Method for calculating equivalent stiffness of dense rib type aileron of airplane
By calculating the unit cell model of the closely spaced aileron using Bloch's theorem and the finite element method, the problem of high computational resource consumption in existing technologies is solved, enabling rapid and accurate calculation of aircraft aileron stiffness and improving design and analysis efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-26
- Publication Date
- 2026-04-14
AI Technical Summary
Existing technologies consume a large amount of computational resources in calculating the stiffness of aircraft aileron structures, making it difficult to achieve fast and accurate stiffness optimization design.
By employing Bloch's theorem and the finite element method, the wave propagation characteristics and equivalent elastic modulus of the unit cell are calculated by extracting the unit cell model of the closely spaced aileron, applying periodic boundary conditions, and obtaining the equivalent stiffness of the aileron.
It enables rapid and accurate calculation of the stiffness of aircraft ribbed ailerons, improving the efficiency of structural design and analysis.
Smart Images
Figure CN121859640A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of aircraft ribbed aileron structure design, and specifically relates to a method for calculating the equivalent stiffness of an aircraft ribbed aileron. Background Technology
[0002] Ailerons are lateral control surfaces located on either side of the wing's trailing edge. Their function is to provide sufficient rolling moment to ensure the aircraft's lateral controllability. The most common aileron structure is the closely spaced ribbed aileron, connected to the fixed trailing edge of the wing via joints. During flight, the aileron primarily bears aerodynamic loads, therefore, its stiffness design is crucial. In conventional aileron design, the use of composite materials, metals, and the assembly of components significantly complicates stiffness calculations. After detailed structural design of the aircraft control surfaces, establishing a refined finite element model to calculate the aileron stiffness consumes enormous computational resources, serving only as a stiffness check and failing to provide timely stiffness optimization for the aileron design. Summary of the Invention
[0003] To address the aforementioned problems, this application provides a method for calculating the equivalent stiffness of an aircraft's closely spaced ailerons, comprising:
[0004] Step S101, Unit cell extraction: Based on the structural design of the aircraft's closely spaced aileron, the aileron structure is approximated as a periodic structure. The aileron structure is cut by two parallel planes with a spacing of a, and representative unit cells are extracted, where the spacing a is the lattice constant.
[0005] Step S102, Finite Element Modeling: The finite element method is used to establish the finite element model of the unit cell. Material parameters and structural parameters are assigned to each component in the unit cell, including the thickness and material properties of the skin, ribs, front beam, and tail edge.
[0006] Step S103: Applying boundary conditions: Based on Bloch's theorem, apply periodic boundary conditions to the unit cell to simulate the wave propagation characteristics in an infinite periodic structure.
[0007] Step S104, Band Structure Calculation: Solve for different wave vectors in the Bloch boundary conditions. from The first three characteristic frequencies within the range are used to obtain the first three dispersion curves of the dense-ribbed aileron unit cell;
[0008] Step S105, Wave velocity extraction: Extract the slopes of the first three dispersion curves within a preset wavelength range, which correspond to the elastic wave propagation velocities in x, y, and z, respectively. , and ;
[0009] Step S106, Equivalent stiffness calculation: Based on the wave velocity calculation formula, combined with the equivalent mass density of the unit cell... The equivalent elastic modulus of the closely spaced ailerons in different directions was obtained.
[0010] Preferably, the single-cell extraction in step S101 includes:
[0011] The ribbed aileron structure includes an upper skin, a lower skin, a front spars, a leading edge, ribs, and a trailing edge;
[0012] The single-cell extraction direction is along the span of the aileron, and the cutting plane spacing 'a' is determined according to the rib spacing, with a range of 50-300 mm.
[0013] The unit cell structure maintains the geometric integrity of the ailerons, including the skin curvature and the arrangement of the ribs.
[0014] Preferably, the finite element modeling in step S102 includes:
[0015] A shell element discrete unit cell structure is adopted, and the mesh size is determined according to the unit cell size, with the element size ranging from a / 10 to a / 20.
[0016] Material parameters include elastic modulus, Poisson's ratio, and density, with values assigned separately for composite materials and metallic materials;
[0017] Structural parameters include skin thickness of 0.5-3mm, rib thickness of 1-5mm, and beam thickness of 2-6mm.
[0018] Preferably, the periodic boundary conditions are applied based on Bloch's theorem, applying displacement constraints to nodes on the relative boundaries of the unit cell. The periodic boundary conditions cover all corresponding faces of the unit cell, including spanwise and chordwise directions.
[0019] Preferably, the band structure calculation in step S104 includes:
[0020] The wave vector k scan interval is [0, π / a], and the number of scan points is 50-200.
[0021] Solving the characteristic frequency problem: (K-ω²M)φ=0, where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and φ is the modal vector;
[0022] The first three dispersive branches are extracted, corresponding to the three lowest-order elastic wave modes.
[0023] Preferably, the first three dispersive branches correspond to the propagation modes of longitudinal waves, transverse shear waves, and bending waves in a periodic structure, respectively.
[0024] Preferably, the wave velocity extraction in step S105 includes:
[0025] Within the range of k to 0, the dispersion curve is linearly fitted, and the slope is the wave speed.
[0026] Wave speed v x Corresponding spanwise wave velocity, v y Corresponding to the chordal wave velocity, v z Corresponding wave velocity in the thickness direction;
[0027] The wave velocity ranges from 100 to 1000 m / s, depending on the material properties and structural parameters.
[0028] Preferably, the equivalent mass density ρ in step S106 is... * It is calculated by dividing the total mass of a single cell by the volume of the single cell.
[0029] Preferably, the equivalent elastic modulus of the closely spaced ailerons along the x, y, and z directions is as follows: , ,and .
[0030] Preferably, the equivalent elastic modulus E x E y E z Used to evaluate the stiffness characteristics of ailerons, including: based on E x and E y Calculate the bending resistance of the aileron; based on E x E y and E z Calculate the torsional resistance of the aileron; predict the natural frequency of the aileron based on the equivalent modulus.
[0031] Preferably, the method further includes step S107, result verification: comparing the calculated equivalent elastic modulus with the detailed finite element analysis results, with the error controlled within 10%.
[0032] Preferably, the method is implemented using finite element software, including ANSYS, Abaqus, or COMSOL, combined with a custom script for wave vector scanning and result extraction.
[0033] Calculating the equivalent stiffness of a ribbed aileron is crucial for analyzing its static and dynamic characteristics. Bloch's theorem is used to analyze the dynamic performance of the unit cell of the ribbed aileron, thereby obtaining its equivalent stiffness. This allows for rapid and accurate calculation of the equivalent stiffness, improving the efficiency of structural design and computational analysis. Attached Figure Description
[0034] Figure 1 This is a schematic diagram of the external shape of a multi-ribbed aileron for an aircraft, which is a general invention.
[0035] Figure 2 This is a schematic diagram of the unit cell structure of an aircraft ribbed aileron based on parameterization in this general invention.
[0036] Figure 3 This is the periodic boundary condition of the unit cell of the aircraft's closely spaced aileron in this general invention.
[0037] Figure 4 This is a finite element model of the aileron control surface based on shell elements in this general invention. Detailed Implementation
[0038] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings. The objective of this invention is to provide a method for calculating the equivalent stiffness of an aircraft ribbed aileron, which can overcome or mitigate at least one of the aforementioned defects of the prior art.
[0039] The technical solution of this invention is: based on the existing structural design pattern of a closely spaced ribbed aircraft aileron, including an upper skin, a lower skin, a front sparsity, a leading edge, ribs, and a tail edge, such as... Figure 1 As shown. Given that the closely spaced aileron structure can be approximated as a periodic structure, i.e., obtained through a periodic array of specific unit cells, the wave propagation characteristics of the unit cell of the aircraft's closely spaced aileron are analyzed using Bloch's theorem and the finite element method. A schematic diagram of the aircraft's closely spaced aileron unit cell is shown below. Figure 2 As shown, by assigning different material and structural parameters to each component in a closely spaced aileron, the equivalent mass density of the aileron unit cell can be calculated. The wave characteristic equations for a closely spaced aileron unit cell are established using the finite element method. Bloch's theorem is used to establish the periodic boundary conditions for the closely spaced aileron unit cell. The band structure of the closely spaced aileron unit cell can be obtained by sweeping the wave vector k in the first irreducible Brillouin zone. At the long-wavelength limit where the wave vector k approaches 0, the slopes of the first three dispersive branches in the band structure are solved, which represent the elastic wave velocities along different directions. , and Furthermore, using the wave velocity calculation formula, the equivalent elastic modulus of the closely spaced ailerons in different directions is obtained as follows: , ,and For detailed calculation procedures, please refer to [link / reference]. Figure 4 .
[0040] Based on the required shape of the aileron control surfaces, including the skin, trailing edge, inner end ribs, outer end ribs, front spars, and leading edge, such as... Figure 1 As shown;
[0041] The shape of the aircraft control surfaces is imported into the finite element software, and the distance is... Two planes are used to cut the closely spaced ailerons to obtain the unit cell structure of the closely spaced aileron, with a length of That is, the lattice constant.
[0042] Assign corresponding material parameters and shell thickness to the skin, trailing edge, ribs, septa, and front spars of the closely spaced aileron unit cell;
[0043] Establish Bloch boundary conditions for the closely spaced aileron unit cell;
[0044] Divide the aileron control surfaces into grids and determine the appropriate grid size and type;
[0045] Solving for different wave vectors in Bloch boundary conditions from The first three characteristic frequencies within the range are used to obtain the first three dispersion curves of the dense-ribbed aileron unit cell;
[0046] Extracting the first three order dispersion curves in the long wavelength range (wave vector) The slopes (approaching 0) correspond to the velocities of elastic waves propagating in different directions. , and .
[0047] Maximum displacement of the trailing edge between the planes containing different connection joint surfaces ;
[0048] Based on the formula for calculating elastic wave velocity, the equivalent elastic modulus of the closely spaced aileron in different directions is obtained as follows: , ,and .
[0049] The advantages of this application are: calculating the equivalent stiffness of a ribbed aileron is crucial for analyzing the static and dynamic characteristics of the ribbed aileron structure. By employing Bloch's theorem to analyze the dynamic performance of the unit cell of the ribbed aileron, the equivalent stiffness of the ribbed aileron can be obtained quickly and accurately, improving the efficiency of structural design and computational analysis.
[0050] This invention patent combines Bloch's theorem and the finite element method to establish a rapid calculation method for the equivalent elastic modulus of the ribbed aileron control surface of an aircraft, which helps to realize the rapid design and analysis of the ribbed aileron of an aircraft.
[0051] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for calculating the equivalent stiffness of a closely spaced aileron in an aircraft, characterized in that, include: Step S101, Unit cell extraction: Based on the structural design of the aircraft's closely spaced aileron, the aileron structure is approximated as a periodic structure. The aileron structure is cut by two parallel planes with a spacing of a, and representative unit cells are extracted, where the spacing a is the lattice constant. Step S102, Finite Element Modeling: The finite element method is used to establish the finite element model of the unit cell. Material parameters and structural parameters are assigned to each component in the unit cell, including the thickness and material properties of the skin, ribs, front beam, and tail edge. Step S103: Applying boundary conditions: Based on Bloch's theorem, apply periodic boundary conditions to the unit cell to simulate the wave propagation characteristics in an infinite periodic structure. Step S104, Band Structure Calculation: Solve for different wave vectors in the Bloch boundary conditions. from The first three characteristic frequencies within the range are used to obtain the first three dispersion curves of the dense-ribbed aileron unit cell; Step S105, Wave velocity extraction: Extract the slopes of the first three dispersion curves within a preset wavelength range, which correspond to the elastic wave propagation velocities in x, y, and z, respectively. , and ; Step S106, Equivalent stiffness calculation: Based on the wave velocity calculation formula, combined with the equivalent mass density of the unit cell... The equivalent elastic modulus of the closely spaced ailerons in different directions was obtained.
2. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The single-cell extraction in step S101 includes: The ribbed aileron structure includes an upper skin, a lower skin, a front spars, a leading edge, ribs, and a trailing edge; The single-cell extraction direction is along the span of the aileron, and the cutting plane spacing 'a' is determined according to the rib spacing, with a range of 50-300 mm. The unit cell structure maintains the geometric integrity of the ailerons, including the skin curvature and the arrangement of the ribs.
3. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The finite element modeling described in step S102 includes: A shell element discrete unit cell structure is adopted, and the mesh size is determined according to the unit cell size, with the element size ranging from a / 10 to a / 20. Material parameters include elastic modulus, Poisson's ratio, and density, with values assigned separately for composite materials and metallic materials; Structural parameters include skin thickness of 0.5-3mm, rib thickness of 1-5mm, and beam thickness of 2-6mm.
4. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The periodic boundary conditions are applied based on Bloch's theorem, imposing displacement constraints on the nodes on the relative boundaries of the unit cell. The periodic boundary conditions cover all corresponding surfaces of the unit cell, including spanwise and chordwise directions.
5. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The band structure calculation in step S104 includes: The wave vector k scan interval is [0, π / a], and the number of scan points is 50-200. Solving the characteristic frequency problem: (K-ω²M)φ=0, where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and φ is the modal vector; The first three dispersive branches are extracted, corresponding to the three lowest-order elastic wave modes.
6. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The first three dispersive branches correspond to the propagation modes of longitudinal waves, transverse shear waves, and flexural waves in periodic structures, respectively.
7. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The wave velocity extraction in step S105 includes: Within the range of k to 0, the dispersion curve is linearly fitted, and the slope is the wave speed. Wave speed v x Corresponding spanwise wave velocity, v y Corresponding to the chordal wave velocity, v z Corresponding wave velocity in the thickness direction; The wave velocity ranges from 100 to 1000 m / s, depending on the material properties and structural parameters.
8. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The equivalent mass density ρ mentioned in step S106 * It is calculated by dividing the total mass of a single cell by the volume of the single cell.
9. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The equivalent elastic moduli of the closely spaced ailerons along the x, y, and z directions are as follows: , ,and .
10. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The equivalent elastic modulus E x E y E z Used to evaluate the stiffness characteristics of ailerons, including: based on E x and E y Calculate the bending resistance of the aileron; based on E x E y and E z Calculate the torsional resistance of the aileron; predict the natural frequency of the aileron based on the equivalent modulus.
11. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The method further includes step S107, result verification: the calculated equivalent elastic modulus is compared with the detailed finite element analysis results, and the error is controlled within 10%.
12. The method for calculating the equivalent stiffness of an aircraft ribbed aileron as described in claim 1, characterized in that, The method is implemented using finite element software, including ANSYS, Abaqus, or COMSOL, combined with custom scripts for wave vector scanning and result extraction.