Modal-based aircraft structure load reconstruction method

Abstract

The invention belongs to the technical field of aerospace, and particularly relates to a modal-based aircraft structure load reconstruction method. The method comprises the following steps: acquiring modal information of a key position of an aircraft structure through a structure finite element model, wherein the modal information comprises a node displacement modal and a unit stress and strain modal matrix; obtaining a node resultant force mode and a profile resultant force / resultant moment mode matrix according to the finite element grid topological relation; and finally, reconstructing the stress / strain intensity of the key position of the structure and the resultant force / resultant moment of the key section from the generalized displacement of the structure according to the modal matrix. The algorithm does not need to process a structural overall rigidity matrix and a damping matrix, and engineering practical application is facilitated.

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 development of aerospace technology, the demand for using high-fidelity finite elements to perform dynamic modeling and analysis on complex structures and even the entire aircraft has increased. However, due to the limitations of computer performance, the modal truncation method is often used in the early stages of aircraft design to improve the computational efficiency of dynamic analysis, which is especially necessary when solving fluid-structure coupling problems. Since solving the dynamic equations after modal reduction can only obtain the generalized displacement, generalized velocity and other responses of the structure, how to reconstruct the physical response based on the generalized dynamic response, including stress, strain, resultant force and resultant moment at key locations of the structure, has become a key technology that must be broken through in aircraft design.

[0003] At present, the load reconstruction methods in the prior art can be mainly divided into two categories from the perspective of force balance: modal displacement method and resultant force method. The resultant force method uses aerodynamic load to subtract the inertial force and damping force of the structure to obtain structural stress, but on the one hand, it is difficult to reconstruct the structural strain and the resultant force and moment at key positions. On the other hand, it also relies on unsteady aerodynamic force solvers, which is only applicable to engineering algorithms and difficult to use for 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, but this method has low computational efficiency and can only restore the equivalent node force and the total force of the structural finite element, and it is difficult to restore the key load information. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention proposes a method for reconstructing aircraft structural loads based on modalities. The modal information of the key positions of the aircraft structure is obtained through the structural finite element model, including the node displacement mode and the unit stress and strain modal matrix; the node resultant force mode and the section resultant force / moment modal matrix are obtained according to the finite element mesh topological relationship; finally, the stress / strain intensity of the key positions of the structure and the resultant force / moment of the key section are reconstructed from the generalized displacement of the structure according to the above modal matrix. The algorithm does not need to process the overall stiffness matrix and damping matrix of the structure, which is convenient for practical engineering applications.

[0005] The technical solution of the present invention is as follows:

[0006] A method for reconstructing aircraft structure loads based on modality 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 ith 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 Where 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 , unit strain matrix E εi and the element stiffness matrix E ki , where E σi and E εi Defined in the local coordinate system of the unit, E ki Defined in the global coordinate system of the structural finite element model;

[0012] Step S2, selecting a section in the structural finite element model, and determining 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 unit stress matrix E σi , unit 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, using the nodal forces in the unit to restore the section resultant force and moment;

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

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

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

[0019] Preferably, in step S2, the principle for determining the unit is: selecting a unit close to the fixed support end or the side of 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 generalized displacement factor of the structure.

[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 section resultant force and moment are expressed as:

[0029]

[0030] Where m represents the total number of units on the section, I3 is a 3×3 unit matrix, 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, all defined in the global coordinate system of the structural finite element model, F x 、F y 、F z are the section force in the x, y, and z directions of the global coordinate system, M x 、M y 、M z They 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 node force modal matrix Φ fi Respectively expressed as:

[0032]

[0033] Preferably, in step S7, the section resultant force and section resultant moment modal matrix Φ F It is 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 ith 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 section 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 section 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 structure 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 structure 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 drawings required for use in the embodiments will be briefly introduced below. The features and advantages of the present invention can be more clearly understood by referring to the drawings. 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 creative work.

[0048] Figure 1 It is a schematic diagram of the finite element model of the flat plate wing structure in Example 1 of the present invention.

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

[0050] Figure 3 It is a unit used for load reconstruction on a certain section of the wing 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 section reconstructed according to the generalized displacement in Example 1 of the present invention.

[0053] Figure 6 It is the section resultant moment response 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 purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments 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 protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0056] Example 1

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

[0058] Figure 2 The following figure shows the structural finite element nodes required to reconstruct a section load in the middle of the wing. Take a section perpendicular to the Y axis in the middle of the wing and select all nodes on the section to participate in the section load reconstruction. The geometric center of the selected node is regarded as the center of the section and as the reference point for the section moment.

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

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

[0061] Step 1: Establish a structural finite element model for the flat wing surface, such as Figure 1 As shown. And follow Figure 2 , Figure 3 As shown, select the nodes on the section to be calculated 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 structural finite element model, 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 node force modal matrix Φ fi A similar method can also be used 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 section resultant force / moment. Select the elements and nodes in the first step, set the reference point to 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 structural generalized displacements based on the obtained section resultant force / moment modal matrix.

[0071] Figure 4The generalized displacement q of the structure shown corresponds to the following working 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 curve of the section in the x, y, and z directions of the global coordinate system is displayed.

[0076] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

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

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

[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope 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 ith 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 Where 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 , unit 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, selecting a section in the structural finite element model, and determining 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 unit stress matrix E σi , unit 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, using the nodal forces in the unit to restore the section resultant force and moment; Step S6: Extracting the unit stress matrix Φ σi , unit strain matrix Φ εi and the node force modal matrix Φ fi ; Step S7: Extract the section resultant force / moment modal matrix Φ F ; Step S8: According to the section resultant force / moment modal matrix Φ F and the structural generalized displacement vectors to recover the structural loads.

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: selecting 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 generalized displacement factor of the structure.

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 section 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, 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, all defined in the global coordinate system of the structural finite element model, F x 、F y 、F z are the section force in the x, y, and z directions of the global coordinate system, M x 、M y 、M z They 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 node 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 It is 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 restored 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 ith element.

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