A topology optimization method for lattice-solid composite structures based on multivariable design

Abstract

The present invention discloses a lattice-solid composite structure topology optimization method based on multivariable design, which solves the problem in the prior art that lattice-solid composite structure optimization cannot realize multivariable design, and has the beneficial effect of expanding the design space of lattice material filling structure. The specific scheme is as follows: A lattice-solid composite structure topology optimization method based on multivariable design, comprising establishing a lattice material structure configuration containing multiple design variables; obtaining macroscopic equivalent physical properties of the lattice material corresponding to different design variables; setting the design definition domain of multiple design variables for the lattice-solid material, and establishing a lattice-solid multi-material interpolation model; constructing a multivariable lattice-solid composite structure topology optimization mathematical model; calculating the objective function value corresponding to the current design variable and the sensitivity information of the current design variable to the objective function and the constraint function; and judging the convergence of the optimization iteration according to the updated design variables.

Description

Technical Field

[0001] The present invention relates to the field of structural optimization, in particular to a topology optimization method for a lattice-solid composite structure based on multivariable design. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In recent years, the rapid development of additive manufacturing technology has enabled the fabrication of structural components with complex geometries. An increasing number of innovative designs have been transformed from concepts into actual products, particularly those using lattice materials. Lattice materials are high-performance, lightweight materials with porous microstructures. They offer multifunctional properties such as heat dissipation, vibration reduction, and sound insulation, and hold broad application prospects in consumer goods, architectural decoration, the automotive industry, and aerospace.

[0004] Structural topology optimization seeks the optimal distribution of materials within the structural design domain based on given boundary conditions and constraints to optimize the target performance of the structure. Using topology optimization methods to design high-performance non-uniform lattice filling structures has become a hot topic in the field of structural optimization design. Compared with complete lattice filling design, lattice-solid composite structures can achieve better mechanical properties. In recent years, there has been some progress in the design of lattice-solid composite structures based on topology optimization methods. However, the inventors found that the existing methods cannot achieve the optimization of lattice-solid composite structures with multivariable design, and cannot achieve the collaborative optimization of lattice-solid materials with multivariable design while constraining the relative density variation range of the lattice materials. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a lattice-solid composite structure topology optimization method based on multivariable design, to realize the optimization of the lattice-solid composite structure with multivariable design, and to achieve the collaborative optimization of the lattice-solid material while constraining the relative density variation range of the lattice material.

[0006] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0007] A topology optimization method for lattice-solid composite structures based on multivariable design includes the following:

[0008] Establishing lattice material structural configurations containing multiple design variables;

[0009] Calculate the data of several sample points, that is, obtain the macroscopic equivalent physical properties of the lattice material corresponding to different design variables;

[0010] Based on a number of sample point data, an interpolation model is established to map the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material;

[0011] Setting the design definition domains of multiple design variables for the lattice-solid material, including the lattice material definition domain and the solid material definition domain, and establishing a lattice-solid multi-material interpolation model based on an interpolation model that maps the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material;

[0012] Construct a mathematical model for topology optimization of multivariable lattice-solid composite structures;

[0013] Based on the lattice-solid multi-material interpolation model and the multivariable lattice-solid composite structure topology optimization mathematical model, the objective function value corresponding to the current design variable and the sensitivity information of the current design variable to the objective function and constraint function are calculated, and the design variables are updated;

[0014] The convergence of the optimization iteration is judged based on the updated design variables. If the iteration converges, the optimization is completed.

[0015] The topology optimization method described above, based on multivariable design, can effectively improve the mechanical properties of lattice-solid composite structures. A lattice-solid multi-material interpolation model is established according to the lattice material definition domain and the solid material definition domain to achieve collaborative optimization of the lattice-solid composite structure with multivariable design.

[0016] A lattice-solid composite structure topology optimization method based on multivariable design as described above, wherein the convergence of the optimization iteration is judged based on the updated design variables, and if the iteration converges, the optimization is completed, otherwise the optimization proceeds to the next step;

[0017] According to the updated design variables, determine whether the current design variables meet the update conditions of the material definition domain. If so, update the material definition domain, otherwise do not update it; and return to calculate the objective function value corresponding to the current design variable and the sensitivity information of the current design variable to the objective function and constraint function.

[0018] As described above, a lattice-solid composite structure topology optimization method based on multivariable design, the multiple design variables refer to the definition parameters of the lattice material, and the definition parameters of the lattice material include the width parameter or length parameter or angle parameter or composition coefficient parameter of the lattice material structural configuration.

[0019] In establishing the structural configuration of lattice materials, the range of variation of design variables is given.

[0020] As described above, in a lattice-solid composite structure topology optimization method based on multivariable design, the macroscopic equivalent physical properties of the lattice material corresponding to different design variables include the relative density of the lattice material and the equivalent elastic matrix of the lattice material.

[0021] In the above-mentioned lattice-solid composite structure topology optimization method based on multivariable design, the fitting relationship of the interpolation model is determined based on the fitting constants calculated based on sample point data and the least squares method and the definition parameters of the lattice material.

[0022] As described above, in a lattice-solid composite structure topology optimization method based on multivariable design, the lattice material definition domain is that multiple design variables are between the minimum value of the definition parameter of the predefined lattice material and the maximum value of the definition parameter of the predefined lattice material.

[0023] As described above, a lattice-solid composite structure topology optimization method based on multivariable design, the solid material definition domain is a maximum value of a plurality of design variables that are greater than the definition parameters of a predefined lattice material. At this time, the plurality of design variables change synergistically, and the range of the synergistic change of the plurality of design variables is between the maximum value of the definition parameters of the lattice material and the maximum value of the design variable change range.

[0024] As described above, a lattice-solid composite structure topology optimization method based on multivariable design is provided, wherein the lattice-solid multi-material interpolation model is obtained based on the lattice material definition domain, the solid material definition domain, the design variables, and an interpolation model that maps the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material.

[0025] As described above, a lattice-solid composite structure topology optimization method based on multivariable design is described. After constructing a multivariable lattice-solid composite structure topology optimization mathematical model, topology optimization structural parameters are defined, and an optimization iteration initial design is set.

[0026] A lattice-solid composite structure topology optimization method based on multivariable design as described above, wherein the material properties corresponding to the design variables at this time are calculated based on the lattice-solid multi-material interpolation model and the multivariable lattice-solid composite structure topology optimization mathematical model, and finite element analysis is performed to calculate the structural displacement, and then the objective function value corresponding to the current design variable is calculated;

[0027] The design variables are updated using the moving evolution method.

[0028] The beneficial effects of the present invention are as follows:

[0029] 1) The present invention provides a topology optimization method based on lattice-solid composite structure design, which can effectively improve the mechanical properties of lattice material-filled structures and greatly expand the design space of lattice material-filled structures.

[0030] 2) The present invention provides a topology optimization method, based on multivariable design, and establishes a lattice-solid multi-material interpolation model according to the lattice material definition domain and the solid material definition domain, thereby realizing the collaborative optimization of the lattice-solid composite structure of multivariable design, and maximizing the design potential of the lattice-solid composite structure; the overall approach has wide applicability to structural optimization problems of various forms of lattice materials and solid composites.

[0031] 3) The present invention sets up a lattice-solid multi-material interpolation model based on the lattice material definition domain and the solid material definition domain, which can effectively control the relative density variation range of the lattice material during the optimization process; and the distribution of the lattice material and the solid material is consistent with the working conditions, combining excellent mechanical properties and the excellent multifunctional properties of the lattice material.

[0032] 4) Based on a number of sample point data, the present invention establishes an interpolation model that maps the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material. This can efficiently predict the material properties corresponding to different design variables, greatly saving calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0034] Figure 1 This is a flow chart of the lattice-solid composite structure topology optimization method based on multivariable design of the present invention;

[0035] Figure 2 is a schematic diagram of design variables in a single structure of the lattice material of the present invention;

[0036] Figure 3 Schematic diagram of the cantilever beam structure and boundary conditions to be optimized in the present invention;

[0037] Figure 4 is a diagram showing the distribution evolution of design variables during the cantilever beam topology optimization process of the present invention;

[0038] Figure 5 It is a structural detail diagram of the cantilever beam topology optimization result of the present invention.

[0039] In the figure: the distances or sizes between parts are exaggerated to show the positions of various parts, and the schematic diagram is for reference only. DETAILED DESCRIPTION

[0040] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0041] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless otherwise clearly indicated in the present invention, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "include" and / or "comprising" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations;

[0042] As introduced in the background technology, there is a problem in the existing technology that it is impossible to achieve the optimization of lattice-solid composite structures with multi-variable design. In order to solve the above technical problems, the present invention proposes a topology optimization method for lattice-solid composite structures based on multi-variable design.

[0043] In a typical embodiment of the present invention, referring to Figure 1 As shown in FIG, a topology optimization method for lattice-solid composite structures based on multivariable design includes the following contents:

[0044] Step 1: Design a lattice material structure configuration containing multiple design variables;

[0045] The multiple design variables refer to definition parameters of the lattice material. The definition parameters of the lattice material can be two, three, four or other numbers. The definition parameters of the lattice material include a width parameter, a length parameter, an angle parameter or a composition coefficient parameter of the structural configuration of the lattice material.

[0046] In establishing the structural configuration of lattice materials, the variation range of the design variables corresponding to the lattice materials is given.

[0047] Specifically, for example Figure 2 The lattice material structure shown in the figure contains four design variables: α, β, γ, and δ, which correspond to the widths of the four rods in the lattice material structure. The range of these four design variables is defined as:

[0048] l1≤α, β, γ, δ≤l2 (1)

[0049] Wherein, l1 and l2 are respectively the minimum value and the maximum value of the definition parameter of the predefined lattice material in the lattice material structure, that is, the minimum value and the maximum value of the definition parameter of the predefined lattice material, that is, the minimum value and the maximum value of the predefined rod width.

[0050] Step 2: Calculate the data of several sample points, that is, obtain the macroscopic equivalent physical properties of the lattice material corresponding to different design variables.

[0051] Specifically, the macroscopic equivalent physical properties of the lattice material include the relative density ρ of the lattice material L and the equivalent elastic matrix D of the lattice material L The relative density of the lattice material ρ L :

[0052]

[0053] Where V lattice is the volume of the lattice material structure, V domain The volume of the design domain for the lattice material structure.

[0054] Equivalent elastic matrix D of lattice material L It can be calculated based on existing numerical homogenization methods.

[0055] Step 3: Based on the data of several sample points, establish an interpolation model that maps the mathematical relationship between the design variables in the lattice material and its macroscopic equivalent physical properties. The fitting relationship of the interpolation model is:

[0056]

[0057] Where, is the equivalent elastic matrix D L The coefficient in u i (i=1-15) is the fitting constant calculated based on the sample points and the least squares method.

[0058] Step 4: Set the design variable definition domains of multiple design variables for lattice-solid materials, namely the lattice material definition domain and the solid material definition domain, and establish a lattice-solid multi-material interpolation model based on the interpolation model that maps the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material.

[0059] Specifically, the domain of the lattice material is defined as the four design variables are between the predefined minimum rod width and the minimum rod width, and at this time the four variables are relatively independent, that is, l1≤α, β, γ, δ≤l2;

[0060] The domain of the solid material definition is that all four design variables are greater than the predefined maximum rod width l2, and at this time, the four design variables vary in a coordinated manner, and the maximum value of the four design variable variation range is set to l3, that is, l2 < α = β = γ = δ ≤ l3. It should be noted that when α = β = γ = δ = l3, corresponding to the complete solid material properties, the material property penalty can be applied to force the corresponding design variables of the solid material to converge to the maximum value of the design variable variation range l3 during the optimization process.

[0061] The lattice-solid multi-material interpolation model includes the equivalent elastic matrix and relative density information of the lattice material. The constructed lattice-solid multi-material interpolation model is as follows:

[0062]

[0063] Where, is the material equivalent elastic matrix D in the multi-material interpolation model E The coefficient in , ρ E is the relative density, p is the material property penalty coefficient, and ω are constants in the interpolation model, which can be obtained by solving the corresponding material properties when α=β=γ=δ=l2 and α=β=γ=δ=l3.

[0064] Step 5: Construct a mathematical model for the topology optimization of a multivariable lattice-solid composite structure. Taking the topology optimization model of minimizing structural flexibility under the constraint of volume fraction as an example, the mathematical model for the topology optimization of a multivariable lattice-solid composite structure is:

[0065]

[0066]

[0067] st:F=KU, (5)

[0068]

[0069] l1≤α E , β E , γ E , δ E ≤l3, E=1, 2, ..., N.

[0070] in, It represents the total function of design variables, including the four design variable information in all finite element units, N is the number of finite element units, C is the structural flexibility, F is the load vector of the structure, U is the displacement, K is the total stiffness matrix of the structure, and U S is the unit displacement, K E is the element stiffness matrix, V is the total volume of the structure during the optimization process, V0 is the volume of the structural design domain, f is the volume fraction constraint, l1 and l3 are the lower and upper limits of the design variable change, respectively.

[0071] Step 6: Define the topology optimization structural parameters and set the initial design for optimization iteration;

[0072] Specifically, the initial design is set as a uniform filling design of lattice material with a set relative density, and the variation range of the four design variables is defined as the lattice material definition domain.

[0073] Step 7: Based on the lattice-solid multi-material interpolation model constructed in step 4, calculate the material properties corresponding to the design variables at this time, and perform finite element analysis to calculate the structural displacement, calculate the objective function value corresponding to the current design variable and the sensitivity information of the current design variable to the objective function and constraint function.

[0074] Specifically, the sensitivity of the current design variable to the objective function is:

[0075]

[0076] Where x E is the total function of the unit design variables, including the four design variable information in the unit, B is the unit strain matrix, Ω E is the finite element unit volume, It can be calculated using the lattice-solid multi-material interpolation model constructed in step 4.

[0077] The sensitivity of the design variables to the constraint function is:

[0078]

[0079] It can be calculated using the lattice-solid multi-material interpolation model constructed in step 4.

[0080] Step 8: Based on the sensitivity information obtained in step 7, the design variables are updated using the MMA algorithm (moving asymptote method).

[0081] Step 9: Determine whether the updated design variables have converged. If not, proceed to Step 10. If so, terminate the solution and output the topology optimization results, which are the optimal distributions of the four design variables at each location in the macrostructure.

[0082] Specifically, the sign of iterative convergence is that the change value of the design variable after being updated by the optimization algorithm is less than the set value or the maximum number of iterations exceeds the preset number.

[0083] Step 10: Input the updated design variables into the checking mechanism of the multivariate material domain and return to step 7.

[0084] Specifically, the checking mechanism of the multivariate material domain is as follows:

[0085] When the multivariable material definition domain is the lattice material definition domain, if the four variables updated by the optimization algorithm simultaneously reach the upper limit of the lattice material definition domain, that is, α=β=γ=δ=l2, then in the next iteration, the material definition domain is changed to the solid material definition domain, otherwise, the material definition domain remains unchanged; when the material definition domain is the solid material definition domain, if the four variables updated by the optimization algorithm simultaneously reach the lower limit of the solid material definition domain, that is, α=β=γ=δ=l2, then in the next iteration, the material definition domain is changed to the lattice material definition domain, otherwise, the material definition domain remains unchanged.

[0086] The following is a further explanation of the lattice-solid composite structure topology optimization method based on multivariable design proposed by the present invention with reference to examples.

[0087] All physical quantities used in this embodiment are assumed to be dimensionless. The dimensions and boundary conditions of the two-dimensional cantilever beam structure are as follows: Figure 3 As shown in the figure, the structure size is defined as 40×20, the finite element mesh size is 1×1, and the volume constraint is 50% of the original. The initial design is to use four lattice materials with equal rod width and relative density of 0.5 for uniform filling.

[0088] Figure 4 It is the evolution of the four design variables during the optimization process. Figure 5 The final optimized lattice-solid composite structure design details are shown.

[0089] from Figure 4 and Figure 5 As can be seen, the multivariable design-based topology optimization method for lattice-solid composite structures provided by the present invention achieves lattice-solid material collaborative optimization while constraining the density variation range of the lattice material, greatly expanding the design space for lattice material-filled structures. In the optimized structure, the solid material and high-density lattice material are distributed in locations with high strain energy in the structural units. The distribution of the lattice and solid materials is consistent with the working conditions, combining excellent mechanical properties with the excellent multifunctional properties of the lattice material. Furthermore, the present topology optimization method has high optimization efficiency and good structural connectivity.

[0090] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A topology optimization method for lattice-solid composite structures based on multivariable design, characterized in that: Includes the following: Establishing lattice material structural configurations containing multiple design variables; Calculate the data of several sample points, that is, obtain the macroscopic equivalent physical properties of the lattice material corresponding to different design variables; Based on a number of sample point data, an interpolation model is established to map the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material; Setting the design definition domains of multiple design variables for the lattice-solid material, including the lattice material definition domain and the solid material definition domain, and establishing a lattice-solid multi-material interpolation model based on an interpolation model that maps the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material; Construct a mathematical model for the topology optimization of a multivariable lattice-solid composite structure; Construct a mathematical model for the topology optimization of a multivariable lattice-solid composite structure. Taking the topology optimization model of minimizing structural flexibility under the set volume fraction constraint as an example, the mathematical model for the topology optimization of a multivariable lattice-solid composite structure is: in, Represents the total function of design variables, which contains the four design variable information in all finite element units. is the number of finite element elements, is the structural flexibility, is the load vector acting on the structure, is the displacement, is the total structural stiffness matrix, is the unit displacement, is the element stiffness matrix, is the total volume of the structure during the optimization process, is the volume of the structural design domain, is the volume fraction constraint, and are the lower and upper limits of the design variable variation, respectively; Based on the lattice-solid multi-material interpolation model and the multivariable lattice-solid composite structure topology optimization mathematical model, the objective function value corresponding to the current design variable and the sensitivity information of the current design variable to the objective function and constraint function are calculated, and the design variables are updated; The convergence of the optimization iteration is judged based on the updated design variables. If the iteration converges, the optimization is completed.

2. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The convergence of the optimization iteration is judged according to the updated design variables. If the iteration converges, the optimization is completed, otherwise the optimization proceeds to the next step. According to the updated design variables, determine whether the current design variables meet the update conditions of the material definition domain. If so, update the material definition domain; otherwise, do not update. And return to calculate the objective function value corresponding to the current design variable and the sensitivity information of the current design variable to the objective function and constraint function.

3. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The multiple design variables refer to definition parameters of the lattice material, and the definition parameters of the lattice material include width parameters, length parameters, angle parameters, or composition coefficient parameters of the lattice material structure configuration; In establishing the structural configuration of lattice materials, the range of variation of design variables is given.

4. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The macroscopic equivalent physical properties of the lattice material corresponding to the different design variables include the relative density of the lattice material and the equivalent elastic matrix of the lattice material.

5. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 3, characterized in that: The fitting relationship of the interpolation model is determined based on the fitting constants calculated based on the sample points and the least square method and the definition parameters of the lattice material.

6. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The lattice material definition domain is a domain where multiple design variables are between a minimum value of a definition parameter of a predefined lattice material and a maximum value of a definition parameter of the predefined lattice material.

7. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The solid material definition domain is a domain in which multiple design variables are all greater than the maximum value of the definition parameters of the predefined lattice material. At this time, the multiple design variables change synergistically, and the range of the synergistic change of the multiple design variables is between the maximum value of the definition parameters of the lattice material and the maximum value of the design variable change range.

8. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The lattice-solid multi-material interpolation model is obtained based on the lattice material definition domain, the solid material definition domain, the design variables and the interpolation model that maps the mathematical relationship between the design variables in the lattice material and the physical properties of the lattice material.

9. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: After constructing the multivariable lattice-solid composite structure topology optimization mathematical model, topology optimization structural parameters are defined, and an optimization iteration initial design is set.

10. The method for topology optimization of a lattice-solid composite structure based on multivariable design according to claim 1, characterized in that: The method is based on the lattice-solid multi-material interpolation model and the multivariable lattice-solid composite structure topology optimization mathematical model to calculate the material properties corresponding to the design variables at this time, perform finite element analysis, calculate the structural displacement, and then calculate the objective function value corresponding to the current design variables; The design variables are updated using the moving evolution method.

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