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CN-122020837-A - Layout optimization design method for airfoil reinforcing rib

CN122020837ACN 122020837 ACN122020837 ACN 122020837ACN-122020837-A

Abstract

The invention belongs to the technical field of aircraft design, and particularly relates to a layout optimization design method of airfoil reinforcing ribs. Conventional airfoil stiffener layout designs rely heavily on the engineering experience of the designer, reference prototypes, and a series of "design-check-modify" trial-and-error procedures. The invention skillfully solves the mathematical solution problem of '0-1' discrete optimization problem through the SIMP model and the penalty factor, and the final result is clear. Through the combined control of volume constraint and filtering technology, the sparse rib layout with the least material consumption and the least quantity can be naturally generated, and the layout is continuous and smooth and is easy to be converted into a practical engineering component. The efficiency of the gradient-based optimization algorithm is far higher than that of gradient-free algorithms such as genetic algorithm when processing large-scale variables, so that the method is suitable for engineering practice.

Inventors

  • ZHOU HAN
  • ZHOU CHUNPING
  • YU JIXUAN

Assignees

  • 中国航空工业集团公司济南特种结构研究所

Dates

Publication Date
20260512
Application Date
20251224

Claims (10)

  1. 1. The layout optimization design method of the aeroplane airfoil reinforcing rib is characterized by comprising the following steps of: Step 1, establishing a finite element model of an airfoil structure according to the aerodynamic shape of the airfoil and interface design, and setting material properties, boundary conditions and analysis types; step 2, presetting a series of alternative choices in the design space of the airfoil surface Establishing material and section attribute for each reinforcing rib to form a mother set S with optimized layout, defining topological variable, and introducing a density variable for each reinforcing rib in the mother set S , ; Step 3, establishing the elastic modulus of the reinforcing rib through a power function interpolation model And density variable The association is established as follows: Wherein, the Is when the density is variable The elastic modulus of the reinforcing rib is 1, In order to be a penalty factor, Is an extremely small positive number introduced for avoiding singular stiffness matrix; step 4, performing simulation calculation on the finite element model, and extracting the structure flexibility ; Step 5, calculating the flexibility of the structure With respect to density variables Sensitivity of (a) The calculation formula is as follows: In the formula, Representing the node displacement vector corresponding to a single rib, Representing a stiffness matrix corresponding to the single stiffening rib; step 6, calculating density variable Corresponding minimum clearance constraint function between reinforcement ribs : In the formula, In order to be a penalty factor, In order to strengthen the minimum inter-rib gap, As a density variable Corresponding stiffening rib and density variable The distance between the corresponding reinforcing ribs; For each density variable Corresponding minimum clearance constraint function between reinforcement ribs Condensing by using p-mean condensing function, and converting into single minimum gap constraint function : In the formula, Is a super-parameter in the p-mean coacervation function, A relaxation factor introduced to avoid overconstraining; Calculating density variables Corresponding maximum intercostal gap constraint function : In the formula, In order to be a penalty factor, In order to strengthen the maximum inter-rib gap, As a distance density variable The corresponding reinforcing ribs do not exceed the maximum clearance Is provided with a number of reinforcing ribs which are arranged in the middle of the steel plate, for each density variable Corresponding maximum gap constraint function Condensing by using p-mean condensing function, and converting into a single maximum gap constraint function : Step 7, optimizing calculation by adopting gradient algorithm, and updating density variable ; Step 8, judging whether the optimization process is converged or not, if not, entering a step 3 to perform a new round of iterative optimization, otherwise, entering a step 9; Step 9, after convergence, according to the density variable of each reinforcing rib And (3) a relation between the final value of the (c) and the threshold value to obtain a discrete rib layout.
  2. 2. The layout optimization design method according to claim 1, wherein in step 3, a RAMP interpolation function is used to calculate the material elastic modulus of the rib unit, and the RAMP interpolation function is as follows: Penalty factor at this time Recommended 16.
  3. 3. The layout optimization design method according to claim 2, wherein the sensitivity calculation formula in step 5 becomes: 。
  4. 4. The layout optimization design method according to claim 1, wherein in step 3, when the reinforcing rib is grid-sectioned by the shell unit, the material property is kept unchanged, and the thickness of the reinforcing rib unit is equal to the thickness of the reinforcing rib unit Interpolation calculation is performed, namely: In the formula, Is the rib element thickness when the density variable x e is 1.
  5. 5. The layout optimization design method according to claim 1, wherein the structural flexibility in step 4 is calculated by using the following formula : In the formula, As the displacement vector of the node, For the node load vector, only the node load vector is required to be extracted from the finite element calculation result And node displacement vector Extraction of the stiffness matrix is avoided.
  6. 6. The layout optimization design method according to claim 1, wherein in step 5, the structure flexibility is calculated by using the following formula With respect to density variables Sensitivity of (a) : Only the node load vector of the reinforcing rib is required to be extracted from the finite element calculation result And node displacement vector 。
  7. 7. The layout optimization design method according to claim 1, wherein in step 6, the p-norm agglomeration function is replaced by KS agglomeration function, and the minimum gap constraint function is obtained And maximum gap constraint function The method comprises the following steps: 。
  8. 8. the layout optimization design method according to claim 1, wherein the gradient class algorithm in the step 7 comprises MMA, an optimization criterion method OC or a sequence quadratic programming method.
  9. 9. The layout optimization design method according to claim 1, wherein the minimum gap constraint function between the reinforcing ribs is designed by adopting a density filtering mode, and the minimum gap constraint between the reinforcing ribs is converted into that the reinforcing ribs in any one of the parent sets S are separated from each other The maximum gap constraint function between the reinforcing ribs is designed by adopting a density filtering mode, and the maximum gap constraint between the reinforcing ribs is converted into that the reinforcing ribs in any parent set S are separated from the reinforcing ribs At least 1 reinforcing rib is provided in the region of the (c).
  10. 10. The layout optimization design method of claim 1, wherein the convergence condition comprises: 1) The number of optimization iterations exceeds the upper limit, and the maximum number of iterations can be set to 200; 2) The maximum variation before and after the updating of the design variable is less than 0.01; Meeting either condition may be considered that the optimization has converged.

Description

Layout optimization design method for airfoil reinforcing rib Technical Field The invention belongs to the technical field of aircraft design, and particularly relates to a layout optimization design method of a wing reinforcing rib of an aviation aircraft. Background The aeroplane surface of the aircraft is a key component for bearing aerodynamic load and maintaining the flying attitude, and the structural design of the aeroplane is directly related to the performance, safety and economy of the aircraft. In airfoil structures, stiffening ribs (simply "ribs") are the longitudinal load bearing members of the core, whose primary functions include transferring aerodynamic loads, maintaining airfoil profile shape, supporting the skin, and improving the overall and local stability of the structure. Thus, the layout design of the stiffening ribs, including the number, location, geometry and size thereof, has a decisive influence on the weight, strength and stiffness of the airfoil structure. Conventional airfoil stiffener layout designs rely heavily on the engineering experience of the designer, reference prototypes, and a series of "design-check-modify" trial-and-error procedures. The designer typically initially determines a rib layout based on aerodynamic load distribution, overall layout requirements, and past success, and then performs strength, stiffness, and stability checks via finite element analysis. If the verification is not passed, the position or the size of the rib is manually adjusted by experience, analysis is performed again, and the process is circulated until the design requirement is met. This approach has the following significant limitations: 1. The subjectivity is strong, the optimal solution is difficult to obtain, the design quality is highly dependent on personal experience, different designers can give schemes with great difference, and whether the solution is the solution with the lightest weight or the optimal performance is difficult to prove. 2. The method has low efficiency and long development period, geometric modeling and finite element analysis are needed to be carried out again for each design change, the whole process is tedious and time-consuming, and the method cannot meet the design requirement of rapid iteration of modern aircrafts. 3. The exploration space is limited, and due to time and cost limitations, designers can only compare in a limited number of schemes, and can not fully explore the wide design space, and better layout forms can be omitted. With the development of computer technology and optimization theory, a structure optimization technology based on parameterized modeling and mathematical programming method appears. Such methods parameterize the rib layout and optimize it using a direct search algorithm. However, conventional optimization methods still face serious challenges in coping with such complex problems as rib placement: 1. The computational cost is high, the stiffening rib layout optimization is a discrete variable optimization problem, and each function evaluation (i.e., finite element analysis in each iteration) requires a significant amount of computational resources. For global optimization, thousands of iterations are required, with the total computation cost being prohibitive. 2. The optimization algorithm is sensitive to the initial value, discrete variables and discontinuous design space are difficult to process, and the optimization algorithm is easy to converge to a local optimal solution instead of a global optimal solution. 3. Convergence problems when the design variables are large (as in the case of optimizing the number and positions of ribs), the complexity of the problem increases dramatically, and conventional optimization algorithms may suffer from convergence difficulties or non-convergence. In addition, topology optimization is also a powerful tool that can find the optimal distribution of materials within a given design area. However, when the conventional continuous topology optimization (such as searching for the optimal stiffener on the skin) is applied to the airfoil integral structure, the result is often complex two-dimensional or three-dimensional material distribution, which has a great gap from the "beam-rib-skin" discretized structure system customarily adopted in aviation engineering, and has poor engineering interpretation and manufacturing feasibility. Disclosure of Invention The field is urgent to need an optimization design method capable of considering both the calculation efficiency and the global optimizing capability, and aiming at the problem of the aircraft wing reinforcing rib layout, so as to quickly and automatically find the optimal or near-optimal layout scheme with lighter weight and performance meeting the requirements in the conceptual design stage. Aiming at the most fundamental layout problem that ribs cannot be automatically created or deleted in the prior art, namely that the problem of 'where