A solid-lattice hybrid aircraft structure optimization design method

Abstract

The application discloses a kind of solid-lattice hybrid aircraft structure optimization design method, belong to aerospace structure light weight and optimization design technical field.The method is established three-dimensional finite element model according to aircraft component and calibrates function area;Adopt homogenization method to evaluate lattice equivalent performance, as anisotropic material phase is introduced into optimization;Determine the optimal layout of solid, lattice and material removal area using multi-material topology optimization;Obtain clear topology configuration by density filtering and projection;Topology result is reconstructed and converted into anisotropic lattice filling;Further, size and orientation collaborative optimization distributes lattice rod diameter.The application realizes solid and lattice collaborative optimization and reasonable distribution of rod size, ensures stiffness while achieving lightweight.

Description

Technical Field

[0001] This invention belongs to the field of aerospace structure and structural optimization design technology, specifically involving a solid-lattice hybrid aircraft structural optimization design method, applicable to the coordinated optimization design of lightweight and stiffness performance of load-bearing components such as aircraft spoilers, control surfaces, and wing boxes. Background Technology

[0002] Lattice structures are a type of porous structure composed of periodic or periodic unit cells arranged in a certain pattern in space. They have high specific strength, specific stiffness, and good energy absorption and distributed load-bearing capacity, and have been widely used in lightweight aerospace components such as satellite support structures, morphing wings, and aircraft spoilers.

[0003] In existing solid-lattice hybrid structure designs, the spatial layout of solid material regions, lattice-filled regions, and material removal regions typically relies on the designer's engineering experience or manual post-processing based on topology optimization results. A systematic design method is lacking that can collaboratively optimize lattice structures with solid materials and openings. Due to the complex load transfer paths and local stress characteristics of aircraft structures, relying solely on experience to determine the distribution of solid and lattice materials can easily lead to inaccurate identification of main load-bearing paths, unreasonable lattice-filled region division, and imbalances in local material configuration. Furthermore, traditional lattice-filling methods often use uniform member dimensions, making it difficult to achieve adaptive distribution based on the load levels and stiffness requirements of different regions. When lattice structures are directly applied to complex aircraft components, discontinuities in the connection between the lattice region and the solid load-bearing structure, external skin, or connecting joints may also exist. Without collaborative layout optimization among solid materials, lattice materials, and openings, and further optimization of lattice member dimensions, it is difficult to simultaneously consider structural stiffness, strength, weight reduction, and manufacturing feasibility, resulting in the underutilization of the lightweight potential of lattice structures in aircraft load-bearing components.

[0004] Topology optimization, a structural optimization method based on mathematical modeling and numerical iteration, can automatically seek a reasonable distribution of materials under given design domain, load conditions, and constraints, providing an effective approach for lightweight design of aircraft structures. Existing research has applied topology optimization methods and lattice filling strategies to aerospace structural design, achieving structural weight reduction and performance improvement to some extent. However, existing methods typically obtain the topology optimization results of the solid structure first, and then introduce lattice filling in certain areas based on experience or local design requirements. There is a lack of a unified layout determination mechanism between the solid load-bearing area, the lattice-filled area, and the material removal area, resulting in the spatial distribution relationship of different areas mainly relying on manual experience, which is difficult to fully adapt to complex load transfer paths and structural function maintenance requirements.

[0005] Therefore, it is necessary to provide a method for optimizing aircraft structures that combines solid and lattice elements. Summary of the Invention

[0006] This invention provides a solid-lattice hybrid aircraft structure optimization design method, which aims to solve the problems in the existing lightweight design of aircraft structures, such as the reliance on experience for lattice filling areas, the difficulty in coordinating the distribution of solid and lattice materials, the insufficient introduction of material removal areas, and the difficulty in further optimizing the size of lattice rods, thereby improving the material utilization efficiency and lightweight design effect of aircraft structures.

[0007] The technical problem to be solved by the present invention is to overcome the defects in the existing lightweight design of aircraft structures, such as reliance on experience for lattice filling areas, difficulty in coordinating the distribution of solid materials and lattice materials, insufficient introduction of material removal areas, and difficulty in further optimizing the size of lattice rods, and to provide a solid-lattice hybrid aircraft structure optimization design method.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A method for optimizing the design of a solid-lattice hybrid aircraft structure includes the following steps: Based on the geometric shape, connection and assembly relationship, load transfer path and lightweight design goal of the aircraft structural components, a three-dimensional finite element model is established, including load conditions, boundary conditions, candidate material types and non-design regions. According to the requirements of maintaining aerodynamic shape, maintaining connection and assembly and maintaining main load-bearing path, the functional region attributes of the three-dimensional finite element model are calibrated, and it is divided into aerodynamic shape maintenance region, connection and assembly region, main load-bearing design region and material removal region, forming a design constraint mapping relationship oriented towards the coordinated distribution of solid material, lattice equivalent material and material removal region.

[0009] Configurations are selected from the lattice unit cell configuration library, and the macroscopic equivalent mechanical properties of the lattice unit cells in different principal directions are calculated using the homogenization method. The equivalent elastic matrix, equivalent density, and direction-dependent performance parameters are obtained. The lattice structure composed of the lattice unit cells is then equivalent to an anisotropic lattice equivalent material phase, which is then introduced into subsequent multi-material topology optimization.

[0010] Based on the load-bearing functional requirements of aircraft structural components, a performance evaluation criterion oriented towards structural deformation suppression and load transfer efficiency improvement is constructed, and material usage constraints and manufacturing feasibility constraints are embedded in the optimization solution process; displacement, stress and flexibility response within the design domain are obtained through finite element response analysis.

[0011] Based on the structural response results, the performance contribution differences of solid materials, lattice equivalent materials, and material removal regions in each design unit are evaluated. Combined with the directional stiffness characteristics of lattice equivalent materials, a sensitivity-driven criterion is formed for load-bearing path preservation, lightweight region identification, and directional stiffness matching. The multi-material design variables are updated according to the criteria, so that solid materials, lattice equivalent materials, and material removal regions can adaptively evolve within the design domain according to the degree of structural contribution and load transfer direction.

[0012] Density filtering and Heaviside projection are applied to the updated multi-material design variables to suppress checkerboard patterns, mesh dependence, and intermediate density regions within the design domain, thereby creating continuous, identifiable, and easily reconstructable boundary lines between the solid material region, the lattice-filled region, and the material removal region.

[0013] Determine whether the optimization iteration meets the preset convergence condition. If it does not meet the condition, return to the previous step and continue the iteration; if it does meet the condition, proceed to the next step.

[0014] Based on the converged multi-material topology results, the spatial distribution characteristics of the solid load-bearing area, the lattice candidate filling area, and the material removal area are extracted. The boundaries of each region are geometrically arranged and the structural regions are reconstructed to generate an initial partitioning model of the solid-lattice hybrid structure that meets the functional preservation requirements.

[0015] The candidate lattice filling regions in the initial partitioning model are transformed into anisotropic lattice filling structures. Based on the load transfer direction, principal stiffness direction, and spatial adjacency relationship between the lattice filling regions and the solid load-bearing regions, the local orientation and arrangement of the lattice unit cells are determined. At the same time, a connection transition region between the solid structure and the lattice structure is constructed to ensure that the solid-lattice hybrid structure remains continuous in terms of geometric boundaries, load transfer paths, and local coordinate directions.

[0016] For the lattice-filled region in the initial model of the solid-lattice hybrid structure, the influence of different lattice cell wall thickness parameters and rod diameter parameters on the structural stiffness, mass and interface load transfer performance is evaluated, and local sensitivity evaluation results for lattice size optimization are established.

[0017] For the anisotropic unit cell configuration of the bar-based lattice, the wall thickness parameter, bar diameter parameter, and unit cell orientation parameter are used as design variables, and the size and orientation are optimized in a coordinated manner based on the local load transfer direction and sensitivity evaluation results. During the size update and orientation adjustment process, the connection continuity between adjacent lattice unit cells is considered so that lattice unit cells of different sizes and orientations are coordinated in spatial arrangement, node connection and load transfer.

[0018] Determine whether the optimized solid-lattice hybrid structure meets the design requirements; if it does not meet the design requirements, return to step S2 and re-optimize using a different lattice configuration; if it meets the requirements, output the final solid-lattice hybrid aircraft structure model.

[0019] Compared with the prior art, the advantages of this invention are as follows: First, a collaborative optimization design method for solid-lattice-material removal regions in complex aircraft structures is proposed. This method treats the lattice structure, after homogenization, as an independent equivalent material phase, and incorporates it, along with the solid material phase and material removal regions, into a multi-material topology optimization framework. This achieves unified layout optimization of the main load-bearing solid region, the lightweight lattice filling region, and the material removal region. Compared to traditional design methods that rely on manual experience to divide lattice regions, this invention can automatically determine the spatial distribution of different material regions based on the load transfer path and structural stress characteristics, thereby improving the rationality of material configuration and the autonomous optimization capability of structural design.

[0020] Second, a highly efficient design mechanism combining macroscopic structural topology optimization and lattice equivalent performance characterization was constructed. The equivalent macroscopic mechanical properties of the lattice structure were obtained through an energy-based homogenization method and introduced as material parameters into the overall structural optimization process. This avoids the modeling complexity and computational scale expansion caused by directly establishing a large number of microscopic lattice members in the macroscopic aircraft structure. This method can significantly improve optimization computational efficiency while maintaining the load-bearing characteristics of the lattice structure in the optimization process, providing a more engineering-applicable technical path for the design of solid-lattice hybrid structures of complex components such as aircraft spoilers, control surfaces, and wing boxes.

[0021] Third, a continuous design process from topology generation to manufacturable model reconstruction has been established. Through density filtering and Heaviside projection, the checkerboard effect is mitigated, mesh dependency is reduced, and intermediate density cells are decreased, resulting in clearer structural boundaries between solid material regions, lattice material regions, and material removal regions. Based on this, through model reconstruction and lattice filling, the topology optimization results are transformed into a solid-lattice hybrid structure with well-defined geometric boundaries and continuous load-bearing paths. This process helps alleviate the discontinuity in the connection between lattice regions and solid structures, improving the reliability and manufacturability of converting optimization results into engineering models.

[0022] Fourth, the material utilization efficiency and load-bearing performance of the solid-lattice hybrid structure are further improved through the optimization of lattice member dimensions. By using the diameter of the lattice members as a dimensional design variable, the dimensions of the lattice members can be spatially adjusted according to the local stress levels in different regions, providing stronger support in high-load areas and reducing material redundancy in low-load areas. Thus, the solid structure bears the main load transfer, while the lattice structure provides lightweight infill and distributed load-bearing, forming a synergistic load-bearing system. This system can improve overall stiffness, deformation response, and stress distribution while reducing structural mass, providing a widely applicable design framework for the lightweight, functional, and engineering applications of complex load-bearing components in aerospace. Attached Figure Description

[0023] 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: Figure 1 A flowchart illustrating a method for optimizing a solid-lattice hybrid aircraft structure provided by the present invention; Figure 2 This is the initial design model of the aircraft structure, taking the spoiler as an example, established in Embodiment 1 of the present invention; Figure 3 This is a diagram of the compliance iteration curve obtained during the optimization process in Embodiment 1 of the present invention; Figure 4 This is a diagram showing the optimized result of topology optimization and reconstruction of the aircraft spoiler structure in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the aircraft spoiler structure lattice optimization process in Embodiment 1 of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] Example 1 This embodiment provides a hybrid solid-lattice aircraft structure optimization design method, specifically applied to the design of aircraft spoilers.

[0026] Step S1: Establish a three-dimensional finite element model and calibrate the functional area attributes; Based on the geometric shape, connection and assembly relationships, load transfer paths, and lightweight design goals of the aircraft structural components, a three-dimensional finite element model was established, including load conditions, boundary conditions, candidate material types, and non-design regions. Functional region attributes were then calibrated. Using the aircraft spoiler as the optimization object, and considering its deceleration, attitude control, and load-bearing functions, design requirements for mass reduction, stiffness maintenance, displacement control, and stress control were determined. Based on the actual load conditions of the spoiler, boundary constraints were applied at six joints, and a uniformly distributed load of 2×10⁻⁶ was applied. -5 GPa acts on the upper surface of the skin. The external aerodynamic profile of the spoiler, the upper and lower skins, the connecting joints, and the assembly interfaces are set as non-evolvable regions to maintain the continuity of the aerodynamic shape and the integrity of the sealed cavity; the internal load-bearing space is set as the structural optimization domain, allowing the material to redistribute and undergo topological evolution during the design iteration process. Thus, the model is divided into an aerodynamic shape preservation region, a connecting assembly region, a main load-bearing design region, and a material removal region, forming a design constraint mapping relationship oriented towards the coordinated distribution of solid materials, lattice equivalent materials, and material removal regions.

[0027] In this step, the initial model weight of 292.6 kg is the overall weight including the aerodynamic shape retention area, the connection and assembly area, and the upper and lower skins.

[0028] like Figure 2 As shown, the spoiler model includes a structural optimization domain and an aerodynamic shape preservation region. In the initial model, the skin thickness is uniformly set to 1 mm, and the initial mass is 292.6 kg. The design domain is discretized using the finite element method, dividing it into 6.55 × 10⁻⁶ sections. 5 Each element is a tetrahedral. The spoiler skin is made of AlSi10Mg aluminum alloy with a density ρ = 2160 kg / m³. 3 The elastic modulus E = 69 GPa and Poisson's ratio ν = 0.3. The internal area of ​​the solid spoiler is entirely made of aluminum alloy; the internal area of ​​the solid-lattice hybrid structure uses both aluminum alloy and lattice materials. Connecting components are made of TC4 titanium alloy, with an elastic modulus E = 110 GPa and a density ρ = 4510 kg / m³. 3 Poisson's ratio ν = 0.33.

[0029] This step, through the above functional area attribute calibration, ensures that the optimization results reduce structural mass while maintaining the aerodynamic integrity of the spoiler, the feasibility of connection and assembly, and the continuity of the main load-bearing path.

[0030] Step S2: Calculate the macroscopic equivalent mechanical properties of the lattice unit cell using a homogenization method; A body-centered cubic unit cell was selected from the lattice unit cell configuration library as the representative configuration of the lattice equivalent material, and its macroscopic equivalent mechanical properties were calculated using a periodic homogenization method. Periodic boundary conditions were applied to the body-centered cubic unit cell so that the displacement difference between corresponding points on the boundary relative to the unit cell met the macroscopic unit strain requirement. ; In the formula, and These represent the displacements of the lattice unit cells relative to the corresponding points on the boundary. and These are the coordinates of the points corresponding to the relative boundaries of the lattice unit cells. This represents the macroscopic unit strain applied to the lattice unit cell.

[0031] Multiple independent macroscopic unit strain conditions are applied to the lattice unit cell, and the periodic perturbation displacement field under each macroscopic unit strain condition is solved. The equivalent stiffness tensor is expressed as: ; In the formula, The equivalent elastic tensor after homogenization of the lattice unit cell. It is a periodic lattice single-cell region. For unit cell volume, For the local material elasticity tensor within a single cell, and The macroscopic unit strain applied to a single cell, and For the corresponding periodic characteristic displacement field, , , , , , , , It is a spatial orientation indicator.

[0032] The equivalent density of the lattice unit cell is determined according to the following formula: ; In the formula, The equivalent density of a lattice unit cell, Density of the parent material The volume of the solid material region in the lattice unit cell. It refers to the solid material region within the lattice unit cell occupied by the parent material.

[0033] This yields the equivalent elastic matrix, equivalent density, and direction-dependent stiffness parameters of the body-centered cubic unit cell, which are then used as lattice equivalent material phases in subsequent multi-material topology optimization of solid materials, lattice equivalent materials, and material removal regions.

[0034] This step obtains the equivalent macroscopic mechanical properties of the lattice structure through an energy-based homogenization method and introduces them as material parameters into the overall structural optimization process. This avoids the modeling complexity and computational scale expansion caused by directly establishing a large number of microscopic lattice members in the macroscopic aircraft structure. It can significantly improve the optimization computation efficiency while maintaining the load-bearing characteristics of the lattice structure in the optimization.

[0035] Step S3: Construct a multi-material topology optimization model; Based on the load-bearing functional requirements of aircraft structural components, a multi-material topology optimization model was constructed, oriented towards structural deformation suppression and load transfer efficiency improvement. Material usage constraints and manufacturing feasibility constraints were embedded into the optimization solution process. Displacement, stress, and compliance responses within the design domain were obtained through finite element response analysis, providing a calculation basis for subsequent multi-material distribution adjustments.

[0036] The multi-material topology optimization model uses the lattice equivalent mechanical properties obtained in step S2 as the lattice equivalent material phase, and participates in the optimization together with the solid material phase and the material removal region to determine the spatial distribution of the solid load-bearing region, the lattice filling region, and the material removal region within the design domain. This topology optimization model characterizes the maximization of structural stiffness by minimizing structural flexibility, and simultaneously applies volume fraction constraints and manufacturing feasibility constraints. Its expression is: ; in, For structural flexibility, For external load vector, For displacement vectors, It is the volume fraction of the material. To preset the upper limit of volume fraction, For design variables, This represents the total number of units within the design area.

[0037] When performing solid topology optimization on the aircraft spoiler, the volume fraction of aluminum alloy is constrained to 0.11. When performing solid-lattice hybrid topology optimization on the aircraft spoiler, both aluminum alloy and lattice equivalent materials are introduced into the design domain, and their volume fraction constraints are both set to 0.1. Simultaneously, to improve manufacturing feasibility, manufacturing feasibility constraints are introduced during modeling to avoid inverted structural configurations. The unidirectional draft direction is defined as the z-direction, and the (th)th... The original design variables for each unit are: Then the one-way draft constraint is: ; in Indicates the ( ) unidirectional draft constraint values ​​at each unit. Indicates the unit layer number along the draft direction.

[0038] In this embodiment, the Method of Moving Asymptotes (MMA) is used to solve the above topology optimization model.

[0039] This step, by introducing manufacturing feasibility constraints, can avoid creating undercut, suspended, or non-demolding structures, ensuring that the optimization results are actually manufacturable.

[0040] Step S4: Sensitivity-driven update of multi-material design variables; Based on the structural response results obtained in step S3, the differences in load-bearing contributions of solid material, lattice equivalent material, and material removal region in each design unit are evaluated. Furthermore, considering the directional stiffness characteristics of the lattice equivalent material, a sensitivity-driven criterion is established for maintaining load-bearing paths, identifying lightweight regions, and matching directional stiffness. Multi-material design variables are updated according to this criterion, enabling the solid material phase, lattice equivalent material phase, and material removal region to adaptively evolve within the design domain according to their structural contribution and load transfer direction.

[0041] Among them, the The material properties of each design element are represented by a multi-material penalty interpolation model, and its element stiffness matrix is: ; in, For the first In the design unit, the first The design variable for each material phase, where p is the penalty factor. For the first The first unit The element stiffness matrix of a material phase.

[0042] Calculate the structural flexibility for the first In the design unit, the first The sensitivity expression for the material phase design variable is: ; Where C represents structural flexibility; For the first The nodal displacement vectors of each design unit; This is the transpose of the element node displacement vector.

[0043] Furthermore, for the lattice equivalent material phase, the equivalent elastic tensor obtained by homogenizing the lattice unit cell is introduced, and its directional equivalent stiffness is calculated based on the local load transmission direction: ; in, For lattice equivalent materials along the local load transfer direction Directional equivalent stiffness, For the lattice equivalent elastic tensor The equivalent flexibility tensor obtained by inverting it, , , , Transfer direction vector for local loads Components in different spatial directions.

[0044] Based on the flexibility sensitivity of each design unit and the directional equivalent stiffness of the lattice material, solid materials are preferentially retained in the main load-bearing path and high stiffness contribution areas. In areas with lower load-bearing requirements but still needing to maintain the continuity of force transmission, lattice equivalent materials are arranged. In areas with lower structural contribution, material removal areas are formed, thereby achieving the coordinated evolution of solid load-bearing areas, lattice filling areas, and material removal areas.

[0045] Step S5: Density filtering and Heaviside projection processing; Density filtering and Heaviside projection are applied to the updated multi-material design variables to suppress checkerboard patterns, mesh dependence, and intermediate density regions within the design domain, thereby creating continuous, identifiable, and easily reconstructable boundary lines between the solid material region, lattice-filled region, and material removal region.

[0046] S5.1, density filtering is performed on the multi-material design variables. The density filtering uses a distance-weighted average method, and its expression is: ; in center spacing Smaller than the filter radius elements The set, For unit With unit i The Euclidean distance between the centers These are the weighting coefficients.

[0047] S5.2, Heaviside projection is applied to the design variables after density filtering to enhance the clarity of material boundaries. The expression is as follows: ; in For projection parameters, This is a preset projection threshold. Because the projection operator is highly nonlinear, an extension strategy is used to avoid the optimization process converging to a local optimum. For example... Figure 3As shown, a smaller projection parameter is used in the initial optimization stage to maintain the continuity of design variables and search stability. Subsequently, the projection parameter is gradually increased as the iteration process progresses, so that the design variables gradually evolve towards a clear material distribution, thereby obtaining a solid-lattice hybrid structure with clear boundaries and easy reconstruction.

[0048] Based on the projected physical design variables The material phases of each design unit are determined, so that the solid material phase forms the solid load-bearing zone, the lattice equivalent material phase forms the lattice filling zone, and the material removal zone phase forms the material removal zone, thereby obtaining a multi-material topology with continuous boundaries, clear regions, and easy subsequent geometric reconstruction.

[0049] Step S6: Determine the convergence condition; Determine if the objective function meets the optimization convergence condition. If not, return to S3 to continue iteration; otherwise, terminate the optimization. The convergence condition is that the maximum change in the design variable between two consecutive iterations is less than a preset threshold. The iterative loop will continue until the maximum change in the design variables meets the preset stopping criterion.

[0050] Step S7: Geometric reconstruction generates the initial partition model; Based on the converged multi-material topology optimization results, the spatial distribution characteristics of the solid load-bearing region, lattice candidate filling region, and material removal region are extracted. The boundaries of each region are then geometrically reconstructed with partition constraints to generate an initial partitioned model of the solid-lattice hybrid structure that meets the requirements of maintaining aerodynamic shape, connection assembly, and load-bearing path. Three-dimensional modeling software is used to geometrically reconstruct the discrete boundaries obtained from topology optimization. By constructing a non-uniform rational B-spline (NURBS) spatial spline surface to fit the boundaries, the discretized topological boundaries are smoothly converted into a continuous and manufacturable three-dimensional geometric solid model. During the reconstruction process, key topological features of the main load-bearing path, connection interface, and lattice candidate filling region are preserved, while small branches, isolated regions, and locally redundant features that do not meet manufacturing size requirements are removed to improve the manufacturability of the model and the stability of subsequent analysis.

[0051] After boundary smoothing and region reconstruction, the topology results are converted from STL format to standard engineering formats such as STEP, forming an initial model of a solid-lattice hybrid structure that can be used for lattice mapping, structural assembly, and finite element verification, such as... Figure 4 As shown, the left figure is the configuration obtained by multi-material topology optimization, and the top and bottom figures on the right are the front view and back view of the same solid-lattice hybrid structure reconstructed from the left figure, respectively.

[0052] Step S8: Filling and constructing the transition region of the anisotropic lattice; The candidate lattice filling regions in the initial partitioning model are transformed into anisotropic lattice filling structures. Based on the load transfer direction within the lattice filling regions, the principal stiffness direction of the lattice unit cells, and their spatial adjacency with the solid load-bearing regions, the local orientation and arrangement of the lattice unit cells are determined. Simultaneously, a connecting transition region is constructed between the solid load-bearing regions and the lattice filling regions to maintain continuity in the geometric boundaries, load transfer paths, and lattice orientation of the solid-lattice hybrid structure.

[0053] Among them, the first in the lattice filling area The local load transfer direction of each design unit is determined by the principal direction of the stress tensor, and its expression is: ; In the formula, For the first Stress tensor of each design unit For the first The local load transfer direction of each design unit These are the corresponding principal stress eigenvalues.

[0054] Based on the correspondence between the local load transfer direction and the principal stiffness direction of the lattice unit cell, a local rotation matrix is ​​constructed. Furthermore, a coordinate transformation is performed on the equivalent elastic tensor obtained by homogenizing the lattice unit cell to obtain the lattice equivalent elastic tensor with local orientation within the e-th design element: ; In the formula, The lattice equivalent elastic tensor after local orientation transformation. Let be the equivalent elastic tensor of the lattice unit cell in the initial local coordinate system. , , , Local rotation matrix The amount.

[0055] Based on the spatial adjacency between the lattice filling area and the solid load-bearing area, a connection transition region is constructed between the solid structure and the lattice structure. This connection transition region is represented as follows: ; ; In the formula, For the solid-to-lattice connection transition region, For the dot matrix filling area, For the solid load-bearing area, This serves as the boundary between the solid load-bearing area and the lattice-filled area. For point To the boundary distance, This represents the width of the transition area.

[0056] Within the connection transition region, the lattice unit cells are trimmed, densified, have gradually changed rod diameters, or have interface node coupling processes to ensure that the solid structure and the lattice structure remain continuous in terms of geometric boundaries, load transfer paths, and local coordinate directions.

[0057] This step, by constructing a connection transition region between the solid structure and the lattice structure, can effectively alleviate the problem of discontinuity in the connection between the lattice region and the solid structure, avoid local stress concentration caused by abrupt changes in rod diameter or insufficient node connection, and improve the reliability and manufacturability of converting optimization results into engineering models.

[0058] Step S9: Establish a local sensitivity evaluation criterion for lattice size optimization; For the body-centered cubic lattice-filled region in the initial model of the solid-lattice hybrid structure, the influence of lattice member diameter parameters on structural stiffness, mass, and interface load transfer performance is evaluated, and a local sensitivity evaluation criterion for optimizing the size of the body-centered cubic lattice is established. The body-centered cubic lattice is a member-based lattice; the member diameter is used as the main dimensional design variable, and combined with the local lattice orientation determined in step S8, dimensional sensitivity analysis is performed on each member.

[0059] For the first in a body-centered cubic lattice The element stiffness matrix of a single member under local orientation is expressed as: ; In the formula, For the first The cross-sectional area of ​​each member, The stiffness matrix per unit cross-sectional area after considering the local orientation of the members and the anisotropic stiffness of the lattice.

[0060] The structural objective function and the sensitivity of volume to bar diameter are expressed as follows: ; ; In the formula, The objective function is a structural strain energy type. For the first The element node displacement vector corresponding to each bar element. For the length of the rod, For the volume of the rod, For the first Stiffness matrix of each bar element.

[0061] Meanwhile, in the transition area between the solid load-bearing zone and the body-centered cubic lattice filling zone, the members near the interface are locally densified, have gradually changed diameters, or are coupled together to improve the continuity of the connection between the solid structure and the lattice structure and avoid local stress concentration caused by abrupt changes in diameter or insufficient node connection.

[0062] Step S10: Co-optimization of size and orientation; For the body-centered cubic lattice-filled region in a solid-lattice hybrid structure, the diameter, cross-sectional area, and local orientation parameters of the lattice members are used as design variables. Based on the local load transfer direction and the sensitivity evaluation results obtained in step S9, the size and orientation of the body-centered cubic lattice are optimized. During the optimization process, the continuity of node connections between adjacent body-centered cubic unit cells and the coordination of changes in member diameter are considered to ensure that lattice unit cells of different sizes and orientations remain continuous in spatial arrangement, node connections, and load transfer paths.

[0063] For the basis point lattice of body-centered cubic rods, the following dimensional and orientation co-optimization model is established: ; In the formula, The set of design variables for the dimensions and orientation of the base point lattice of the member. For the first Local orientation matrix of a single unit cell of a rod-based lattice The overall stiffness matrix, The diameter of all lattice members; The overall stiffness matrix is ​​determined and assembled from the diameters and local orientations of the lattice members. Let be the total nodal displacement vector. The overall external load vector; This represents the total volume of the bar-based lattice structure under the current design variables. This is the upper limit of the total volume of the preset rod base point lattice.

[0064] After updating the size and adjusting the orientation of the lattice unit cells, a connectivity correction method based on shared boundary cutting control points is used to perform geometric connectivity processing on adjacent lattice unit cells. The lattice filling region is divided into multiple unit cell structures, and shared cutting control points are set on the common boundary of adjacent unit cells. The height parameter of the cutting control points is used as a geometric control variable to ensure that adjacent unit cells adopt the same cutting height at the common boundary, thereby ensuring that the cutting surfaces of adjacent lattice unit cells match each other at the common boundary.

[0065] The optimization model corresponding to the connectivity correction is expressed as follows: ; In the formula, This is a set of height parameters for cutting control points. For the first The height parameters of each cutting control point This represents the total number of cutting control points. Let S be the objective function for structural flexibility. For the first The relative volume corresponding to a single cell structure or coarse grid unit. The number of unit cells or coarse grid cells. This is the preset desired volume fraction.

[0066] Based on the above optimization model, the height parameters of the shared cutting control points are adjusted so that adjacent lattice units have a consistent cutting height at the common boundary, and the lattice structure with optimized dimensions maintains geometric connectivity and continuous load transfer between adjacent units.

[0067] Step S11: Multi-index finite element verification and performance comparison; Finite element numerical verification and multi-index performance check were performed on the solid-lattice hybrid structure after lattice size optimization. Performance parameters such as structural mass, maximum displacement, maximum stress, structural flexibility and stiffness improvement rate were extracted and compared with traditional solid structure or hybrid structure without lattice size optimization to evaluate the comprehensive performance of the solid-lattice hybrid structure in terms of lightweighting, deformation suppression, stress control and load transfer continuity.

[0068] The results show that, compared with traditional solid structures, the optimized structure obtained by this invention maintains good load-bearing performance while reducing the total mass by 47.16%. Specifically, the maximum displacement is reduced by 9.47%, the stiffness is increased by 9.94%, and the maximum stress index is improved by 47.25%. These results demonstrate that this solid-lattice hybrid structure can significantly reduce structural mass while improving material utilization efficiency, and simultaneously meet the requirements for structural stiffness, displacement control, and stress control.

[0069] Table 1 Comparison of performance of two types of spoiler structures Note: In Table 1, the 81.39 kg for the "traditional structural model" refers to the internal design domain mass after material removal through topology optimization; the 292.6 kg for the initial overall model includes the aerodynamic shape maintenance area, the connection and assembly area, and the upper and lower skins. The statistical methods for the two are different.

[0070] Step S12: Determine whether the design requirements are met; Determine whether the optimized solid-lattice hybrid structure meets the design requirements. Specifically, compare and analyze the optimized solid-lattice hybrid structure with the traditional solid structure. If the optimized structure meets the preset design requirements in terms of displacement, stress, and stiffness while reducing mass, then output the final solid-lattice hybrid aircraft structural model. If it does not meet the design requirements, return to step S2 and use a different lattice configuration until a structural model that meets the requirements for lightweighting and load-bearing performance is obtained.

[0071] Figure 5 The flowchart illustrates the optimization of the spoiler structure using a lattice. Based on multi-material topology optimization results, body-centered cubic (BCC) lattice unit cells are filled within the equivalent material region of the lattice, resulting in a hybrid structure consisting of a solid load-bearing portion and a BCC lattice filling portion. Subsequently, using the diameter or cross-sectional area of ​​the BCC members as design variables, the dimensions of the lattice members are optimized under a volume fraction constraint of 0.3. This allows the member dimensions to be redistributed according to local stress requirements, further reducing the structural mass and improving material utilization efficiency while ensuring the overall stiffness and load-bearing capacity of the spoiler.

[0072] This step optimizes the size of the lattice members by spatially adjusting their dimensions according to the local stress levels in different areas. This provides stronger support to high-load areas and reduces material redundancy in low-load areas, thereby improving overall stiffness and stress distribution while reducing structural mass.

[0073] In summary, this invention provides a solid-lattice hybrid aircraft structure optimization design method. By introducing a lattice unit cell homogenization method to obtain equivalent material parameters of the lattice, and employing a multi-material topology optimization method to collaboratively determine the spatial distribution of solid materials, lattice materials, and material removal regions, combined with density filtering, Heaviside projection, and lattice size optimization strategies, it can stably obtain solid-lattice hybrid structural configurations with clear main load-bearing paths, reasonable lattice filling, and high material utilization. This method not only avoids the problem of traditional lattice filling regions relying on empirical division, but also allows for further dimensional optimization of the diameter or cross-sectional area of ​​lattice members based on the topology optimization results. This enables the lattice structure to redistribute materials according to local load-bearing requirements, thereby balancing structural lightweighting, stiffness improvement, and stress control. This method realizes a complete design process from finite element modeling, multi-material topology optimization, model reconstruction to lattice size optimization and numerical verification, providing a new technical path for the design, optimization, and engineering application of high-performance lightweight structures in the aerospace field.

[0074] The solid-lattice hybrid aircraft structural optimization design method provided by this invention can be widely applied to the lightweight design and stiffness performance improvement of complex load-bearing components such as aircraft spoilers, control surfaces, and wing boxes. Through the synergistic layout optimization of solid and lattice materials and the rational allocation of lattice member dimensions, this invention can significantly reduce structural mass while improving overall stiffness, deformation response, and stress distribution, demonstrating significant industrial practical value and promising prospects for widespread application.

Claims

1. A method for optimizing the design of a solid-lattice hybrid aircraft structure, characterized in that, Includes the following steps: Step S1: Based on the geometric shape, connection and assembly relationship, load transfer path and lightweight design goal of the aircraft structural components, establish a three-dimensional finite element model including load conditions, boundary conditions, candidate material types and non-design regions; and according to the requirements of maintaining aerodynamic shape, maintaining connection and assembly and maintaining main load-bearing path, perform functional region attribute calibration on the three-dimensional finite element model, divide it into aerodynamic shape maintenance region, connection and assembly region, main load-bearing design region and material removal region, and form a design constraint mapping relationship oriented towards the coordinated distribution of solid materials, lattice equivalent materials and material removal regions; Step S2: Select a configuration from the lattice unit cell configuration library, use the homogenization method to calculate the macroscopic equivalent mechanical properties of the lattice unit cell in different principal directions, obtain the equivalent elastic matrix, equivalent density and direction-related performance parameters, and convert the lattice structure composed of the lattice unit cells into an anisotropic lattice equivalent material phase, and introduce the anisotropic lattice equivalent material phase into subsequent multi-material topology optimization; Step S3: Based on the load-bearing functional requirements of the aircraft structural components, construct a performance evaluation criterion oriented towards structural deformation suppression and load transfer efficiency improvement, and embed material usage limits and manufacturing feasibility constraints into the optimization solution process; Displacement, stress, and compliance responses within the design domain are obtained through finite element response analysis. Step S4: Based on the structural response results, evaluate the performance contribution differences of solid material, lattice equivalent material and material removal region in each design unit, and combine the directional stiffness characteristics of lattice equivalent material to form a sensitivity-driven criterion for maintaining load-bearing path, identifying lightweight regions and matching directional stiffness. The multi-material design variables are updated according to the aforementioned criteria, so that the solid material, lattice equivalent material, and material removal region can adaptively evolve within the design domain according to the degree of structural contribution and the direction of load transfer. Step S5: Density filtering and Heaviside projection processing are applied to the updated multi-material design variables to suppress checkerboard phenomenon, mesh dependence and intermediate density regions in the design domain, so that continuous, identifiable and easy-to-reconstruct boundary lines are formed between the solid material area, the lattice filling area and the material removal area. Step S6: Determine whether the optimization iteration meets the preset convergence condition. If it does not meet the condition, return to step S3 to continue the iteration; if it does meet the condition, proceed to step S7. Step S7: Based on the converged multi-material topology results, extract the spatial distribution characteristics of the solid load-bearing area, the lattice candidate filling area and the material removal area, and perform geometric processing and structural region reconstruction on the boundaries of each region to generate an initial partitioning model of the solid-lattice hybrid structure that meets the functional preservation requirements. Step S8: The candidate lattice filling region in the initial partitioning model is transformed into anisotropic lattice filling structure. Based on the load transfer direction, principal stiffness direction and spatial adjacency relationship between the lattice filling region and the solid load-bearing region, the local orientation and arrangement of the lattice unit cell are determined. At the same time, a connection transition region between the solid structure and the lattice structure is constructed to ensure that the solid-lattice hybrid structure remains continuous in geometric boundaries, load transfer paths and local coordinate directions. Step S9: For the lattice-filled region in the initial model of the solid-lattice hybrid structure, evaluate the influence of different lattice cell wall thickness parameters and rod diameter parameters on the structural stiffness, mass and interface load transfer performance, and establish local sensitivity evaluation results for lattice size optimization. Step S10: For the anisotropic unit cell configuration of the bar base lattice, the wall thickness parameter, bar diameter parameter and unit cell orientation parameter are used as design variables, and the size and orientation are optimized in a coordinated manner based on the local load transfer direction and sensitivity evaluation results. During the size update and orientation adjustment process, the continuity of connection between adjacent lattice unit cells is considered so that lattice unit cells of different sizes and orientations can maintain coordination in spatial arrangement, node connection and load transfer. Step S11: Determine whether the optimized solid-lattice hybrid structure meets the design requirements; If the design requirements are not met, return to step S2 and re-optimize using a different lattice configuration; If satisfied, the final solid-lattice hybrid aircraft structure model will be output.

2. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, In step S2, the anisotropic lattice equivalent material phase is obtained through a periodic unit cell homogenization method: at least one lattice unit cell configuration is selected from a preset lattice unit cell configuration library, the lattice unit cell configuration including rod-based lattice unit cells or surface-based lattice unit cells, and periodic boundary conditions are applied to the lattice unit cells: ; In the formula, and These represent the displacements of the lattice unit cells relative to the corresponding points on the boundary. and These are the coordinates of the points corresponding to the relative boundaries of the lattice unit cells. The macroscopic unit strain applied to the lattice unit cell; Multiple independent macroscopic unit strain conditions are applied to the lattice unit cell, and the periodic perturbation displacement field under each macroscopic unit strain condition is solved. The equivalent stiffness tensor is expressed as: ; In the formula, The equivalent elastic tensor after homogenization of the lattice unit cell. It is a periodic lattice single-cell region. For unit cell volume, For the local material elasticity tensor within a single cell, and The macroscopic unit strain applied to a single cell, and For the corresponding periodic characteristic displacement field, , , , , , , , The spatial orientation index; the equivalent density of the lattice unit cell is determined according to the following formula: ; In the formula, The equivalent density of a lattice unit cell, Density of the parent material The volume of the solid material region in the lattice unit cell. It refers to the solid material region within the lattice unit cell occupied by the parent material.

3. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, In step S3, the constructed topology optimization model is a multi-material topology optimization model. The multi-material topology optimization model uses the lattice equivalent mechanical properties obtained in step S2 as the lattice equivalent material phase, and participates in the optimization together with the solid material phase and the material removal region to determine the spatial distribution of the solid load-bearing region, the lattice filling region and the material removal region in the design domain. The topology optimization model characterizes structural stiffness maximization by minimizing structural flexibility, and imposes volume fraction constraints and manufacturing feasibility constraints. Its expression is as follows: ； in, For structural flexibility, For external load vector, For displacement vectors, It is the volume fraction of the material. To preset the upper limit of volume fraction, For design variables, The total number of units within the design area; the manufacturing feasibility constraints include unidirectional draft constraints, the expression of which is: ,in Indicates the ( ) unidirectional draft constraint values ​​at each unit. Indicates the unit layer number along the draft direction.

4. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, In step S4, the first The material properties of each design element are represented by a multi-material penalty interpolation model, and its element stiffness matrix is: ; in, For the first In the design unit, the first The design variable for each material phase, where p is the penalty factor. For the first The first unit The element stiffness matrix of the first material phase; structural flexibility relative to the first... In the design unit, the first The sensitivity expression for the material phase design variable is: ; Where C represents structural flexibility; For the first The nodal displacement vectors of each design unit; This is the transpose of the element nodal displacement vector; for the lattice equivalent material phase, an equivalent elastic tensor obtained by homogenizing the lattice unit cell is introduced, and its directional equivalent stiffness is calculated based on the local load transfer direction: in, For lattice equivalent materials along the local load transfer direction Directional equivalent stiffness, For the lattice equivalent elastic tensor The equivalent flexibility tensor obtained by inverting it, , , , Transfer direction vector for local loads Components in different spatial directions.

5. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, Step S5 specifically includes: S5.1, the density filtering process uses a distance-weighted filtering method, the expression of which is: ; ; in center spacing Smaller than the filter radius elements The set, For unit With unit The Euclidean distance between the centers, of which center spacing Smaller than the filter radius elements A set; S5.2, the design variables after density filtering are processed using Heaviside projection, the expression of which is: ; in For projection parameters, The preset projection threshold; Based on the projected physical design variables The material phases of each design unit are determined, so that the solid material phase forms a solid load-bearing area, the lattice equivalent material phase forms a lattice filling area, and the material removal area phase forms a material removal area, thus obtaining a multi-material topology with continuous boundaries and clear regions.

6. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, In step S7, based on the converged multi-material topology optimization results, the spatial distribution characteristics of the solid load-bearing area, the lattice candidate filling area, and the material removal area are extracted, and the boundaries of each region are partitioned and constrained for geometric reconstruction. During the reconstruction process, the aerodynamic shape retention area, the connection assembly area, and the load input area are used as functional retention areas. Continuous surface fitting is performed on the solid load-bearing area, a fillable spatial boundary is established for the lattice candidate filling area, the material removal area is spatially reorganized to reduce weight, and the transition interface between the solid area and the lattice area is smoothed. The discrete topological boundary is converted into a continuous and editable three-dimensional geometric model through a non-uniform rational B-spline spatial spline surface, and output as a three-dimensional geometric model in STEP or STL format.

7. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, In step S8, the direction of local load transfer is determined by the principal direction of the stress tensor, satisfying: ; In the formula, For the first Stress tensor of each design unit For the first The local load transfer direction of each design unit The corresponding principal stress eigenvalues ​​are used; based on the correspondence between the local load transfer direction and the principal stiffness direction of the lattice unit cell, a local rotation matrix is ​​constructed. And perform coordinate transformation on the equivalent elastic tensor obtained by homogenizing the lattice unit cell to obtain the first... The lattice equivalent elastic tensor with local orientation within each design unit: ; In the formula, The lattice equivalent elastic tensor after local orientation transformation. Let be the equivalent elastic tensor of the lattice unit cell in the initial local coordinate system. , , , Local rotation matrix The components; the connection transition region is represented as: ; ; In the formula, For the solid-to-lattice connection transition region, For the dot matrix filling area, For the solid load-bearing area, This serves as the boundary between the solid load-bearing area and the lattice-filled area. For point To the boundary distance, This represents the width of the transition area.

8. The method for optimizing the structure of a solid-lattice hybrid aircraft according to claim 1, characterized in that, In step S9, for the base lattice of the rods, the diameter of the rods in the lattice is used as a dimensional design variable. The element stiffness matrix of a lattice member under local orientation is expressed as: ; In the formula, For the first The cross-sectional area of ​​each member, The stiffness matrix per unit cross-sectional area is given by considering the local orientation of the members and the anisotropic stiffness of the lattice. The structural objective function and the sensitivity of the volume to the member diameter are expressed as follows: ; ; In the formula, The objective function is a structural strain energy type. For the first The element node displacement vector corresponding to each bar element. For the length of the rod, For the volume of the rod, For the first Stiffness matrix of each bar element; For a surface-based lattice, the wall thickness of the lattice surface is used as a dimensional design variable. The stiffness matrix of a surface-based lattice element is expressed as: ; In the formula, For the first The wall thickness of each surface-based lattice element Let be the area of ​​the mid-surface of this surface-based lattice element. The membrane strain-displacement matrix, For the strain-displacement matrix, Let be the anisotropic equivalent elastic tensor or equivalent elastic matrix after local orientation transformation; the structural objective function and the sensitivity of volume to wall thickness are expressed as: ; ; In the formula, For the first Stiffness matrix of a surface-based lattice element For the first The mid-surface area of ​​each surface-based lattice element Let be the volume of the lattice wall.

9. The method for optimizing the structure of a solid-lattice hybrid aircraft according to claim 1, characterized in that, In step S10, for the rod base point lattice, the size and orientation co-optimization model is expressed as: ; In the formula, Design the set of variables for the dimensions and orientation of the base point lattice of the member. For the first Local orientation matrix of a single unit cell of a rod-based lattice For displacement vectors, The overall stiffness matrix, The diameter of all lattice members; The overall stiffness matrix is ​​determined and assembled from the diameters and local orientations of the lattice members. Let be the total nodal displacement vector. The overall external load vector; This represents the total volume of the bar-based lattice structure under the current design variables. This is the upper limit of the total volume of the preset rod base point lattice; For a surface-based lattice, the size and orientation co-optimization model is expressed as: ; In the formula, The set of design variables for the size and orientation of the surface base lattice.

10. The solid-lattice hybrid aircraft structure optimization design method according to claim 1, characterized in that, In step S10, after updating the size and adjusting the orientation of the lattice unit cells, a connectivity correction method based on shared boundary cutting control points is further used to perform geometric connectivity processing on adjacent lattice unit cells: the lattice filling region is divided into multiple unit cell structures, and shared cutting control points are set on the common boundary of adjacent unit cells. The height parameter of the cutting control points is used as a geometric control variable to ensure that adjacent unit cells use the same cutting height at the common boundary, thus ensuring that the cutting surfaces of adjacent lattice unit cells match each other at the common boundary; the optimization model corresponding to the connectivity correction is expressed as: ; In the formula, This is a set of height parameters for cutting control points. For the first The height parameters of each cutting control point This represents the total number of cutting control points. Let S be the objective function for structural flexibility. For displacement vectors, The overall stiffness matrix, For the first The relative volume corresponding to a single cell structure or coarse grid unit. The number of unit cells or coarse grid cells. The desired volume fraction is set as a preset value. The height parameter of the shared cutting control point is adjusted according to the above optimization model so that adjacent lattice units have a consistent cutting height at the common boundary, and the lattice structure with optimized dimensions maintains geometric connectivity and load transfer continuity between adjacent units.

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