A topological optimization design method of a multi-physical field multi-performance integrated lattice structure

Abstract

The application provides a kind of multi-physical field multi-performance integrated lattice structure topology optimization design method, belongs to aerospace lightweight and multifunctional structure design field.The application takes lattice cell design domain as object, faces the comprehensive demand of aerospace structure under the service condition of multiple field coupling such as bearing and thermal management, establishes multi-objective optimization model including mechanical performance, thermal conductivity, electrical conductivity and mass transport capacity based on normalization and weight method, realizes the coordinated promotion of multiple performances under multiple constraint conditions, so as to avoid the engineering adaptation problem that function fragmentation, performance conflict is difficult to coordinate and is difficult to meet complex service conditions caused by design based on single physical field or single performance index.The application overcomes the function fragmentation problem caused by traditional single physical field design, realizes the multi-performance integrated design of bearing / heat / electricity / mass transfer, and is suitable for engineering implementation of high-performance lattice structure in aerospace field.

Description

Technical Field

[0001] This invention belongs to the field of aerospace structural optimization design technology, specifically relating to a topology optimization design method for a multi-physics, multi-performance integrated lattice structure. Background Technology

[0002] With the increasing demand for high-performance, lightweight structures in the aerospace field, lattice structures, as a novel material form, have received widespread attention in recent years in areas such as aerospace vehicles, engines, and thermal management systems. Lattice structures not only possess low weight and excellent mechanical properties, but also exhibit potential advantages in heat transfer, electrical conductivity, and permeability, thus holding significant application prospects in multi-performance integrated designs. The design of lattice structures is typically based on topology optimization techniques, adjusting the material distribution to optimize its mechanical and thermal properties to meet specific application requirements.

[0003] In related technologies, most optimization design methods for lattice structures in the aerospace field primarily focus on single-physics performance (such as mechanical properties or thermal conductivity), neglecting the need for multi-physics collaborative optimization. Especially in aircraft structures, lattice materials often face complex interactions of multiple boundary conditions, including loads, temperature, electromagnetics, and mass transfer. Traditional lattice structure optimization methods often cannot simultaneously consider the complex coupling between these multi-physics fields, limiting their application in high-performance aerospace vehicles. Existing optimization methods often struggle to balance and weigh these performance characteristics within a unified framework. Multi-material multi-physics topology optimization suffers from non-convergence, the inability of material penalties to drive multiple material variables towards 0 / 1, and the inability to satisfy multiple constraints, making it impossible to design lattice structures that meet the specific application scenarios, i.e., the multi-physics performance requirements.

[0004] Therefore, it is necessary to provide a topology optimization design method for a multi-physics, multi-performance integrated lattice structure to solve the above problems. Summary of the Invention

[0005] This invention provides a topology optimization design method for multi-physics, multi-performance integrated lattice structures, aiming to overcome the limitations of existing lattice structure optimization methods under multi-physics performance requirements. By introducing a multi-objective optimization framework, an optimization design method capable of simultaneously considering multiple physics performances is constructed, achieving efficient optimization under different operating conditions and boundary conditions. Based on the load, thermal, electrical, and mass transfer boundary conditions of the aircraft's macroscopic structure, the required multi-physics performance indicators for the lattice structure are analyzed and determined, and these performance indicators are selected and allocated according to priority. By constructing an optimization function with multiple performance objectives and considering the constraints of performance indicators, the optimization algorithm can effectively meet multiple functional requirements while comprehensively improving the mechanical, thermal, electrical, and mass transfer capabilities of the lattice structure. Furthermore, the energy homogenization method, multi-material linear model, and implicit floating projection constraints employed in this invention ensure the efficiency and feasibility of the optimization process, providing a high-performance, multi-functional integrated lattice structure optimization design scheme for the aerospace field, effectively solving at least one of the technical problems mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the present invention is implemented as follows:

[0007] A topology optimization design method for a multi-physics, multi-performance integrated lattice structure includes the following steps:

[0008] Step S1: Based on the load, thermal, electrical and mass transfer boundary conditions of the aircraft's macroscopic structure, analyze and determine the multiphysics performance requirements of the lattice structure, form a set of performance indicators to be optimized and their priorities, and select a subset of performance indicators to participate in this optimization from the set of performance indicators.

[0009] Step S2: Construct the objective function and constraints. Select one or more performance indicators with higher priority from the subset of performance indicators as optimization objectives, select the remaining performance indicators as constraints, and use mass or volume fraction as one of the constraints.

[0010] Step S3: Select materials and input optimization parameters according to the performance requirements to establish a finite element model of a lattice unit cell; wherein, the material distribution within the unit cell is characterized based on a linear material model to construct multiphysics control equations and corresponding finite element discrete models.

[0011] Step S4: Calculate the equivalent performance parameters of the lattice unit cell based on the energy homogenization method. The equivalent performance parameters include one or more of the following: mechanical performance parameters, thermal conductivity parameters, electrical conductivity parameters, and equivalent permeability.

[0012] Step S5: Calculate the constraint values ​​based on the equivalent performance parameters obtained in step S4 and calculate the objective function based on the weighting method. At the same time, calculate the sensitivity of the objective function and the constraint conditions to the design variables.

[0013] Step S6: Update the design variables, filter variables, and physical variables, and apply implicit floating projection constraints;

[0014] Step S7: Determine whether the constraints are met and whether the process has converged. If the constraints are not met or the process has not converged, return to step S4 to continue iterating. If the constraints are met and the process has converged, proceed to the subsequent smooth design steps.

[0015] Step S8: After the constraints are met and convergence is achieved, perform smooth design and determine whether the smooth design result meets the error standard. If it does not meet the standard, return to step S4 to continue iteration. If it does meet the standard, output the final topology optimization result of the lattice structure and end the process.

[0016] As a preferred improvement, the subset of performance indicators used in this optimization was determined based on the functional component types of the spacecraft's macrostructure, mission conditions, and boundary conditions for loads, heat, electricity, and mass transfer. G ={ B , G , k , l , D},in, B Represents the equivalent bulk modulus of the lattice structure. G Represents the equivalent shear modulus of the lattice structure. k This represents the equivalent thermal conductivity of the lattice structure. l This represents the equivalent conductivity of the lattice structure. D This represents the equivalent permeability of the lattice structure.

[0017] As a preferred improvement, the selection of the performance index subset includes: selecting a predetermined number of performance indicators to participate in optimization according to their priority, or selecting performance indicators with a priority higher than a predetermined threshold to participate in optimization; and selecting equivalent performance parameters corresponding to one or more performance indicators with higher priority from the performance index subset to construct an objective function, and constructing the equivalent performance parameters corresponding to the remaining performance indicators in the performance index subset, as well as the mass or volume fraction, as constraints.

[0018] As a preferred improvement, the linear material model is used to map design variables to the material parameter distribution of each physical field within the lattice unit cell. The linear material model performs linear interpolation on the elastic parameters, thermal conductivity parameters, electrical conductivity parameters, and equivalent permeability parameters, respectively, so that the material parameters change continuously with the design variables among candidate material parameters.

[0019]

[0020] In the formula, , 、 and Representation unit e Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability; Indicates the first α Unit of a type of material e Design variables; , 、 and They represent the first α Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability of the material; , 、 and They represent the first i The model describes the Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability of various materials. The linear interpolation model encompasses elastic parameters, thermal conductivity parameters, electrical conductivity parameters, and equivalent permeability parameters, providing a unified characterization of material parameter distributions in a lattice unit cell under multi-physics conditions. When only a subset of physics needs to be considered in the actual optimization task, the corresponding interpolation formula can be selected for calculation based on the selection results of the performance index subset. This multi-material linear interpolation model effectively avoids the numerical problems such as non-convergence and poor optimization ability caused by traditional material penalty models, improving the stability and efficiency of the algorithm.

[0021] As a preferred improvement, the equivalent properties of the lattice structure can be calculated and predicted using a homogenization method. According to Einstein's summation convention, the equivalent elastic tensor, equivalent thermal conductivity tensor, equivalent electrical conductivity tensor, and equivalent permeability can be obtained. Using an energy-based homogenization method, these physical quantities are written in energy-based form:

[0022]

[0023] In the formula, , 、 and These represent the equivalent elastic tensor, equivalent thermal conductivity tensor, equivalent electrical conductivity tensor, and equivalent permeability obtained after energy homogenization. N Indicates the total number of finite element elements; , Represents the element displacement vector; T represents the matrix transpose; Represents the element stiffness matrix; , Represents the unit temperature vector; Represents the thermal conductivity matrix of the unit cell; , Represents the unit potential vector; Represents the unit conductivity matrix; , Represents the cell diffusion vector; Represents the cell penetration matrix; i , j , k , l Indicates the direction of the test vector for different physical fields; The integral region is represented by two-dimensional structures, which represent the area of ​​the design region, and three-dimensional structures, which represent the volume of the design region. Energy-based homogenization methods are more efficient and easier to integrate into topology optimization frameworks than traditional asymptotic homogenization methods.

[0024] As a preferred improvement, the mathematical model of the objective function and constraint function is established according to step S2:

[0025] ;

[0026] In the formula, Represent the objective function; This indicates that the weighting factors are calculated using either linear weighting or compromise programming methods. This indicates the number of sub-objectives included in the objective function; Indicates from G ={ B , G , k , l , D The normalized representation of the equivalent performance parameters selected in}; Indicates the quality of the optimized structure; Indicates structural mass constraints; Indicates the minimum design variables; This indicates the number of optimization objectives in the objective function; This represents the total number of performance indices in the objective function and constraints. Indicates the part that serves as a constraint. G ={ B , G , k , l , D The normalized representation of the equivalent performance parameters selected in} This indicates the number of sub-constraints within a constraint. Sensitivity can be calculated using the adjoint method, numerical difference method, finite difference method, or other numerical optimization methods to obtain the sensitivity of the objective function and constraints with respect to the design variables. A multi-objective topology optimization mathematical model is established to avoid the limitations of designing around a single performance objective.

[0027] As a preferred improvement, the single variable is divided into design field variables. Filter field variables and design variables The design field variables are updated using the moving asymptote method. The upper and lower limits of this update require calculations of +0.01 and -0.01 respectively, based on the original values. Additionally, to ensure physical meaning, [further details are needed]. The process of implicit floating projection is represented as follows:

[0028] ;

[0029] In the formula, This represents the density after projection; y The threshold value is determined using a binary search method. β This represents the 0 / 1 smoothing parameter, used to smooth the degree to which design variables tend towards 0 / 1. β A larger value indicates fewer design variables whose 0 / 1 constraints are strictly in the middle range. Traditional material penalties have drawbacks in smoothing 0 / 1 design variables: the degree of smoothing is uncontrollable, resulting in a large number of design variables in the 0-1 middle range in multi-material topology optimization, leading to a very ambiguous structure and a lack of physical meaning. In contrast, implicit floating projection is a physically based numerical method that can effectively smooth multiple design variables simultaneously in multi-material optimization, with controllable smoothing, resulting in clear optimization results.

[0030] As a preferred improvement, the convergence condition is that the change in the design field variable during iteration is less than or equal to 0.001, i.e. , where k represents the number of iterations, and this threshold is less than the convergence criterion of ordinary algorithms to achieve more stable optimization.

[0031] As a preferred improvement, a level set function is introduced to smooth the optimization results. To determine the error introduced by the level set function, the smoothed structure is projected back to the original mesh. Subsequently, various performance indicators of the structure are calculated and compared with the structure before smoothing. If the error of each indicator is less than 1%, the smoothed design is considered to meet the error standard. If it does not meet the standard, the projection smoothing parameters in step S6 are increased. β To enhance the 0 / 1 requirement for design field variables, return to step S4 and repeat the iterative process. Smooth design avoids the jagged boundaries caused by traditional element-based topology optimization, while also reducing design errors.

[0032] A multi-physics, multi-performance integrated lattice structure is constructed using the aforementioned topology optimization design method for a multi-physics, multi-performance integrated lattice structure.

[0033] The beneficial effects of this invention are as follows:

[0034] (1) The optimized design is highly compatible with practical applications. By innovatively combining multi-physics field requirements and multi-objective optimization framework, this invention can effectively address complex multi-field coupling problems in practical applications, has strong engineering application value, can significantly improve the integration of materials-structure-function, and promote the rapid development of high-performance structural materials;

[0035] (2) Achieving multi-physics collaborative optimization and improving overall performance. This invention is the first to achieve simultaneous optimization of the performance of lattice structures in multiple physical fields (mechanical, thermal, electrical and mass transfer, etc.) under the same framework. Compared with traditional single-performance design, it not only improves the overall performance of lattice structures under multiple physical fields, but also greatly releases their application potential in aerospace, energy and advanced manufacturing fields, showing great industrialization potential and scientific value;

[0036] (3) Breaking through the bottleneck of traditional optimization and achieving efficient global optimization. This invention adopts a combination of multi-material linear material interpolation model and floating projection technology, and improves the moving asymptote method. It significantly overcomes the difficulties in convergence caused by the penalty model in traditional topology optimization methods, the inability to achieve multi-variable 0 / 1 control and the unclear physical meaning, greatly enhances the optimization effect under complex multi-physics conditions, and promotes the development of topology optimization technology;

[0037] (4) The energy homogenization method is extended to the optimization of electrical conductivity and equivalent permeability. This invention uses the energy homogenization method to calculate the equivalent performance parameters of the lattice unit cell. This method is traditionally used to optimize mechanical stiffness and thermal conductivity. However, in this invention, it is innovatively extended to the optimization of electrical conductivity and equivalent permeability. Through precise energy distribution, the balance and optimization effect of the structure under multi-physics field performance are ensured, thus providing a new approach for the design and application of conductive materials and fluid transport. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0039] Figure 1A flowchart illustrating the topology optimization design method for a multi-physics, multi-performance integrated lattice structure provided by this invention;

[0040] Figure 2 This diagram illustrates the design domain and optimized design results in the embodiments.

[0041] Figure 3 This is a comparison diagram showing the optimized design results in Example 1 with the single-material, single-objective optimized structure. Detailed Implementation

[0042] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] like Figure 1-Figure 3 As shown, this embodiment provides a topology optimization design method for a multi-physics, multi-performance integrated lattice structure, including the following steps:

[0044] Step S1: Based on the load, thermal, electrical and mass transfer boundary conditions of the aircraft's macroscopic structure, analyze and determine the multiphysics performance requirements of the lattice structure, form a set of performance indicators to be optimized and their priorities, and select a subset of performance indicators to participate in this optimization from the set of performance indicators.

[0045] In this embodiment, the requirements of a spacecraft thermal control system are selected as an example. Spacecraft require a highly efficient thermal control system to ensure the normal operation of internal electronic equipment and other sensitive components in the long-term space environment. A thermal control system typically includes a load-bearing structure, a multi-layered thermal shielding structure, heat conduction devices, and gas flow paths. The lattice material needs excellent mechanical properties and thermal conductivity, while also possessing permeability to regulate gas flow in different areas, ensuring effective heat conduction and dissipation. The performance priority, from highest to lowest, is: mechanical properties—thermal conductivity—equivalent permeability. The subset of performance indicators involved in this optimization is... G ={ B , G , k , D},in, B Represents the equivalent bulk modulus of the lattice structure. G Represents the equivalent shear modulus of the lattice structure. k This represents the equivalent thermal conductivity of the lattice structure. D This represents the equivalent permeability of the lattice structure. Conductivity is not included in this subset of performance metrics.

[0046] Step S2: Construct the objective function and constraints. Select one or more performance indicators with higher priority from the subset of performance indicators as optimization objectives, select the remaining performance indicators as constraints, and use mass or volume fraction as one of the constraints.

[0047] In this embodiment, a predetermined number of performance indicators are selected for optimization based on their priority. The objective function is constructed using the equivalent bulk modulus, shear modulus, and thermal conductivity, which have higher priority, while the equivalent permeability and mass fraction, which have lower priority, are used as constraints.

[0048] Step S3: Select materials and input optimization parameters according to the performance requirements to establish a finite element model of a lattice unit cell; wherein, the material distribution within the unit cell is characterized based on a linear material model to construct multiphysics control equations and corresponding finite element discrete models.

[0049] In this embodiment, for ease of explanation, dimensionless materials are selected. Material 1 has a Young's modulus of 10 and a thermal conductivity of 100, making it more suitable as a load-bearing material. Material 2 has a Young's modulus of 100 and a thermal conductivity of 10, making it more suitable as a heat-conducting material. Both materials have a density of 1, a Poisson's ratio of 0.3, and an equivalent permeability of 1. Optimized parameter settings: Projection parameters β The initial value is 3. The linear material model is used to map design variables to the material parameter distribution of each physical field within the lattice unit cell. The linear material model includes linear interpolation of elastic parameters, thermal conductivity parameters, and equivalent permeability parameters. (It should be noted that conductivity is not included in the performance index subset of this embodiment.) Therefore, no interpolation was performed on the conductivity parameters. However, when the performance requirements include conductivity, the model can also perform linear interpolation on the conductivity parameters (the interpolation form is similar to that of the thermal conductivity parameters), allowing the material parameters to change continuously among the candidate material parameters as the design variables change.

[0050]

[0051] In the formula, , 、 and Representation unit e Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability; Indicates the first α Unit of a type of material e The design variables, among which α= 1 , 2 ,...,θ , i The total number of materials; , 、 and They represent the first α Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability of the material; , 、 and They represent the first i The model describes the Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability of various materials. The linear interpolation model encompasses elastic parameters, thermal conductivity parameters, electrical conductivity parameters, and equivalent permeability parameters, providing a unified characterization of material parameter distributions in a lattice unit cell under multi-physics conditions. When only a subset of physics needs to be considered in the actual optimization task, the corresponding interpolation formula can be selected for calculation based on the selection results of the performance index subset. This multi-material linear interpolation model effectively avoids the numerical problems such as non-convergence and poor optimization ability caused by traditional material penalty models, improving the stability and efficiency of the algorithm.

[0052] Step S4: Calculate the equivalent performance parameters of the lattice unit cell based on the energy homogenization method. The equivalent performance parameters include one or more of the following: mechanical performance parameters, thermal conductivity parameters, electrical conductivity parameters, and equivalent permeability.

[0053] In this embodiment, according to Einstein's summation convention, the equivalent properties of the lattice structure can be calculated and predicted using an energy-based homogenization method:

[0054] ;

[0055] In the formula, , 、 and These represent the equivalent elastic tensor, equivalent thermal conductivity tensor, equivalent electrical conductivity tensor, and equivalent permeability obtained after energy homogenization. N Indicates the total number of finite element elements; , Represents the element displacement vector; T represents the matrix transpose; Represents the element stiffness matrix; , Represents the unit temperature vector; Represents the thermal conductivity matrix of the unit cell; , Represents the cell diffusion vector; Represents the cell penetration matrix; i , j , k , l This indicates the direction of the test vector for different physical fields, taking a value of 1 or 2; The integral region is represented by two-dimensional structures, which represent the area of ​​the design region, and three-dimensional structures, which represent the volume of the design region. Energy-based homogenization methods are more efficient and easier to integrate into topology optimization frameworks than traditional asymptotic homogenization methods.

[0056] Step S5: Calculate the constraint values ​​based on the equivalent performance parameters obtained in step S4 and calculate the objective function based on the weighting method. At the same time, calculate the sensitivity of the objective function and the constraint conditions to the design variables.

[0057] In this embodiment, the weights of bulk modulus, shear modulus, and thermal conductivity are set to 0.4, 0.4, and 0.2, respectively; the equivalent permeability constraint is set to be greater than or equal to 0.35; and the mass constraint is set to 0.5. The mathematical model for the objective function and constraint function is established as follows:

[0058] ;

[0059] In the formula, Represent the objective function; This indicates that the weighting factor is calculated using linear weighting or compromise programming methods, and its value ranges from 0 to 1. This indicates the number of sub-objectives included in the objective function; Indicates from G ={ B , G , k , l , D The normalized representation of the equivalent performance parameters selected in}; Indicates the quality of the optimized structure; Indicates structural mass constraints; Indicates the minimum design variables; This indicates the number of optimization objectives in the objective function; This represents the total number of performance indices in the objective function and constraints. Indicates the part that serves as a constraint. G ={ B , G , k , l , D The normalized representation of the equivalent performance parameters selected in} This indicates the number of sub-constraints contained in the constraint; all the above performance values ​​are normalized, that is, the obtained value is divided by the maximum value obtained through HS theory, so as to effectively measure each performance and avoid the inability to accurately obtain design preferences by weight due to excessively large performance values.

[0060] Sensitivity can be calculated using the adjoint method, numerical difference method, finite difference method, or other numerical optimization methods to obtain the sensitivity of the objective function and constraints with respect to the design variables.

[0061]

[0062]

[0063]

[0064] in, This represents the element stiffness matrix with unit Young's modulus; This represents a single-unit thermal conductivity matrix; This represents a unit permeability matrix with a unit equivalent permeability. This represents the Young's modulus of the first material; This represents the thermal conductivity of the first material; This represents the equivalent permeability of the first material; , , These represent the partial derivatives of the equivalent elastic tensor, equivalent thermal conductivity tensor, and equivalent permeability with respect to the design variables, respectively.

[0065] A multi-objective topology optimization mathematical model was established to avoid the limitations of designing around a single performance.

[0066] Step S6: Update the design variables, filter variables, and physical variables, and apply implicit floating projection constraints;

[0067] In this embodiment, the single variable is divided into design field variables. Filter field variables and design variables The design field variables are updated using the moving asymptote method. The upper and lower limits of this update require calculations of +0.01 and -0.01 respectively, based on the original values. Additionally, to ensure physical meaning, [further details are needed]. .

[0068] In multi-material, multi-objective topology optimization, most methods use material penalties to drive the 0 / 1 design of design variables, which effectively solves the optimization problem. However, using material penalty models in multi-material topology optimization cannot guarantee that they apply to multiple design variables, resulting in a large number of intermediate values ​​that affect the algorithm's convergence performance and cause structural ambiguity. Linear material interpolation avoids this drawback by driving the 0 / 1 design of design variables through implicit floating projection. The implicit floating projection process is represented as follows:

[0069] ;

[0070] In the formula, This represents the density after projection; y The threshold value is determined using a binary search method. β This represents the 0 / 1 smoothing parameter, used to smooth the degree to which design variables tend towards 0 / 1. β A larger value indicates fewer design variables whose 0 / 1 constraints are strictly in the middle range. Traditional material penalties have drawbacks in smoothing 0 / 1 design variables: the degree of smoothing is uncontrollable, resulting in a large number of design variables in the 0-1 middle range in multi-material topology optimization, leading to a very ambiguous structure and a lack of physical meaning. In contrast, implicit floating projection is a physically based numerical method that can effectively smooth multiple design variables simultaneously in multi-material optimization, with controllable smoothing, resulting in clear optimization results.

[0071] Step S7: Determine whether the constraints are met and whether the process has converged. If the constraints are not met or the process has not converged, return to step S4 to continue iterating. If the constraints are met and the process has converged, proceed to the subsequent smooth design steps.

[0072] In this embodiment, the convergence condition is determined when the change in the design field variable during iteration is less than or equal to 0.001, i.e. , where k represents the number of iterations, and this threshold is less than the convergence criterion of ordinary algorithms to achieve more stable optimization.

[0073] Step S8: After the constraints are met and convergence is achieved, perform smooth design and determine whether the smooth design result meets the error standard. If it does not meet the standard, return to step S4 to continue iteration. If it does meet the standard, output the final topology optimization result of the lattice structure and end the process.

[0074] In this embodiment, a level set function is introduced to smooth the optimization results. To determine the error introduced by the level set function, the smoothed structure is projected back to the original mesh. Subsequently, various performance indicators of the structure are calculated and compared with the structure before smoothing. If the error of each indicator is less than 1%, the smoothed design is considered to meet the error standard. If it does not meet the standard, the projection smoothing parameters in step S6 are increased. β To enhance the 0 / 1 requirement for design field variables, return to step S4 and repeat the iterative process. Smooth design avoids the jagged boundaries caused by traditional element-based topology optimization, while also reducing design errors. During this process, β The increment is set to 1.

[0075] Example 1

[0076] like Figure 2As shown, in this embodiment, the design domain of the lattice structure is a square region with a hole in the center. Materials 1 and 2 are evenly distributed around it. The weights for bulk modulus, shear modulus, and thermal conductivity are set to 0.4, 0.4, and 0.2, respectively. The equivalent permeability constraint is set to be greater than or equal to 0.35, the mass constraint is 0.5, and the mass constraint for both materials is 0.25. The optimization model is expressed as follows:

[0077]

[0078] Input optimization parameters, where Material 1 has a Young's modulus of 10 and a thermal conductivity of 100, making it more suitable as a load-bearing material. Material 2 has a Young's modulus of 100 and a thermal conductivity of 10, making it more suitable as a heat-conducting material. Both materials have a density of 1, a Poisson's ratio of 0.3, and an equivalent permeability of 1. Optimization parameter settings: Projection parameters β The initial value is 3. The optimization design is performed using the optimization design method provided by this invention.

[0079] Figure 2 The paper also showcases the optimized structure, including the microstructure unit cell, periodic array, and effective performance. The final structure has a bulk modulus of 8.95, a shear modulus of 7.14, a thermal conductivity of 9.28, an equivalent permeability of 0.35, and a mass of 0.5. The optimized structure exhibits clear material interfaces and boundaries, and the output can be directly used for manufacturing. The periodic array structure, using the 5×3 periodic array as an example, can actually output any periodic form.

[0080] Figure 3 This paper compares the structural properties obtained based on the method of this invention with those of lattice structures designed using a single material and a single objective (focusing only on thermal conductivity). As shown in the figure, the structure designed by the multi-physics, multi-performance integrated lattice structure design method proposed in this invention maintains the same level of thermal conductivity. This is because all materials are used for heat conduction, while the bulk modulus and shear modulus are increased by 61% and 70% respectively, and the equivalent permeability is increased by 13%. Overall performance is improved, not only meeting thermal conductivity requirements but also bearing load, preventing structural instability and failure under high loads, and meeting the equivalent permeability requirements. Compared with traditional single-physics, single-objective design, the design method of this invention achieves a comprehensive performance improvement while avoiding common problems such as convergence difficulties, unclear physical meaning, and structural ambiguity. This method can find the optimal balance under multiple physical field requirements, enabling the lattice structure to achieve optimal comprehensive effects in terms of load-bearing capacity, thermal conductivity, and mechanical properties, providing strong performance support and practical feasibility for applications in aerospace, energy, and other fields.

[0081] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A topology optimization design method for a multi-physics, multi-performance integrated lattice structure, characterized in that, Includes the following steps: Step S1: Based on the load, thermal, electrical, and mass transfer boundary conditions of the aircraft's macrostructure, analyze and determine the multiphysics performance requirements of the lattice structure, forming a set of performance indicators to be optimized and their priorities. Then, select a subset of performance indicators from this set to participate in the optimization. The subset of performance indicators participating in this optimization is determined based on the functional component types of the aircraft's macrostructure, mission conditions, and the load, thermal, electrical, and mass transfer boundary conditions. Г ={ B , G , κ , λ , D },in, B Represents the equivalent bulk modulus of the lattice structure. G Represents the equivalent shear modulus of the lattice structure. κ This represents the equivalent thermal conductivity of the lattice structure. λ This represents the equivalent conductivity of the lattice structure. D This represents the equivalent permeability of the lattice structure; Step S2: Construct the objective function and constraints. Select one or more performance indicators with higher priority from the subset of performance indicators as optimization objectives, select the remaining performance indicators as constraints, and use mass or volume fraction as one of the constraints. Step S3: Select materials and input optimization parameters according to the performance requirements to establish a finite element model of the lattice unit cell; wherein, the material distribution within the unit cell is characterized based on a linear material model to construct multiphysics control equations and corresponding discrete finite element models; the linear material model is used to map design variables to the material parameter distribution of each physical field within the lattice unit cell, and the linear material model performs linear interpolation on elastic parameters, thermal conductivity parameters, electrical conductivity parameters, and equivalent permeability parameters, so that the material parameters change continuously with the design variables among candidate material parameters: In the formula, , 、 and Representation unit e Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability; Indicates the first α Unit of a type of material e Design variables; , 、 and They represent the first α Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability of the material; , 、 and They represent the first θ Young's modulus, thermal conductivity, electrical conductivity, and equivalent permeability of the material; Step S4: The equivalent performance parameters of the lattice unit cell are calculated using an energy-based homogenization method. These equivalent performance parameters include one or more of the following: mechanical properties, thermal conductivity, electrical conductivity, and equivalent permeability. The equivalent performance parameters of the lattice structure are predicted using the homogenization method. According to Einstein's summation convention, the equivalent elastic tensor, equivalent thermal conductivity tensor, equivalent electrical conductivity tensor, and equivalent permeability are obtained. Using the energy-based homogenization method, these physical quantities are written in energy-based form. In the formula, , 、 and These represent the equivalent elastic tensor, equivalent thermal conductivity tensor, equivalent electrical conductivity tensor, and equivalent permeability obtained after energy homogenization. N Indicates the total number of finite element elements; , Represents the element displacement vector; T represents the matrix transpose; Represents the element stiffness matrix; , Represents the unit temperature vector; Represents the thermal conductivity matrix of the unit cell; , Represents the unit potential vector; Represents the unit conductivity matrix; , Represents the cell diffusion vector; Represents the cell penetration matrix; i , j , k , l Indicates the direction of the test vector for different physical fields; The integral region is represented by the two-dimensional structure, which represents the area of ​​the design region, and the three-dimensional structure, which represents the volume of the design region. Step S5: Calculate the constraint values ​​based on the equivalent performance parameters obtained in step S4 and calculate the objective function based on the weighting method. At the same time, calculate the sensitivity of the objective function and the constraint conditions to the design variables. Step S6: Update the design field variables, filter field variables, and design variables, and apply implicit floating projection constraints; Step S7: Determine whether the constraints are met and whether the process has converged. If the constraints are not met or the process has not converged, return to step S4 to continue iterating. If the constraints are met and the process has converged, proceed to the subsequent smooth design steps. Step S8: After the constraints are met and convergence is achieved, perform smooth design and determine whether the smooth design result meets the error standard. If it does not meet the standard, return to step S4 to continue iteration. If it does meet the standard, output the final topology optimization result of the lattice structure and end the process.

2. The topology optimization design method for a multi-physics, multi-performance integrated lattice structure according to claim 1, characterized in that, In step S2, the selection of the performance index subset includes: selecting a preset number of performance indicators to participate in optimization according to the priority of the performance indicators, or selecting performance indicators with a priority higher than a preset threshold to participate in optimization; and selecting equivalent performance parameters corresponding to one or more performance indicators with higher priority from the performance index subset to construct an objective function, and constructing the equivalent performance parameters corresponding to the remaining performance indicators in the performance index subset and the mass or volume fraction as constraints.

3. The topology optimization design method for a multi-physics, multi-performance integrated lattice structure according to claim 1, characterized in that, In step S5, the mathematical model of the objective function and constraint function is established according to step S2: ； In the formula, Represent the objective function; This indicates that the weighting factors are calculated using either linear weighting or compromise programming methods. This indicates the number of sub-objectives included in the objective function; Indicates from Г ={ B , G , κ , λ , D The normalized representation of the equivalent performance parameters selected in}; Indicates the quality of the optimized structure; Indicates structural mass constraints; Indicates the minimum design variables; This indicates the number of optimization objectives in the objective function; This represents the total number of performance indices in the objective function and constraints. Indicates the part that serves as a constraint. Г ={ B , G , κ , λ , D The normalized representation of the equivalent performance parameters selected in} This indicates the number of sub-constraints contained within a constraint.

4. The topology optimization design method for a multi-physics, multi-performance integrated lattice structure according to claim 3, characterized in that, In step S6, the single variable is divided into design field variables. Filter field variables and design variables The design field variables are updated using the moving asymptote method. The upper and lower limits of this update require calculations of +0.01 and -0.01 respectively, based on the original values. Additionally, to ensure physical meaning, [further details are needed]. The process of implicit floating projection is represented as: ； In the formula, This represents the density after projection; y Indicates the threshold; β This represents the smoothing parameter.

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