A modal-based method for reconstructing aircraft structural loads

Abstract

The present invention belongs to the technical field of aerospace, and particularly relates to a modal-based method for reconstructing aircraft structural loads. This method uses a structural finite element model to obtain modal information at key locations of the aircraft structure, including nodal displacement modes and element stress and strain modal matrices. Based on the topological relationships of the finite element mesh, nodal resultant force modes and section resultant force / moment modal matrices are derived. Finally, based on these modal matrices, the stress / strain intensity at key locations and the resultant force / moment at key sections are reconstructed from the generalized displacements of the structure. This algorithm does not require processing the overall stiffness and damping matrices of the structure, facilitating practical engineering applications.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace, and in particular relates to a modal-based aircraft structure load reconstruction method. Background Art

[0002] In recent years, with the advancement of aerospace technology, there has been an increasing demand for high-fidelity finite element methods to perform dynamic modeling and analysis of complex structures and even entire aircraft. However, due to limitations in computer performance, modal truncation is often used in the early stages of aircraft design to improve the computational efficiency of dynamic analysis. This is particularly necessary when solving fluid-structure interaction problems. Since solving the dynamic equations after modal reduction can only produce generalized displacements and generalized velocities of the structure, reconstructing the physical response based on the generalized dynamic response, including stresses, strains, resultant forces, and resultant moments at key locations of the structure, has become a key technological breakthrough that must be made in aircraft design.

[0003] The load reconstruction methods in the existing technology can be mainly divided into two categories from the perspective of force balance: the modal displacement method and the resultant force method. The resultant force method uses the aerodynamic load to subtract the inertial force and damping force of the structure to obtain the structural stress, but on the one hand, it is difficult to reconstruct the structural strain and the resultant force and moment at the key position. On the other hand, it also relies on the unsteady aerodynamic force solver, which is only applicable to engineering algorithms and difficult to use in computational fluid dynamics (CFD). The modal displacement method is based on the linear superposition principle of displacement. It uses the modal matrix of the structure to reconstruct physical responses such as node displacement and velocity from the generalized dynamic response, and then combines the structural stiffness matrix to restore the structural load. For example, a Chinese patent application with publication number CN106650077A discloses a method for reconstructing aircraft dynamic loads based on the modal displacement method. However, this method has low computational efficiency and can only restore the equivalent node force and the total force of the structural finite element, making it difficult to restore key load information. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this paper proposes a modal-based method for reconstructing aircraft structural loads. This method uses a finite element model to obtain modal information at key locations of the aircraft structure, including nodal displacement modes and element stress and strain modal matrices. Based on the topological relationships of the finite element mesh, the nodal resultant force modes and section resultant force / moment modal matrices are derived. Finally, based on these modal matrices, the stress / strain intensities at key locations and the resultant forces / moments at key sections are reconstructed from the generalized displacements. This algorithm eliminates the need to process the overall structural stiffness and damping matrices, facilitating practical engineering applications.

[0005] The technical solutions of the present invention are as follows:

[0006] A modal-based aircraft structural load reconstruction method comprises the following steps:

[0007] Step S1, establishing a structural finite element model for the aircraft structure;

[0008] In all structural finite element models, forces and moments are defined in the global coordinate system G of the structural finite element model, and stresses and strains are defined in the local coordinate system E of the element. i In the following, i represents the element number, and the transformation relationship of the node displacement from the local coordinate system to the global coordinate system is u (g) =Γ i u (ei) ;

[0009] Among them, u (ei) represents the node displacement in the local coordinate system of the i-th unit, u (g) represents the node displacement in the global coordinate system, Γ i is the coordinate transformation matrix from the local coordinate system of the i-th unit to the global coordinate system;

[0010] Assume that the node has 6 degrees of freedom in the global coordinate system of the structural finite element model, including displacement and rotation in three directions, then the node displacement vector is u j =[u xj ,u yj ,u zj ,R xj ,R yj ,R zj ] T , the node displacement modal matrix is Among them, j represents the node number, u xj ,u yj ,u zj ,R xj ,R yj ,R zj They represent the displacement of node j in the x direction, the displacement in the y direction, the displacement in the z direction, the rotation in the x direction, the rotation in the y direction, and the rotation in the z direction, respectively. n represents the order of the mode. represents the component of the r-th order modal vector at the node j degree of freedom, r = 1, 2, …, n;

[0011] The element properties of element i include the element stress matrix E σi , element strain matrix E εi and the element stiffness matrix E ki , where E σi and E εi Defined in the unit local coordinate system, E ki Defined in the global coordinate system of the structural finite element model;

[0012] Step S2: Select a section in the structural finite element model and determine all nodes and elements on the section;

[0013] Step S3, using the node displacement modal matrix to restore the node displacement vector;

[0014] Step S4: Using the element stress matrix E σi , element strain matrix E εi and the element stiffness matrix E ki Restore the stress σ in the unit i , strain ε i and nodal forces [F] i ;

[0015] Step S5: Recover the section resultant force and moment using the nodal forces within the unit;

[0016] Step S6: Extract the element stress matrix Φ σi , unit strain matrix Φ εi and the nodal force modal matrix Φ fi ;

[0017] Step S7: Extract the cross-section resultant force / moment modal matrix Φ F ;

[0018] Step S8: According to the cross-section resultant force / moment modal matrix Φ F and the structural generalized displacement vector to recover the structural load.

[0019] Preferably, in step S2, the principle for determining the unit is: selecting the unit close to the fixed support end or the center of gravity of the aircraft.

[0020] Preferably, in step S3, the node displacement vector is expressed as:

[0021] u j =Φ j q

[0022] Where q is the structural generalized displacement factor.

[0023] Preferably, the stress σ in unit i in step S4 is i , strain ε i and nodal forces [F] i Respectively expressed as:

[0024]

[0025]

[0026]

[0027] Where p represents the total number of nodes in unit i, F s represents the nodal force at node s in element i, s=1,2,…p,F s =[f xs fys f zs m xs m ys m zs ] T , f xs 、f ys 、f zs 、m xs 、m xs 、m xs They represent the displacement of node s in the x direction, the displacement in the y direction, the displacement in the z direction, the rotation in the x direction, the rotation in the y direction, and the rotation in the z direction respectively.

[0028] Preferably, in step S5, the cross-sectional resultant force and resultant moment are expressed as:

[0029]

[0030] Where m represents the total number of units on the section, I3 is a 3×3 unit matrix, and 03 is a 3×3 zero matrix. r0=[x0 y0 z0] T is the coordinate of the reference point of the resultant force on the section, r is =[x is y is z is ] T is the coordinate of node s in element i, both defined in the global coordinate system of the structural finite element model, F x 、F y 、F z are the resultant forces of the cross section in the x, y, and z directions of the global coordinate system, M x 、M y 、M z are the resultant moments of the section in the x, y, and y directions of the global coordinate system, respectively.

[0031] Preferably, in step S6, the unit stress matrix Φ σi , unit strain matrix Φ εi and the nodal force modal matrix Φ fi Respectively expressed as:

[0032]

[0033] Preferably, in step S7, the modal matrix of the section resultant force and the section resultant moment Φ F Expressed as:

[0034]

[0035] T i =diag(A1,A2,…,A p )

[0036]

[0037] 06 is a 6×6 zero matrix.

[0038] Preferably, the structural load restored in step S8 is expressed as:

[0039] σ i =Φ σi q

[0040] ε i =Φ εi q

[0041] [F x F y F z M x M y M z ]=Φ F q

[0042] Among them, σ i represents the stress of the i-th unit, ε i represents the strain of the i-th element.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) Compared with the resultant force method in the prior art, the present invention does not rely on an unsteady aerodynamic force solver and can reconstruct unit stress, strain, and cross-sectional resultant force and moment.

[0045] (2) Compared with the structural load reconstruction method based on the modal displacement method in the prior art, the present invention can reconstruct the cross-sectional resultant force / moment and does not require the overall stiffness matrix of the structural finite element, which improves the calculation efficiency and is more convenient for practical engineering applications.

[0046] (3) The modal-based aircraft structural load reconstruction method proposed in the present invention is not limited by aerodynamic modeling methods, structural complexity, etc., and can not only be used to solve the problem of aircraft structural load reconstruction in the aviation field, but can also be extended to various complex structures in the engineering field, such as ships, vehicles, large bridges, buildings, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention can be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0048] Figure 1 Schematic diagram of the finite element model of the flat-plate airfoil structure in Example 1 of the present invention.

[0049] Figure 2 It is the node on the left side of a certain section of the airfoil in Example 1 of the present invention used for load reconstruction.

[0050] Figure 3 It is a unit used for load reconstruction on a certain section of the airfoil in Example 1 of the present invention.

[0051] Figure 4 It is the gust response of the first 10 modes of the plane airfoil under a certain working condition in Example 1 of the present invention.

[0052] Figure 5 It is the resultant force response of the cross section reconstructed based on the generalized displacement in Example 1 of the present invention.

[0053] Figure 6 It is the resultant moment response of the cross section of the generalized displacement reconstruction of the structure in Example 1 of the present invention. DETAILED DESCRIPTION

[0054] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features therein can be combined with each other without conflict.

[0055] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0056] Example 1

[0057] like Figure 1 As shown, a swept parallelogram flat airfoil is symmetrical, with a thickness of 1.04 mm, a chord length of 52.6 mm, a span of 140.337 mm, and a sweep angle of 15°. The global coordinate system has the X-axis oriented chord-wise, the Z-axis pointing upward perpendicular to the airfoil, and the Y-axis direction determined by the right-hand rule.

[0058] Figure 2 The figure shows the structural finite element nodes required to reconstruct the loads for a section in the middle of the wing. A section perpendicular to the Y-axis is taken in the middle of the wing, and all nodes in the section are selected for section load reconstruction. The geometric center of the selected node is considered the center of the section and serves as the reference point for the resultant moment of the section.

[0059] Figure 3The following figure shows the structural finite element elements required to reconstruct the loads for a section in the middle of the wing. Following engineering practice, the finite element elements near the fixed end or the center of gravity of the aircraft are selected for the section load reconstruction.

[0060] For the flat wing, the modal-based aircraft structure load reconstruction method of the present invention is used to perform load reconstruction, specifically as follows:

[0061] Step 1: Establish a structural finite element model for the flat plate wing, such as Figure 1 As shown. And follow Figure 2 、 Figure 3 As shown, select the nodes on the cross section to be solved and the elements close to the fixed end.

[0062] Preferably, 72 units and 75 nodes are selected.

[0063] Step 2: Perform modal analysis on the finite element model of the structure, calculate the first 10 modes and output the stress, strain and node force of the unit under each mode. σi For example, it can be expressed as:

[0064]

[0065] in represents the stress vector of element i in the sth mode, which can be obtained by declaring an output request in modal analysis. Similarly, the strain modal matrix Φ εi and the nodal force modal matrix Φ fi A similar method can also be used through and When declaring output, you can specify the calculation scope to be the selected grid and nodes to improve the calculation efficiency and optimize the size of the result file.

[0066] Step 3: Extract the modal matrix of the resultant force / moment of the section. Select the elements and nodes in the first step, set the reference point as the center of the section, and calculate the sum matrix T of each element. i and the section resultant force / moment under each mode

[0067]

[0068] Then assemble the section resultant force / moment modal matrix:

[0069]

[0070] Step 4: Recover the structural loads from the generalized displacements of the structure based on the obtained section resultant force / moment modal matrix.

[0071] Figure 4The generalized displacement q of the structure shown corresponds to the following operating conditions: the wing is in level flight at 0 angle of attack, Ma = 3.0, and the sea level air density is 1.225 kg / m 3 Converted dynamic pressure, airspeed 460m / s, step gust amplitude 50m / s.

[0072] Reconstruct the section resultant force / moment as follows:

[0073] F=Φ F q

[0074] Where F=[F x F y F z M x M y M z ] T

[0075] The reconstruction result is as follows Figure 5 、 6 shown. Figure 5 The resultant force response curve of the cross section in the x, y, and z directions of the global coordinate system is shown. Figure 6 The resultant moment response curves of the cross section in the x, y, and z directions of the global coordinate system are displayed.

[0076] In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "connect," "fixed," etc. should be understood broadly. For example, they may refer to fixed connection, detachable connection, or integration; mechanical connection or electrical connection; direct connection or indirect connection through an intermediate medium; internal communication between two components or interaction between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0077] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0078] In the present invention, the terms "first", "second", "third", and "fourth" are used for descriptive purposes only and should not be understood as indicating or implying relative importance. The term "plurality" refers to two or more, unless otherwise clearly defined.

[0079] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A modal-based aircraft structural load reconstruction method, characterized in that: The following steps are involved: Step S1, establishing a structural finite element model for the aircraft structure; In all structural finite element models, forces and moments are defined in the global coordinate system G of the structural finite element model, and stresses and strains are defined in the local coordinate system E of the element. i In the following, i represents the element number, and the transformation relationship of the node displacement from the local coordinate system to the global coordinate system is u (g) =Γ i u (ei) ; Among them, u (ei) represents the node displacement in the local coordinate system of the i-th unit, u (g) represents the node displacement in the global coordinate system, Γ i is the coordinate transformation matrix from the local coordinate system of the i-th unit to the global coordinate system; Assume that the node has 6 degrees of freedom in the global coordinate system of the structural finite element model, including displacement and rotation in three directions, then the node displacement vector is u j =[u xj ,u yj ,u zj ,R xj ,R yj ,R zj ] T , the node displacement modal matrix is Among them, j represents the node number, u xj ,u yj ,u zj ,R xj ,R yj ,R zj They represent the displacement of node j in the x direction, the displacement in the y direction, the displacement in the z direction, the rotation in the x direction, the rotation in the y direction, and the rotation in the z direction, respectively. n represents the order of the mode. represents the component of the r-th order modal vector at the node j degree of freedom, r = 1, 2, …, n; The element properties of element i include the element stress matrix E σi , element strain matrix E εi and the element stiffness matrix E ki , where E σi and E εi Defined in the unit local coordinate system, E ki Defined in the global coordinate system of the structural finite element model; Step S2: Select a section in the structural finite element model and determine all nodes and elements on the section; Step S3, using the node displacement modal matrix to restore the node displacement vector; Step S4: Using the element stress matrix E σi , element strain matrix E εi and the element stiffness matrix E ki Restore the stress σ in the unit i , strain ε i and nodal forces [F] i ; Step S5: Recover the section resultant force and moment using the nodal forces within the unit; Step S6: Extract the element stress matrix Φ σi , unit strain matrix Φ εi and the nodal force modal matrix Φ fi ; Step S7: Extract the cross-section resultant force / moment modal matrix Φ F ; Step S8: According to the cross-section resultant force / moment modal matrix Φ F and the structural generalized displacement vector to recover the structural load.

2. The modal-based aircraft structure load reconstruction method according to claim 1, characterized in that: In step S2, the principle for determining the unit is to select the unit close to the fixed support end or the center of gravity of the aircraft.

3. The modal-based aircraft structure load reconstruction method according to claim 1, characterized in that: In step S3, the node displacement vector is expressed as: you j =Φ j q Where q is the structural generalized displacement factor.

4. The modal-based aircraft structure load reconstruction method according to claim 1, characterized in that: The stress σ in the element i in step S4 i , strain ε i and nodal forces [F] i Respectively expressed as: Where p represents the total number of nodes in unit i, F s represents the nodal force at node s in element i, s=1,2,…p,F s =[f xs f ys f zs m xs m ys m zs ] T , f xs 、f ys 、f zs 、m xs 、m xs 、m xs They represent the displacement of node s in the x direction, the displacement in the y direction, the displacement in the z direction, the rotation in the x direction, the rotation in the y direction, and the rotation in the z direction respectively.

5. The modal-based aircraft structure load reconstruction method according to claim 4, characterized in that: In step S5, the cross-sectional resultant force and moment are expressed as: Where m represents the total number of units on the section, I3 is a 3×3 unit matrix, and O3 is a 3×3 zero matrix. r0=[x0 y0 z0] T is the coordinate of the reference point of the resultant force on the section, r is =[x is y is z is ] T is the coordinate of node s in element i, both defined in the global coordinate system of the structural finite element model, F x 、F y 、F z are the resultant forces of the cross section in the x, y, and z directions of the global coordinate system, M x 、M y 、M z are the resultant moments of the section in the x, y, and y directions of the global coordinate system, respectively.

6. The modal-based aircraft structure load reconstruction method according to claim 5, characterized in that: In step S6, the unit stress matrix Φ σi , unit strain matrix Φ εi and the nodal force modal matrix Φ fi Respectively expressed as:

7. The modal-based aircraft structure load reconstruction method according to claim 6, characterized in that: In step S7, the modal matrix of the section resultant force and the section resultant moment Φ F Expressed as: T i =diag(A1,A2,…,A p ) 06 is a 6×6 zero matrix.

8. The modal-based aircraft structure load reconstruction method according to claim 7, characterized in that: The structural load recovered in step S8 is expressed as: s i =Φ σi q e i =Φ εi q [F x F y F z M x M y M z ]=Φ F q among them, σ i represents the stress of the i-th unit, ε i represents the strain of the i-th element.

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