A method for discretizing the mass of a wing structure based on a lagrange operator

Abstract

The application belongs to the field of aeronautical engineering, and particularly relates to a wing surface structure mass discrete method based on a Lagrange operator. The method firstly defines a parameterization of a thin-walled box section structure containing a plate and a rib, and establishes a structure finite element model. Then, a mass model is constructed by assigning material density. Then, the core processing is divided into two parts: firstly, for the concentrated mass in the model, the Lagrange multiplier method is adopted, and according to the minimum deformation energy and the static force equivalent principle, the concentrated mass is accurately distributed to the specified distributed grid nodes; secondly, for the continuous distributed mass of the shell element, the mass is equivalent to be dispersed to the element nodes through isoparametric transformation and shape function. Finally, all the distributed masses are collected to form a complete discrete mass model. The application realizes the automatic and high-precision conversion from the detailed structure finite element model to the concentrated mass model for system analysis, and significantly improves the efficiency and accuracy of the mass distribution analysis in the aircraft scheme design stage.

Description

Technical Field

[0001] This application belongs to the field of aeronautical engineering, and specifically relates to a method for discretizing the mass of airfoil structures based on Lagrange operators. Background Technology

[0002] To improve performance and reduce weight, modern aircraft commonly employ thin-walled stiffened structures in their airframe design. Wings, tails, and other structures typically utilize thin-walled box-section structures to enhance load-bearing efficiency.

[0003] Structural mass distribution is an important original basis for design and analysis in fields such as overall aircraft design, flight mechanics, strength, and flutter.

[0004] Structural mass distribution is also an essential raw parameter for calculating the static and dynamic mass of an aircraft.

[0005] A structural finite element model (FEM) is a mathematical model that reflects the stiffness of a structure. It describes the deformation and internal mass under the action of external mass. Modern aircraft design often uses FEMs for simulation-aided design in the early stages. FEMs contain a large number of structural design parameters, including mass distribution information of the aircraft structure. This mass distribution information can be used as design input in areas such as overall aircraft design, flight mechanics, strength, and flutter. Summary of the Invention

[0006] To address the aforementioned problems, this application provides a method for discretizing the mass of airfoil structures based on Lagrange operators, comprising the following steps:

[0007] S1: Define the structural parameters of the thin-walled box segment structure of the aircraft, including parameters of plate structures and parameters of stiffened structures;

[0008] S2: Based on the structural parameters, establish a finite element model of the thin-walled box segment structure of the aircraft;

[0009] S3: Based on the aforementioned finite element model, define a mass finite element model to complete the conversion from the structural finite element model to the mass finite element model;

[0010] S4: Using the Lagrange multiplier method, the lumped mass in the mass finite element model is discretized and distributed to the specified mass distribution grid nodes;

[0011] S5: Discretize and distribute the continuously distributed mass in the finite element model to specified discrete points, thus completing the mass discretization of the entire structure.

[0012] Preferably, in step S1:

[0013] The descriptive parameters of the plate-type structure include plate thickness, material, and serial number;

[0014] The reinforced structures are managed in groups. The description parameters of a single group of reinforcements include the number of reinforcements, the reinforcement arrangement, the plate number to which they are connected, and the reinforcement list information. The description parameters of a single reinforcement include the start and end points, the shape and area of ​​the upper and lower edge strips, the web thickness, the material, and the number.

[0015] Preferably, in step S2, the finite element model includes the geometric parameters of the structure, the mechanical properties of the materials, the boundary constraints, and the layup sequence information of the composite materials, and the elements constituting the model are grouped according to the structural form and stress characteristics.

[0016] Preferably, step S3 specifically includes:

[0017] S31: Based on the finite element model, input the material density of each component to establish a mass model;

[0018] S32: Input the mass weighting coefficient to adjust the mass of each component to match the theoretically calculated mass;

[0019] S33: Perform the entire quality model calculation and output the element quality data of each component.

[0020] Preferably, the mass allocation using the Lagrange multiplier method in step S4 is specifically as follows:

[0021] Construct the Lagrangian function based on the principle of minimizing deformation energy and the static equivalent condition;

[0022] By solving the Lagrangian function, the node mass assigned to each mass distribution grid node is calculated.

[0023] The final quality of a node is obtained by summing the quality assigned to the same node.

[0024] Preferably, in step S5, the continuously distributed mass is discretized for both triangular and quadrilateral units;

[0025] For triangular elements, they are transformed into regular triangles in the natural coordinate system through coordinate interpolation, and the equivalent nodal forces are calculated based on shape functions and Jacobi matrices, thereby completing the discretization of mass to the nodes;

[0026] For quadrilateral elements, they are transformed into regular squares in the natural coordinate system through coordinate interpolation, and the equivalent nodal forces are calculated based on shape functions and Jacobi matrices, thereby completing the discretization of mass to the nodes.

[0027] This invention enables automated and high-precision conversion from detailed structural finite element models to lumped mass models for system analysis, significantly improving the efficiency and accuracy of mass distribution analysis in the aircraft design phase. Attached Figure Description

[0028] Figure 1 This is a flowchart of the finite element model creation process;

[0029] Figure 2 This is a schematic diagram illustrating the transformation from a single mass point to n nodes;

[0030] Figure 3 This is a schematic diagram of the isoparametric transformation of a triangular unit;

[0031] Figure 4 This is a schematic diagram of the isoparametric transformation of a quadrilateral element. Detailed Implementation

[0032] 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 of this application without creative 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. Figures 1-4 As shown:

[0033] The first step is to parametrically describe the constituent elements of thin-walled box-section structures (such as the main box sections of wings and tail fins) to provide input for modeling. The structures are mainly divided into two categories:

[0034] Plates: including wall panels, ribs, webs, skins, etc. Each plate requires the following parameters to be defined: ① thickness, ② material type, ③ unique identification number.

[0035] Reinforcement: Including beams, longitudinal walls, trusses, etc., used to enhance the stability of slabs. For ease of management, it is defined in groups. The parameters of a reinforcement group include: the number of reinforcements in the group, the arrangement method (e.g., equal spacing), and the slab number it connects to. The parameters of each individual reinforcement in the group include: ① coordinates of the start and end points, ② cross-sectional shape and area of ​​the upper and lower edge bars, ③ web thickness, ④ material type, ⑤ number, and ⑥ whether it is a reinforcing bar.

[0036] Based on the above parameters, a finite element analysis model of the structure is established in finite element preprocessing software (such as MSC Patran). The model must include complete geometric, material properties, element properties, boundary conditions, and other information. Element types are selected according to the structural characteristics: rod elements (CROD), beam elements (CBAR), triangular shell elements (CTRIA3), and quadrilateral shell elements (CQUAD4). A key step is to group the elements according to the structural form and stress characteristics. For example, all quadrilateral elements on the same panel are grouped together, and all beam elements on the same beam are grouped together. This grouping is the basis for subsequent output of mass information by substructure.

[0037] This step completes the conversion from the "structural finite element model" to the "mass finite element model":

[0038] a) Based on the established structural finite element model, assign the correct mass density parameter to each material.

[0039] b) As needed for the design, a mass weighting factor can be entered for a specific component or material to fine-tune its mass so that it matches the theoretical calculation or target value.

[0040] c) Run the mass calculation function to output data such as the mass, centroid position, and moment of inertia of each element or element group in the model. At this time, the mass information is still attached to the original element, including concentrated mass points (such as the nodal mass of beam element) and distributed mass (such as the surface mass of shell element).

[0041] Discretize lumped mass using the Lagrange multiplier method

[0042] This step deals with concentrated masses attached to element nodes in the mass model (e.g., equivalent mass at beam element nodes). The goal is to rationally distribute these concentrated masses to a specified, sparser set of "mass distribution grid" nodes based on the principles of "static equivalence" and "minimum deformation energy".

[0043] 1. Establish a coordinate system. Taking the wing coordinate system as an example, define the intersection of the leading edge of the wing and the axis of symmetry of the aircraft as the origin O, with the X-axis pointing backward, the Z-axis along the spanwise direction, and the Y-axis pointing vertically downward to form a right-handed coordinate system.

[0044] 2. For a mass PA and coordinate (x... A ,z A Given a concentrated mass point A, it needs to be distributed among n surrounding mass distribution grid nodes. Let the coordinates of the j-th mass node be (x, y). j ,z j The allocated mass is P. j Its distance from point A is L. j .

[0045] 3. According to the deformation energy theory, for a cantilever beam with a mass point as a fixed support, the mass distribution grid nodes at its free end are distributed to the mass... Its deformation energy is

[0046]

[0047] In the formula: EJ — bending stiffness of the hypothetical beam;

[0048] — The distance from point A to point j.

[0049] Therefore, the deformation energy of the entire space is

[0050]

[0051] To minimize the deformation energy of the space, the static equivalence condition must also be satisfied.

[0052]

[0053]

[0054]

[0055] Where: n — number of nodes in the mass distribution grid;

[0056] —The quality of the points used for allocation;

[0057] —The x-coordinate of the point used for assignment;

[0058] — The z-coordinate of the point used for assignment.

[0059] The Lagrange multiplier method is used to establish the Lagrange function.

[0060]

[0061] In the formula: , ;

[0062] , , It is a Lagrange multiplier.

[0063] In order to make Take the minimum value, let

[0064]

[0065] have to

[0066]

[0067] Substituting equation (3) into equation (2), we finally obtain...

[0068]

[0069] Solve from equation (6) , , Substituting back into equation (5) yields the node mass assigned to each mass distribution grid node. Finally, the mass assigned to the same node is summed to obtain the mass of that node.

[0070] Fifth, discretize the continuously distributed mass to specified discrete points to complete the discretization of the mass:

[0071] The surface distribution quality of the finite element model of the thin-walled box segment structure of the aircraft mainly targets planar triangular and quadrilateral elements. That is, isoparametric triangular elements and isoparametric quadrilateral elements.

[0072] Any triangular element in the global coordinate system can be converted into a regular triangle in the natural coordinate system through interpolation, such as... Figure 3 .

[0073] in

[0074] , (8)

[0075] (9)

[0076] At this point, the equivalent nodal force in any triangular element can be calculated as follows:

[0077] (10)

[0078] in The determinant of the Jacobi matrix

[0079]

[0080] (11)

[0081] Any quadrilateral element in the global coordinate system can be converted into a regular square in the natural coordinate system through interpolation, such as... Figure 4 .

[0082] in

[0083] , (15)

[0084] Shape function The expression is the same as formula (12) in section 3.1.

[0085] The effective nodal forces in any quadrilateral element can be calculated as follows:

[0086] (16)

[0087] (17)

[0088] By summing up the calculated node-assigned masses, we obtain the discrete mass matrix of the entire thin-walled box segment structure across all specified mass distribution grid nodes. This matrix can be directly used for subsequent calculations of overall aircraft mass characteristics, dynamic stiffness analysis, flutter analysis, etc., achieving a rapid and accurate conversion from a detailed structural finite element model to a lumped mass model suitable for system-level analysis.

[0089] Through the above steps, this invention proceduralizes and automates the complex structural mass discretization process, significantly improving the efficiency and accuracy of mass distribution analysis during the aircraft design phase.

[0090] 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 discretizing the mass of an airfoil structure based on Lagrange operators, characterized in that, Includes the following steps: S1: Define the structural parameters of the thin-walled box segment structure of the aircraft, including parameters for plate structures and parameters for stiffened structures; S2: Based on the structural parameters, establish a finite element model of the thin-walled box segment structure of the aircraft; S3: Based on the aforementioned finite element model, define a mass finite element model to complete the conversion from the structural finite element model to the mass finite element model; S4: Using the Lagrange multiplier method, the lumped mass in the mass finite element model is discretized and distributed to the specified mass distribution grid nodes; S5: Discretize and distribute the continuously distributed mass in the finite element model to specified discrete points, thus completing the mass discretization of the entire structure.

2. The method for discretizing the mass of an airfoil structure based on Lagrange operators as described in claim 1, characterized in that, In step S1: The descriptive parameters of the plate-type structure include plate thickness, material, and serial number; The reinforced structures are managed in groups. The description parameters of a single group of reinforcements include the number of reinforcements, the reinforcement arrangement, the plate number to which they are connected, and the reinforcement list information. The description parameters of a single reinforcement include the start and end points, the shape and area of ​​the upper and lower edge strips, the web thickness, the material, and the number.

3. The method for discretizing the mass of an airfoil structure based on Lagrange operators as described in claim 1, characterized in that, In step S2, the finite element model includes the geometric parameters of the structure, the mechanical properties of the materials, the boundary constraints, and the information on the layup sequence of the composite materials. The elements that make up the model are grouped according to the structural form and stress characteristics.

4. The method for discretizing the mass of an airfoil structure based on Lagrange operators as described in claim 1, characterized in that, Step S3 specifically includes: S31: Based on the finite element model, input the material density of each component to establish a mass model; S32: Input the mass weighting coefficient to adjust the mass of each component to match the theoretically calculated mass; S33: Perform the entire quality model calculation and output the element quality data of each component.

5. The method for discretizing the mass of an airfoil structure based on Lagrange operators as described in claim 1, characterized in that, The mass allocation using the Lagrange multiplier method described in step S4 is as follows: Construct the Lagrangian function based on the principle of minimizing deformation energy and the static equivalent condition; By solving the Lagrangian function, the node mass assigned to each mass distribution grid node is calculated. The final quality of a node is obtained by summing the quality assigned to the same node.

6. The method for discretizing the mass of an airfoil structure based on Lagrange operators as described in claim 1, characterized in that, In step S5, the continuously distributed mass is discretized for both triangular and quadrilateral units; For triangular elements, they are transformed into regular triangles in the natural coordinate system through coordinate interpolation, and the equivalent nodal forces are calculated based on shape functions and Jacobi matrices, thereby completing the discretization of mass to the nodes; For quadrilateral elements, they are transformed into regular squares in the natural coordinate system through coordinate interpolation, and the equivalent nodal forces are calculated based on shape functions and Jacobi matrices, thereby completing the discretization of mass to the nodes.

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