A load conversion method based on radial basis functions

Abstract

The application provides a load conversion method based on a radial basis function, and the method comprises the following steps: determining a radial basis function, calculating a matrix C ss and a matrix A as based on the radial basis function; setting a block in the lower left of a diagonal line of the matrix C ss and the matrix A as to be a zero matrix, and obtaining a matrix C ssb and a matrix A asb ; obtaining converted structural node load f s based on aerodynamic node load f a , the matrix C ssb and the matrix A asb , so as to realize the function of load conversion between different models and simultaneously meet the conservation of multi-section force and moment; the application sets the block in the lower left of a diagonal line of the matrix C ss and the matrix A as to be a zero matrix by block processing of C a , A ss and f as , and provides a calculation method which is simple in form, high in performance, can be used for load conversion between different engineering physical models, and simultaneously meets the conservation of arbitrary multi-section force and moment.

Description

Technical Field

[0001] The present application belongs to the technical field of helicopter load conversion, and in particular relates to a load conversion method based on radial basis functions. Background Art

[0002] Design requirements such as high maneuverability and fuel economy necessitate meticulous design for modern aircraft. This is particularly true for aircraft wing structures, which often require aeroelastic analysis, strength analysis, or fluid-structure interaction analysis. These analytical methods, which involve converting aerodynamic node loads to structural node loads, require the use of various load conversion algorithms. Furthermore, due to the specifics of frame-beam layouts in wing designs, there is a practical need to conserve forces and moments at multiple cross-sections during load conversion.

[0003] Traditional load conversion methods such as radial basis functions (RBFs) and multi-point arrays cannot directly satisfy the conservation of multi-section forces and moments. To meet this demand, this application provides a load conversion method based on radial basis functions that can simultaneously satisfy the conservation of multi-section forces and moments. Summary of the Invention

[0004] In order to solve the above technical problems, the present application provides a load conversion method based on radial basis functions, which includes:

[0005] Determine the radial basis function

[0006] Based on the radial basis function Calculate the matrix C ss and matrix A as ;

[0007] The matrix C ss and matrix A as The block on the lower left of the diagonal is set to 0 matrix, and the matrix C is obtained ssb and matrix A asb ;

[0008] Based on the aerodynamic node load f a , the matrix C ssb and matrix A asb , and obtain the converted structural node load f s , thereby realizing the function of load conversion between different models and satisfying the conservation of multi-section forces and moments;

[0009] Wherein, the radial basis function is determined Previously, it also included:

[0010] Step S1: Calculate and obtain the aerodynamic load value f of the wing surface a and aerodynamic node coordinate Xa , discretize the physical surface of the structure and obtain the structural node coordinates X s ;

[0011] Step S2: grouping the aerodynamic loads, aerodynamic node coordinates, and structural node coordinates according to the determined cross-sectional positions where force and moment conservation must be maintained before and after load conversion;

[0012] Wherein, the radial basis function Calculate the matrix C ss and matrix A as ,include:

[0013] Based on the radial basis function Calculate the matrix C ss and matrix A as Elements of

[0014] Based on the preset rules and the determined cross-sectional positions where the forces and moments before and after the load conversion need to be maintained, the matrix C ss and matrix A as Arrange the elements of to get the matrix C ss and matrix A as ; The preset rule is that elements of the same group are in the same area of ​​the matrix;

[0015] The matrix C ss and matrix A as The block on the lower left of the diagonal is set to 0 matrix, and the matrix C is obtained ssb and matrix A asb ,include:

[0016] Step S3: Based on the grouping relationship determined in step S2 and the property that the rows or columns of the matrix can be exchanged, C ss 、A as Matrix and f a The vectors are grouped and sorted so that the elements belonging to the same group are in the same area of ​​the matrix;

[0017] Step S4: C ss and A as The lower left block of the matrix diagonal is set to 0 matrix, and the processed transformation matrix is ​​recorded as C ssb and A asb .

[0018] Preferably, the radial basis function include:

[0019]

[0020] Where k is the distance between mesh nodes of different models during load conversion; r0 represents the effective distance set artificially.

[0021] Preferably, the cross-sectional position is determined according to a physical position in a physical model that needs to satisfy the force and moment conservation requirements.

[0022] Preferably, the aerodynamic node load f a , the matrix C ssb and matrix A asb , and obtain the converted structural node load f s Previously, it also included:

[0023] Determine the aerodynamic node load f a and structural node loads f s The relationship between them.

[0024] Preferably, the determination of the aerodynamic node load f a and structural node loads f s The relationships between

[0025] Create an interpolation surface based on the coordinates of the structural nodes:

[0026]

[0027] The coefficients in the formula are obtained by the definite solution conditions, which are:

[0028] s(X si )=u si (i=1,2,…,N)

[0029] After determining the coefficients, the aerodynamic node displacement u can be obtained from the interpolation surface a and structural node displacement u s The relationship between:

[0030]

[0031] Where,

[0032]

[0033] Combined load and displacement relationship:

[0034]

[0035] Right now:

[0036]

[0037] The aerodynamic node load f can be obtained a and the structural node load f s The relationship between:

[0038]

[0039] Preferably, the aerodynamic node load f a , the matrix C ssb and matrix A asb , and obtain the converted structural node load f s ,include:

[0040] Based on the aerodynamic node load f a and the structural node load f s The relationship between the matrix C ssb and matrix A asb , get the converted structural node load

[0041] Beneficial technical effects of this application:

[0042] This application is submitted to C ss 、A as Matrix and f a The vector is divided into blocks and the C ss and A as The lower left block of the matrix diagonal is set to 0, which provides a simple and efficient calculation method that can convert loads between different engineering physics models and simultaneously meet the conservation of forces and moments in any multiple sections. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A schematic diagram of aerodynamic node loads for the M6 ​​wing model provided in an embodiment of the present application;

[0044] Figure 2 This is a schematic diagram of the converted structural node load provided in an embodiment of the present application. DETAILED DESCRIPTION

[0045] See also Figure 1-Figure 2 This application is based on the fact that aerodynamic loads are gradually superimposed from the wing tip to the wing root, and the C ss and A as The matrix is ​​divided into blocks, and the transformation matrix C that satisfies the conservation of multi-section force and moment is constructed by setting the corresponding matrix blocks to 0 matrices. ss and A as , which can not only realize the demand for node load conversion between different grids or grid point groups, but also simultaneously meet the conservation of multi-section forces and moments.

[0046] In the embodiment of the present application, the specific technical solution involved in the present application is as follows: a load conversion method based on radial basis functions that satisfies multi-section conservation, comprising:

[0047] Step S1: Calculate and obtain the aerodynamic load value f of the wing surface a and aerodynamic node coordinate X a , discretize the physical surface of the structure and obtain the structural node coordinates X s ;

[0048] Step S2: grouping the aerodynamic loads, aerodynamic node coordinates, and structural node coordinates according to the determined cross-sectional positions where force and moment conservation must be maintained before and after load conversion;

[0049] Step S3: Select the specific form of radial basis function Create an interpolation surface based on the coordinates of the structural nodes:

[0050]

[0051] Where ‖·‖ is the 2-norm, representing the distance between points; N is the number of nodes on the surface of the structure; the coefficient α can be obtained from the definite solution condition, which is:

[0052] s(X si )=u si (i=1,2,…,N)

[0053] After determining the coefficients, the aerodynamic node displacement u can be obtained from the interpolation surface a and structural node displacement u s The relationship between:

[0054]

[0055] Where,

[0056]

[0057] Combined load and displacement relationship:

[0058]

[0059] Right now:

[0060] The aerodynamic node load f can be obtained a and the structural node load f s The relationship between:

[0061]

[0062] In the actual calculation process, it is only necessary to determine the radial basis function Then directly calculate C ss and A as matrix.

[0063] Step S4: Based on the grouping relationship determined in step 2 and the property that the rows or columns of the matrix can be exchanged, C is intentionally grouped according to the grouping relationship. ss 、A as Matrix and f a The vectors are grouped and sorted so that the elements belonging to the same group are in the same area of ​​the matrix. In fact, when the grid is divided, the node coordinate information is sorted according to the corresponding rules. ss and A as Matrix and f a The vector is sorted into blocks.

[0064] Step S5: C ss and A as The lower left block of the matrix diagonal is set to 0 matrix, and the processed transformation matrix is ​​recorded as C ssb and A asb ;

[0065] Step S6: According to the aerodynamic node load f in step 3 a and the structural node load f s The converted structural node loads are calculated based on the relationship between:

[0066]

[0067] Here are three cross-sectional forces and moments under conservation conditions: ss3 and A as3 Matrix form:

[0068]

[0069] The above-mentioned load conversion method based on radial basis function satisfies multi-section conservation. In this method, the radial basis function described in step 2 has multiple forms, among which the most common one is the C2 basis function, which has the following form:

[0070]

[0071] Where k is the distance between mesh nodes of different models during load conversion; r0 represents the effective distance set artificially.

[0072] This application is submitted to C ss 、A as Matrix and f a The vector is divided into blocks and the C ss and A as The lower left block of the matrix diagonal is set to 0, which provides a simple and efficient calculation method that can convert loads between different engineering physics models and simultaneously meet the conservation of forces and moments in any multiple sections.

Claims

1. A load conversion method based on radial basis function, characterized in that: The method comprises: Determine the radial basis function Based on the radial basis function Calculate the matrix C ss and matrix A as ; The matrix C ss and matrix A as The block on the lower left of the diagonal is set to 0 matrix, and the matrix C is obtained ssb and matrix A asb ; Based on the aerodynamic node load f a , the matrix C ssb and matrix A asb , and obtain the converted structural node load f s , thereby realizing the function of load conversion between different models and satisfying the conservation of multi-section forces and moments; Wherein, the radial basis function is determined Previously, it also included: Step S1: Calculate and obtain the aerodynamic load value f of the wing surface a and aerodynamic node coordinate X a , discretize the physical surface of the structure and obtain the structural node coordinates X s ; Step S2: grouping the aerodynamic loads, aerodynamic node coordinates, and structural node coordinates according to the determined cross-sectional positions where force and moment conservation must be maintained before and after load conversion; Wherein, the radial basis function Calculate the matrix C ss and matrix A as ,include: Based on the radial basis function Calculate the matrix C ss and matrix A as Elements of Based on the preset rules and the determined cross-sectional positions where the forces and moments before and after the load conversion need to be maintained, the matrix C ss and matrix A as Arrange the elements of to get the matrix C ss and matrix A as ; The preset rule is that elements of the same group are in the same area of ​​the matrix; The matrix C ss and matrix A as The block on the lower left of the diagonal is set to 0 matrix, and the matrix C is obtained ssb and matrix A asb ,include: Step S3: Based on the grouping relationship determined in step S2 and the property that the rows or columns of the matrix can be exchanged, C ss 、A as Matrix and f a The vectors are grouped and sorted so that the elements belonging to the same group are in the same area of ​​the matrix; Step S4: C ss and A as The lower left block of the matrix diagonal is set to 0 matrix, and the processed transformation matrix is ​​recorded as C ssb and A asb .

2. The method according to claim 1, characterized in that The radial basis function include: Where k is the distance between mesh nodes of different models during load conversion; r0 represents the effective distance set artificially.

3. The method according to claim 1, characterized in that The cross-sectional position is determined based on the physical position in the physical model that needs to satisfy the force and moment conservation requirements.

4. The method according to claim 1, wherein The aerodynamic node load f a , the matrix C ssb and matrix A asb , and obtain the converted structural node load f s Previously, it also included: Determine the aerodynamic node load f a and structural node loads f s The relationship between them.

5. The method according to claim 4, characterized in that Determining the aerodynamic node load f a and structural node loads f s The relationships between Create an interpolation surface based on the coordinates of the structural nodes: The coefficients in the formula are obtained by the definite solution conditions, which are: s(X si )=u si (i=1,2,…,N) After determining the coefficients, the aerodynamic node displacement u can be obtained from the interpolation surface a and structural node displacement u s The relationship between: Where, Combined load and displacement relationship: Right now: The aerodynamic node load f can be obtained a and the structural node load f s The relationship between:

6. The method according to claim 5, characterized in that The aerodynamic node load f a , the matrix C ssb and matrix A asb , and obtain the converted structural node load f s ,include: Based on the aerodynamic node load f a and the structural node load f s The relationship between the matrix C ssb and matrix A asb , get the converted structural node load

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