Entity gradient dot matrix mixed structure multi-scale topological optimization method

Abstract

The invention provides a multi-scale topological optimization method for an entity gradient dot matrix mixed structure, and belongs to the field of structural topological optimization design, and the off-line stage comprises the following steps: constructing parameterized entity microstructure and dot matrix microstructure unit cells, establishing a sample database and an agent model, and realizing rapid mapping of unit density and unit cell mechanical attributes; the online stage comprises the following steps: defining double design variables of entity unit density and dot matrix unit density, minimizing structural flexibility as a multi-scale topological optimization model of a target function, introducing a Heaviside function to project the entity unit density, completing model reconstruction of the unit density and a corresponding entity gradient dot matrix structure, and obtaining a multi-scale topological optimization model of the target function. And obtaining a mixed structure topological configuration in which a solid structure and a gradient lattice structure are reasonably distributed. According to the method, co-parallel topological optimization of the entity structure and the gradient lattice structure is achieved, the comprehensive mechanical property of the structure is remarkably improved, and a new method is provided for entity gradient lattice mixed configuration design.

Description

Technical Field

[0001] The present invention mainly relates to the technical field related to structural topology optimization design, and specifically to a multi-scale topology optimization method for a solid gradient lattice hybrid structure. Background Art

[0002] As an intelligent design method, topology optimization provides a huge degree of design freedom for the design of innovative structural configurations. Compared with the single-scale topology optimization method, multi-scale design can obtain the optimal topological structure at both the macro and micro levels, and has attracted widespread attention in lattice structure design.

[0003] Lattice structures have excellent mechanical properties such as low density, high specific stiffness / strength, energy absorption and vibration reduction, and are widely used in the design of key structures in aerospace, medical bone implants, vehicle equipment and other fields. Multi-scale topology optimization methods can be divided into two categories based on the type of microstructure used. The first method is to establish a multi-scale optimization design model based on the uniform distribution of a single type of microstructure in the macrostructure to achieve the optimal design of the macroscopic performance of the structure. The second method is to consider the topological optimization design of the gradient lattice structure of multiple types of microstructures, which can greatly improve the target performance of the structure compared with the first method.

[0004] Although the gradient lattice structure has achieved a relatively excellent mechanical performance design by changing the density distribution of the microstructure unit cells in space, the strength and stiffness of the lattice structure are still difficult to meet the high-strength performance design requirements under load-bearing conditions. Especially in the main force transmission path of the structure, it is difficult for the lattice structure to achieve mechanical properties close to those of pure solid materials. On the other hand, the macroscopic topological configuration design that only includes pure solid structures has excellent stiffness performance, but its comprehensive mechanical properties are insufficient, such as structural lightweight, robustness, and buckling stability. Therefore, in the structural design that considers comprehensive mechanical properties such as lightweight, high performance, and multi-function, both pure lattice design and pure solid design face performance improvement bottlenecks. Summary of the invention

[0005] The present invention mainly provides a multi-scale topology optimization method of a solid gradient lattice hybrid structure to solve the technical problems raised in the above-mentioned background technology.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] A multi-scale topology optimization method for a solid gradient lattice hybrid structure, characterized in that the method comprises an offline stage and an online stage, and the offline stage comprises the following steps:

[0008] O1: Establishing the level set function of lattice microstructure;

[0009] O2: Get the density distribution of entity-lattice mixed unit cells;

[0010] O3: Calculate the performance of the solid-lattice unit cell under different parameters;

[0011] O4: Build a single cell database and proxy model;

[0012] The online phase includes the following steps:

[0013] S1: Design domain discretization and parameter definition;

[0014] S2: Construct a dual-constraint multi-scale topology optimization model;

[0015] S3: Conduct finite element analysis and sensitivity calculations;

[0016] S4: Solve the optimization model and update the design variables;

[0017] S5: Projecting entity unit cell density and updating true density;

[0018] S6: Calculate the objective function and constraints;

[0019] S7: Iteration convergence condition judgment; if the convergence condition is not met, repeat the above steps S3-S7;

[0020] S8: Geometric boundary processing and model reconstruction.

[0021] Furthermore, in the present invention, the offline stage step O1 establishes the initial level set function φ0(x) of the lattice microstructure unit cell based on the implicit description method; according to the level set model expression criteria, microstructures with different volume fractions are obtained at different cutting heights, and the volume fraction of the lattice microstructure is regulated by the parameter t2, and its mathematical expression is as follows:

[0022]

[0023] Where φ(x) is the level set function of the lattice microstructure, t2 is the parameter that controls the volume fraction of the microstructure unit cell, the area where φ(x)>0 represents the area containing material in the microstructure unit cell, the area where φ(x)<0 represents the blank area that does not contain material in the microstructure unit cell, the area where φ(x)=0 represents the boundary area between the microstructure unit cell material and the void, D represents the predefined shape area of ​​the entire microstructure unit cell, Ω represents the evolution area of ​​the microstructure unit cell during optimization, Represents the boundary of the microstructure unit cell.

[0024] Furthermore, in the present invention, the offline stage step O2 first defines the entity unit cell density matrix ρ(t1), and the density of the entity unit cell is regulated by the control parameter t1; then the level set function φ(x) of the microstructure unit cell is converted into the microstructure unit cell density matrix ρ(t2); finally, the entity unit cell density matrix ρ(t1) and the microstructure unit cell density matrix ρ(t2) are Boolean summed to obtain the density matrix ρ(t1, t2) of the entity-lattice mixed unit cell;

[0025] The mathematical expression of density Boolean summation is as follows: ρ(t1, t2) = max(ρ(t1), ρ(t2)).

[0026] 4. According to the multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, it is characterized in that the offline stage step O4 is based on a certain number of solid-lattice hybrid unit cell sample data obtained in step O3, including density sample data and performance sample data, and then constructs a proxy model, establishes a mapping relationship between the solid unit cell volume fraction x and the lattice unit cell volume fraction y with respect to the three elastic components CH11, CH12 and CH33 in the elastic matrix, and simultaneously establishes a mapping relationship between the solid unit cell volume fraction x and the lattice unit cell volume fraction y and the solid-lattice hybrid unit cell volume fraction z; on this basis, calculates the partial derivative information (sensitivity information) of the three elastic components with respect to the solid unit cell volume fraction x and the lattice unit cell volume fraction y, and Then, a proxy model is constructed to establish the mapping relationship between the solid unit cell volume fraction x, the lattice unit cell volume fraction y and the partial derivative information of the three elastic components.

[0028] Further, in the present invention, the online stage step S2 constructs a multi-scale topology optimization model with the solid unit density x and the microstructure unit density y as design variables, the overall structure volume of the solid-lattice mixture and the solid structure volume as double constraints, and the minimization of structural flexibility as the objective function;

[0029]

[0030] Wherein, the subscript i represents the i-th unit in the design domain, that is, the i-th unit cell in the solid-lattice hybrid structure, c represents the total flexibility of the structure, which is the objective function, K, U, and F are the overall stiffness matrix, overall displacement matrix, and overall load matrix of the structure, respectively, ui is the displacement vector of unit i, ki is the stiffness matrix of unit i, f(x) is the overall volume fraction constraint function of the solid-lattice structure, f is the given overall volume fraction constraint value of the solid-lattice structure, g(x) is the overall volume fraction constraint function of the lattice structure, g is the given volume fraction constraint value of the solid structure, v0 is the unit volume (value 1), V0 is the overall volume of the design domain before optimization, z*i is the volume fraction of the final solid-lattice unit cell, that is, the unit density participating in the finite element analysis;

[0031] The stiffness matrix of the unit i can be expressed as:

[0032]

[0033] Where ΩE represents the domain of the unit, B is the strain-displacement matrix of the unit, and Di is the elastic matrix of the unit, which is expressed as follows:

[0034]

[0035] For the orthogonal isotropic structure, CH11=CH22, CH21=CH12, and the elastic components in the elastic matrix of the unit are obtained according to the mapping relationship constructed in the offline stage.

[0036] Furthermore, in the present invention, the online stage step S3 introduces the Heaviside function to project the density of the solid unit so that its intermediate density approaches 0-1, updates the volume fraction x* of the solid unit, and obtains the volume fraction of the final solid-lattice structure unit according to the mapping relationship; the Heaviside function projection operation is as follows:

[0037]

[0038] Where the parameter β controls the slope of the threshold function.

[0039] Furthermore, in the present invention, the online stage S4 performs finite element analysis on the entire solid-lattice structure to obtain the unit displacement vector ui and the overall displacement matrix U, and then calculates the partial derivative of the objective function (structural flexibility) with respect to the design variables;

[0040]

[0041] In the formula, the partial derivative of the elastic matrix D with respect to the design variables is calculated as follows:

[0042]

[0043] The partial derivative of the elastic component in the elastic matrix of the unit with respect to the design variable is obtained according to the mapping relationship constructed in the offline stage;

[0044] Compute the partial derivatives of the volume constraint function with respect to the design variables:

[0045]

[0046] Furthermore, in the present invention, the online stage step S5 uses a gradient-based optimization algorithm to solve the dual-constraint topology optimization model based on the sensitivity information obtained in step S4, and updates the design variables.

[0047] Furthermore, in the present invention, the online stage step S6 calculates the structural flexibility and volume fraction after this iteration based on the finite element result information obtained in step S4 and the updated design variables obtained in step S5.

[0048] Further, in the present invention, the convergence criterion in step S7 includes reaching a given threshold or reaching a maximum number of iterations, which is defined as follows:

[0049] or n≥n max

[0050] Where δ is the given threshold and nmax represents the given maximum number of iterations.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1. The present invention provides a data-driven multi-scale topology optimization method for a solid-gradient lattice hybrid structure, innovatively proposes a hybrid modeling method of solid unit cell density and lattice unit cell density, obtains a solid-lattice hybrid unit cell sample database under different parameters, and introduces a proxy model to construct a correlation between unit density and mechanical properties of solid-lattice hybrid units, thereby realizing a rapid mapping of unit density and unit cell mechanical properties and reducing the computational cost of multi-scale topology optimization;

[0053] 2. At the same time, the present invention introduces the Heaviside function in the optimization to project the entity unit density, so that its intermediate density approaches 0-1, eliminates the intermediate unit density that has no physical meaning, and obtains a clearer entity unit density distribution. After Boolean summation with the lattice unit cell density, it provides effective data for the reconstruction of the entity-lattice structure model;

[0054] 3. In addition, the present invention realizes flexible regulation of the volume proportion of the solid structure and the lattice structure in the design domain by constructing a multi-scale topology optimization model with the overall structure volume of the solid-lattice mixture and the solid structure volume as dual constraints and minimization of structural flexibility as the objective function, and obtains a hybrid configuration of a solid structure with clear boundaries and a geometrically continuous gradient lattice structure. The corresponding multi-scale topology optimization strategy provides a solution for the efficient design of large-scale solid-gradient lattice structures.

[0055] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of a data-driven multi-scale topology optimization method of a solid-gradient lattice hybrid structure provided by the present invention;

[0057] Figure 2 It is a schematic diagram of the cutting of the level set function of the lattice microstructure of the present invention;

[0058] Figure 3 It is a schematic diagram of the hybrid data of the entity and lattice microstructure of the present invention;

[0059] Figure 4 Surface diagrams of the mapping relationship between unit density and unit cell properties constructed by the present invention: (a) is the mapping surface of xy-CH11 based on the Kriging proxy model, (b) is the mapping surface of xy-CH12 based on the Kriging proxy model, (c) is the mapping surface of xy-CH33 based on the Kriging proxy model, and (d) is the mapping surface of xyz based on the Kriging proxy model;

[0060] Figure 5 The surface diagram of the mapping relationship between the unit density and the elastic component partial derivative constructed by the present invention: (af) are respectively based on the Kriging proxy model The mapping surface of

[0061] Figure 6 It is a diagram of the process of density projection of entity unit cell and Boolean summation with lattice unit cell of the present invention;

[0062] Figure 7 It is a schematic diagram of the geometric boundary processing of the gradient lattice of the present invention;

[0063] Figure 8 is a schematic diagram of the design domain of a two-dimensional Michell beam structure in Example 2 of the present invention;

[0064] Fig. 9 is an optimization iteration curve diagram of the objective function and volume fraction in the preferred embodiment 2 of the present invention;

[0065] Fig.10 Schematic diagram of optimized configuration of Michell beam entity-gradient lattice in preferred embodiment 2 of the present invention: (a) is a configuration diagram of entity structure; (b) is a topological configuration diagram of gradient lattice structure; (c) is a topological configuration diagram of entity-gradient lattice hybrid structure;

[0066] Fig.11 is a schematic diagram of a two-dimensional femoral structure design domain in Example 3 of the present invention;

[0067] Fig.12 is an optimization iteration curve diagram of the objective function and volume fraction in the preferred embodiment 3 of the present invention;

[0068] Fig.13 This is a schematic diagram of the optimized configuration of the two-dimensional femoral structure entity-gradient lattice in the preferred embodiment 3 of the present invention: (a) is the density distribution diagram of the topological structure unit; (b) is the reconstructed topological configuration diagram. DETAILED DESCRIPTION

[0070] To facilitate understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. Several embodiments of the present invention are given in the drawings, but the present invention can be implemented in different forms and is not limited to the embodiments described in the text. On the contrary, these embodiments are provided to make the content disclosed in the present invention more thorough and comprehensive.

[0071] It should be noted that when an element is referred to as being "fixed on" another element, it may be directly on the other element or there may be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be a central element at the same time. The terms "vertical", "horizontal", "left", "right" and similar expressions used in this article are for illustrative purposes only.

[0072] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by technicians in the technical field to which the present invention belongs. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0073] Embodiment 1:

[0074] See also Figure 1-Figure 7 The present invention provides a data-driven multi-scale topology optimization method for a solid-gradient lattice hybrid structure, the method comprising the following steps:

[0075] The offline phase includes the following steps:

[0076] O1: Establishing the level set function of lattice microstructure;

[0077] Furthermore, the offline stage step O1 is based on an implicit description method. In this example, the signed distance function is used to establish the initial level set function φ0(x) of the lattice microstructure unit cell. According to the level set model expression criteria, microstructures with different volume fractions are obtained at different cutting heights. The volume fraction of the lattice microstructure is regulated by the parameter t2, and its mathematical expression is as follows:

[0078]

[0079] Where φ(x) is the level set function of the lattice microstructure, t2 is the parameter that controls the volume fraction of the microstructure unit cell, the area where φ(x)>0 represents the area containing material in the microstructure unit cell, the area where φ(x)<0 represents the blank area that does not contain material in the microstructure unit cell, the area where φ(x)=0 represents the boundary area between the microstructure unit cell material and the void, D represents the predefined shape area of ​​the entire microstructure unit cell, Ω represents the evolution area of ​​the microstructure unit cell during optimization, Represents the boundary of the microstructure unit cell.

[0080] O2: Get the density distribution of entity-lattice mixed unit cells;

[0081] Furthermore, in the offline stage step O2, the entity unit cell density matrix ρ(t1) is first defined, and the density of the entity unit cell is regulated by the control parameter t1; then the level set function φ(x) of the microstructure unit cell is converted into the microstructure unit cell density matrix ρ(t2); finally, the entity unit cell density matrix ρ(t1) and the microstructure unit cell density matrix ρ(t2) are Boolean summed to obtain the density matrix ρ(t1, t2) of the entity-lattice mixed unit cell.

[0082] Furthermore, the mathematical expression of the Boolean summation of the density matrix is ​​as follows:

[0083] ρ(t1,t2)=max(ρ(t1),ρ(t2))

[0084] O3: Calculate the performance of the solid-lattice unit cell under different parameters;

[0085] Furthermore, in the offline stage step O3, based on the density matrix of the solid-lattice hybrid unit cell obtained in step O2, the elastic properties of the microstructure are calculated based on the homogenization method to obtain the elastic matrix of the hybrid microstructure controlled by different parameters t1 and t2.

[0086] Furthermore, the volume fractions x and y of the solid unit cell and the microstructure unit cell are calculated according to the solid unit cell density matrix ρ(t1) and the microstructure unit cell density matrix ρ(t2), and the volume fraction z of the mixed unit cell is obtained according to the density matrix ρ(t1, t2) of the solid-lattice mixed unit cell.

[0087] O4: Build a single cell database and proxy model;

[0088] Furthermore, the offline stage step O4 is based on a certain number of entity-lattice mixed unit cell sample data obtained in step O3, including density sample data and performance sample data.

[0089] Furthermore, a mapping relationship between the volume fraction of the solid unit cell x and the volume fraction of the lattice microstructure unit cell y with respect to the three elastic components CH11, CH12 and CH33 in the elastic matrix is ​​constructed, and a mapping relationship between the volume fraction of the solid unit cell x and the volume fraction of the lattice unit cell y and the volume fraction of the solid-lattice mixed unit cell z is constructed. This implementation example establishes a proxy model by introducing the Kriging algorithm;

[0090] Furthermore, the partial derivative information (sensitivity information) of the three elastic components with respect to the solid unit cell volume fraction x and the lattice unit cell volume fraction y is calculated, namely: Then, a mapping relationship between the volume fraction x of the entity unit cell and the volume fraction y of the lattice unit cell and the partial derivative information of the three elastic components is constructed. This implementation example establishes a proxy model by introducing the Kriging algorithm.

[0091] The online phase includes the following steps:

[0092] S1: Design domain discretization and parameter definition;

[0093] Furthermore, in the online stage step S1, the design domain is first discretized into a number of quadrilateral units for unit cell matching, the number of discrete units in the design domain is N, and then the solid unit density x and the microstructure unit density y are defined as dual design variables, and the solid unit density x and the lattice microstructure unit density y are equivalent to the solid unit cell volume fraction x and the lattice microstructure unit cell volume fraction y.

[0094]

[0095] S2: Construct a dual-constraint multi-scale topology optimization model;

[0096] Furthermore, in the online stage step S2, a multi-scale topology optimization model is constructed with the solid unit density x and the microstructure unit density y as design variables, the solid structure volume and the overall structure volume of the solid-lattice mixture as double constraints, and minimization of structural flexibility as the objective function.

[0097]

[0098] Wherein, the subscript i represents the i-th unit in the design domain, that is, the i-th unit cell in the solid-lattice hybrid structure, c represents the total flexibility of the structure, which is the objective function, K, U, and F are the overall stiffness matrix, overall displacement matrix, and overall load matrix of the structure, respectively, ui is the displacement vector of unit i, ki is the stiffness matrix of unit i, f(x) is the overall volume fraction constraint function of the solid-lattice structure, f is the given overall volume fraction constraint value of the solid-lattice structure, g(x) is the overall volume fraction constraint function of the lattice structure, g is the given volume fraction constraint value of the solid structure, v0 is the unit volume (value 1), V0 is the overall volume of the design domain before optimization, and z*i is the volume fraction of the final solid-lattice unit cell, that is, the unit density participating in the finite element analysis.

[0099] Furthermore, the stiffness matrix of the unit i can be expressed as:

[0100]

[0101] Where ΩE represents the domain of the unit, B is the strain-displacement matrix of the unit, and Di is the elastic matrix of the unit, which is expressed as follows:

[0102]

[0103] Furthermore, for the orthogonal isotropic structure, CH11=CH22, CH21=CH12, and the elastic components in the elastic matrix of the unit are obtained according to the mapping relationship constructed in the offline stage.

[0104] S3: Conduct finite element analysis and sensitivity calculations;

[0105] Furthermore, the online stage step S3 introduces the Heaviside function to project the entity unit density so that its intermediate density approaches 0-1, thereby avoiding the intermediate unit density that has no physical meaning.

[0106] Furthermore, the volume fraction of the solid unit (or unit density) is updated, and the volume fraction of the final solid-lattice structure unit is obtained according to the mapping relationship.

[0107] Furthermore, the Heaviside function projection operation is as follows:

[0108]

[0109] Wherein, x* is the volume fraction of the projected solid unit, and the parameter β controls the slope of the threshold function, which is 8 in this embodiment.

[0110] S4: Solve the optimization model and update the design variables;

[0111] Furthermore, in the online stage step S4, finite element analysis is performed on the entire solid-lattice structure to obtain the unit displacement vector ui and the overall displacement matrix U, and then the partial derivative of the objective function (structural flexibility) with respect to the design variables is calculated:

[0112]

[0113] In the formula, the partial derivative of the elastic matrix D with respect to the design variables is calculated as follows:

[0114]

[0115] Furthermore, the partial derivative of the elastic component in the elastic matrix of the unit with respect to the design variable is obtained according to the mapping relationship constructed in the offline stage.

[0116] Furthermore, the partial derivatives of the volume constraint function with respect to the design variables are calculated:

[0117]

[0118] S5: Solve the optimization model and update the design variables;

[0119] Furthermore, in the online stage step S5, based on the sensitivity information obtained in step S4, a gradient-based optimization algorithm is used to solve the dual-constraint topology optimization model. In this example, the MMA algorithm is used to update the design variables.

[0120] S6: Calculate the objective function and constraints;

[0121] Furthermore, the online stage step S6 calculates the structural flexibility and volume fraction after this iteration based on the finite element result information obtained in step S4 and the updated design variables obtained in step S5.

[0122] S7: Iteration convergence condition judgment;

[0123] Furthermore, the convergence criterion in the online step S7 includes reaching a given threshold or reaching a maximum number of iterations, which is defined as follows:

[0124] or n≥n max

[0125] Where δ is the given threshold and nmax represents the given maximum number of iterations.

[0126] S8: Geometric boundary processing and model reconstruction.

[0127] Furthermore, in the online stage step S8, based on the optimized solid unit and microstructure unit densities, the unit density is converted into the node density, so as to realize the inverse mapping between the unit node density and the level set unit cell control parameters.

[0128] Furthermore, the corresponding solid microstructure unit cells and lattice microstructure unit cells are filled into the corresponding units in the design domain according to the control parameters. Finally, the solid structure and the lattice microstructure are Boolean summed to achieve the reconstruction of the solid-gradient lattice hybrid structure model with good geometric boundary continuity.

[0129] Example 2: See Figure 8-Figure 10 Shown is a preferred embodiment according to the present invention.

[0130] Furthermore, this example performs solid-gradient lattice optimization on a two-dimensional Michell beam. Figure 8 As shown in the figure, the size of the Michell beam is: L×H=120×40, the design domain is discretized into 120×40 quadrilateral units, the lower left corner and the lower right corner of the design domain structure are set with simple support and fixed constraints respectively, and a vertical concentrated load F=1N is applied to the middle of the lower boundary. Two-dimensional solid unit cells and X-shaped unit cells are used for optimization. The overall volume fraction constraint of the solid-lattice structure is set to 0.5, and the volume fraction constraint of the solid structure is set to 0.2. After 42 iterations, the structural flexibility converges to 26.09, the macrostructure volume fraction converges to 0.5, and the solid structure volume fraction converges to 0.2. The iteration curve is shown in Fig. 9 After the optimization, the optimal unit density parameters are obtained, and the mapping and reconstruction are performed to obtain the topological optimization configuration design of the mixed entity and gradient lattice. The entity structure is continuously distributed, and the lattice structure presents a continuous gradient distribution, as shown in Fig.10 shown.

[0131] Example 3: See Figure 11-13 Shown is a preferred embodiment according to the present invention.

[0132] Furthermore, this example performs solid-gradient lattice topology optimization on a two-dimensional femoral structure based on a data-driven solid-gradient lattice hybrid structure multi-scale topology optimization method provided by the present invention. Fig.11As shown, the dimensions of the femur are: L×H=85×90, the design domain is discretized into 185×90 quadrilateral units, the bottom of the design domain is fixed, and two external loads F1=10N and F2=20N are applied to the upper part. The outer contour of the femur is set with a skin with a width of 2. The skin is a non-design domain and does not participate in the optimization process. Two-dimensional solid unit cells and X-shaped unit cells are used for optimization. The overall volume fraction constraint of the solid-lattice structure is set to 0.5, and the volume fraction constraint of the solid structure is set to 0.25. After 48 iterations, the structural flexibility converged to 2952.46, the macroscopic structure volume fraction converged to 0.5, and the solid structure volume fraction converged to 0.2. The iteration curve is shown in Fig.12 After the optimization, the optimal unit density parameters are obtained, and the mapping and reconstruction are performed to obtain the topological optimization configuration design of the mixed entity and gradient lattice. The entity structure is continuously distributed, and the lattice structure presents a continuous gradient distribution, as shown in Fig.13 shown.

[0133] The above examples show that the data-driven solid-gradient lattice hybrid structure multi-scale topology optimization method provided by the present invention still has good applicability and stability in the topology optimization process of irregular and complex structures.

[0134] The above is an exemplary description of the present invention in combination with the accompanying drawings. It is obvious that the specific implementation of the present invention is not limited to the above-mentioned method. As long as such non-substantial improvements are made by adopting the method concept and technical solution of the present invention, or the concept and technical solution of the present invention are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A multi-scale topology optimization method for solid gradient lattice hybrid structure, It is characterized in that, The method includes an offline phase and an online phase. The offline phase includes the following steps: O1: Establishing the level set function of lattice microstructure; O2: Get the density distribution of entity-lattice mixed unit cells; O3: Calculate the performance of the solid-lattice unit cell under different parameters; O4: Build a single cell database and proxy model; The online phase includes the following steps: S1: Design domain discretization and parameter definition; S2: Construct a dual-constraint multi-scale topology optimization model; S3: Conduct finite element analysis and sensitivity calculations; S4: Solve the optimization model and update the design variables; S5: Projecting entity unit cell density and updating true density; S6: Calculate the objective function and constraints; S7: Iteration convergence condition judgment; if the convergence condition is not met, repeat the above steps S3-S7; S8: Geometric boundary processing and model reconstruction.

2. According to the multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, It is characterized in that In the offline stage, step O1 is based on an implicit description method to establish an initial level set function φ0(x) of the lattice microstructure unit cell; according to the level set model expression criteria, microstructures with different volume fractions are obtained at different cutting heights, and the volume fraction of the lattice microstructure is regulated by the parameter t2, and its mathematical expression is as follows: Where φ(x) is the level set function of the lattice microstructure, t2 is the parameter that controls the volume fraction of the microstructure unit cell, the area where φ(x)>0 represents the area containing material in the microstructure unit cell, the area where φ(x)<0 represents the blank area that does not contain material in the microstructure unit cell, the area where φ(x)=0 represents the boundary area between the microstructure unit cell material and the void, D represents the predefined shape area of ​​the entire microstructure unit cell, Ω represents the evolution area of ​​the microstructure unit cell during optimization, Represents the boundary of the microstructure unit cell.

3. According to claim 1, a multi-scale topology optimization method for a solid gradient lattice hybrid structure, It is characterized in that In the offline stage, step O2 first defines the entity cell density matrix ρ(t1), and controls the density of the entity cell by the control parameter t1; then converts the level set function φ(x) of the microstructure cell into the microstructure cell density matrix ρ(t2); finally, the entity cell density matrix ρ(t1) and the microstructure cell density matrix ρ(t2) are Boolean summed to obtain the density matrix ρ(t1, t2) of the entity-lattice hybrid cell; The mathematical expression of density Boolean summation is as follows: ρ(t 1 ,t 2 )=max(ρ(t 1 ),ρ(t 2 )).

4. According to claim 1, a multi-scale topology optimization method for a solid gradient lattice hybrid structure, It is characterized in that The offline stage step O4 is based on a certain number of entity-lattice hybrid unit cell sample data obtained in step O3, including density sample data and performance sample data, and then constructs a proxy model, establishes a mapping relationship between the entity unit cell volume fraction x and the lattice unit cell volume fraction y with respect to the three elastic components CH11, CH12 and CH33 in the elastic matrix, and simultaneously establishes a mapping relationship between the entity unit cell volume fraction x and the lattice unit cell volume fraction y and the entity-lattice hybrid unit cell volume fraction z; on this basis, calculates the partial derivative information (sensitivity information) of the three elastic components with respect to the entity unit cell volume fraction x and the lattice unit cell volume fraction y, and Then, a proxy model is constructed to establish the mapping relationship between the solid unit cell volume fraction x, the lattice unit cell volume fraction y and the partial derivative information of the three elastic components.

5. According to claim 1, a multi-scale topology optimization method for a solid gradient lattice hybrid structure, It is characterized in that The online stage step S2 constructs a multi-scale topology optimization model with the solid unit density x and the microstructure unit density y as design variables, the overall structure volume of the solid-lattice mixture and the solid structure volume as double constraints, and minimization of structural flexibility as the objective function; find{x i ,y i } Τ ,i=1,…,N stKU=F 0:ρ min ≤x i ,y i ≤1,i=1,…,N; Wherein, the subscript i represents the i-th unit in the design domain, that is, the i-th unit cell in the solid-lattice hybrid structure, c represents the total flexibility of the structure, which is the objective function, K, U, and F are the overall stiffness matrix, overall displacement matrix, and overall load matrix of the structure, respectively, ui is the displacement vector of unit i, ki is the stiffness matrix of unit i, f(x) is the overall volume fraction constraint function of the solid-lattice structure, f is the given overall volume fraction constraint value of the solid-lattice structure, g(x) is the overall volume fraction constraint function of the lattice structure, g is the given volume fraction constraint value of the solid structure, v0 is the unit volume (value 1), V0 is the overall volume of the design domain before optimization, z*i is the volume fraction of the final solid-lattice unit cell, that is, the unit density participating in the finite element analysis; The stiffness matrix of the unit i can be expressed as: Where ΩE represents the domain of the unit, B is the strain-displacement matrix of the unit, and Di is the elastic matrix of the unit, which is expressed as follows: For the orthogonal isotropic structure, CH11=CH22, CH21=CH12, and the elastic components in the elastic matrix of the unit are obtained according to the mapping relationship constructed in the offline stage.

6. The multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, It is characterized in that The online stage step S3 introduces the Heaviside function to project the density of the solid unit so that its intermediate density approaches 0-1, updates the volume fraction x* of the solid unit, and obtains the volume fraction of the final solid-lattice structure unit according to the mapping relationship; the Heaviside function projection operation is as follows: Where the parameter β controls the slope of the threshold function.

7. The multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, It is characterized in that The online stage S4 performs finite element analysis on the entire solid-lattice structure to obtain the unit displacement vector ui and the overall displacement matrix U, and then calculates the partial derivative of the objective function (structural flexibility) with respect to the design variables; In the formula, the partial derivative of the elastic matrix D with respect to the design variables is calculated as follows: The partial derivative of the elastic component in the elastic matrix of the unit with respect to the design variable is obtained according to the mapping relationship constructed in the offline stage; Compute the partial derivatives of the volume constraint function with respect to the design variables:

8. The multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, It is characterized in that The online stage step S5 solves the dual-constraint topology optimization model based on the sensitivity information obtained in step S4, and updates the design variables using a gradient-based optimization algorithm.

9. The multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, It is characterized in that The online stage step S6 calculates the structural flexibility and volume fraction after this iteration based on the finite element result information obtained in step S4 and the updated design variables obtained in step S5.

10. The multi-scale topology optimization method of a solid gradient lattice hybrid structure according to claim 1, It is characterized in that The convergence criteria in step S7 include reaching a given threshold or reaching a maximum number of iterations, which are defined as follows: or n≥n max Where δ is the given threshold and nmax represents the given maximum number of iterations.

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