Multi-scale optimization intelligent design method for special-shaped structure

Abstract

The invention relates to a multi-scale optimization intelligent design method for a special-shaped structure, and belongs to the field of spacecraft structure mechanism additive manufacturing. Comprising the following steps: constructing a special-shaped lattice structure by adopting a level set function, and performing interpolation and correction; setting relative density sample points and performing polynomial interpolation to establish a geometric agent model; obtaining a constitutive matrix through numerical value homogenization and establishing a constitutive agent model; based on a constitutive agent model and an isogeometric topological optimization method, performing iterative solution by taking minimization of the flexibility of the special-shaped sandwich structure as a target to obtain optimal density distribution; and the optimal density distribution is substituted into a geometric agent model to output an interpolation coefficient, and an implicit model of the special-shaped sandwich structure is generated through gradient lattice filling. According to the method, the implicit model of the special-shaped sandwich structure filled with the conformal continuous gradient special-shaped lattice structure is constructed, and the special-shaped sandwich structure is generated through additive manufacturing based on the implicit model, so that the problem that a multi-scale optimization design method for the gradient lattice filled special-shaped sandwich structure is lacked at present is solved.

Description

Technical Field

[0001] The present invention relates to the field of additive manufacturing of spacecraft structural mechanisms, and in particular to a multi-scale optimization intelligent design method for special-shaped structures. Background Art

[0002] As the demand for weight reduction of spacecraft models becomes more and more urgent, the application of lightweight structures based on additive manufacturing in spacecraft is gradually increasing. The special-shaped sandwich structure is a typical high-stiffness, high-strength lightweight structure, which is widely used in the field of spacecraft. The performance of the special-shaped sandwich structure mainly depends on the type of sandwich, including random sandwich (such as foam) and periodic sandwich (such as lattice). Although random sandwiches are easy to manufacture, their mechanical properties are unpredictable, while periodic sandwiches are composed of repeatedly arranged porous units, so they have predictable mechanical properties. By adjusting the geometry and distribution of the lattice, better performance control can be achieved.

[0003] With the development of additive manufacturing technology, the design space of special-shaped sandwich structures has been greatly expanded. However, existing sandwich structures are usually designed based on regular shapes and are difficult to be directly applied to special-shaped sandwich structures. In addition, when designing periodic sandwich structures, they are usually based on classic orthogonal enveloping lattices. There are discontinuous connections between the lattices, and there is a geometric mismatch between the lattice and the special-shaped sandwich structure, which not only leads to a decrease in local stress concentration and strength of the structure, but also affects the overall performance of the structure.

[0004] It can be seen that providing a multi-scale optimization intelligent design method for special-shaped structures to achieve the optimal design and preparation of gradient lattice-filled special-shaped sandwich structures is an urgent problem to be solved. Summary of the invention

[0005] In view of the above analysis, the present invention aims to provide a multi-scale optimization intelligent design method for special-shaped structures to solve the problem of the current lack of optimization design and preparation method of gradient lattice filled special-shaped sandwich structures.

[0006] The present invention provides a multi-scale optimization intelligent design method for special-shaped structures, the method comprising the following steps: A shaped lattice structure is constructed by using a level set function, and a conformal gradient shaped lattice structure is obtained by interpolating and correcting the shaped lattice structure; relative density sample points are set, and the relationship between the interpolation coefficient and the relative density sample points is calculated based on the conformal gradient shaped lattice structure, and a geometric proxy model is established by performing polynomial interpolation on the relative density sample points; a constitutive matrix corresponding to the relative density sample points is obtained by numerical normalization based on the conformal gradient shaped lattice structure, and a constitutive proxy model is established by performing polynomial interpolation on the relative density sample points; Based on the constitutive surrogate model and isogeometric topology optimization method, the optimal density distribution is obtained by iterative solution with the goal of minimizing the flexibility of the special-shaped sandwich structure. The optimal density distribution is substituted into the geometric proxy model to output the interpolation coefficient, the interpolation coefficient is corrected by the NURBS basis function, and the implicit model of the special-shaped sandwich structure is generated by gradient lattice filling.

[0007] Furthermore, a geometric space of the irregular lattice structure is constructed, and the constitutive matrix corresponding to the relative density sample points after interpolation is obtained by performing polynomial interpolation on the relative density sample points. The constitutive matrix space of the irregular lattice structure is constructed, and the mapping relationship from the geometric space to the constitutive matrix space is determined to establish a constitutive proxy model.

[0008] Furthermore, the constitutive proxy model is input into the CAD software, and the isogeometric model is constructed based on the NURBS basis function. The isogeometric model is refined through k-refinement, and the boundary conditions and constraints are defined. The density distribution function is established, and the objective function is established to minimize the flexibility of the special-shaped sandwich structure. Sensitivity analysis is performed based on the density distribution function, and the objective function is iteratively solved through the MMA algorithm to obtain the optimal density distribution.

[0009] Furthermore, the relationship between the interpolation coefficient and the aspect ratio and relative density sample points is calculated by formulas (8)-(10): , (8) , (9) , (10) in, is the Heaviside function, is the relative density of the gradient shaped lattice structure, is the aspect ratio of the conformal gradient shaped lattice structure, is the interpolation coefficient of the conformal gradient shaped lattice structure, are the polynomial interpolation coefficients, is the interpolation order, is the maximum interpolation order, represents the level set function, represents the design domain; The expression of the geometric proxy model is as follows: , (11) in, Represents a geometric proxy model.

[0010] Furthermore, the implicit modeling expression of a single shaped lattice structure is: , (3) Among them, Void represents the void in the special-shaped lattice structure, Boundary represents the boundary of the special-shaped lattice structure, and Solid represents the area of ​​the special-shaped lattice filled with material.

[0011] Furthermore, the optimal density distribution is substituted into the geometric proxy model established by formulas (10) and (11) to output the interpolation coefficients, and the interpolation coefficients are corrected by the NURBS basis function to obtain the corrected interpolation coefficients. Based on the corrected interpolation coefficients and the conformal gradient shaped lattice structure, a conformal continuous gradient shaped lattice structure is constructed by the level set function, and the implicit model of the shaped sandwich structure filled by the conformal continuous gradient shaped lattice structure is output by formula (3).

[0012] Furthermore, the corrected interpolation coefficient is obtained by the following formula: , (20) in, is the corrected interpolation coefficient.

[0013] Furthermore, a gradient shaped lattice structure with continuous shape is constructed by the following formula: , , (twenty one) in, is the global level set function of the shape-continuous gradient shaped lattice structure, C is the Cth shaped lattice structure, N is the number of shaped lattice structures, and X is the set of all shaped lattice structures in the physical space.

[0014] Furthermore, the relationship between the interpolation coefficient and the aspect ratio as well as the relative density after interpolation is calculated by performing polynomial interpolation on the relative density sample points, thereby establishing a geometric proxy model.

[0015] Furthermore, based on the generated implicit model, a special-shaped sandwich structure is produced by additive manufacturing.

[0016] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. The present invention solves the problem of the current lack of multi-scale optimization design methods for shaped sandwich structures filled with gradient lattices by constructing an implicit model of a shaped sandwich structure filled with a continuous gradient shaped lattice structure, and generating the shaped sandwich structure by additive manufacturing based on the implicit model.

[0017] 2. The present invention expands the density distribution of a small number of control points to the density distribution of a large number of parameter points through interpolation coefficients, corrects the interpolation coefficients through NURBS basis functions, and updates the LSF function based on the corrected interpolation coefficients, thereby achieving a smooth transition between local LSF functions, thereby achieving continuous connection between lattice structures, effectively solving the connectivity problem between gradient lattice structures under orthogonal envelopes, and significantly improving the quality of special-shaped sandwich structure design and manufacturability in engineering.

[0018] 3. The present invention can quickly evaluate the mechanical properties of the special-shaped lattice structure under different key geometric parameters by constructing a constitutive proxy model, avoiding the calculation of the constitutive matrix of each lattice one by one, reducing the amount of calculation and improving the calculation efficiency. In addition, through polynomial interpolation, the mechanical properties of the special-shaped lattice structure with different relative density, aspect ratio and deflection angle can be predicted efficiently and accurately.

[0019] 4. The present invention implicitly constructs various shapes of shaped lattice structures through the level set function, which can not only obtain shaped lattice structures of various topological forms, but also obtain gradient shaped lattice structures with the same topological configuration but different characteristic sizes through interpolation. The present invention constructs a shape-dependent shaped lattice structure by modifying the level set function corresponding to the gradient shaped lattice structure through the NURBS basis function, and realizes the adaptive matching between the lattice structure and the shaped sandwich structure.

[0020] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components; Figure 1 A flowchart of a multi-scale optimization intelligent design method for special-shaped structures according to an embodiment of the present invention; Figure 2 A schematic diagram of using the LSF function to construct a special-shaped lattice structure according to an embodiment of the present invention; Figure 3 (a) is a schematic diagram of a special-shaped BCC lattice structure and its envelope domain according to an embodiment of the present invention; Figure 3 (b) is a schematic diagram of key geometric characteristic parameters of the special-shaped BCC lattice structure according to an embodiment of the present invention; Figure 4is the constitutive matrix corresponding to the special-shaped BCC lattice structure of the embodiment of the present invention when the relative density is 30%; Figure 5 (a) is a schematic diagram of the geometric space of the special-shaped BCC lattice structure according to an embodiment of the present invention; Figure 5 (b) is a schematic diagram of a constitutive proxy model according to an embodiment of the present invention; Figure 5 (c) is an embodiment of the present invention , The mapping relationship from the geometric space of the heterogeneous BCC lattice structure to the constitutive matrix space; Figure 5 (d) is an embodiment of the present invention , The mapping relationship from the geometric space of the heterogeneous BCC lattice structure to the constitutive matrix space; Figure 6 (a) is the global LSF function of the discontinuous shaped BCC lattice structure of the embodiment of the present invention; Figure 6 (b) is a schematic diagram of the control point density distribution and the parameter point density distribution before interpolation of the arc sandwich structure according to an embodiment of the present invention; Figure 6 (c) is the global LSF function of the connected heterogeneous BCC lattice structure according to an embodiment of the present invention; Figure 6 (d) is a schematic diagram of a discontinuous special-shaped BCC lattice structure according to an embodiment of the present invention; Figure 6 (e) is a schematic diagram of a connected special-shaped BCC lattice structure according to an embodiment of the present invention; Figure 6 (f) is a schematic diagram of the control point density distribution and the parameter point density distribution after interpolation of the three-dimensional arc sandwich structure according to an embodiment of the present invention; Figure 6 (g) is a schematic diagram of a shape-continuous gradient BCC lattice structure filled in a circular arc sandwich structure according to an embodiment of the present invention; Figure 6 (h) is a schematic diagram of a substrate BCC lattice structure filled in a circular arc sandwich structure according to an embodiment of the present invention; Figure 7 (a) shows the design domain and boundary conditions of the three-point bending semicircular arc sandwich structure according to an embodiment of the present invention; Figure 7 (b) is a uniform heterogeneous lattice structure of an embodiment of the present invention; Figure 7 (c) is a partial enlarged view of the gradient shaped lattice structure along the YOZ plane of an embodiment of the present invention; Figure 7 (d) is a partial enlarged view of the gradient shaped lattice structure along the XOY plane of an embodiment of the present invention; Figure 7 (e) is an overall schematic diagram of a gradient shaped lattice structure according to an embodiment of the present invention; Figure 7 (f) is a schematic diagram of removing the first layer of the lattice structure of the gradient profiled lattice structure according to an embodiment of the present invention; Figure 7 (g) is a schematic diagram of the gradient special-shaped lattice structure of an embodiment of the present invention after removing 1 / 4 of the overall lattice structure; Figure 8 (a) is the output of the gradient lattice structure optimization model of the embodiment of the present invention; Figure 8 (b) shows the three-stage bending test and DIC characterization of the orthogonal uniform lattice structure of the embodiment of the present invention; Figure 8 (c) shows the three-stage bending test and DIC characterization of the uniform lattice structure of the embodiment of the present invention; Figure 8 (d) shows the three-stage bending test and DIC characterization of the lattice structure with uniform gradient in an embodiment of the present invention; Figure 8 (e) is the force-displacement curve of the semicircular arc orthogonal uniform, irregular uniform, and irregular gradient lattice structures according to the embodiment of the present invention; Figure 8 (f) shows the bending modulus and ultimate strength of the semicircular arc orthogonal uniform, irregular uniform, and irregular gradient lattice structures according to the embodiment of the present invention; Fig. 9 Schematic diagram of the design, preparation and test of the special-shaped gradient lattice structure of the rudder plate according to the embodiment of the present invention; Fig.10 (a) is a test structure of an orthogonal uniform lattice structure according to an embodiment of the present invention; Fig.10 (b) is a test structure of a profiled gradient lattice structure according to an embodiment of the present invention; Fig.10 (c) is a schematic diagram of the interior of an orthogonal uniform lattice rudder plate and a fracture diagram of the rudder shaft according to an embodiment of the present invention; Fig.10 (d) is a schematic diagram of the interior of the special-shaped gradient lattice rudder plate and an enlarged view of the rudder shaft according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0023] Example 1 A specific embodiment of the present invention discloses a multi-scale optimization intelligent design method for special-shaped structures. Figure 1 As shown, the method comprises the following steps: S1. Constructing a special-shaped lattice structure using a level set function, and obtaining a conformal gradient special-shaped lattice structure by interpolating and correcting the special-shaped lattice structure; setting relative density sample points, calculating the relationship between the interpolation coefficient and the relative density sample points based on the conformal gradient special-shaped lattice structure, and establishing a geometric proxy model by performing polynomial interpolation on the relative density sample points; obtaining a constitutive matrix corresponding to the relative density sample points by numerical normalization based on the conformal gradient special-shaped lattice structure, and establishing a constitutive proxy model by performing polynomial interpolation on the relative density sample points; S2. Based on the constitutive proxy model and isogeometric topology optimization method, the optimal density distribution is obtained by iterative solution with the goal of minimizing the flexibility of the special-shaped sandwich structure; S3, substituting the optimal density distribution into the geometric proxy model to output the interpolation coefficient, correcting the interpolation coefficient through the NURBS basis function, and generating an implicit model of the special-shaped sandwich structure by gradient lattice filling.

[0024] Specifically, in step S1, the expression for constructing a single heteromorphic lattice structure using a local level set function is: , (1) in, Represents a set of physical space coordinate points of a single shaped lattice structure, represents the sampling points of the local level set function, represents the local level set function corresponding to a single shaped lattice structure, represents a single shaped lattice structure boundary, Indicates that the level set function is defined using the signed distance function.

[0025] Specifically, the special-shaped lattice structure is interpolated by the following formula: , (2) in, is the interpolation coefficient.

[0026] Specifically, the implicit modeling expression of a single heterogeneous lattice structure is obtained from formulas (1) and (2): , (3) Among them, Void represents the void in the special-shaped lattice structure, Boundary represents the boundary of the special-shaped lattice structure, and Solid represents the area of ​​the special-shaped lattice filled with material.

[0027] It should be noted that the shaped sandwich structure is filled with a large number of lattice structures. The lattice structure is the basic building block of the shaped sandwich structure. The modeling method of the lattice structure has a significant impact on the performance of the shaped sandwich structure. Therefore, it is crucial to select an appropriate lattice structure modeling method. The present invention adopts a level set function (LSF) implicit modeling method based on a signed distance function (SDF). The boundary of the shaped lattice structure is implicitly represented by the zero isosurface of the high-dimensional LSF. Compared with the model generated by the traditional modeling software, the implicit model has higher accuracy and smaller data volume, and can conveniently realize batch modeling of a large number of lattice structures, thereby improving the modeling efficiency. The present invention can implicitly construct shaped lattice structures of various shapes through the level set function (LSF). Therefore, based on the above formulas (1)-(3), not only can shaped lattice structures of various topological forms be obtained, but also gradient shaped lattice structures with the same topological configuration but different characteristic sizes can be obtained by interpolation.

[0028] For example, several typical heteromorphic lattice structures are constructed, such as Figure 2 As shown, it includes two-dimensional X-shaped structure and X-Box structure and three-dimensional body-centered cubic (BCC) structure and face-centered cubic (FCC) structure. Among them, "Prototype LSF" represents the special-shaped lattice structure constructed by level set function, and "Update LSF" represents the corresponding special-shaped lattice structure obtained by interpolating the special-shaped lattice structure. Figure 2 It can be seen that the LSF function corresponding to the "Prototype LSF" updates the zero isosurface projection of the LSF function after interpolation, thereby generating an "Update LSF" with the same topological configuration but different feature sizes.

[0029] Furthermore, the constructed and interpolated special-shaped lattice structures are modified by NURBS basis functions to obtain a conformal gradient special-shaped lattice structure.

[0030] Specifically, the expression of the B-spline basis function is: , (4) in, Represents the i-th node of the NURBS basis function; Represents NURBS basis function; represents the node vector, which is a non-decreasing ordered parameter set; n represents the number of B-spline basis functions, that is, the number of control points; p is the polynomial order.

[0031] It should be noted that the B-spline curve is defined by the B-spline basis function, and the value interval of each B-spline basis function is [0,1], so it is non-zero in a specific interval and zero outside the interval, so that the B-spline basis function can flexibly control the curve. Each parameter in the node vector of the B-spline basis function represents a node, and all nodes divide the entire definition domain into multiple sub-intervals, each sub-interval corresponds to one or more non-zero intervals of the B-spline basis function, thereby determining the local control characteristics of the curve.

[0032] Specifically, the expression of NURBS basis function is: , (5) It should be noted that NURBS basis functions Obtained by weighted averaging of B-spline basis functions within the unit decomposition framework. NURBS (Non-Uniform Rational B-Spline) basis functions have stronger generalization capabilities than B-spline basis functions, and can better control curve shapes and improve flexibility.

[0033] It should be noted that the special-shaped lattice structure constructed by the level set function is an orthogonal geometric envelope. When filling the special-shaped sandwich configuration, the redundant lattice structure can only be cut out by Boolean operation, resulting in a geometric mismatch between the lattice structure and the special-shaped sandwich structure. The present invention modifies formula (1) through the NURBS basis function to construct a special-shaped lattice structure that changes with the shape, thereby realizing adaptive matching between the lattice structure and the special-shaped sandwich structure.

[0034] Exemplarily, according to formula (1), a three-dimensional shaped lattice structure is constructed by using a local level set function, and the three-dimensional shaped lattice structure is modified by a NURBS basis function, and the expression of the three-dimensional shaped lattice structure with a conformal gradient is obtained as follows: , (6) , (7) in, represents the sampling points in the parameter space, Represents the physical coordinates corresponding to the sampling points of the local level set function, is the LSF function corresponding to the modified heterogeneous lattice structure, R represents the basis function of formula (5) extended from one dimension to three dimensions, and P is the coordinate of the control point.

[0035] Furthermore, relative density sample points are set, and key geometric characteristic parameters are extracted according to the geometric changes of the conformal gradient shaped lattice structure, wherein the key geometric characteristic parameters include the relative density, aspect ratio and deflection angle of the conformal gradient shaped lattice structure; and the Heaviside function is used to calculate the relationship between the interpolation coefficient and the aspect ratio and relative density sample points.

[0036] Specifically, the relative density sample point refers to the relative density value set according to experience and actual needs. The relationship between the interpolation coefficient, the aspect ratio and the relative density sample point is calculated by formulas (8)-(10).

[0037] , (8) , (9) , (10) in, is the Heaviside function, is the relative density of the gradient shaped lattice structure, is the aspect ratio of the conformal gradient shaped lattice structure, is the interpolation coefficient of the conformal gradient shaped lattice structure, are the polynomial interpolation coefficients, is the interpolation order, is the maximum interpolation order, represents the level set function, Represents the design domain.

[0038] Preferably, in this application, b is 2.

[0039] For example, a shaped BCC lattice structure is selected as the conformal gradient shaped lattice structure, and the shaped BCC lattice structure and its envelope domain are as follows: Figure 3 As shown in (a), the key geometric characteristic parameters are obtained based on the geometric changes of the special-shaped BCC lattice structure, such as Figure 3 (b) shown.

[0040] It should be noted that the BCC lattice structure can withstand multi-axial forces from different directions, has high specific stiffness and high specific strength, and is easy to realize through additive manufacturing processes. Figure 3 (b) It can be seen that the interpolation coefficient is related to the relative density and aspect ratio, but not to the deflection angle. It does not matter, so the calculation and and The relationship between.

[0041] Furthermore, the relationship between the interpolation coefficient and the aspect ratio and the relative density after interpolation is calculated by performing polynomial interpolation on the relative density sample points, thereby establishing a geometric proxy model. The expression of the geometric proxy model is as follows: , (11) in, Represents a geometric proxy model.

[0042] It should be noted that the geometric proxy model includes the relationship between the interpolation coefficient and the set and interpolated relative density sample points, so the relationship between the interpolation coefficient and any relative density can be obtained through the geometric proxy model.

[0043] Furthermore, based on the shape-conforming gradient shaped lattice structure, each component of the elastic tensor of the shaped lattice structure is calculated by numerical normalization, so as to obtain the constitutive matrix corresponding to the shaped lattice structure at the relative density sample point.

[0044] Specifically, each component of the elasticity tensor is calculated by the following formula: , (12) in, , is a user-defined uniform strain field, , is the true strain generated by the custom strain field, is the volume of the heterogeneous lattice structure, Represents the Young's modulus of the shaped lattice structure.

[0045] Specifically, the constitutive matrix is ​​the elastic coefficient matrix composed of each component of the elastic tensor.

[0046] For example, the shaped BCC lattice structure is an anisotropic structure with one elastic symmetry plane. Based on the shaped BCC lattice structure, the constitutive matrix corresponding to the relative density of 30% is solved by numerical homogenization, such as Figure 4 As shown. Figure 4 It can be seen that when the angle of the shaped BCC lattice structure is deflected, tension-shear coupling occurs, resulting in the non-zero element corresponding to the tension-shear coupling term in the constitutive matrix, and the absolute value of the element corresponding to the tension-shear coupling term increases with the increase of the deflection angle. In addition, as the aspect ratio of the shaped BCC lattice structure decreases, it becomes flatter, which significantly affects the element corresponding to the second direction in the constitutive matrix.

[0047] Furthermore, the constitutive matrix corresponding to the interpolated relative density sample points is obtained by performing polynomial interpolation on the relative density sample points, thereby establishing a constitutive proxy model.

[0048] Specifically, a geometric space of a heterogeneous lattice structure is constructed, and a constitutive matrix space of the heterogeneous lattice structure is constructed by performing polynomial interpolation on relative density sample points to obtain a constitutive matrix corresponding to the interpolated relative density sample points, and a mapping relationship from the geometric space to the constitutive matrix space is determined to establish a constitutive proxy model.

[0049] Specifically, the geometric space is a three-dimensional space composed of relative density, aspect ratio and deflection angle, and each element in the geometric space represents a special-shaped lattice structure with specific geometric characteristics. The expression of the geometric space is as follows: , , , , (13) in, A geometric space representing a shaped lattice structure.

[0050] Specifically, polynomial interpolation is performed using the following formula: , (14) Where s is the row in the constitutive matrix; t is the column in the constitutive matrix; m is the order of the polynomial interpolation; Indicates when , When fixed, the interpolation coefficient of the sth row, tth column, and mrth item of the constitutive matrix.

[0051] Specifically, each element in the constitutive matrix space represents the constitutive matrix of a shaped lattice structure with specific geometric characteristics. The expression of the constitutive matrix space is as follows: , (15) in, Represent the constitutive matrix space of shaped lattice structures.

[0052] Specifically, the expression of the constitutive proxy model is as follows: , (16) in, Represents the constitutive surrogate model.

[0053] For example, the geometric space of the shaped BCC lattice structure is as follows Figure 5 As shown in (a), the constitutive proxy model of the heterogeneous BCC lattice structure under different relative density, deflection angle and aspect ratio is predicted by polynomial interpolation. Figure 5 (b). Figure 5 (b) It can be seen that the sensitivity of the elements in the constitutive matrix to different geometric parameters varies. Under the premise of large symmetry of the constitutive matrix, the main diagonal elements are more sensitive to the aspect ratio and relative density than the deflection angle, while the elements corresponding to the tension-shear coupling coefficient are less sensitive to the aspect ratio and relative density than the deflection angle. Figure 5 (c) and 5 (d) show that when the aspect ratio and the deflection angle are fixed, the mapping relationship from the geometric space of the heterogeneous BCC lattice structure to the constitutive matrix space satisfies the continuous differentiable relationship with the relative density.

[0054] It should be noted that if the constitutive matrix of each lattice is repeatedly calculated each time during the multi-scale optimization process of the special-shaped lattice structure, the amount of calculation is large and time-consuming. Therefore, the present invention can quickly evaluate the mechanical properties of the special-shaped lattice structure under different key geometric parameters by constructing a constitutive proxy model, avoiding the calculation of the constitutive matrix of each lattice one by one, reducing the amount of calculation and improving the calculation efficiency. In addition, through polynomial interpolation, the mechanical properties of the special-shaped lattice structure with different relative density, aspect ratio and deflection angle can be predicted efficiently and accurately.

[0055] Specifically, in step S2, the constitutive proxy model is input into the CAD software, an isogeometric model is constructed based on the NURBS basis function, the isogeometric model is refined through k-refinement, boundary conditions and constraints are defined, a density distribution function is established, an objective function is established with the goal of minimizing the flexibility of the special-shaped sandwich structure, a sensitivity analysis is performed based on the density distribution function, and the objective function is iteratively solved through the MMA algorithm to obtain the optimal density distribution.

[0056] It should be noted that k-refinement is a local refinement method in isogeometric analysis (IGA). By increasing the order of the NURBS basis function, the specific area of ​​the isogeometric model is refined without changing the overall topological structure of the lattice, so as to improve the accuracy and efficiency of the isogeometric analysis.

[0057] Specifically, the density distribution function is as follows: , (17) in, represents the density distribution function, , , are the coordinates of the control points in the parameter space of the isogeometric model, , , , represents the NURBS basis function, Represents the density distribution of control points, where l, m, and n are the maximum number of nodes in the three parameter directions.

[0058] Specifically, the objective function established with the goal of minimizing the flexibility of the special-shaped sandwich structure is as follows: , , , , , (18) in, Indicates the flexibility of the special-shaped sandwich structure, It's strain. is the constitutive matrix, is the displacement column vector, is the global force vector of the profiled sandwich structure, is the volume fraction of the special-shaped sandwich structure, represents the constitutive stiffness matrix of the special-shaped sandwich structure, is the volume fraction of the optimal setting.

[0059] Specifically, sensitivity analysis is performed using the following formula: , , (19) in, , , are the coordinates of the Gaussian points in the parameter space of the isogeometric model, represents the stiffness matrix of the shaped lattice structure in finite element analysis, Represents the displacement vector of the heteromorphic lattice structure.

[0060] It should be noted that the control points refer to the control points of the NURBS basis function. The present invention calculates the constitutive matrix by the Gaussian integral method, so the corresponding Gaussian points are obtained through the control points.

[0061] Specifically, in step S3, the optimal density distribution is substituted into the geometric proxy model established by formula (10) to output the interpolation coefficient, the interpolation coefficient is corrected by the NURBS basis function to obtain the corrected interpolation coefficient, based on the corrected interpolation coefficient and the conformal gradient shaped lattice structure, a conformal continuous gradient shaped lattice structure is constructed by using the level set function, and the implicit model of the shaped sandwich structure filled by the conformal continuous gradient shaped lattice structure is output by formula (3).

[0062] Furthermore, the corrected interpolation coefficient is obtained by the following formula: , (20) in, is the corrected interpolation coefficient.

[0063] Furthermore, a gradient shaped lattice structure with continuous shape is constructed by the following formula: , , (twenty one) in, is the global level set function of the shape-continuous gradient shaped lattice structure, C is the Cth shaped lattice structure, N is the number of shaped lattice structures, and X is the set of all shaped lattice structures in the physical space.

[0064] It should be noted that the interpolation coefficients are scalar field interpolation coefficients. The level set function for constructing a single shaped lattice structure is a local level set function. In order to generate a shaped sandwich structure, N shaped lattice structures need to be connected, so N local level set functions need to be combined to construct a global level set function.

[0065] For example, four 2D X-shaped gradient lattice structures with increasing relative density are filled in the arc-shaped sandwich structure, and the global LSF function is as follows: Figure 6 As shown in (a), the zero-value surface projection of the global LSF function is used to generate a shape-dependent gradient lattice structure, such as Figure 6 (d). However, Figure 6 As shown in (b), from the distribution of control point density and parameter point density (the size of the point indicates the size of the equivalent density), there is a discontinuous connection phenomenon between the heterogeneous gradient lattice structures, which leads to severe stress concentration and easily causes structural failure. The interpolation coefficient is corrected by the NURBS basis function, and the LSF function is updated based on the corrected interpolation coefficient. Figure 6 As shown in (c), a smooth transition between local LSF functions is achieved, and a continuous connection between heterogeneous gradient lattice structures is achieved through low-dimensional projection. Figure 6 (e) As shown. Figure 6 (f) and Figure 6 As shown in (g), this method can be easily extended to three-dimensional lattice structures, such as BCC and P-FCC lattice structures, to solve the connectivity problem between lattice structures.

[0066] It can be understood that the present invention expands the density distribution of a small number of control points to the density distribution of a large number of parameter points through interpolation coefficients, corrects the interpolation coefficients through NURBS basis functions, and updates the LSF function based on the corrected interpolation coefficients, thereby achieving a smooth transition between local LSF functions, thereby achieving continuous connection between lattice structures, effectively solving the connectivity problem between gradient lattice structures under orthogonal envelopes, and significantly improving the quality of special-shaped sandwich structure design and manufacturability in engineering.

[0067] Example 2 Another specific embodiment of the present invention generates a special-shaped sandwich structure by additive manufacturing based on the implicit model generated above.

[0068] Specifically, an STL format file is output based on the implicit model, and the STL format file is input into a 3D printer for additive manufacturing and printing to generate a special-shaped sandwich structure.

[0069] It should be noted that compared with the models generated by traditional modeling software, implicit models have higher accuracy and smaller data volume, and are more suitable for engineering manufacturing.

[0070] Example 3 Another specific embodiment of the present invention realizes the multi-scale optimization design and experimental verification of the three-point bent semicircular arc sandwich structure.

[0071] Specifically, the design domain and boundary conditions of the three-point bending semicircular arc sandwich structure are as follows: Figure 7 (a) shows the external load The distributed force is applied to the middle position of the upper surface of the semicircle, the middle positions of the bottom ends on both sides are fixed, and displacement constraints are applied in three directions to limit the degree of freedom. Young's modulus of the substrate , Poisson's ratio ,density . Design domain outer diameter , inner diameter ,width , discretize the design domain into units to optimize the filling of the special-shaped BCC lattice structure. During the optimization iteration process, when the maximum value of the control point density distribution change is less than 0.01 or the maximum number of iterations reaches 300, the iteration is terminated. The objective function is set to minimize the structural flexibility, and the relative volume fraction is limited to 0.3. Figure 7 (b) shows the semicircular arc uniform lattice structure generated at the same relative density. The results of multi-scale optimization design of gradient shaped lattice structure are shown in Figure 2. Figure 7 As shown in (e), it can be seen that the high-density special-shaped BCC lattice structure forms a continuous force transmission path from the middle of the semicircular arc top to the support end, while a large number of medium and low-density special-shaped BCC lattices are distributed on the secondary force transmission path, which can effectively resist shear deformation and stably support the upper and lower solid panels. Figure 7 (c) and Figure 7 As shown in (d), the irregular BCC lattice structures are continuously connected. After removing the first layer of the lattice structure of the optimized gradient irregular lattice structure, its internal structure is observed, as shown in Figure 7 As shown in (f), it can be found that the high-density lattice structure is clearly distributed on the force transmission path to resist structural deformation and enhance structural stiffness. Figure 7 (g) shows a schematic diagram of the semicircular gradient lattice structure after removing 1 / 4 of the overall lattice structure. It can be seen that there are four force transmission paths that form an angle of about 30° with the XOY plane, which improves the stability of the sandwich structure.

[0072] Specifically, Figure 8 (a) shows the connectivity between the lattice structures of the gradient lattice structure optimization model. In order to verify the performance of the gradient lattice structure provided by the present invention, a semicircular arc sandwich structure filled with orthogonal uniform, irregular uniform and irregular gradient lattice structures was prepared by 3D printing and subjected to a three-point bending test. All samples were printed by the same printer under the same conditions and subjected to a three-point bending test on a Strong universal testing machine. First, the load The preload force is then The load was then applied at a speed of 200 until all samples broke. When the indenter displacement was 5 mm, the three-point bending test and DIC results of the orthogonal uniform lattice structure, the profiled uniform lattice structure, and the profiled gradient lattice structure were as follows: Figure 8 (b)- Figure 8 As shown in (d), it can be seen that the orthogonal uniform lattice structure has strain concentration near the load application point. Since the low-density area is prone to buckling and softening under the load, the overall structure is destroyed; the strain distribution of the special-shaped uniform lattice structure is relatively more uniform, but there are still local high-strain areas near the load application point and the support end, and the risk of local failure is still relatively large; the strain distribution of the special-shaped gradient lattice structure is more uniform, and the high-density area is concentrated on the main force transmission path, which effectively enhances the stiffness of the load transfer path and reduces the risk of local buckling. Figure 8 As shown in (e), at the same volume fraction, the strength and stiffness of the semicircular gradient lattice structure (GLSS) are better than those of the semicircular uniform lattice structure (CLSS) and the orthogonal uniform lattice structure (ULSS). The slope of the load-displacement curve of GLSS is 89.8% higher than that of ULSS, and the ultimate strength is 18.7% higher. At the same time, ULSS exhibits obvious local buckling during loading, while GLSS maintains a high degree of stability. Figure 6 As shown in (f), the flexural modulus and ultimate load of GLSS are better than those of CLSS and ULSS.

[0073] The experimental results show that compared with the traditional orthogonal uniform lattice structure filling, the lattice structure intelligent filling method provided by the present invention reasonably optimizes the lattice structure density distribution, sets high-density lattices on the main force path to improve the bearing capacity, and uses low-density lattices as auxiliary support structures. It significantly improves the bearing capacity, bending stiffness and tensile strength of the semi-circular arc sandwich structure, thereby improving the stability of the overall structure and effectively reducing the risk of local strain concentration and buckling failure, and has broad engineering application potential.

[0074] Example 4 Another specific embodiment of the present invention realizes the optimized design and preparation of the tail windward rudder of the aircraft.

[0075] Specifically, the windward rudder surface is distributed in a '+' or 'x' shape, with a wedge-shaped cross-section that contracts forward to reduce aerodynamic drag. The rudder surface adopts a hexahedral lattice filling design and is optimized under wind pressure load conditions. Fig. 9 As shown in the figure, the optimization design results of the special-shaped gradient lattice structure for the rudder plate structure show that the high-density lattice structure is mainly concentrated in the area extending from the fixed end to the force-bearing end, forming the main load-bearing path, effectively alleviating local buckling deformation and improving the stiffness and strength of the overall structure. In addition, the high-density lattice structure is concentrated near the rudder shaft and the rudder surfaces on both sides, increasing the moment of inertia of the bending section and significantly improving the bending resistance of the rudder plate.

[0076] In order to verify the performance of the above-mentioned optimized design of the rudder plate structure, the present invention adopts metal additive manufacturing to prepare the rudder plate filled with orthogonal uniform lattice structure (ULSS-R) and special-shaped gradient lattice structure (CGLSS-R). An L-PBF machine with a maximum laser power of , the spot size is Fiber laser, metal powder Prepare.

[0077] like Fig.10 (a) and Fig.10(b) shows the two-point loading test results of the rudder plate structure filled with orthogonal uniform lattice structure and special-shaped gradient lattice structure respectively; the initial pressure of the hydraulic support rod is set to 2000N, the gain coefficient is 5, and the custom peak load is 10000N; in the rudder plate structure filled with uniform lattice, when the peak force of the loading point reaches 7620.5N and 6820.2N respectively, the rudder shaft breaks, and the corresponding loading point displacements are 14000 and 6820.2N respectively. and 7000 In the rudder plate structure filled with gradient lattices, when the peak forces at the loading points are 9700N and 9500N, the corresponding loading point displacements are 4800 and 9500N, respectively. and 12000 It can be seen that the peak force of the rudder plate structure filled with gradient lattice is about 45.6% higher than that of the rudder plate structure filled with uniform lattice, and the displacement is reduced by about 28.7%. Fig.10 (c) and Fig.10 As shown in (d), in the rudder plate structure filled with orthogonal uniform lattices, the lattice structure showed significant fracture in the arc transition area of ​​the rudder axis, while no fracture occurred in the rudder plate structure filled with gradient lattices.

[0078] The test results show that the gradient lattice structure has no cracks or microcracks in the transition area between the rudder shaft and the rudder surface, which significantly improves the bending stiffness and tensile strength of the rudder plate structure, effectively reduces the risk of local buckling and crack propagation, and thus improves the overall reliability and service life of the structure.

[0079] Compared with the prior art, the multi-scale optimization intelligent design method for special-shaped structures provided by the present invention has the following beneficial effects: 1. The present invention solves the problem of the current lack of multi-scale optimization design methods for shaped sandwich structures filled with gradient lattices by constructing an implicit model of a shaped sandwich structure filled with a continuous gradient shaped lattice structure, and generating the shaped sandwich structure through additive manufacturing based on the implicit model.

[0080] 2. The present invention expands the density distribution of a small number of control points to the density distribution of a large number of parameter points through interpolation coefficients, corrects the interpolation coefficients through NURBS basis functions, and updates the LSF function based on the corrected interpolation coefficients, thereby achieving a smooth transition between local LSF functions, thereby achieving continuous connection between lattice structures, effectively solving the connectivity problem between gradient lattice structures under orthogonal envelopes, and significantly improving the quality of special-shaped sandwich structure design and manufacturability in engineering.

[0081] 3. The present invention can quickly evaluate the mechanical properties of the special-shaped lattice structure under different key geometric parameters by constructing a constitutive proxy model, avoiding the calculation of the constitutive matrix of each lattice one by one, reducing the amount of calculation and improving the calculation efficiency. In addition, through polynomial interpolation, the mechanical properties of the special-shaped lattice structure with different relative density, aspect ratio and deflection angle can be predicted efficiently and accurately.

[0082] 4. The present invention implicitly constructs various shapes of shaped lattice structures through the level set function, which can not only obtain shaped lattice structures of various topological forms, but also obtain gradient shaped lattice structures with the same topological configuration but different characteristic sizes through interpolation. The present invention constructs a shape-dependent shaped lattice structure by modifying the level set function corresponding to the gradient shaped lattice structure through the NURBS basis function, and realizes the adaptive matching between the lattice structure and the shaped sandwich structure.

[0083] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0084] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A multi-scale optimization intelligent design method for special-shaped structures, characterized in that: The method comprises the following steps: A shaped lattice structure is constructed by using a level set function, and a conformal gradient shaped lattice structure is obtained by interpolating and correcting the shaped lattice structure; relative density sample points are set, and the relationship between the interpolation coefficient and the relative density sample points is calculated based on the conformal gradient shaped lattice structure, and a geometric proxy model is established by performing polynomial interpolation on the relative density sample points; a constitutive matrix corresponding to the relative density sample points is obtained by numerical normalization based on the conformal gradient shaped lattice structure, and a constitutive proxy model is established by performing polynomial interpolation on the relative density sample points; Based on the constitutive surrogate model and isogeometric topology optimization method, the optimal density distribution is obtained by iterative solution with the goal of minimizing the flexibility of the special-shaped sandwich structure. The optimal density distribution is substituted into the geometric proxy model to output the interpolation coefficient, the interpolation coefficient is corrected by the NURBS basis function, and the implicit model of the special-shaped sandwich structure is generated by gradient lattice filling.

2. The multi-scale optimization intelligent design method for special-shaped structures according to claim 1 is characterized in that: The geometric space of the heterogeneous lattice structure is constructed, and the constitutive matrix corresponding to the relative density sample points after interpolation is obtained by polynomial interpolation of the relative density sample points, and the constitutive matrix space of the heterogeneous lattice structure is constructed. The mapping relationship from the geometric space to the constitutive matrix space is determined to establish a constitutive proxy model.

3. The multi-scale optimization intelligent design method for special-shaped structures according to claim 1 is characterized in that: The constitutive proxy model is input into the CAD software, and the isogeometric model is constructed based on the NURBS basis function. The isogeometric model is refined through k-refinement, and the boundary conditions and constraints are defined. The density distribution function is established, and the objective function is established to minimize the flexibility of the special-shaped sandwich structure. Sensitivity analysis is performed based on the density distribution function, and the objective function is iteratively solved through the MMA algorithm to obtain the optimal density distribution.

4. The multi-scale optimization intelligent design method for special-shaped structures according to claim 1 is characterized in that: The relationship between the interpolation coefficient, aspect ratio and relative density sample points is calculated by formulas (8)-(10): ， (8) ， (9) ， (10) in, is the Heaviside function, is the relative density of the gradient shaped lattice structure, is the aspect ratio of the conformal gradient shaped lattice structure, is the interpolation coefficient of the conformal gradient shaped lattice structure, are the polynomial interpolation coefficients, is the interpolation order, is the maximum interpolation order, represents the level set function, represents the design domain; The expression of the geometric proxy model is as follows: ， (11) in, Represents a geometric proxy model.

5. The multi-scale optimization intelligent design method for special-shaped structures according to claim 4 is characterized in that: The implicit modeling expression for a single shaped lattice structure is: ， （3） Among them, Void represents the void in the special-shaped lattice structure, Boundary represents the boundary of the special-shaped lattice structure, and Solid represents the area of ​​the special-shaped lattice filled with material.

6. The multi-scale optimization intelligent design method for special-shaped structures according to claim 5 is characterized in that: The optimal density distribution is substituted into the geometric proxy model established by formulas (10) and (11) to output the interpolation coefficients. The interpolation coefficients are corrected by the NURBS basis function to obtain the corrected interpolation coefficients. Based on the corrected interpolation coefficients and the conformal gradient shaped lattice structure, a conformal continuous gradient shaped lattice structure is constructed by the level set function. The implicit model of the shaped sandwich structure filled by the conformal continuous gradient shaped lattice structure is output by formula (3).

7. The multi-scale optimization intelligent design method for special-shaped structures according to claim 6 is characterized in that: The corrected interpolation coefficient is obtained by the following formula: ，(20) in, is the corrected interpolation coefficient.

8. The multi-scale optimization intelligent design method for special-shaped structures according to claim 6 is characterized in that: The gradient shaped lattice structure with continuous shape is constructed by the following formula: ， ， (21) in, is the global level set function of the shape-continuous gradient shaped lattice structure, C is the Cth shaped lattice structure, N is the number of shaped lattice structures, and X is the set of all shaped lattice structures in the physical space.

9. The multi-scale optimization intelligent design method for special-shaped structures according to claim 1, characterized in that: The geometric proxy model is established by performing polynomial interpolation on relative density sample points to calculate the relationship between the interpolation coefficient, the aspect ratio and the relative density after interpolation.

10. The multi-scale optimization intelligent design method for special-shaped structures according to claim 1, characterized in that: Based on the generated implicit model, a special-shaped sandwich structure is produced by additive manufacturing.

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