A complex variable density lattice mirror homogenization force-thermal coupling fast simulation method

Abstract

This invention discloses a rapid simulation method for homogenized mechanical-thermal coupling of complex variable-density lattice mirrors, solving the problems of limited computational resources, frequent errors, and inaccuracies in the mechanical-thermal coupling simulation of complex variable-density lattice mirrors. In this invention, equivalent elastic performance models and equivalent thermal conductivity models at the microscale are constructed. Through a custom material subroutine, the spatial relative density scalar field is dynamically converted into a continuously changing equivalent elastic modulus scalar field and an equivalent thermal conductivity scalar field. This spatially variable property field accurately maps the influence of density gradient on local stiffness and heat conduction path, ensuring the realism and physical rigor of the deformation behavior of the macroscopic continuum under mechanical-thermal coupling loads.

Description

Technical Field

[0001] This invention relates to space optical remote sensors and advanced optomechanical structure optimization methods, specifically to a rapid simulation method for homogenization of complex variable density lattice mirrors using force-thermal coupling. Background Technology

[0002] With the rapid development of space optical remote sensing technology, the demand for large-aperture, high-resolution space optical cameras is increasing. As the core optical component of a space optical camera, the surface accuracy of the mirror directly determines the imaging quality of the entire system. To meet the stringent weight restrictions of space launch vehicles and to ensure the high stiffness and thermal stability of the mirror under complex space thermal environments and gravity release, the mechanical-thermal coupling co-optimization design has become an important aspect of mirror development.

[0003] In recent years, Triply Periodic Minimal Surfaces (TPMS) lattice structures have shown great application potential in the optimization design of mirror structures due to their smooth and continuous surfaces, lack of stress concentration, good self-support, and excellent specific stiffness and thermal conductivity. To further explore the performance limits of materials, advanced optomechanical structure optimization design often no longer uses uniformly distributed TPMS lattices, but instead generates spatially continuously varying density TPMS lattice structures (e.g., high density near support holes and low density at the edges) based on the stress and heat transfer requirements of different parts of the mirror.

[0004] However, when conducting force-thermal coupling simulation analysis on such complex variable-density TPMS mirrors, existing conventional finite element calculation methods face insurmountable engineering and technical bottlenecks, specifically in the following aspects:

[0005] The demand for computing resources is increasing exponentially, exceeding the capabilities of conventional hardware. Traditional finite element simulations typically require meshing the full-scale solid model of the mirror. TPMS microstructures possess extremely complex spatial surface morphologies, and their variable density design causes the cell wall thickness to constantly change in space. To capture these extremely complex lattice structures, tens of millions or even hundreds of millions of high-order tetrahedral meshes must be generated. This exponentially increasing number of mirror meshes leads to problems such as memory overflow and extremely long solution times, far exceeding the memory and computing power limits of conventional high-performance workstations.

[0006] Microscopic meshes are highly susceptible to distortion, making convergence extremely difficult in force-thermal coupling analysis. In thin-walled regions, low-density porous regions, and at the interface with the macroscopic outer shell of variable-density TPMS, traditional mesh generation algorithms readily produce elongated, distorted, and low-quality distorted meshes. During force-thermal coupling simulations, the superposition of multiple boundary conditions, including heat conduction, thermal stress deformation, and gravity, leads to singular or ill-conditioned finite element stiffness matrices, causing severe non-convergence problems and forcing simulation interruptions.

[0007] Existing homogenization methods have limitations, lacking accurate characterization of the equivalent mechanical-thermal coupling performance of variable-density lattice mirrors. To address computational limitations, some researchers have proposed homogenization methods that treat the lattice structure as equivalent to a solid material. However, most existing homogenization simulations are limited to "uniform density lattices," assigning a single equivalent material property to each unit cell. For the "variable-density field" generated by optimization design, this single equivalent method completely ignores the significant impact of local density gradients on structural stiffness and heat conduction paths, leading to substantial errors in macroscopic mechanical-thermal coupling simulation results and failing to provide reliable guidance for the accurate design of mirrors. Summary of the Invention

[0008] The purpose of this invention is to solve the problems of limited computational resources, easy calculation errors, and inaccurate calculations in the mechanical-thermal coupling simulation of complex variable-density lattice mirrors, and to provide a homogenized mechanical-thermal coupling fast simulation method for complex variable-density lattice mirrors.

[0009] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0010] A rapid simulation method for homogenization of complex variable-density lattice mirrors using force-thermal coupling is characterized by the following steps:

[0011] S1. Within the modeling system, construct a macroscopic reflector geometric model, and spatially separate the reflector geometric model into two continuous entities: the outer shell region and the internal design domain.

[0012] S2. Generate unit cell models with different wall thicknesses based on the isosurface function in the modeling system, calculate the relative density of each unit cell model, and use a nonlinear regression algorithm to fit and establish the mapping relationship between the relative density of the unit cell model and the wall thickness of the unit cell model.

[0013] S3. Construct a relative density scalar field within the internal design domain;

[0014] S4. For cell models with different relative densities, apply unit strain loads independently, solve for the equivalent elastic matrix, calculate the equivalent elastic modulus based on the equivalent elastic matrix, fit the equivalent elastic modulus of the cell model with the relative density, and construct the equivalent elastic performance model.

[0015] S5. For unit cell models with different relative densities, apply unit temperature gradient loads independently, solve the equivalent thermal conductivity matrix, fit the values ​​in the equivalent thermal conductivity matrix with the relative density of the unit cell model, and construct an equivalent thermal conductivity performance model.

[0016] S6. Using the relative density scalar field, the equivalent elastic modulus scalar field and the equivalent thermal conductivity scalar field are dynamically generated in space by combining the equivalent elastic performance model and the equivalent thermal conductivity performance model, respectively. The internal design domain is given equivalent material properties, and the matrix material of the shell region is given isotropic properties. The mapping relationship between the relative density of the cell model and the wall thickness of the cell model is combined to obtain the macro equivalent model. The macro equivalent model is meshed to obtain the macro equivalent finite element model.

[0017] S7. Apply actual thermodynamic boundary conditions to the macroscopic equivalent finite element model, perform finite element mechanical-thermal coupling calculations, solve the temperature field distribution by calling the equivalent material properties, and determine the macroscopic displacement field based on the temperature field distribution.

[0018] S8. Extract the nodal normal displacement data within the effective diameter range of the deformed macroscopic equivalent finite element model based on the macroscopic displacement field, and fit and calculate the surface accuracy of the reflecting mirror.

[0019] Furthermore, in S1, the outer shell area includes a mirror panel, a central light-transmitting hole, a back support hole, and an outer ring.

[0020] Furthermore, in S2, the expression for the isosurface function is:

[0021]

[0022] In the formula, Let C represent the isosurface function, and let C represent the isosurface constant. () indicates the coordinate positions of the X-axis, Y-axis, and Z-axis in a three-dimensional coordinate system.

[0023] Furthermore, the relative density scalar field described in S3 is constructed based on the distance field between any spatial node in the internal design domain and the back support hole, or based on the density field obtained from the topology optimization of the internal design domain, or based on an arbitrary function field.

[0024] Furthermore, S3 specifically refers to:

[0025] The distance field between any spatial node in the internal design domain and the back support hole is mapped to a relative density scalar field through a decreasing linear function, where the value of the relative density scalar field ranges from 0.2 to 0.8.

[0026] Furthermore, S4 specifically refers to:

[0027] S41. Perform finite element mesh generation on the cell model of each relative density, and independently apply 6 macroscopic unit strain loads along the three orthogonal normal directions X, Y, and Z and the three shear directions XY, YZ, and XZ at the boundary of the cell model. Obtain the stress results through finite element analysis and solve for the equivalent elastic matrix D that reflects the mechanical properties of the structure.

[0028] S42. Calculate the equivalent elastic modulus of the unit cell model for each relative density based on the equivalent elastic matrix D. ;

[0029] S43. By fitting the relative density of the unit cell model to the corresponding equivalent elastic modulus using the exponential function form of the Gibson-Ashby model, a continuous mathematical mapping function is constructed, resulting in the equivalent elastic performance model of the unit cell model, expressed as:

[0030] ;

[0031] In the formula, The relative density is represented by the unit cell model. The elastic modulus of a solid material; Let n be the density of the solid material, and n represent the sensitivity index.

[0032] Furthermore, S5 specifically refers to:

[0033] S51. Perform finite element mesh generation for each relative density unit cell model, apply unit temperature gradient load independently along the X direction, extract the total heat flux density through the boundary of the unit cell model through steady-state solution, and calculate the equivalent thermal conductivity matrix describing the thermal conductivity characteristics of the unit cell model.

[0034] S52. Using each relative density of the unit cell model as the independent variable and the value in the equivalent thermal conductivity matrix corresponding to each relative density as the dependent variable, a continuous mathematical mapping function is fitted by a polynomial to construct the equivalent thermal conductivity performance model of the unit cell model.

[0035] The feature is that, in S6, the mesh used in the meshing of the macroscopic equivalent model is a high-order tetrahedral finite element mesh.

[0036] Furthermore, in S7, the actual thermodynamic boundary conditions include the actual fixed constraint of the reflector, the actual mechanical load, and the actual heat flow load.

[0037] Furthermore, in S1, the construction of the macroscopic mirror geometric model specifically involves: determining the basic parameters of the mirror according to the optical design requirements, and constructing the macroscopic mirror geometric model in combination with the actual working conditions.

[0038] Compared with the prior art, the present invention has the following beneficial technical effects:

[0039] 1. Significantly reduces computational resource consumption, breaking through the computational bottleneck of complex variable-density lattice reflectors. This invention equates the complex internal design domain to a macroscopic continuum, allowing for modeling using a relatively coarse high-order tetrahedral finite element mesh. During force-thermal coupling simulation, the solver directly calls the equivalent material properties at each location within the internal design domain, enabling rapid solution of the macroscopic nodal displacement field of the entire reflector in a very short time, greatly saving computation time and hardware costs.

[0040] 2. Eliminates mesh distortion and computational non-convergence caused by microscopic porosity. This invention abandons the direct subdivision of complex microscopic real geometry and fundamentally avoids the problem of microscopic matrix mesh generation by establishing a macroscopic equivalent finite element model, thus ensuring the mesh quality of the finite element model and the extremely high stability of the mechanical-thermal coupling calculation.

[0041] 3. High-fidelity reproduction of the non-uniform force and heat conduction characteristics of variable-density lattices, ensuring solution accuracy. Unlike traditional methods that simplify the entire lattice region as a single homogeneous material, this invention constructs equivalent elastic performance models and equivalent heat conduction performance models at the microscale. Through a custom material subroutine, the spatial relative density scalar field is dynamically converted into continuously varying equivalent elastic modulus scalar fields and equivalent thermal conductivity scalar fields. This spatially variable property field accurately maps the influence of density gradient on local stiffness and heat conduction path, ensuring the realism and physical rigor of the deformation behavior of the macroscopic continuum under force-thermal coupling loads. Attached Figure Description

[0042] Figure 1 This is a flowchart of an embodiment of the rapid simulation method for homogenization of complex variable density lattice mirrors using force-thermal coupling according to the present invention.

[0043] Figure 2 This is a schematic diagram of the macroscopic mirror geometric model in an embodiment of the rapid simulation method for homogenization of complex variable density lattice mirrors using force-thermal coupling according to the present invention.

[0044] Figure 3 This is a diagram illustrating the composition of the macroscopic mirror geometric model in an embodiment of the rapid simulation method for homogenization, force-thermal coupling, and homogenization of complex variable density lattice mirrors according to the present invention.

[0045] Figure 4 This is a schematic diagram of a variable density lattice mirror model constructed with a relative density scalar field in an embodiment of a rapid simulation method for homogenization, force-thermal coupling, and homogenization of a complex variable density lattice mirror according to the present invention.

[0046] Figure 5 This is a graph showing the equivalent elastic modulus versus relative density mapping function of a unit cell model in an embodiment of a rapid simulation method for homogenization and thermal coupling of complex variable density lattice mirrors according to the present invention.

[0047] Figure 6 This is a graph showing the equivalent thermal conductivity versus relative density mapping function of the unit cell model in an embodiment of the rapid simulation method for homogenization of complex variable density lattice mirrors according to the present invention.

[0048] Figure 7 This is a temperature field cloud map of the macroscopic equivalent finite element model for force-thermal coupling simulation analysis in an embodiment of a rapid simulation method for homogenizing complex variable density lattice mirrors according to the present invention.

[0049] Among them, (a) is the temperature field cloud map of the force-thermal coupling simulation analysis of the mirror surface; (b) is the temperature field cloud map of the force-thermal coupling simulation analysis of the back of the mirror.

[0050] Figure 8 This is a displacement cloud diagram of the macroscopic equivalent finite element model for force-thermal coupling simulation analysis in an embodiment of the rapid simulation method for homogenization of complex variable density lattice mirrors of the present invention.

[0051] Among them, (a) is the displacement cloud map of the force-thermal coupling simulation analysis of the mirror surface; (b) is the displacement cloud map of the force-thermal coupling simulation analysis of the back of the reflector.

[0052] The attached figures are labeled as follows:

[0053] 1-Mirror panel; 2-Central light-transmitting hole; 3-Back support hole; 4-Outer ring; 5-Internal design area; 6-Outer shell area. Detailed Implementation

[0054] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0055] This embodiment provides a rapid simulation method for homogenizing the force-thermal coupling of complex variable-density lattice mirrors, such as... Figure 1 As shown, it includes the following steps:

[0056] S1. Determine the basic parameters of the reflector (including reflector aperture, mirror curvature, mirror thickness, etc.) according to the optical design requirements. Select the reflector material, back structure, and support scheme based on the actual working conditions. Construct a macroscopic geometric model of the reflector using 3D modeling software, such as... Figure 2 and Figure 3 As shown, the reflector in this embodiment adopts a three-point back support method, which separates the geometric model of the reflector into two continuous entities in space: the internal design domain 5 and the outer shell region 6. The outer shell region 6 includes a mirror panel 1, a central light-transmitting hole 2, three back support holes 3 and an outer ring 4, wherein the three back support holes 3 are distributed at 120 degrees on the back plate of the mirror panel 1.

[0057] S2. In the modeling software, the TPMS structure is constructed using isosurface functions. To generate, Let C represent the isosurface function, and C represent the isosurface constant; the isosurface is the boundary between solid material and pores. In this embodiment, the isosurface function can generate unit cell models with different wall thicknesses, and then the relative density of each unit cell model can be calculated. A nonlinear regression algorithm is used to fit and establish the mapping relationship between the relative density of the unit cell model and the wall thickness of the unit cell model.

[0058] In this embodiment, the cell model can be of various types, such as TPMS Gyroid, Diamond, Primitive, Schwarz, IWP, and Lidinoid.

[0059] Taking the TPMS Gyroid-type unit cell model as an example, its mathematical expression is:

[0060]

[0061] In the formula, Represents the isosurface function of the TPMS Gyroid-type unit cell model. These represent the periodic dimensions (i.e., the size of the unit cell model) of the TPMS Gyroid type unit cell model along the X, Y, and Z axes in a three-dimensional coordinate system, respectively. () represents the coordinate positions of the X, Y, and Z axes in a three-dimensional coordinate system. The input parameter for generating a TPMS Gyroid-type unit cell model is usually the wall thickness. The wall thickness parameter controls the degree of surface offset, which in turn determines the relative density of the unit cell.

[0062] Because the relationship between relative density and wall thickness in the structure of TPMS unit cells is complex and nonlinear, there is no simple formula that can be directly applied. Therefore, it is necessary to establish a mapping relationship between the relative density and wall thickness parameters of TPMS unit cells. Taking a TPMS Gyroid-type unit cell model with dimensions of 10mm × 10mm × 10mm as an example, a series of unit cell models with wall thicknesses ranging from 1 to 4mm and a step size of 0.1mm are generated; the actual relative density of each unit cell thickness is calculated; and the mapping relationship between relative density and wall thickness is fitted using a polynomial nonlinear regression algorithm.

[0063] S3. Construct a relative density scalar field within the internal design domain. This can be done by constructing a density field based on the distance field between any spatial node in the internal design domain and the back support hole, or based on the density field obtained from the topology optimization of the internal design domain, or based on an arbitrary function field.

[0064] In this embodiment, the distance field based on the three back support holes 3 is mapped to the relative density scalar field of the internal design domain through a linear function. The relative density of the unit cell model is set to 0.8 at a distance of 0 mm from the outer wall of the support hole, and 0.2 at a distance of 30 mm from the outer wall of the support hole; a linear transition is observed between 0 and 30 mm. This achieves a variable density effect where the relative density of the unit cell model decreases with increasing distance from the support hole. The variable density lattice mirror model constructed from this relative density scalar field is shown below. Figure 4 As shown, this model is for visualization purposes only.

[0065] Linear mapping function:

[0066] (0≤L≤30);

[0067] The internal design domain is divided into regions based on its distance from the three back support holes 3. L is the distance from a point in the internal design domain to the outer wall of the corresponding back support hole 3 in that region. The relative density is represented by the unit cell model.

[0068] S4. According to Hooke's Law, the stress of the element... Elasticity matrix and strain The following relationship exists:

[0069] =D ;

[0070] Therefore, a certain amount of displacement (i.e. strain) is applied to the unit cell model. The corresponding stress can be obtained through finite element calculation. This allows us to inversely calculate the values ​​in the elasticity matrix D.

[0071] Based on the above analysis, in this embodiment, unit strain loads are applied independently to unit cell models with different relative densities, the equivalent elastic matrix is ​​solved, the equivalent elastic modulus is calculated based on the equivalent elastic matrix, and the equivalent elastic modulus of the unit cell model is fitted with the relative density to construct an equivalent elastic performance model; specifically:

[0072] S41. Perform finite element mesh generation on the cell model of each relative density, and independently apply 6 macroscopic unit strain loads (i.e., apply strain in only one direction at a time, and set the other strains to 0) along the three orthogonal normal directions X, Y, and Z and the three shear directions XY, YZ, and XZ at the boundary of the cell model. Obtain the stress results through finite element analysis and solve for the equivalent elastic matrix D that reflects the mechanical properties of the structure.

[0073] For example, the TPMS Gyroid-type unit cell model has perfect cubic symmetry in space. This means that its mechanical properties are exactly the same in the three orthogonal directions of X, Y, and Z.

[0074] The equivalent elastic matrix D of the unit cell is expressed as:

[0075]

[0076] Among them, D 11 D 12 D 44 All values ​​are from the equivalent elasticity matrix D, where D is a value from the equivalent elasticity matrix D. 11 D represents the stress required to produce a unit strain along the x-direction. 12 D represents the stress required in the x-direction to maintain a constant length in the x-direction when a unit strain is generated along the y-direction. 44 This represents the shear stress required in the x-direction to produce a unit shear strain in the yz-plane.

[0077] S42. Calculate the equivalent elastic modulus of the unit cell model for each relative density based on the equivalent elastic matrix D. .

[0078] Since the TPMS Gyroid-type unit cell model is approximately isotropic, it is only necessary to extract and The value of is then its equivalent elastic modulus. The expression can be represented as:

[0079] .

[0080] S43. By fitting the relative density of the unit cell model to the corresponding equivalent elastic modulus using the exponential function form of the Gibson-Ashby model, a continuous mathematical mapping function is constructed to establish the equivalent elastic performance model of the unit cell model, such as... Figure 5 As shown, the expression is:

[0081] ;

[0082] In the formula, The relative density is represented by the unit cell model. The elastic modulus of a solid material; Let n be the density of the solid material, and n represent the sensitivity index.

[0083] S5. For unit cell models with different relative densities, apply a unit temperature gradient load independently, solve for the equivalent thermal conductivity matrix, and fit the values ​​in the equivalent thermal conductivity matrix with the relative density of the unit cell model to construct an equivalent thermal conductivity performance model; specifically:

[0084] S51. According to Fourier's law, the thermal conductivity of the TPMS Gyroid-type unit cell model... Heat flux density and temperature gradient The relationship between them can be represented as:

[0085] .

[0086] For each relative density unit cell model, a finite element mesh is generated, and a unit temperature gradient load is applied independently along the X direction (i.e., The total heat flux density passing through the boundary of the unit cell model is extracted by steady-state solution, and the equivalent thermal conductivity matrix describing the thermal conductivity characteristics of the unit cell model is calculated.

[0087] S52. Taking each relative density of the unit cell model as the independent variable and the values ​​in the equivalent thermal conductivity matrix corresponding to each relative density as the dependent variable, a continuous mathematical mapping function is fitted using a polynomial to construct the equivalent thermal conductivity performance model of the unit cell model, such as... Figure 6 As shown.

[0088] S6. Using the relative density scalar field, combined with the equivalent elastic performance model and the equivalent thermal conductivity performance model, the equivalent elastic modulus scalar field and the equivalent thermal conductivity scalar field that are continuously varying in space are dynamically generated. The internal design domain is given equivalent material properties, and the shell region is given isotropic properties of the matrix material (AlSi10Mg) to obtain the macroscopic equivalent model. The macroscopic equivalent model is divided into a high-order tetrahedral finite element mesh. The mesh nodes of the shell region mesh and the internal design domain mesh are kept to share, so as to ensure the continuity of the physical field; thus, the macroscopic equivalent finite element model is obtained.

[0089] S7. Apply actual thermodynamic boundary conditions to the macroscopic equivalent finite element model. These conditions include applying fixed constraints to the three back support holes 3 distributed at 120-degree angles on the back plate of the mirror panel 1, adding a self-weight load along the vertical direction of the optical axis, and a heat flow load uniformly distributed on the mirror surface. Perform finite element mechanical-thermal coupling calculations on the macroscopic equivalent finite element model. Use the solver to call the equivalent material properties to solve for the temperature field distribution, and determine the macroscopic displacement field based on the temperature field distribution. Perform mechanical-thermal coupling simulation analysis of the macroscopic equivalent finite element model, as shown in the temperature field cloud diagram. Figure 7 As shown, the displacement contour plot of the macroscopic equivalent finite element model under force-thermal coupling simulation analysis is as follows: Figure 8 As shown.

[0090] according to Figure 7 and Figure 8 It can be known that: Figure 7 The temperature field gradient is extremely small, indicating that the reflector structure has good thermal conductivity; Figure 8 The overall deformation is at the submicron level, consistent with the mechanical and thermal analysis characteristics of precision optical mirrors. Based on this macroscopic displacement field, the mirror nodal displacement data extracted in subsequent steps can accurately and quantitatively reflect the local deformation effects of mirror support and mechanical and thermal load conditions on the mirror surface.

[0091] S8. Extract the nodal normal displacement data within the effective aperture range of the deformed macro equivalent finite element model (within the effective aperture range of the reflector) based on the macro displacement field. Use Zernike polynomials to fit the nodal normal displacement data to obtain the total displacement field. Separate and filter out rigid body displacements from the total displacement field, extract the uncompensated residual distortion displacements, and calculate the surface accuracy of the reflector (RMS value and PV value).

[0092] Through the above methods, this invention provides a rapid simulation method for homogenized mechanical-thermal coupling of complex variable-density lattice mirrors, constructing equivalent elastic performance models and equivalent thermal conductivity models at the microscale. By using a custom material subroutine, the spatial relative density scalar field is dynamically converted into a continuously changing equivalent elastic modulus scalar field and an equivalent thermal conductivity scalar field. This spatially variable property field accurately maps the influence of the density gradient on local stiffness and heat conduction path, ensuring the realism and physical rigor of the deformation behavior of the macroscopic continuum under mechanical-thermal coupling loads.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A rapid simulation method for homogenization, force, and thermal coupling of complex variable-density lattice mirrors, characterized in that, Includes the following steps: S1. Within the modeling system, construct a macroscopic reflector geometric model, and spatially separate the reflector geometric model into two continuous entities: the outer shell region and the internal design domain. S2. Generate unit cell models with different wall thicknesses based on the isosurface function in the modeling system, calculate the relative density of each unit cell model, and use a nonlinear regression algorithm to fit and establish the mapping relationship between the relative density of the unit cell model and the wall thickness of the unit cell model. S3. Construct a relative density scalar field within the internal design domain; S4. For cell models with different relative densities, apply unit strain loads independently, solve for the equivalent elastic matrix, calculate the equivalent elastic modulus based on the equivalent elastic matrix, fit the equivalent elastic modulus of the cell model with the relative density, and construct the equivalent elastic performance model. S5. For unit cell models with different relative densities, apply unit temperature gradient loads independently, solve the equivalent thermal conductivity matrix, fit the values ​​in the equivalent thermal conductivity matrix with the relative density of the unit cell model, and construct an equivalent thermal conductivity performance model. S6. Using the relative density scalar field, the equivalent elastic modulus scalar field and the equivalent thermal conductivity scalar field are dynamically generated in space by combining the equivalent elastic performance model and the equivalent thermal conductivity performance model, respectively. The internal design domain is given equivalent material properties, and the matrix material of the shell region is given isotropic properties. The mapping relationship between the relative density of the cell model and the wall thickness of the cell model is combined to obtain the macro equivalent model. The macro equivalent model is meshed to obtain the macro equivalent finite element model. S7. Apply actual thermodynamic boundary conditions to the macroscopic equivalent finite element model, perform finite element mechanical-thermal coupling calculations, solve the temperature field distribution by calling the equivalent material properties, and determine the macroscopic displacement field based on the temperature field distribution. S8. Extract the nodal normal displacement data within the effective diameter range of the deformed macroscopic equivalent finite element model based on the macroscopic displacement field, and fit and calculate the surface accuracy of the reflecting mirror.

2. The rapid simulation method for homogenization, force-thermal coupling, of a complex variable-density lattice mirror according to claim 1, characterized in that: In S1, the outer shell area includes a mirror panel, a central light-transmitting hole, a back support hole, and an outer ring.

3. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 1, characterized in that, In S2, the expression for the isosurface function is: ； In the formula, Let C represent the isosurface function, and let C represent the isosurface constant. () indicates the coordinate positions of the X-axis, Y-axis, and Z-axis in a three-dimensional coordinate system.

4. The rapid simulation method for homogenization, force-thermal coupling, of a complex variable-density lattice mirror according to claim 2, characterized in that: The relative density scalar field described in S3 is constructed based on the distance field between any spatial node in the internal design domain and the back support hole, or based on the density field of the topology optimization result of the internal design domain, or based on an arbitrary function field.

5. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 4, characterized in that, S3 specifically refers to: The distance field between any spatial node in the internal design domain and the back support hole is mapped to a relative density scalar field through a decreasing linear function, where the value of the relative density scalar field ranges from 0.2 to 0.

8.

6. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 1, characterized in that, S4 specifically refers to: S41. Perform finite element mesh generation on the cell model of each relative density, and independently apply 6 macroscopic unit strain loads along the three orthogonal normal directions X, Y, and Z and the three shear directions XY, YZ, and XZ at the boundary of the cell model. Obtain the stress results through finite element analysis and solve for the equivalent elastic matrix D that reflects the mechanical properties of the structure. S42. Calculate the equivalent elastic modulus of the unit cell model for each relative density based on the equivalent elastic matrix D. ; S43. By fitting the relative density of the unit cell model to the corresponding equivalent elastic modulus using the exponential function form of the Gibson-Ashby model, a continuous mathematical mapping function is constructed, resulting in the equivalent elastic performance model of the unit cell model, expressed as: ； In the formula, The relative density is represented by the unit cell model. The elastic modulus of a solid material; Let n be the density of the solid material, and n represent the sensitivity index.

7. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 1, characterized in that, S5 specifically refers to: S51. Perform finite element mesh generation for each relative density unit cell model, apply unit temperature gradient load independently along the X direction, extract the total heat flux density through the boundary of the unit cell model through steady-state solution, and calculate the equivalent thermal conductivity matrix describing the thermal conductivity characteristics of the unit cell model. S52. Using each relative density of the unit cell model as the independent variable and the value in the equivalent thermal conductivity matrix corresponding to each relative density as the dependent variable, a continuous mathematical mapping function is fitted by a polynomial to construct the equivalent thermal conductivity performance model of the unit cell model.

8. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 1, characterized in that, In S6, the mesh for meshing the macroscopic equivalent model is a high-order tetrahedral finite element mesh.

9. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 1, characterized in that, In S7, the actual thermodynamic boundary conditions include the actual fixed constraint of the reflector, the actual mechanical load, and the actual heat flow load.

10. The rapid simulation method for homogenization, force, and thermal coupling of a complex variable-density lattice mirror according to claim 1, characterized in that, In S1, the construction of the macroscopic mirror geometric model specifically involves: determining the basic parameters of the mirror according to the optical design requirements, and constructing the macroscopic mirror geometric model in combination with the actual working conditions.

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