Full-scale parallel topology optimization method and system for solid-lattice hybrid configuration

Abstract

The present invention belongs to the field of structural topology optimization design, and specifically discloses a full-scale parallel topology optimization method and system for a solid-lattice hybrid configuration, which includes: constructing the level set function of the solid microstructure and the lattice microstructure, and obtaining the global parameterized level set function of the solid-lattice hybrid by introducing the control parameter; bringing it into the Hamilton-Jacobi partial differential equation to obtain the ordinary differential equation; taking the control parameters of the solid structure and the lattice structure as the dual design variables, taking the minimization of the macroscopic structure flexibility as the objective function, and establishing a topology optimization mathematical model with the solid structure volume and the macroscopic structure volume as the dual constraints; calculating the sensitivity information, and then using the gradient-based optimization algorithm to solve the topology optimization model. The present invention can overcome the problem of insufficient mechanical properties of pure solid macroscopic topological structures and single lattice structures, realize the configuration design of solid-lattice parallel optimization, and effectively improve the mechanical properties of the structure.

Description

Technical Field

[0001] The present invention belongs to the field of structural topology optimization design, and more specifically, relates to a full-scale parallel topology optimization method and system for a solid-lattice hybrid configuration. Background Art

[0002] The lattice structure is obtained through a periodic array of microstructures (lattice microstructures). It has excellent mechanical properties such as low density, energy absorption and vibration reduction, heat dissipation and thermal insulation, and is widely used in the design of key structures in the fields of aircraft, rail transportation, and medical bone implants. However, the periodic lattice structure has a single function, insufficient mechanical properties, and a complex coupling relationship between mechanical properties and macroscopic distribution, which leads to the inadequate application potential of the lattice structure, and there is a large gap between the actual use requirements of functional structural parts.

[0003] Topology optimization methods provide a powerful optimization tool for the mechanical performance design of lattice structures. Topology optimization methods can optimize the macroscopic structural distribution and microstructural configuration of lattice structures in parallel to achieve functionally graded lattice design, thereby obtaining mechanical properties that are better than periodic lattice structures. In terms of functionally graded lattice topology optimization, topology optimization methods can be divided into layer-by-layer optimization, domain-by-domain optimization, and point-by-point optimization. Although functionally graded lattice structures achieve relatively good designs through the spatial configuration distribution of variable density microstructures, in practical applications, the mechanical properties of lattice structures are difficult to meet the performance design requirements of lightweight and high strength, especially in the main force transmission path of high-load structural conditions. The lattice structure cannot provide mechanical properties similar to those of solid materials. On the other hand, the topological configuration of pure solid structures can provide greater stiffness performance, but faces design conflicts in terms of comprehensive performance such as structural lightweight, robustness, and buckling stability. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a full-scale parallel topological optimization method and system for a solid-lattice hybrid configuration, which aims to achieve coordinated regulation of the topological configuration of the solid structure and the lattice structure, and effectively improve the mechanical properties of the structure.

[0005] To achieve the above object, according to one aspect of the present invention, a full-scale parallel topology optimization method for a solid-lattice hybrid configuration is proposed, comprising the following steps:

[0006] S1: Introduce control parameters to construct the level set function of the solid microstructure and lattice microstructure on the unit cell, and then obtain the global parameterized level set function of the solid-lattice hybrid structure;

[0007] S2: A mathematical model for topology optimization is established with the control parameters of the solid structure and the lattice structure as dual design variables, minimization of the overall structural flexibility as the objective function, and the solid structure volume and the macroscopic structure volume as dual constraints;

[0008] S3: Substitute the global parameterized level set function into the Hamilton-Jacobi partial differential equation to obtain the ordinary differential equation;

[0009] S4: Based on ordinary differential equations, determine the sensitivity formula of the objective function and constraint conditions with respect to the design variables and obtain sensitivity information;

[0010] S5: Based on the sensitivity information, the topology optimization model is solved using a gradient-based optimization algorithm to obtain dual design variables, thereby determining the optimal solid-crystal hybrid configuration.

[0011] As a further preferred embodiment, in step S1, the global parameterized level set function is specifically:

[0012]

[0013] Where Φ(x, t) is the level set function of the solid structure, θ(x, t) is the level set function of the lattice structure, T(t) and H(t) are the control parameters of the solid structure and the lattice structure, i.e., the design variables; is the level set function of the solid microstructure with a volume fraction of 1, γ(x) is the level set function of the lattice microstructure with a predefined small volume fraction, is the control coefficient of the entity microstructure level set function, C γ is the control coefficient of the lattice microstructure level set function, N(x) is the linear interpolation shape function; Г(x, t) is the global parameterized level set function of the solid-lattice hybrid macrostructure, the area where Г(x, t)>0 represents the position containing material in the structure, the area where Г(x, t)<0 represents the blank position without material in the structure, the area where Г(x, t)=0 represents the boundary area between material and void in the design domain, D represents the predefined entire design domain, Ω represents the junction evolution region in the optimization, Represents the boundaries of a structure.

[0014] As a further preferred embodiment, the control coefficient C γ The calculation method is as follows:

[0015]

[0016] As a further preferred embodiment, in step S2, the topology optimization mathematical model is specifically:

[0017] find:{T(t),H(t)}

[0018]

[0019]

[0020] Where J(Г) is the overall flexibility of the solid-lattice hybrid structure, ε and u are the strain field and displacement field of the discrete unit in the structure, and B is the material equivalent elastic matrix; Ф (u,v) is the strain energy functional, l Ф (v) is the work done by the external force on the virtual displacement, U is the displacement field of the structure, g(Г) is the volume constraint function of the macro structure, f(Φ) is the volume constraint function of the solid structure, ζ is the given volume fraction constraint value of the macro structure, δ is the given volume fraction constraint value of the solid structure, V represents the initial complete volume of the design domain, Ω macro is the region of entity-lattice structure evolution during optimization, Ω solid is the physical structure evolution area during optimization; T k (t) represents the design variable of the physical structure on the kth unit cell, H k (t) represents the design variable of the lattice structure on the kth unit cell, and m is the number of unit cells in the design domain.

[0021] As a further preferred embodiment, in step S3, the ordinary differential equation obtained is as follows:

[0022]

[0023]

[0024] Where t is pseudo time, They are the normal velocities of boundary evolution of solid structure and lattice structure during the optimization process, respectively.

[0025] As further preferred, step S4, determining the sensitivity formula of the objective function with respect to the design variables, comprises:

[0026] Based on the ordinary differential equation, the normal velocity expression is determined and substituted into the sensitivity formula of the objective function with respect to the pseudo-time t, and the sensitivity formula of the objective function with respect to the design variable is obtained as follows:

[0027]

[0028]

[0029] In the formula, is the sensitivity of the objective function with respect to the physical structure design variables, is the sensitivity of the objective function to the design variables of the lattice structure; δ is the derivative of the Heaviside function with respect to the level set function; G(Г) is the node strain energy.

[0030] As a further preferred embodiment, in step S4, the sensitivity of the constraint condition to the design variable is expressed as:

[0031]

[0032]

[0033] In the formula, is the sensitivity of the macrostructure volume constraint function with respect to the dual design variables, is the sensitivity of the volume constraint function of the solid structure to its own design variables.

[0034] As a further preferred method, the design domain is discretized in advance, including:

[0035] The design domain is divided into a certain number of regular quadrilateral regions or regular hexahedral regions, each region matches a microstructure unit cell of a corresponding size, and each region is further divided into fine grids to form a finite element analysis grid;

[0036] Two sets of meshes are obtained by the above method to match the solid microstructure and the lattice microstructure respectively; two design variables are defined on the nodes of the two sets of meshes respectively.

[0037] As a further preferred embodiment, in step S5, a gradient-based optimization algorithm is used to solve the topology optimization model, and the design variables are iteratively updated; when the convergence criterion is met, the iteration is stopped, and the dual design variable values ​​at this time are used as the final values;

[0038] The convergence criterion is:

[0039]

[0040] In the formula, σ is the given threshold, n max is the maximum number of given iterations; J(Γ) n is the objective function value of the nth iteration.

[0041] According to another aspect of the present invention, a full-scale parallel topology optimization system for a solid-lattice hybrid configuration is provided, comprising a processor for executing the full-scale parallel topology optimization method for the solid-lattice hybrid configuration.

[0042] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0043] 1. The present invention constructs a parameterized level set function by introducing dual design variables, completes the decoupling of the Hamilton-Jacobi partial differential equation, establishes dual constraints on the volume of the macro structure and the volume of the solid structure, realizes the coordinated regulation of the topological configuration of the solid structure and the lattice structure, obtains a solid-lattice mixed configuration design, avoids the parallel optimization process of splitting the solid and lattice structures, can overcome the problem of insufficient mechanical properties of pure solid macro topological structures and single lattice structures, effectively improves the mechanical properties of the structure, and provides a new method for expanding the design freedom and engineering application scope of the lattice structure.

[0044] 2. The present invention converts the topological configuration control and geometric boundary continuity of the preset microstructure into design variables embedded in the optimization framework, and ensures the continuous distribution of the solid structure in the design domain and the gradient distribution of the lattice microstructure based on the full-scale finite element, ensuring the continuous transition of the geometric boundaries of the solid structure and the lattice structure. Compared with the solid-uniform lattice design, the solid-gradient lattice hybrid innovative configuration provided by the present invention expands the design space and design freedom, and can greatly improve the mechanical properties of the structure.

[0045] 3. The present invention realizes flexible and coordinated regulation of the volume proportion of the solid structure and the lattice structure in the design domain by constructing dual constraints of the volume of the macrostructure and the volume of the solid structure. That is, under any given dual volume constraints, the mechanical properties of the optimized structure can be precisely regulated and optimized and the corresponding solid-lattice configuration can be obtained, ensuring the reasonable distribution and parallel design of the two structural configurations in space, providing a new idea for improving the mechanical properties of lightweight and high-strength structures. The present invention can better balance the comprehensive factors such as structural lightweight, stiffness, robustness, and buckling stability, and provides a practical and feasible configuration innovation design technology solution for customized performance design requirements and engineering application needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of a full-scale parallel topology optimization method for a solid-lattice hybrid configuration provided by an embodiment of the present invention;

[0047] Figure 2 Schematic diagram of design domain discretization and dual design variable definition in an embodiment of the present invention;

[0048] Figure 3 is a schematic diagram of a hybrid design of a solid and lattice microstructure according to an embodiment of the present invention;

[0049] Figure 4 is a schematic diagram of the design domain of the two-dimensional cantilever beam structure in Example 1 of the present invention;

[0050] Figure 5Schematic diagram of the optimized configuration of the cantilever beam structure entity and lattice in Example 1 of the present invention, wherein (a) is a configuration diagram of the entity structure in the macro structure, (b) is a configuration diagram of the X-shaped unit cell gradient lattice distribution in the macro structure, and (c) is an optimized entity-lattice mixed configuration diagram;

[0051] Figure 6 (a) and (b) are the objective function and volume fraction optimization iteration curves in Example 1 of the present invention;

[0052] Figure 7 (a) to (f) are optimized configuration diagrams of the cantilever beam under different parameters in Example 1 of the present invention;

[0053] Figure 8 is a schematic diagram of the design domain of a two-dimensional Michell beam structure in Example 2 of the present invention;

[0054] Fig. 9 Schematic diagram of optimized configuration of Michell beam entity and lattice in Example 2 of the present invention, wherein (a) is a configuration diagram of entity structure in macro structure, (b) is a configuration diagram of X-shaped unit cell gradient lattice distribution in macro structure, and (c) is an optimized entity-lattice mixed configuration diagram;

[0055] Fig.10 (a) and (b) are the objective function and volume fraction optimization iteration curves in Example 2 of the present invention;

[0056] Fig.11 is a schematic diagram of the design domain of a three-dimensional MBB beam structure in Example 3 of the present invention;

[0057] Fig.12 Schematic diagram of optimized configuration of MBB beam entity and lattice in Example 3 of the present invention, wherein (a) is a configuration diagram of entity structure in macro structure, (b) is a configuration diagram of body-centered cubic unit cell gradient lattice distribution in macro structure, and (c) is an optimized entity-lattice mixed configuration diagram;

[0058] Fig.13 (a) and (b) are the objective function and volume fraction optimization iteration curves in Example 3 of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0060] The embodiment of the present invention provides a full-scale parallel topology optimization method for a solid-lattice hybrid configuration, such as Figure 1 As shown, the following steps are included:

[0061] S1: Construction of bivariate parameterized level set function;

[0062] The entity and microstructure level set functions constructed based on the implicit modeling method are introduced by introducing the dual control parameters T k (t) and T k (t) Establish the bivariate level set function Φ of the local unit cell k (x,t) and θ k (x, t), is defined as follows:

[0063]

[0064] In the formula, the coefficient T k (t) and H k (t) is the control parameter about pseudo time t, i.e., the design variable in the subsequent optimization process. k (t) represents the design variable of the physical microstructure on the kth unit cell, H k (t) represents the design variable of the lattice microstructure on the kth unit cell, is the level set function of the solid microstructure with a volume fraction of 1, γ(x) is the level set function of the lattice microstructure with a predefined small volume fraction, is the control coefficient of the entity microstructure level set function, C γ is the control coefficient of the lattice microstructure level set function, and N(x) is the linear interpolation shape function. Control coefficient and C γ The definition is as follows:

[0065]

[0066] According to the defined two-variable level set function, the level set function Г of the local unit cell of the k-th solid-lattice hybrid structure in the discrete design domain is obtained through Boolean summation operation. k (x, t), the summation operation is defined as follows:

[0067] G k (x,t)=max(Φ k (x,t),θ k (x,t)

[0068] By assembling the microstructure unit cells (i.e., solid microstructure or lattice microstructure), the entire solid structure or lattice structure can be obtained. Based on the level set function of the local unit cells, the parameterized level set function of the entire structure is obtained, which is defined as follows:

[0069]

[0070]

[0071] Where Φ(x, t) is the parameterized level set function of the solid structure, θ(x, t) is the parameterized level set function of the lattice structure, T(t) is the global design variable of the solid structure, H(t) is the global design variable of the lattice structure, Г(x, t) is the macroscopic structure level set function of the solid-lattice mixture, the area where Г(x, t)>0 represents the position containing material in the structure, the area where Г(x, t)<0 represents the blank position without material in the structure, and Г(x, t)=0 represents the boundary area between material and void in the design domain; D represents the entire predefined design domain, Ω represents the junction evolution region in the optimization, Represents the boundaries of a structure.

[0072] Specifically, for a two-dimensional structure, a unit cell has 4 nodes, T k (t) and H k (t) dimensions are all 4×1; for a three-dimensional structure, a unit cell has 8 nodes, T k (t) and H k (t) The dimensions are all 8×1.

[0073] Specifically, the volume fraction of the lattice microstructure unit cell is predefined before optimization, and its volume fraction may vary between 0 and 1, or may be arbitrarily predefined within the range of 0 to 1. In this embodiment, the predefined minimum volume fraction is 0.06.

[0074] Furthermore, for the dual design variables, the design domain is discretized:

[0075] The discretization of the design domain is to divide the design domain into a certain number of regular quadrilateral regions (two-dimensional structure) or regular hexahedral regions (three-dimensional structure). The above regions are used to match the microstructure unit cells of corresponding sizes. Each region is further divided into fine grids to form a finite element analysis grid. After the actual design domain is discretized, it actually contains two sets of "virtual" grids of the same size to match the physical structure and lattice structure. The design variables (control parameters) are defined on the nodes of the two sets of "virtual" grids. The two sets of design variables are written in column vector form and defined as follows:

[0076] T(t)=[T1(t) T2(t) T3(t) … T m (t)] T

[0077] H(t)=[H1(t) H2(t) H3(t) … H m (t)] T

[0078] Where T(t) and H(t) represent the predefined design variables of the solid and lattice microstructures, m is the number of design variables, corresponding to the number of unit cell nodes in the design domain; the control parameter T of the unit cell is k (t) and H k (t) are obtained from T(t) and H(t).

[0079] S2: Establishment of mathematical model for multi-constraint topology optimization;

[0080] Taking the control parameters of the solid structure and lattice structure as design variables and minimizing the structural flexibility (maximizing the stiffness) as the objective function, a topology optimization mathematical model with the solid structure and the macroscopic structure volume as dual constraints was established; the details are as follows:

[0081] find:{T(t),H(t)}

[0082]

[0083]

[0084] Where J(Г) is the flexibility of the solid-lattice hybrid structure, which is set as a dimensionless value, ε and u are the strain field and displacement field of the structure, B is the material equivalent elastic matrix, and a Ф (u,v)=l Ф (v) is the weak form of the elastic equilibrium equation, a Ф (u,v) is the strain energy functional, l Ф (v) is the work done by the external force on the virtual displacement, U is the displacement field of the structure; g(Г) is the volume constraint function of the macro structure, f(Φ) is the volume constraint function of the solid structure, ζ is the volume fraction constraint value of the given macro structure, δ is the volume fraction constraint value of the given solid structure, represents the initial full volume of the design domain; Ω macro is the region of entity-lattice structure evolution during optimization, Ω solid It is the region where the physical structure evolves during optimization.

[0085] S3: Decoupling of Hamilton-Jacobi partial differential equations;

[0086] The level set function changes dynamically with pseudo time t, and the process of structural topology optimization can be described as a process that makes the level set function change dynamically with time. Therefore, its dynamic model is expressed as:

[0087]

[0088] Differentiating both sides of the above equation with respect to pseudo-time t yields a Hamilton-Jacobi type partial differential equation:

[0089]

[0090] Considering the normal velocity v n =v·n, and the normal vector n is defined as This gives the Hamilton-Jacobi partial differential equation:

[0091]

[0092] The global parameterized level set function of the defined solid structure and lattice structure is brought into the original Hamilton-Jacobi differential equation, and the partial differential equation is transformed into an ordinary differential equation, whose expression is as follows:

[0093]

[0094]

[0095] The mathematical expression of normal velocity can be obtained:

[0096]

[0097]

[0098] S4: Structural finite element analysis and sensitivity information calculation;

[0099] Define the same number of finite element analysis grids according to the number of discrete units, apply constraints and loads according to the given boundary conditions, carry out finite element analysis to obtain the strain field and displacement field of the structure, and then calculate the strain energy of the unit and convert it into the nodal strain energy G(Г) of the unit cell.

[0100] Then determine the calculation method of sensitivity information:

[0101] (1) The sensitivity of the objective function with respect to the two sets of design variables is expressed as:

[0102]

[0103]

[0104] Substitute the normal velocity in step S2 into the following equation:

[0105]

[0106]

[0107] According to the chain rule:

[0108]

[0109]

[0110] Then the sensitivity of the objective function to the two sets of design variables can be obtained by comparing the above formulas:

[0111]

[0112]

[0113] In the formula, is the sensitivity of the objective function with respect to the physical structure design variables, is the sensitivity of the objective function to the design variables of the lattice structure, and δ is the derivative of the Heaviside function with respect to the level set function.

[0114] (2) The sensitivity of the constraint function with respect to the two sets of design variables is expressed as:

[0115]

[0116]

[0117] In the formula, is the sensitivity of the macrostructure volume constraint with respect to the dual design variables, It is the sensitivity of the volume constraint of the solid structure to its own design variables.

[0118] S5: Optimization model solution and dual design variable update;

[0119] Based on the sensitivity information, the topology optimization model is solved by a gradient-based optimization algorithm, and the design variables are updated. During the solution process, if the convergence criterion is not met, the process returns to step S3. When the convergence criterion is met, the iteration is stopped, and the dual design variable values ​​at this time are taken as the final values.

[0120] Furthermore, a dual optimization criterion method is used for solving the problem, and a moving asymptote optimization algorithm can also be used for solving the model.

[0121] Furthermore, the convergence criterion is to reach a given threshold or reach the maximum number of iterations, which is defined as follows:

[0122]

[0123] In the formula, σ is the given threshold, n max represents the maximum number of given iterations, J(Γ) n is the objective function value of the nth iteration.

[0124] The following are specific examples:

[0125] Example 1

[0126] The optimized structure is a two-dimensional cantilever beam, such as Figure 4 As shown, the size of the two-dimensional cantilever beam is: L×H=400×200, the left side of the design domain structure is fixed, and a concentrated load F=1N is applied vertically downward at the lower right corner. The design domain contains 20×10 unit cells, and the unit cell size is 20×20. Solid unit cells and X-shaped unit cells are used for optimization. The solid-lattice parallel topology optimization method provided by the present invention is used to carry out the optimization design of the two-dimensional cantilever beam. The objective function is to maximize the structural stiffness (minimize the flexibility), the macroscopic structure volume fraction constraint is 0.5, the solid structure volume fraction constraint is 0.3, and the lattice structure is freely optimized under the macroscopic volume constraint. After 57 iterations, the optimization is completed, and the following is obtained. Figure 5 The topological optimization configuration design of the mixed solid and lattice is shown. The solid structure is continuously distributed, and the lattice structure presents a gradient distribution. The structural flexibility converges to 177.65, the macrostructure volume fraction converges to 0.5, and the solid structure volume fraction converges to 0.3. Figure 6 It can be seen from the iteration curve that the algorithm shows good convergence and both dual constraints satisfy the given set values.

[0127] In order to further illustrate the applicability and stability of the method of the present invention, the volume constraint (Vol_solid) of the solid structure is changed and set to Vol_solid: 0, 0.1, 0.2, 0.3, 0.4, 0.5 respectively, and the volume fraction of the macro structure (Vol_Macro) is all set to 0.5, and the optimization is carried out according to the above 6 sets of constraint conditions. The results are as follows Figure 7 As shown in the figure, a clear and correct configuration design can be obtained under each set of constraints, verifying the effectiveness of the method provided by the present invention. As the volume fraction of the solid structure in the design domain increases, the lower the flexibility value (Comp) of the structure, the higher the stiffness of the structure. However, the design of a pure solid structure without considering the lattice has poor robustness and is prone to buckling instability.

[0128] Example 2

[0129] The optimized structure is a two-dimensional Michell beam, such as Figure 8 As shown in the figure, the size of the Michell beam is: L×H=600×200, 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. The design domain contains 30×10 unit cells, and the solid unit cells and X-shaped unit cells are also used for optimization. After the optimization, the topological optimization configuration design of the mixed solid and lattice is obtained. The solid structure is continuously distributed, and the lattice structure presents a gradient distribution, as shown in Fig. 9 After 57 iterations, the structural flexibility converged to 28.48, the macrostructure volume fraction converged to 0.5, and the solid structure volume fraction converged to 0.3. The iteration curve is shown in Fig.10Different structural examples verify the applicability and stability of the full-scale parallel topology optimization method for a solid-lattice hybrid configuration design provided by the present invention.

[0130] Example 3

[0131] The optimized structure is a three-dimensional MBB beam, such as Fig.11 As shown in the figure, the size of the MBB beam is: L×H×W=280×70×42, the bottom of the left and right sides of the design domain are fixed and simply supported, and a vertical downward force load F=10N is applied to the middle of the top. The design domain contains 20×5×3 unit cells, and the unit cell size is selected from three-dimensional solid unit cells and body-centered cubic unit cells, with a size of 14×14×14. After 67 iterations, the optimization is completed, and a topological optimization configuration design of a mixture of solid and lattice is obtained. The solid structure is continuously distributed, and the lattice structure presents a gradient distribution, as shown in Fig.12 The structural flexibility converges to 492007.88, the macrostructure volume fraction converges to 0.5, and the solid structure volume fraction converges to 0.3. The iterative curve is shown in Fig.13 shown.

[0132] The above three-dimensional calculation examples show that the method of the present invention still has good applicability and stability in the topology optimization process of three-dimensional structures.

[0133] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A full-scale parallel topology optimization method for a solid-lattice hybrid configuration, characterized in that: The steps include: S1: Introduce control parameters to construct the level set function of the solid microstructure and lattice microstructure on the unit cell, and then obtain the global parameterized level set function of the solid-lattice hybrid structure; The global parameterized level set function is specifically: Where Φ(x, t) is the level set function of the solid structure, θ(x, t) is the level set function of the lattice structure, T(t) and H(t) are the control parameters of the solid structure and the lattice structure, i.e., the design variables; is the level set function of the solid microstructure with a volume fraction of 1, γ(x) is the level set function of the lattice microstructure with a predefined small volume fraction, is the control coefficient of the entity microstructure level set function, C γ is the control coefficient of the lattice microstructure level set function, N(x) is the linear interpolation shape function; Г(x, t) is the global parameterized level set function of the solid-lattice hybrid macrostructure, the area where Г(x, t)>0 represents the position containing material in the structure, the area where Г(x, t)<0 represents the blank position without material in the structure, the area where Г(x, t)=0 represents the boundary area between material and void in the design domain, D represents the predefined entire design domain, Ω represents the structural evolution area in the optimization, Indicates the boundaries of a structure; S2: A mathematical model for topology optimization is established with the control parameters of the solid structure and the lattice structure as dual design variables, minimization of the overall structural flexibility as the objective function, and the solid structure volume and the macroscopic structure volume as dual constraints; S3: Substitute the global parameterized level set function into the Hamilton-Jacobi partial differential equation to obtain the ordinary differential equation; S4: Based on ordinary differential equations, determine the sensitivity formula of the objective function and constraint conditions with respect to the design variables and obtain sensitivity information; S5: Based on the sensitivity information, the topology optimization model is solved using a gradient-based optimization algorithm to obtain dual design variables, thereby determining the optimal solid-crystal hybrid configuration.

2. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to claim 1, characterized in that: Control coefficient C γ The calculation method is as follows:

3. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to claim 1, characterized in that: Step S2, the topology optimization mathematical model is specifically: find:{T(t),H(t)} min: s.t: Where J(Г) is the overall flexibility of the solid-lattice hybrid structure, ε and u are the strain field and displacement field of the discrete unit in the structure, and B is the material equivalent elastic matrix; Ф (u,v) is the strain energy functional, l Ф (v) is the work done by the external force on the virtual displacement, U is the displacement field of the structure, g(Г) is the volume constraint function of the macro structure, f(Φ) is the volume constraint function of the solid structure, ξ is the given volume fraction constraint value of the macro structure, δ is the given volume fraction constraint value of the solid structure, represents the initial full volume of the design domain, Ω macro is the region of entity-lattice structure evolution during optimization, Ω solid It is the region where the physical structure evolves during optimization; T k (t) represents the design variable of the physical structure on the kth unit cell, H k (t) represents the design variable of the lattice structure on the kth unit cell, and m is the number of unit cells in the design domain.

4. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to claim 3, characterized in that: Step S3, the ordinary differential equation obtained is as follows: Where t is pseudo time, They are the normal velocities of boundary evolution of solid structure and lattice structure during the optimization process, respectively.

5. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to claim 4, characterized in that: Step S4, determining the sensitivity formula of the objective function with respect to the design variables, including: Based on the ordinary differential equation, the normal velocity expression is determined and substituted into the sensitivity formula of the objective function with respect to the pseudo-time t, and the sensitivity formula of the objective function with respect to the design variable is obtained as follows: In the formula, is the sensitivity of the objective function with respect to the physical structure design variables, is the sensitivity of the objective function to the design variables of the lattice structure; δ is the derivative of the Heaviside function with respect to the level set function; G(Г) is the node strain energy.

6. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to claim 5, characterized in that: Step S4, the sensitivity of the constraint conditions to the design variables is listed as: In the formula, is the sensitivity of the macrostructure volume constraint function with respect to the dual design variables, is the sensitivity of the volume constraint function of the solid structure to its own design variables.

7. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to claim 1, characterized in that: Pre-discretization of the design domain, including: The design domain is divided into a certain number of regular quadrilateral regions or regular hexahedral regions, each region matches a microstructure unit cell of a corresponding size, and each region is further divided into fine grids to form a finite element analysis grid; Two sets of meshes are obtained by the above method to match the solid microstructure and the lattice microstructure respectively; two design variables are defined on the nodes of the two sets of meshes respectively.

8. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration according to any one of claims 1 to 7, characterized in that: Step S5, using a gradient-based optimization algorithm to solve the topology optimization model and iteratively update the design variables; when the convergence criterion is met, the iteration is stopped and the dual design variable values ​​at this time are taken as the final values; The convergence criterion is: or n≥n max In the formula, σ is the given threshold, n max is the maximum number of given iterations; J(Γ) n is the objective function value of the nth iteration.

9. A full-scale parallel topology optimization system for a solid-lattice hybrid configuration, characterized in that: It includes a processor, which is used to execute the full-scale parallel topology optimization method of the solid-lattice hybrid configuration as described in any one of claims 1-8.

Images