method, and the spatial transformation parameters are extracted from the complex exponential function; the relative angle of the multi-scale structure and the mesoscopic structure size parameters are represented by the rotation matrix and the scaling coefficient, and the transformed spatial transformation parameters are calculated according to the rotation matrix and the scaling coefficient; based on the transformed spatial transformation parameters, the signed distance function of the irregular two-dimensional multi-scale structure is calculated by the least squares method; the relative density parameter is used as the projection function of the signed distance function to calculate the irregular two-dimensional multi-scale structure voxel model that meets the requirements of multiple design parameters.

[0025] The irregular two-dimensional multi-scale structure modeling based on Fourier transform is specifically as follows:

[0026] Establishing a global coordinate system on a two-dimensional parameter domain , the design parameters are expressed by two-dimensional functions, including the relative density two-dimensional function , relative angle two-dimensional function and a two-dimensional function of the microstructure size Specific steps include:

[0027] 1) Calculate the signed distance function The Fourier series of

[0028] According to the signed distance function of the microstructure , calculated using two-dimensional discrete Fourier transform The Fourier series of is calculated as:

[0029] (3)

[0030] in, is a two-dimensional function representing the spectrum, and Represents the local coordinate system Coordinates on ; and Is a constant, representing the local coordinate system The size of the microstructure at the corresponding coordinate in ;

[0031] According to formula (4), the spatial transformation parameters in the frequency domain are defined as :

[0032] (4)

[0033] 2) Use rotation matrix and scaling coefficient to transform spatial parameters Perform spatial transformation;

[0034] According to design parameters and , calculate the transformed spatial transformation parameters through the rotation matrix and scaling coefficient :

[0035] (5)

[0036] 3) Constructing a least squares problem to solve the irregular two-dimensional multi-scale structure signed distance function ;

[0037] According to the transformed space transformation parameters , the signed distance function of the irregular two-dimensional multi-scale structure is calculated :

[0038] (6)

[0039] in, and is a two-dimensional parameter domain coordinate system The coordinates on ;

[0040] Define a two-dimensional function , and write formula (6) as:

[0041] (7)

[0042] Construct a least squares optimization problem and solve :

[0043] (8)

[0044] in, represents a two-dimensional parameter domain;

[0045] From the perspective of numerical calculation, combined with the finite difference method, the least squares optimization problem expressed in formula (8) is solved to obtain , and substitute it into formula (7) to calculate the signed distance function of the irregular two-dimensional multi-scale structure ;

[0046] 4) Using relative density parameters as projection functions to calculate irregular two-dimensional multi-scale structure voxel models;

[0047] (9)

[0048] in, Voxel models representing irregular two-dimensional multiscale structures.

[0049] The method for generating the irregular curved surface thin-walled multi-scale structure geometric model is as follows: first, an isosurface method and a triangulation method are used to extract an irregular two-dimensional multi-scale structure grid model from the irregular two-dimensional multi-scale structure voxel model. ; Based on the irregular two-dimensional multi-scale structure grid model and 2D parametric domain mesh models , the interpolation method is used to calculate the irregular three-dimensional multi-scale structure single-layer grid model ; For irregular three-dimensional multi-scale structure single-layer grid model The geometric model of irregular three-dimensional thin-walled multi-scale structure is calculated using the normal vector weighted offset method.

[0050] The specific steps include:

[0051] 1) Extracting grid models of irregular two-dimensional multi-scale structures ;

[0052] Based on the irregular two-dimensional multi-scale structure voxel model, the contour extraction method is used to extract the structure contour, and the triangulation method is used to obtain the grid model of the irregular two-dimensional multi-scale structure. ;

[0053] 2) Irregular 3D multi-scale structure single-layer grid model ;

[0054] According to the irregular two-dimensional multi-scale structured grid model 2D parametric domain mesh model for surface design domain , calculate the three-dimensional coordinate system Mesh model of medium-scale structure; a point in the plane where the spatial triangle is located , expressed as a linear combination of the three vertices of the triangle, and the interpolation coefficients are obtained by solving the linear equations shown in formula (10) , , :

[0055] (10)

[0056] in, 2D parametric domain mesh model for surface design domain The node coordinates of Irregular two-dimensional multi-scale structured grid model Node coordinates of

[0057] The interpolation coefficients , , Substitute into the surface design domain mesh model In the coordinates of , the irregular three-dimensional multi-scale structure single-layer grid model is calculated Node coordinates on :

[0058] (11)

[0059] 3) Establishing geometric models of irregular three-dimensional thin-walled multi-scale structures;

[0060] Design domain mesh model based on surface , specify the thickness of irregular three-dimensional thin-walled multi-scale structures , using the normal vector weighted offset method to calculate the offset surface design domain mesh model ; The vertex offset normal vector is calculated by weighting the normal vector angle of the adjacent face, and the surface design domain mesh model The vertex weighted offset normal vector calculation formula is:

[0061] (12)

[0062] in, is a node The vertex normal vector, is the number of adjacent faces of the node, For adjacent faces At the node The angle at which

[0063] The original surface is forward offset and the interpolation method is used to calculate the offset of the irregular three-dimensional multi-scale structure single-layer grid model , connect the irregular three-dimensional multi-scale structure single-layer grid model with the original surface grid nodes to obtain a multi-scale structure; reversely offset the original surface, where Represents the thickness of the outer thin-walled skin; connect the reverse offset surface and the original surface mesh nodes to obtain the curved thin-walled structure; merge the multi-scale structure and the curved thin-walled structure to obtain an irregular three-dimensional curved thin-walled multi-scale structure model.

[0064] Beneficial effects of the present invention:

[0065] (1) A method for implicitly modeling the mesostructure of curved, thin-walled, multi-scale structures is provided. Compared with the traditional B-rep method, the method of the present invention can define the mesostructure topological information and quickly calculate the mesostructure signed distance function, which can be used to model irregular two-dimensional gradient lattice structures. The method of the present invention avoids the complex geometric feature Boolean operations and the individual adjustment of feature size parameters in the traditional B-rep method, simplifying the modeling of complex mesostructures.

[0066] (2) A two-dimensional irregular multi-scale structure modeling method based on the Fourier transform method is provided. Compared with the existing multi-scale structure modeling method with only variable relative density parameters, the multi-scale structure established by the method of the present invention has variable relative density, relative angle and micro-structure size parameters at the same time, realizing a smooth transition between micro-structures with different relative density, relative angle and micro-structure size parameters, thereby ensuring the connectivity of the overall structure.

[0067] (3) A method for generating geometric models of curved thin-walled multi-scale structures is provided. Compared with the existing multi-scale structure modeling methods that use regular two-dimensional and three-dimensional structures as design domains, the above method can establish irregular multi-scale structures with complex curved surface structures as design domains, and can establish irregular multi-scale structures with curved thin walls. The generated models can be used for additive manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is an overall flow chart of the modeling and design method of curved thin-walled multi-scale structures;

[0069] Figure 2 It is the calculation method of the mesoscopic structure signed distance function;

[0070] Figure 3 It is the two-dimensional parameter domain of the conformal mapping calculation surface;

[0071] Figure 4 It is a node coordinate interpolation method for multi-scale structured grid models;

[0072] Figure 5 It is a normal vector weighted offset method for multi-scale structured grid models;

[0073] Figure 61 is a modeling input of a specific embodiment example, (a) is a hyperbolic paraboloid, (b) is a Kagome honeycomb, (c) is a multi-scale structure relative density design parameter, (d) is a multi-scale structure relative angle design parameter, and (e) is a multi-scale structure micro-structure size design parameter;

[0074] Figure 7 is the mesoscopic structure of the multi-scale structure, (a) is the mesoscopic structure distance function, and (b) is the relative density control function;

[0075] Figure 8 is the two-dimensional parameter domain of the hyperbolic parabola, (a) is the mesh model of the hyperbolic parabola, and (b) is the two-dimensional parameter domain of the hyperbolic parabola;

[0076] Figure 9 It is the modeling of irregular three-dimensional surface multi-scale structure, (a) is the irregular two-dimensional multi-scale structure grid model, (b) is the irregular surface multi-scale structure single-layer grid model, (c) is the irregular surface multi-scale structure model;

[0077] Figure 10 It is an irregular three-dimensional curved thin-walled multi-scale structure model. DETAILED DESCRIPTION

[0078] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples, but the embodiments of the present invention are not limited thereto.

[0079] Specifically, a modeling and design method for curved thin-walled multi-scale structures is provided. First, characteristic edges are used to represent the topological information of the mesostructure, and the signed distance function of the mesostructure is calculated based on the characteristic edges. Compared with the traditional modeling method based on B-rep, this method can quickly obtain a mesostructure voxel model by defining characteristic edges in combination with a projection function, thereby avoiding repeated Boolean operations on complex geometric features. For mesostructures with variable relative density, the traditional B-rep modeling method needs to adjust the size of the structural features one by one. The method of the present invention simplifies the modeling of mesostructures with variable relative density by defining a two-dimensional projection function. The mesostructure signed distance function obtained by the method of the present invention provides the geometric information of the mesostructure for the subsequent modeling of irregular multi-scale structures with multiple variable design parameters.

[0080] Based on the periodic characteristics of regular multiscale structures, the structural geometric information is decomposed into a weighted sum of complex exponential wave functions. A rotation matrix and scaling coefficients are then used to spatially transform the complex exponential wave in the frequency domain. Finally, based on a specified projection function, a voxel model of an irregular two-dimensional multiscale structure is calculated that meets multiple design parameter requirements. The irregular multiscale structure established by the present method meets the designer's specified parameters for relative density, relative angle, and microscopic structural size gradient, ensuring structural connectivity.

[0081] The isosurface method and triangulation are used to extract a single-layer mesh model of the multiscale structure. Then, based on the two-dimensional parameter domain calculated using the conformal mapping method, an interpolation method is used to calculate the multiscale structure model in three-dimensional space. Finally, a normal vector weighted migration algorithm is used to calculate the geometric model of the curved, thin-walled, multiscale structure. This method is suitable for curved, thin-walled, multiscale structures with complex microstructures and multiple variable design parameters. The generated model can be used for additive manufacturing.

[0082] Figure 1 The modeling and design process of curved thin-walled multi-scale structures mainly consists of four parts, including:

[0083] Based on the topological information of the mesostructure, the mesostructure is implicitly modeled to obtain the signed distance function of the mesostructure; the two-dimensional parameter domain of the surface design domain is calculated using the conformal mapping method;

[0084] Based on Fourier transform, irregular two-dimensional multi-scale structure modeling is carried out, and the relative angle and microscopic structure size parameters of irregular two-dimensional multi-scale structures are established to obtain the signed distance function of irregular two-dimensional multi-scale structure. The relative density function of irregular two-dimensional multi-scale structure is used as the projection function, and the irregular two-dimensional multi-scale structure voxel model is obtained based on the signed distance function of irregular two-dimensional multi-scale structure. Based on the two-dimensional parameter domain and the voxel model of irregular two-dimensional multi-scale structure, the single-layer grid model of irregular three-dimensional multi-scale structure and the three-dimensional multi-scale structure model are obtained, and then the irregular three-dimensional curved thin-wall multi-scale structure geometric model with specified curved thin wall and multi-scale structure thickness is established.

[0085] (1) Implicit modeling of the mesostructure of multi-scale structures;

[0086] The present invention uses a signed distance function to implicitly represent the mesostructure of multi-scale structures, giving full play to the efficiency of implicit modeling in modeling complex geometric features, and providing mesostructure geometric information for subsequent multi-scale structure modeling with multiple variable design parameters. The modeling process of the mesostructure signed distance function is as follows:

[0087] 1) Establish characteristic edges representing the topological configuration information of the microstructure:

[0088] Establishing a local coordinate system , in the local coordinate system In the example, the two endpoints of the feature edge are and , the endpoint coordinates are and , the design domain range is specified as A point on a plane Relative Distance of feature edges The calculation method is as follows Figure 2 As shown, the calculation formula is:

[0089]

[0090] in, is the number of the feature edge, and like Figure 2 As shown, it indicates that the two endpoints of the feature edge are The angle between the connecting line and the feature edge, point The coordinates satisfy .

[0091] 2) Calculate the mesostructure signed distance function

[0092] Signed distance function of microstructure It can be calculated by formula (2):

[0093]

[0094] in, Used to indicate the Feature edges, is the number of characteristic edges.

[0095] (2) Calculation of two-dimensional parameter domain of surfaces based on conformal mapping;

[0096] The present invention uses the conformal mapping method to calculate the two-dimensional parameter domain of the surface to achieve the above-mentioned two-dimensional multi-scale structural model filling. Conformal mapping is an important theoretical tool for exploring the mapping and transformation between surfaces, which can map the surface in space to a simple parameter domain. The angle of the surface geometric features does not change before and after mapping, and has the characteristic of angle preservation. The conformal mapping theory is based on the differential geometry on the Riemann manifold. Given a surface design domain grid model 2D parametric domain mesh model for surface design domain Reversible mapping between , if the mapping satisfy:

[0097]

[0098] say is a conformal mapping where represents the pullback measure, yes The metric tensor on , yes The metric tensor on , is a positive scalar function, Represents the scaling factor between metrics. The calculation method of the two-dimensional parameter domain refers to the method in the paper "Sawhney R, Crane K. Boundary First Flattening[J].ACM Transactions onGraphics (TOG), 2017, 37(1):1-14."

[0099] like Figure 3 As shown, given the surface , the two-dimensional parameter domain mesh model of the surface design domain can be calculated through conformal mapping , the calculated two-dimensional parameter domain can be used to establish a two-dimensional multi-scale structure.

[0100] (3) Irregular two-dimensional multi-scale structure modeling based on Fourier transform method;

[0101] In the two-dimensional parameter domain, regular multi-scale structures can be regarded as formed by the periodic arrangement of mesostructures, while the signed distance function of the periodic structure in the time domain can be decomposed into a Fourier series in the frequency domain through the two-dimensional discrete Fourier transform. According to the scaling and rotation properties of the Fourier transform, the relative angle of the multi-scale structure and the size parameters of the mesostructure are introduced into the complex exponential function of the Fourier series, and the complex exponential function after the spatial transformation is calculated using the rotation matrix and the scaling coefficient. The signed distance function of the irregular multi-scale structure in the time domain is calculated by the inverse Fourier transform, and the irregular multi-scale structure voxel model is obtained by the projection function calculation. This method can obtain an irregular two-dimensional multi-scale structure voxel model with gradual changes in relative density, relative angle and mesostructure size, while maintaining the connectivity of the structure.

[0102] Modeling input is local coordinate system Signed distance function of microstructure And multi-scale structure relative density, relative angle and micro-structure size design parameters. Establish a global coordinate system on the two-dimensional parameter domain , the design parameters are expressed as two-dimensional functions, including the relative density of multi-scale structures , relative angle and microstructure size The specific steps of the modeling process for irregular two-dimensional multi-scale structures include:

[0103] 1) Calculate the signed distance function Fourier series of

[0104] According to the signed distance function of the microstructure , calculated using two-dimensional discrete Fourier transform The Fourier series of is calculated as:

[0105]

[0106] in, is a two-dimensional function representing the spectrum, and Represents the local coordinate system The coordinates on . and Is a constant, representing the local coordinate system The size of mesostructures.

[0107] According to formula (6), the spatial variation parameter in the frequency domain is defined as :

[0108]

[0109] 2) Use rotation matrix and scaling coefficient to perform spatial transformation on complex exponential function

[0110] According to design parameters and , calculate the transformed spatial variation parameters through the rotation matrix and scaling coefficient :

[0111]

[0112] in, and It is a two-dimensional function representing the design parameters of relative angles and microstructure dimensions.

[0113] 3) Constructing a least squares problem to solve the irregular two-dimensional multi-scale structure signed distance function

[0114] According to the transformed space transformation parameters , the signed distance function of the irregular two-dimensional multi-scale structure is calculated :

[0115]

[0116] in, and is a two-dimensional parameter domain coordinate system The coordinates on .

[0117] Define a two-dimensional function , and write formula (8) as:

[0118]

[0119] Construct a least squares optimization problem and solve :

[0120]

[0121] in, represents a two-dimensional parameter domain.

[0122] From the perspective of numerical calculation, combined with the finite difference method, the least squares optimization problem expressed in formula (10) is solved to obtain , and substitute it into formula (9) to calculate the signed distance function of the irregular two-dimensional multi-scale structure .

[0123] 4) Using projection functions to calculate voxel models of irregular two-dimensional multi-scale structures

[0124] Finally, the projection function is used to calculate the voxel model of the irregular two-dimensional multi-scale structure:

[0125]

[0126] in, Voxel models representing irregular two-dimensional multiscale structures.

[0127] Using the above method, an irregular two-dimensional multi-scale structural voxel model that satisfies the relative density, relative angle and microscopic structure size in the two-dimensional parameter domain can be obtained.

[0128] (4) Modeling of irregular three-dimensional thin-walled multi-scale structures

[0129] Based on the calculated voxel model of the irregular two-dimensional multi-scale structure, the contour extraction method is used to extract the structure contour, and the triangulation algorithm is used to obtain the grid model of the irregular two-dimensional multi-scale structure.

[0130] First, the three-dimensional coordinate system is calculated based on the two-dimensional multi-scale structural model and the two-dimensional parameter domain calculated by the conformal mapping method. Mesh model of medium-scale structure. At a point in the plane where the spatial triangle is located , can be expressed as a linear combination of the three vertices of a triangle, such as Figure 4 As shown, by solving the linear equations shown in formula (12), the interpolation coefficients are obtained , , :

[0131]

[0132] in, 2D parametric domain mesh model for surface design domain The node coordinates of Irregular two-dimensional multi-scale structured grid model The node coordinates of .

[0133] The interpolation coefficients , , Substitute into the surface design domain mesh model In the coordinates of , the irregular three-dimensional multi-scale structure single-layer grid model is calculated Node coordinates on :

[0134]

[0135] The above method is used to calculate the node coordinates of the three-dimensional multi-scale structure, and then the grid model of the three-dimensional curved thin-walled multi-scale structure can be obtained.

[0136] Secondly, a geometric model of curved, thin-walled, multi-scale structures for additive manufacturing is established. This paper proposes a method that combines weighted normal vector migration in the design domain with an interpolation method. This method can effectively avoid the problems of mesh intersection and boundary distortion when migrating complex multi-scale structures. is the original surface, is the offset surface, Represents the thickness of the inner multi-scale structure. Figure 5 As shown, the vertex offset normal vector is calculated by weighting the normal vector angles of adjacent faces. The vertex offset normal vector calculation formula is:

[0137]

[0138] in, is a node The vertex normal vector, is the number of adjacent faces of the node, For adjacent faces At the node The angle at which the

[0139] The original surface is forward offset, and the multi-scale structure single-layer grid model on the offset surface is calculated using the interpolation method. The multi-scale structure single-layer grid model is connected with the grid nodes of the original surface to obtain the multi-scale structure. The original surface is reverse offset, and the offset thickness is ,in Represents the thickness of the outer thin-walled skin. Connecting the reverse offset surface to the original surface mesh nodes yields a curved thin-walled structure. Combining the multiscale structure with the curved thin-walled structure yields a curved thin-walled multiscale structure model.

[0140] Specific implementation 1: The design domain of this example is as follows Figure 6 The hyperbolic paraboloid (saddle surface) shown in (a) has a microscopic structure as follows Figure 6 (b) The Kagome honeycomb, the relative density, relative angle and microstructure size design parameters of the multi-scale structure are as follows Figure 6 (c) shown. Among them, the design parameters meet , , The method of the present invention is used to generate a geometric model of an irregular three-dimensional curved surface thin-walled multi-scale structure, specifically in the following steps:

[0141] (1) According to the implicit modeling method of the Kagome configuration microstructure, the signed distance function of the Kagome configuration microstructure is calculated as follows Figure 7 As shown in (a), define the two-dimensional projection function as Figure 7 (b) shown.

[0142] (2) According to the surface two-dimensional parameter domain calculation method based on conformal mapping, specify Figure 8 (a) The hyperbolic paraboloid , calculate the two-dimensional parameter domain of the hyperbolic paraboloid like Figure 8 (b) shown.

[0143] (3) According to the irregular two-dimensional multi-scale structure modeling method based on Fourier transform, based on the mesoscopic structure signed distance function and the two-dimensional parameter domain obtained in steps 1 and 2, the Fourier series of the Kagome configuration mesoscopic structure signed distance function is calculated; the Fourier series is converted into the two-dimensional parameter domain coordinate system. In the array; according to Figure 6 The relative density, relative angle and microscopic structure size design parameters of the multi-scale structure shown are spatially transformed by the complex exponential function through the rotation matrix and scaling coefficient; a least squares problem is constructed to calculate the signed distance function of the irregular multi-scale structure after the spatial transformation; based on the calculated signed distance function, the projection function is used to calculate the voxel model of the irregular two-dimensional multi-scale structure.

[0144] (4) According to the irregular three-dimensional curved surface thin-walled multi-scale structure modeling method, on the basis of the irregular two-dimensional multi-scale structure voxel model obtained in step 3, the irregular two-dimensional multi-scale structure grid model is obtained by isoline extraction and triangulation method as shown in FIG. Figure 9 (a) shows that the three-dimensional coordinate system is obtained by interpolation method. The grid model is as follows Figure 9 (b) shows the original surface and the offset surface calculated by the normal vector weighted offset algorithm. Figure 9 (c) As shown. Connect the nodes of the original surface and the offset surface using the above method to obtain the geometric model of the irregular surface thin-walled multi-scale structure as shown in Figure 10 shown.

[0145] The above-mentioned curved thin-walled multi-scale structure modeling method is implemented using the MATLAB language, and input and output interfaces are written. The input is a common discrete mesh model file and a text file used to specify the microstructure topology configuration, and the output is a discrete mesh geometry model file that can be used for additive manufacturing.

Claims

1. A modeling and design method for curved thin-walled multi-scale structures, characterized in that: Based on the topological information of the mesostructure, the mesostructure is implicitly modeled to obtain the signed distance function of the mesostructure; the two-dimensional parameter domain of the surface design domain is calculated using the conformal mapping method; Based on Fourier transform, irregular two-dimensional multi-scale structure modeling is carried out, and the relative angle and microscopic structure size parameters of irregular two-dimensional multi-scale structures are established to obtain the signed distance function of irregular two-dimensional multi-scale structure. The relative density function of irregular two-dimensional multi-scale structure is used as the projection function, and the irregular two-dimensional multi-scale structure voxel model is obtained based on the signed distance function of irregular two-dimensional multi-scale structure. Based on the two-dimensional parameter domain and the voxel model of irregular two-dimensional multi-scale structure, the single-layer grid model of irregular three-dimensional multi-scale structure and the three-dimensional multi-scale structure model are obtained, and then the irregular three-dimensional curved thin-wall multi-scale structure geometric model with specified curved thin wall and multi-scale structure thickness is established.

2. The method for modeling and designing a curved thin-walled multi-scale structure according to claim 1, wherein: The implicit modeling of the mesostructure is specifically as follows: characteristic edges are used to represent the topological information of the mesostructure; and the signed distance function of the mesostructure is calculated according to the topological information of the mesostructure.

3. The modeling and design method of curved thin-walled multi-scale structures according to claim 2, characterized in that: The specific steps of the implicit modeling of the mesostructure are: 1) Establish characteristic edges representing microscopic structural topology information: Establishing a local coordinate system , in the local coordinate system In the example, the two endpoints of the feature edge are and The endpoint coordinates are and , the design domain range is specified as ; A point on the local coordinate plane Relative Distance of feature edges The calculation formula is: (1), where is the number of the feature edge, and Represents the two endpoints of the feature edge and The angle between the connecting line and the feature edge, point The coordinates satisfy ; 2) Calculate the signed distance function of the microstructure ; Signed distance function of microstructure Calculated by formula (2): (2), where Used to indicate the Feature edges, is the number of characteristic edges.

4. The method for modeling and designing a curved, thin-walled, multi-scale structure according to claim 1, wherein: The irregular two-dimensional multi-scale structure modeling based on Fourier transform is specifically as follows: according to the periodic characteristics of regular two-dimensional multi-scale structures, the geometric information of the mesoscopic structure is decomposed into a complex exponential function by using the Fourier transform method, and the spatial transformation parameters are extracted from the complex exponential function; the relative angle of the multi-scale structure and the mesoscopic structure size parameters are represented by the rotation matrix and the scaling coefficient, and the transformed spatial transformation parameters are calculated according to the rotation matrix and the scaling coefficient; based on the transformed spatial transformation parameters, the signed distance function of the irregular two-dimensional multi-scale structure is calculated by the least squares method; the relative density parameter is used as the projection function of the signed distance function to calculate the irregular two-dimensional multi-scale structure voxel model that meets the requirements of multiple design parameters.

5. The method for modeling and designing a curved thin-walled multi-scale structure according to claim 4, wherein: The irregular two-dimensional multi-scale structure modeling based on Fourier transform is specifically as follows: Establishing a global coordinate system on a two-dimensional parameter domain , the design parameters are expressed by two-dimensional functions, including the relative density two-dimensional function , relative angle two-dimensional function and a two-dimensional function of the microstructure size ; The specific steps include: 1) Calculate the signed distance function The Fourier series of According to the signed distance function of the microstructure , calculated using two-dimensional discrete Fourier transform The Fourier series of is calculated as: (3), where is a two-dimensional function representing the spectrum, and Represents the local coordinate system Coordinates on ; and Is a constant, representing the local coordinate system The size of the microstructure at the corresponding coordinate in ; According to formula (4), the spatial transformation parameters in the frequency domain are defined as : （4） 2) Use rotation matrix and scaling coefficient to transform spatial parameters Perform spatial transformation; According to design parameters and , calculate the transformed spatial transformation parameters through the rotation matrix and scaling coefficient : (5) 3) Constructing a least squares problem to solve the irregular two-dimensional multi-scale structure signed distance function ; According to the transformed space transformation parameters , the signed distance function of the irregular two-dimensional multi-scale structure is calculated : (6) , where and is a two-dimensional parameter domain coordinate system The coordinates on ; Define a two-dimensional function , and write formula (6) as: (7) , construct the least squares optimization problem and solve : (8) , among which, represents a two-dimensional parameter domain; From the perspective of numerical calculation, combined with the finite difference method, the least squares optimization problem expressed in formula (8) is solved to obtain , and substitute it into formula (7) to calculate the signed distance function of the irregular two-dimensional multi-scale structure ; 4) Using relative density parameters as projection functions to calculate irregular two-dimensional multi-scale structure voxel models; (9) , where Voxel models representing irregular two-dimensional multiscale structures.

6. The method for modeling and designing a curved thin-walled multi-scale structure according to claim 1, wherein: The method for generating the irregular curved surface thin-walled multi-scale structure geometric model is as follows: first, an isosurface method and a triangulation method are used to extract an irregular two-dimensional multi-scale structure grid model from the irregular two-dimensional multi-scale structure voxel model. ; Based on the irregular two-dimensional multi-scale structure grid model and 2D parametric domain mesh models , the interpolation method is used to calculate the irregular three-dimensional multi-scale structure single-layer grid model ; For irregular three-dimensional multi-scale structure single-layer grid model The geometric model of irregular three-dimensional thin-walled multi-scale structure is calculated using the normal vector weighted offset method. The specific steps include: 1) Extracting grid models of irregular two-dimensional multi-scale structures ; Based on the irregular two-dimensional multi-scale structure voxel model, the contour extraction method is used to extract the structure contour, and the triangulation method is used to obtain the grid model of the irregular two-dimensional multi-scale structure. ; 2) Irregular 3D multi-scale structure single-layer grid model ; According to the irregular two-dimensional multi-scale structured grid model 2D parametric domain mesh model for surface design domain , calculate the three-dimensional coordinate system Mesh model of medium-scale structure; a point in the plane where the spatial triangle is located , expressed as a linear combination of the three vertices of the triangle, and the interpolation coefficients are obtained by solving the linear equations shown in formula (10) , , : (10) , where 2D parametric domain mesh model for surface design domain The node coordinates of Irregular two-dimensional multi-scale structured grid model Node coordinates of The interpolation coefficients , , Substitute into the surface design domain mesh model In the coordinates of , the irregular three-dimensional multi-scale structure single-layer grid model is calculated Node coordinates on : (11) 3) Establishing geometric models of irregular three-dimensional thin-walled multi-scale structures; Design domain mesh model based on surface , specify the thickness of irregular three-dimensional thin-walled multi-scale structures , using the normal vector weighted offset method to calculate the offset surface design domain mesh model ; The vertex offset normal vector is calculated by weighting the normal vector angle of the adjacent face, and the surface design domain mesh model The vertex weighted offset normal vector calculation formula is: (12) , where is a node The vertex normal vector, is the number of adjacent faces of the node, For adjacent faces At the node The angle at which The original surface is forward offset and the interpolation method is used to calculate the offset of the irregular three-dimensional multi-scale structure single-layer grid model , connect the irregular three-dimensional multi-scale structure single-layer grid model with the original surface grid nodes to obtain a multi-scale structure; reversely offset the original surface, where Represents the thickness of the outer thin-walled skin; connect the reverse offset surface and the original surface mesh nodes to obtain the curved thin-walled structure; merge the multi-scale structure and the curved thin-walled structure to obtain an irregular three-dimensional curved thin-walled multi-scale structure model.

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