A fast equivalent analysis method for structural characteristics of integrated joint wing configuration design

Abstract

The present invention proposes a fast equivalent analysis method for structural characteristics of an integrated connecting wing configuration design. First, the design parameters of the connecting wing configuration are obtained, and the connecting wing is regarded as a structural form of a space rigid frame composed of a front wing, a rear wing and an end plate, which is simplified into a space six-degree-of-freedom rigid frame structure; secondly, the connecting wing is divided into a number of sections according to the front wing, the rear wing and the end plate at set intervals, and each section is regarded as a node; then the inertia moment and torsional stiffness of each node under the rigid center coordinate axis system are calculated, the overall stiffness matrix of the structure is established, and the node load is calculated, the load vector is established, and then the structural equation is established based on the overall stiffness matrix and the load vector; finally, the structural equation is solved to obtain the structural characteristics of the integrated connecting wing configuration. The method of the present invention divides the connecting wing configuration into multiple sections as nodes to ensure the calculation accuracy. At the same time, compared with the solid unit finite element method, there are fewer nodes, which can effectively improve the calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the field of aircraft structure analysis, and in particular to a fast equivalent analysis method of structural characteristics for integrated connecting wing configuration design. Background Art

[0002] In the field of traditional long-flight UAV platform design, the traditional large-swept, large-aspect-ratio aerodynamic layout design has the advantages of good aerodynamic characteristics, high critical Mach number, and high cruise lift-to-drag ratio, but poor structural characteristics, especially low stiffness and large wingtip deformation, which makes it difficult to meet the application requirements of local large-load unmanned aerial vehicle platforms such as microwave energy transmission. The unmanned aerial platform with an integrated linked-wing structure can solve the above problems, providing sufficient stiffness to meet the load requirements while ensuring good aerodynamic characteristics.

[0003] However, the structural characteristics analysis methods used for traditional aircraft configurations are not suitable for integrated wing configurations. At present, the structural characteristics analysis methods for wing configurations mainly include the piecewise linear stiffness method and the solid unit finite element method. However, the piecewise linear stiffness method cannot adapt well to the special stiffness configuration of the wing configuration and has the problem of insufficient accuracy. The solid unit finite element method requires the use of a large number of units and nodes, and the analysis is time-consuming and computationally expensive. Summary of the invention

[0004] To solve the above problems, the present invention proposes a rapid equivalent analysis method for structural characteristics of integrated connecting wing configuration design. The finite element equivalent beam method based on engineering beam theory, on the one hand, combines the classical structural force transmission model of engineering beam theory, and on the other hand, adds a finite element beam model. It can be used to analyze the configuration of special stiffness distribution of connecting wings, and provide an efficient and accurate evaluation method for the structural design of connecting wings, so that it can be applied to the design of long-flight UAV platforms to meet the application requirements of large-load unmanned aerial vehicle platforms.

[0005] The technical solution of the present invention specifically comprises the following steps:

[0006] Step 1: According to the coupling wing configuration scheme to be analyzed, obtain its design parameters, regard the coupling wing as a spatial rigid frame structure composed of a front wing, a rear wing and a connecting end plate, and simplify it into a spatial six-degree-of-freedom rigid frame structure model;

[0007] Step 2: In the spatial six-degree-of-freedom rigid frame structure model, the front wing, the rear wing and the connecting end plate are divided into a number of sections at equal intervals according to the set intervals, and the leading edge point coordinates of each section in the global coordinate system are obtained; wherein the sections of the front wing and the rear wing are parallel to the longitudinal symmetry plane of the aircraft where the connecting wing is located, and the section of the connecting end plate is perpendicular to the longitudinal symmetry plane of the aircraft where the connecting wing is located;

[0008] Step 3: Based on the design parameters and the leading edge coordinates of each section, calculate the coordinates of each section in the global coordinate system The centroid coordinates under the cross section are taken as the origin to establish the centroid coordinate system of each cross section, and the three-axis directions of the centroid coordinate system are parallel to the three-axis directions of the global coordinate system;

[0009] Step 4: Calculate the X-axis moment of inertia of each section in step 2 in its own centroid coordinate system and the Z-axis moment of inertia ;

[0010] Step 5: Calculate the rigid center coordinates of each section in step 2 in its own centroid coordinate system, establish the rigid center coordinate system of each section with the rigid center of each section as the origin, and the three-axis directions of the rigid center coordinate system are parallel to the three-axis directions of the centroid coordinate system;

[0011] Step 6: Calculate the X-axis moment of inertia of each section in step 2 in its respective rigid center coordinate system , Z-axis moment of inertia and torsional stiffness ;

[0012] Step 7: The X-axis moment of inertia of each section in its respective rigid center coordinate system obtained in step 6 , Z-axis moment of inertia and torsional stiffness , establish the unit overall stiffness matrix of each unit and assemble to obtain the structural overall stiffness matrix of the spatial six-degree-of-freedom rigid frame structure model ;

[0013] Step 8: Based on the overall stiffness matrix of the structure obtained in step 7, the structural equation is established and solved to obtain the displacement deflection of each node of the connecting wing structure and the overall structural characteristics.

[0014] Furthermore, the design parameters in step 1 include structural size parameters, structural layout parameters and material property parameters, wherein the structural size parameters include:

[0015] First front spar web thickness: , the thickness of the web of the second front spar: ;

[0016] The flange area of ​​the first front spar: , the lower flange area of ​​the first front wing spar: ;

[0017] Second front wing spar upper flange area: , the lower flange area of ​​the second front wing spar: ;

[0018] Front rib thickness: ;

[0019] Front wing skin thickness: ;

[0020] First rear spar web thickness: , the second rear spar web thickness: ;

[0021] The flange area of ​​the first rear spar: , the lower flange area of ​​the first rear wing spar: ;

[0022] Second rear wing spar upper flange area: , the lower flange area of ​​the second rear wing spar: ;

[0023] Rear wing rib thickness: ;

[0024] Rear wing skin thickness: ;

[0025] Structural layout parameters include:

[0026] First front spar position: , second front spar position: ;

[0027] Front wing rib spacing: ;

[0028] First rear spar location: , second rear spar position: ;

[0029] Rear wing rib spacing: ;

[0030] Material property parameters include:

[0031] Young's modulus of the reference material: ;

[0032] Shear modulus of the reference material: .

[0033] Furthermore, in step 3, the specific steps of establishing a cross-section centroid coordinate system are as follows:

[0034] Step 3.1: Calculate the total structural area of ​​the section ;

[0035]

[0036] In the formula, is the reduction factor; is the skin thickness of the section corresponding area, is the arc length of the skin; is the beam web thickness in the section corresponding area, is the arc length of the beam web; is the flange area of ​​the kth type spar in the corresponding area of ​​the section;

[0037] Step 3.2: Calculate the total static moment of the section on the X-axis of the global coordinate system Total static moment of Z axis ;

[0038]

[0039]

[0040] In the formula, is the Z-coordinate of the arc length element of the skin in the corresponding area of ​​the cross section in the global coordinate system, is the Z-coordinate of the arc length of the beam web in the corresponding area of ​​the section in the global coordinate system, is the Z-coordinate of the k-th wing spar flange in the corresponding area of ​​the cross section in the global coordinate system; is the X-coordinate of the skin arc length element in the corresponding area of ​​the cross section in the global coordinate system, is the X-coordinate of the arc length of the beam web in the corresponding area of ​​the section in the global coordinate system, is the X-coordinate of the k-th wing spar flange in the corresponding area of ​​the cross section in the global coordinate system;

[0041] Step 3.3: Calculate the centroid coordinates of the section ;

[0042]

[0043]

[0044] Move the origin of the global coordinate system to the centroid coordinates , and obtain the centroid coordinate system corresponding to the section.

[0045] Furthermore, in step 4, the X-axis moment of inertia of a section in its centroid coordinate system is and the Z-axis moment of inertia Calculated by the following formula:

[0046]

[0047]

[0048] Furthermore, in step 5, the rigid center coordinates of a certain section It is obtained by the following calculation formula:

[0049]

[0050]

[0051] in, is the total static moment of the section on the X-axis of the centroid coordinate system, is the total static moment of the section on the Z axis of the centroid coordinate system, is the vertical distance from the shear force of the skin arc length element in the corresponding area of ​​the section to the reference point of the set moment, is the vertical distance from the shear force of the beam web arc length microelement in the corresponding area of ​​the section to the reference point of the set moment, It is twice the area contained by the closed curve of the single closed chamber corresponding to the skin arc length microelement of the section. It is twice the area contained by the arc length of the beam web in the corresponding area of ​​the section corresponding to the closed curve of the single closed chamber. is the shear modulus of the reference material.

[0052] Furthermore, in step 6, according to the formula

[0053]

[0054]

[0055] Calculate the rigid center coordinate system The X-axis moment of inertia and the Z-axis moment of inertia ;

[0056] According to the formula

[0057]

[0058] Obtain the torsional stiffness per unit length of the equivalent beam .

[0059] Furthermore, the step 7 comprises the following sub-steps:

[0060] Step 7.1: According to the moment of inertia and torsional stiffness of each section in its own rigid center coordinate system obtained in step 6, establish the local stiffness matrix in the unit local coordinate system ; The local coordinate system of the unit is expressed as: is the origin, Axis as Node and nodes Connection, Axis and Node The coordinate system of the rigid center of the section Axis coincidence, Axis and Axis and The axes form a right-handed coordinate system;

[0061] Specifically, each section is regarded as a node, the location of the node is the rigid center of the section, and two adjacent nodes and nodes The simplified configuration of the connecting wing is a six-degree-of-freedom rigid frame in space, so each node has 6 degrees of freedom and each unit has 12 degrees of freedom. The inertia moment and torsional stiffness obtained in step 6 are used to obtain the node and nodes The element local stiffness matrix of the constituent elements :

[0062]

[0063] In the formula, For Node The total structural area, For Node The total structural area, and For Node X-axis moment of inertia in its rigid center coordinate system and the Z-axis moment of inertia, , and For Node X-axis moment of inertia in its rigid center coordinate system and the Z-axis moment of inertia, , is the unit length, i.e. the distance between two sections; columns 1-6 of the matrix correspond to nodes In the local coordinate system of the element Direction displacement ( )、 Direction displacement ( )、 Direction displacement ( )、 Direction Angle ( )、 Direction Angle ( )、 Direction Angle ( ); Similarly, columns 7-12 of the matrix correspond to nodes 6 degrees of freedom;

[0064] Step 7.2: Using the principle of coordinate system transformation, transform the local stiffness matrix of the unit in the local coordinate system The element global stiffness matrix converted to the global coordinate system Specifically, there are angles in three directions between the local coordinate system of the unit and the global coordinate system. Using the principle of coordinate transformation, the local stiffness matrix of the unit is transformed into the global stiffness matrix of the unit;

[0065]

[0066]

[0067]

[0068] In the formula, is the coordinate transformation matrix, is the Euler transformation matrix, is the unit global stiffness matrix, It is the unit local coordinate system to the global coordinate system Euler angles of three-axis rotation;

[0069] Step 7.3: Assemble the unit global stiffness matrix of each unit to obtain the structural global stiffness matrix ;

[0070] Specifically, the unit global stiffness matrix of each unit is assembled into the structural global stiffness matrix in sequence according to the node number of the unit, and the node number determines its position in the structural global stiffness matrix.

[0071] Furthermore, the step 8 comprises the following sub-steps:

[0072] Step 8.1: Establish the structural equation, specifically:

[0073] 1) Load handling:

[0074] Obtain nodes based on CFD methods or in the form of elliptical distribution Load , the node Load It is expressed as:

[0075]

[0076] In the formula, For Node Force loads in three directions in the global coordinate system, For Node Moment loads in three directions in the global coordinate system;

[0077] Assembling load vectors , expressed as:

[0078]

[0079] For the number of nodes The configuration of which the load vector is a size of is a column vector consisting of the loads at each node.

[0080] Assemble to obtain load vector Finally, combined with the structural overall stiffness matrix obtained in step 7 , the structural equation is established ,in is the displacement vector matrix to be solved, which contains displacements and rotations in three directions, namely Direction displacement, Direction displacement, Directional displacement; Direction angle, Direction angle, Direction angle;

[0081] 2) Boundary condition processing:

[0082] Set the degrees of freedom in the six directions of the front wing root and the rear wing root to 0, that is, The displacement vectors of the nodes corresponding to the wing root of the front wing and the wing root of the rear wing are limited to 0; and the displacement vectors of the nodes corresponding to the connecting end plates are limited to 0;

[0083] Step 8.2: Solve the structural equations, specifically:

[0084] 1) By structural equation Available , get the deflection and rotation of each node;

[0085] The deflection and rotation of each node include the following six parameters:

[0086] Direction displacement: , Direction displacement: , Direction displacement: ;

[0087] Direction Angle: , Direction Angle: , Direction Angle: ;

[0088] 2) According to the deflection and rotation of each node, the shape function of the deflection and rotation is interpolated for each element, that is, the deflection and rotation of any point in the element are obtained, as follows:

[0089] X-direction displacement shape function:

[0090]

[0091] In the formula Is the unit in position The displacement along the X direction, is the unknown coefficient, obtained by interpolation;

[0092] Y-direction displacement shape function:

[0093]

[0094] In the formula Is the unit in position The displacement along the Y direction, is the unknown coefficient, obtained by interpolation;

[0095] Z-direction displacement shape function:

[0096]

[0097] In the formula Is the unit in position The displacement along the Z direction, is the unknown coefficient, obtained by interpolation;

[0098] Shape function of rotation around the X axis:

[0099]

[0100] In the formula Is the unit in position The rotation angle around the X axis, is the unknown coefficient, obtained by interpolation;

[0101] Shape function of rotation around the Y axis:

[0102]

[0103] In the formula Is the unit in position The rotation angle around the Y axis, is the unknown coefficient, obtained by interpolation;

[0104] Shape function of rotation around the Z axis:

[0105]

[0106] In the formula Is the unit in position The rotation angle around the Z axis, is the unknown coefficient, obtained by interpolation;

[0107] 3) According to the obtained displacement shape functions in the X, Y, and Z directions, the stress on the unit is calculated as follows:

[0108] According to the displacement shape function, the linear strain along the X-axis, Y-axis, and Z-axis is obtained:

[0109]

[0110]

[0111]

[0112] In the formula is the linear strain along the X-axis, is the linear strain along the Y-axis, is the linear strain along the Z axis;

[0113] According to the displacement shape function, the shear strain along the XY plane, YZ plane, and ZX plane is obtained:

[0114]

[0115]

[0116]

[0117] In the formula is the shear strain in the XY plane, is the shear strain in the YZ plane, is the shear strain in the ZX plane;

[0118] Based on the obtained linear strain, the normal stress is calculated as follows:

[0119]

[0120]

[0121]

[0122] In the formula, is the Poisson's ratio of the material;

[0123] Based on the obtained shear strain, the shear stress is calculated as follows:

[0124]

[0125]

[0126]

[0127] Based on the obtained normal stress and shear stress, the stress state tensor is obtained:

[0128]

[0129] Solve its characteristic equation: ; Get the eigenvalue , that is, the three principal stresses of the element , , , is the identity matrix;

[0130] Based on the three principal stresses , , , the fourth strength theory is used to calculate the unit equivalent stress :

[0131] σ= 1 2 [ s 1 - s 2 2 + s 2 - s 3 2 + s 3 - s 1 2 ] ;

[0132] 4) Calculate the mass of the entire connecting wing configuration based on the parameters of each section , the specific calculation formula is as follows:

[0133] m = ∑ i=1 n [D x i * A i+1 + A i 2 ] r mean

[0134] In the formula, , Node The total structural area of ​​the section, For Node The distance, n is the number of nodes, is the average density of the cross section.

[0135] Beneficial Effects

[0136] The present invention provides a fast equivalent analysis method for structural characteristics of an integrated connecting wing configuration design. The finite element equivalent beam principle of engineering beam theory is used to divide the connecting wing configuration into multiple sections as nodes, which can accurately describe its special piecewise nonlinear stiffness distribution and ensure calculation accuracy. Compared with the solid unit finite element method, a small number of nodes are used to describe the connecting wing configuration structure, which can effectively improve the calculation efficiency. Therefore, the method of the present invention can effectively solve the problems of insufficient accuracy and long analysis time of the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0137] Figure 1 This is a flowchart of the implementation of the solution of the embodiment of the present invention;

[0138] Figure 2 It is a simplified front configuration of a double beam connecting wing according to an embodiment of the present invention;

[0139] Figure 3It is a simplified structure of the double beam connecting wing of the embodiment of the present invention;

[0140] Figure 4 It is a schematic diagram of the cross-section division of a double-beam connecting wing according to an embodiment of the present invention;

[0141] Figure 5 It is a solid unit finite element mesh division diagram of the example of the present invention;

[0142] Figure 6 This is a diagram of the solid unit finite element results of the example of the present invention.

[0143] Among them: 1-first front wing spar; 2-second front wing spar; 3-front wing rib; 4-front wing skin; 5-first rear wing spar; 6-second rear wing spar; 7-rear wing rib; 8-rear wing skin; 9-connecting end plate. DETAILED DESCRIPTION

[0144] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer and more understandable, and to enable those skilled in the art to better understand the solutions of the present invention, the present invention is further described and fully described in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0145] This embodiment takes a double-beam coupled wing long-flight UAV platform as an example, and adopts the structural characteristic fast equivalent analysis method for integrated coupled wing configuration design proposed in the present invention to analyze the structural characteristics of the coupled wing. When describing the position, deflection and rotation angle in the structural characteristic analysis, the global coordinate system is used, and the origin of the global coordinate system is Based on the design center of the double-beam linked wing long-flight UAV platform, The axis points to the rear of the platform along the section chord line. The axis lies in the section plane perpendicular to Axially, The vertical section of the axis faces inside the platform, satisfying the right-hand system.

[0146] like Figure 1 As shown, this embodiment specifically includes the following steps:

[0147] Step 1: According to the connecting wing configuration scheme to be analyzed, obtain its design parameters, regard the connecting wing as a spatial rigid frame structure composed of the front wing, the rear wing and the connecting end plate, and simplify it into a spatial six-degree-of-freedom rigid frame structure model; the "rigid frame" here refers to a rigid frame structure, not a flexible structure.

[0148] The structure of the connecting wing before simplification of this embodiment is as follows Figure 2 As shown in FIG. 1 , the configuration has propellers for vertical take-off and landing arranged at both ends of the two connecting end plates, a total of 4 propellers, which are shown in FIG. Figure 2The total weight of the double beam wing structure is 300kg, and the anhedral angle of the front wing is , rear wing anhedral , and obtain its design parameters as follows:

[0149] Structural dimension parameters include:

[0150] Front spar web thickness: ;

[0151] First front spar flange area: ;

[0152] Second front spar flange area: ;

[0153] Rear spar web thickness: ;

[0154] First rear spar flange area: ;

[0155] Second rear spar flange area: ;

[0156] Front and rear rib thickness: ;

[0157] Front wing skin and rear wing skin thickness: ;

[0158] Structural layout parameters include:

[0159] First front spar position: , second front spar position: ;

[0160] Front wing rib spacing: ;

[0161] First rear spar location: , second rear spar position: ;

[0162] Rear wing rib spacing: ;

[0163] The spar position here uses the dimensionless parameter Indicates that is the distance between the spar in the section and the leading edge of the section, is the section chord length;

[0164] Material property parameters include:

[0165] Young's modulus of the reference material: ;

[0166] Shear modulus of the reference material: .

[0167] Pick Figure 2 The connecting wing structure shown in the figure is regarded as a space rigid frame structure composed of a front wing, a rear wing and a connecting end plate, and is simplified into a space six-degree-of-freedom rigid frame structure model; the simplified model is shown in Figure 3 shown.

[0168] Step 2: In the spatial six-degree-of-freedom rigid frame structure model, the front wing, the rear wing and the connecting end plate are divided into a number of sections at equal intervals according to the set intervals, and the leading edge point coordinates of each section in the global coordinate system are obtained; wherein the sections of the front wing and the rear wing are parallel to the longitudinal symmetry plane of the aircraft where the connecting wing is located, and the section of the connecting end plate is perpendicular to the longitudinal symmetry plane of the aircraft where the connecting wing is located.

[0169] In this embodiment, the spatial six-degree-of-freedom rigid frame structure model is divided into sections according to the following two principles. The division diagram is shown in FIG. Figure 4 As shown:

[0170] 1) The front wing and rear wing need to be divided into enough sections to accurately describe the global stiffness. The front wing has 9 sections at an interval of 0.3m, and the rear wing has 5 sections at an interval of 0.275m.

[0171] 2) The stiffness of the connecting end plate contributes little to the global stiffness, so four sections are taken at equal intervals;

[0172] The method for obtaining the coordinates of the leading edge points of each section is to first obtain the coordinates of the leading edge points of the sections at both ends of the front wing, rear wing and connecting end plate and the sections at the connection as follows:

[0173] #1 (-0.8505, 0, 0.1610);

[0174] #5 (-0.4058, -1.1, 0.1347);

[0175] #9 (0.1197, -2.4, 0.1035);

[0176] #10 (0.5633, 0, 0.3579);

[0177] #14 (-0.0569, -1.1, 0.2173);

[0178] #15 (-1.158, -1.1, 0.263);

[0179] #18 (0.842, -1.1, 0.263);

[0180] Then the coordinates of the remaining front edge points of the cross section are calculated through geometric relationships.

[0181] Step 3: Based on the design parameters and the leading edge coordinates of each section, calculate the coordinates of each section in the global coordinate system The centroid coordinates under the cross section are taken as the origin to establish the centroid coordinate system of each cross section, and the three-axis directions of the centroid coordinate system are parallel to the three-axis directions of the global coordinate system;

[0182] Let's take the front wing root section as an example, that is, section #1, and calculate its centroid coordinates. And get its centroid coordinate system , which specifically includes the following sub-steps:

[0183] Step 3.1: Calculate the total structural area of ​​the section ;

[0184]

[0185] In the formula, is the reduction factor or conversion factor, which represents the ratio of the Young's modulus of the material used to the reference material. In this embodiment, the materials used are all aluminum alloys, so the reduction factor is ; is the skin thickness of the corresponding area of ​​the cross section. For example, in this embodiment, the cross section is the root cross section of the front wing. is the front wing skin thickness , is the arc length of the skin; is the thickness of the beam web in the corresponding area of ​​the cross section. In this embodiment, is the front spar web thickness , is the arc length of the beam web; is the kth type of spar flange area in the section corresponding region. In this embodiment, there are 4 types of spar flanges in the section corresponding region of the front wing root, which are the upper flange area of ​​the first front spar , the lower flange area of ​​the first front spar , flange area on the second front spar and the lower flange area of ​​the second front spar .

[0186] Step 3.2: Calculate the total static moment of the section on the X-axis of the global coordinate system Total static moment of Z axis ;

[0187]

[0188]

[0189] In the formula, is the Z-coordinate of the arc length element of the skin in the corresponding area of ​​the cross section in the global coordinate system, is the Z-coordinate of the arc length of the beam web in the corresponding area of ​​the section in the global coordinate system, is the Z-coordinate of the k-th wing spar flange in the corresponding area of ​​the cross section in the global coordinate system; is the X-coordinate of the skin arc length element in the corresponding area of ​​the cross section in the global coordinate system, is the X-coordinate of the arc length of the beam web in the corresponding area of ​​the section in the global coordinate system, is the X-coordinate of the kth wing spar flange in the corresponding area of ​​the section in the global coordinate system.

[0190] Step 3.3: Calculate the centroid coordinates ;

[0191]

[0192]

[0193] The global coordinate system is Direction of movement ,Towards Direction of movement That is, the centroid coordinate system of section #1 is obtained.

[0194] Step 4: Calculate the X-axis moment of inertia of each section in step 2 in its own centroid coordinate system and the Z-axis moment of inertia ;

[0195] The details are as follows: Since the angle between the centroid coordinate system and the section principal inertia axis coordinate system is small, the centroid coordinate system is regarded as the principal inertia axis coordinate system, so that the moment of inertia of the section divided by step 2 about the principal inertia axis, that is, the centroid axis, is and It is obtained by the following calculation formula:

[0196]

[0197]

[0198] Step 5: Using engineering beam theory, calculate the rigid center coordinates of each section in step 2 in its own centroid coordinate system, and establish the rigid center coordinate system of each section with the rigid center of each section as the origin, and the three-axis directions of the rigid center coordinate system are parallel to the three-axis directions of the centroid coordinate system;

[0199] The specific description is as follows, taking section #1 as an example:

[0200] Using engineering beam theory, the wing is considered as a beam supported on the fuselage. According to the moment of inertia of section #1 in the centroid coordinate system obtained in step 4, and , the rigid center position of section #1 It is obtained by the following calculation formula:

[0201]

[0202]

[0203] in, is the total static moment of the section on the X-axis of the centroid coordinate system, is the total static moment of the section on the Z axis of the centroid coordinate system, is the vertical distance from the shear force of the skin arc length element in the corresponding area of ​​the section to the reference point of the set moment, is the vertical distance from the shear force of the beam web arc length microelement in the corresponding area of ​​the section to the reference point of the set moment, It is twice the area contained by the closed curve of the single closed chamber corresponding to the skin arc length microelement of the section. It is twice the area contained by the arc length of the beam web in the corresponding area of ​​the section corresponding to the closed curve of the single closed chamber. is the shear modulus of the reference material.

[0204] The centroid coordinate system is Direction of movement ,Towards Direction of movement That is, the rigid center coordinate system of section #1 is obtained.

[0205] Step 6: Calculate the X-axis moment of inertia of each section in step 2 in its respective rigid center coordinate system , Z-axis moment of inertia and torsional stiffness ;

[0206] The specific description is as follows, taking section #1 as an example:

[0207] The rigid center coordinates of the section are obtained from step 5 , use the calculation method in step 4 to calculate the rigid center coordinate system Section moment of inertia and :

[0208]

[0209]

[0210] The torsional stiffness per unit length of the equivalent beam is obtained according to the engineering beam theory.

[0211]

[0212] In this embodiment, the calculation results of the stiffness parameters of some sections are shown in the following table:

[0213]

[0214] Step 7: Establish the overall stiffness matrix of the spatial six-degree-of-freedom rigid frame structure model, which specifically includes the following sub-steps:

[0215] Step 7.1: According to the moment of inertia and torsional stiffness of each section in its own rigid center coordinate system obtained in step 6, establish the local stiffness matrix in the unit local coordinate system ; The local coordinate system of the unit is expressed as: is the origin, Axis as Node and nodes Connection, Axis and Node The coordinate system of the rigid center of the section Axis coincidence, Axis and Axis and The axes form a right-handed coordinate system;

[0216] Specifically, each section is regarded as a node, the location of the node is the rigid center of the section, and two adjacent nodes and nodes The simplified configuration of the connecting wing is a spatial six-degree-of-freedom rigid frame structure, so each node has 6 degrees of freedom and each unit has 12 degrees of freedom. Taking the unit composed of node 1 and node 2 as an example, the unit local stiffness matrix of the unit composed of node 1 and node 2 is obtained from the moment of inertia and torsional stiffness obtained in step 6: for:

[0217]

[0218] Matrix columns 1-6 correspond to nodes In the local coordinate system of the element Direction displacement ( )、 Direction displacement ( )、 Direction displacement ( )、 Direction Angle ( )、 Direction Angle ( )、 Direction Angle ( ); Similarly, columns 7-12 of the matrix correspond to nodes 6 degrees of freedom;

[0219] Step 7.2: Using the principle of coordinate system transformation, transform the local stiffness matrix of the unit in the local coordinate system The element global stiffness matrix converted to the global coordinate system ; Specifically: there are angles in three directions between the local coordinate system of the unit and the global coordinate system. Using the principle of coordinate transformation, the local stiffness matrix of the unit is transformed into the global stiffness matrix of the unit;

[0220]

[0221]

[0222]

[0223] In the formula, is the coordinate transformation matrix, is the Euler transformation matrix, is the unit global stiffness matrix, It is the unit local coordinate system to the global coordinate system Euler angles of three-axis rotation;

[0224] In this embodiment, the angles between the local coordinate system of the unit composed of node 1 and node 2 and the global coordinate system in three directions are , so we have:

[0225]

[0226] Then we get the coordinate transformation matrix And the element global stiffness matrix ;

[0227] Step 7.3: Assemble the unit global stiffness matrix of each unit to obtain the structural global stiffness matrix ;

[0228] Specifically: the unit overall stiffness matrix is ​​assembled into the structural overall stiffness matrix in sequence according to the node number of the unit. The node number determines its position in the structural overall stiffness matrix. The assembled structural overall stiffness matrix can well describe this nonlinear and segmented form, and can make the calculation results more accurate.

[0229] In this embodiment, the structural material properties of the skin, ribs and spars are combined to obtain the overall structural stiffness matrix according to step 7: The matrix size is It is no longer displayed.

[0230] Step 8: According to the overall stiffness matrix of the structure obtained in step 7, the structural equation is established and solved to obtain the displacement deflection of each node of the connecting wing structure and the overall structural characteristics (the following are all processed in the global coordinate system). The specific sub-steps include the following:

[0231] Step 8.1: Establish the structural equation, specifically:

[0232] 1) Load handling:

[0233] Obtaining nodes by CFD methods Load , the node Load It is expressed as:

[0234]

[0235] In the formula, For Node Force loads in three directions in the global coordinate system, For Node Moment loads in three directions in the global coordinate system.

[0236] Assembling load vectors , expressed as:

[0237]

[0238] For the number of nodes The configuration of which the load vector is a size of is a column vector consisting of the loads at each node.

[0239] In this embodiment, four propellers are arranged at the end of the end plate of the configuration. In order to verify the calculation accuracy and efficiency of the vertical yaw state, the diagonal rotor in the vertical yaw control state increases the lift to 1.5 times. Therefore, a 2250N upward concentrated load is set at the front end of the end plate (node ​​15), and the other nodes are unloaded, then:

[0240]

[0241] Assemble to obtain load vector Finally, combined with the overall structural stiffness matrix obtained in step 7 , the structural equation is established ,in is the displacement vector matrix to be solved, which contains displacements and rotations in three directions, namely Direction displacement, Direction displacement, Directional displacement; Direction angle, Direction angle, Direction angle;

[0242] 2) Boundary condition processing:

[0243] The wing roots of the front and rear wings of this configuration are fixed constraints, so the degrees of freedom in the six directions of the front wing root (node ​​1) and the rear wing root (node ​​10) are all 0; in addition, for the connection end plate, since the stiffness here is composed of the common stiffness of the connection end plate and the front and rear wing connection, no additional boundary condition attributes are required; then the displacement vector matrix No. to OK, to The row limit is 0.

[0244] Step 8.2: Solve the structural equations, specifically:

[0245] 1) By structural equation Available , get the deflection and rotation of each node;

[0246] The deflection and rotation of each node include the following six parameters:

[0247] Direction displacement: , Direction displacement: , Direction displacement: ;

[0248] Direction Angle: , Direction Angle: , Direction Angle: ;

[0249] 2) According to the deflection and rotation of each node, the shape function of the deflection and rotation is interpolated for each unit, that is, the deflection and rotation of any point in the unit are obtained. Here, the unit in the front wing is taken as an example, as follows:

[0250] X-direction displacement shape function:

[0251]

[0252] In the formula Is the unit in position The displacement along the X direction;

[0253] Y-direction displacement shape function:

[0254]

[0255] In the formula Is the unit in position The displacement along the Y direction;

[0256] Z-direction displacement shape function:

[0257]

[0258] In the formula Is the unit in position The displacement along the Z direction;

[0259] Shape function of rotation around the X axis:

[0260]

[0261] In the formula Is the unit in position The rotation angle around the X axis;

[0262] Shape function of rotation around the Y axis:

[0263]

[0264] In the formula Is the unit in position The rotation angle around the Y axis;

[0265] Shape function of rotation around the Z axis:

[0266]

[0267] In the formula Is the unit in position The rotation angle around the Z axis;

[0268] 3) Based on the obtained displacement shape functions in the X, Y, and Z directions, the stress on the unit is calculated as follows:

[0269] According to the displacement shape function, the linear strain along the X-axis, Y-axis, and Z-axis is obtained:

[0270]

[0271]

[0272]

[0273] In the formula is the linear strain along the X-axis, is the linear strain along the Y-axis, is the linear strain along the Z axis;

[0274] According to the displacement shape function, the shear strain along the XY plane, YZ plane, and ZX plane is obtained:

[0275]

[0276]

[0277]

[0278] In the formula is the shear strain in the XY plane, is the shear strain in the YZ plane, is the shear strain in the ZX plane;

[0279] Based on the obtained linear strain, the normal stress is calculated as follows:

[0280]

[0281]

[0282]

[0283] In the formula, is the Poisson's ratio of the material;

[0284] Based on the obtained shear strain, the shear stress is calculated as follows:

[0285]

[0286]

[0287]

[0288] Based on the obtained normal stress and shear stress, the stress state tensor is obtained:

[0289]

[0290] Solve its characteristic equation: ; Get the eigenvalue , that is, the three principal stresses of the element , , , is the identity matrix;

[0291] Based on the three principal stresses , , , the fourth strength theory is used to calculate the unit equivalent stress :

[0292] σ= 1 2 [ s 1 - s 2 2 + s 2 - s 3 2 + s 3 - s 1 2 ] ;

[0293] 4) Calculate the mass of the entire connecting wing configuration based on the parameters of each section , the specific calculation formula is as follows:

[0294] m = ∑ i=1 n [D x i * A i+1 + A i 2 ] r mean

[0295] In the formula, , Node The total structural area of ​​the section, For Node The distance, n is the number of nodes, is the average density of the cross section.

[0296] In order to verify the calculation efficiency and accuracy of this patent, the calculation results of the solid unit finite element method are used as a benchmark for verification and comparison; this model focuses on the structural response size at the wing tip, and selects the node 9 where the wing tip is located as the result comparison point. The calculation results are compared as shown in the following table:

[0297]

[0298] As shown in the table above, the response error of the patented structure is less than 10%, among which the wing tip The directional deformation error is only -3.21%, which meets the accuracy requirements of the project. In addition, the solid unit finite element method takes 4.17 minutes, while the patented method takes 7 seconds, which improves the calculation efficiency by more than 30 times. Figure 5 As shown, there are 114898 mesh elements and 216875 nodes; the finite element results of the solid element are as follows Figure 6 As shown, the deformation of the connected wing structure gradually increases from the wing root to the wing tip, and a more significant torsional deformation occurs. The maximum deformation position of the wing is at the wing tip, with a size of 0.01028m.

[0299] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A fast equivalent analysis method for structural characteristics of integrated joint wing configuration design, characterized by: The steps include: Step 1: According to the coupling wing configuration scheme to be analyzed, obtain its design parameters, regard the coupling wing as a spatial rigid frame structure composed of a front wing, a rear wing and a connecting end plate, and simplify it into a spatial six-degree-of-freedom rigid frame structure model; Step 2: In the spatial six-degree-of-freedom rigid frame structure model, the front wing, the rear wing and the connecting end plate are divided into a number of sections at equal intervals according to the set intervals, and the leading edge point coordinates of each section in the global coordinate system are obtained; wherein the sections of the front wing and the rear wing are parallel to the longitudinal symmetry plane of the aircraft where the connecting wing is located, and the section of the connecting end plate is perpendicular to the longitudinal symmetry plane of the aircraft where the connecting wing is located; Step 3: Based on the design parameters and the leading edge coordinates of each section, calculate the coordinates of each section in the global coordinate system The centroid coordinates under the cross section are taken as the origin to establish the centroid coordinate system of each cross section, and the three-axis directions of the centroid coordinate system are parallel to the three-axis directions of the global coordinate system; Step 4: Calculate the X-axis moment of inertia of each section in step 2 in its own centroid coordinate system and the Z-axis moment of inertia ; Step 5: Calculate the rigid center coordinates of each section in step 2 in its own centroid coordinate system, establish the centroid coordinate system of each section with the rigid center of each section as the origin, and the three-axis directions of the rigid center coordinate system are parallel to the three-axis directions of the centroid coordinate system; Step 6: Calculate the X-axis moment of inertia of each section in step 2 in its respective rigid center coordinate system , Z-axis moment of inertia and torsional stiffness ; Step 7: The X-axis moment of inertia of each section in its respective rigid center coordinate system obtained in step 6 , Z-axis moment of inertia and torsional stiffness , establish the unit overall stiffness matrix of each unit and assemble to obtain the structural overall stiffness matrix of the spatial six-degree-of-freedom rigid frame structure model ; Step 8: Based on the overall stiffness matrix of the structure obtained in step 7, the structural equation is established and solved to obtain the displacement deflection of each node of the connecting wing structure and the overall structural characteristics.

2. The structural characteristics rapid equivalent analysis method for integrated joint wing configuration design according to claim 1 is characterized by: The design parameters in step 1 include structural size parameters, structural layout parameters and material property parameters, where the structural size parameters include: First front spar web thickness: , the thickness of the web of the second front spar: ; The flange area of ​​the first front spar: , the lower flange area of ​​the first front wing spar: ; Second front wing spar upper flange area: , the lower flange area of ​​the second front wing spar: ; Front rib thickness: ; Front wing skin thickness: ; First rear spar web thickness: , the second rear spar web thickness: ; The flange area of ​​the first rear spar: , the lower flange area of ​​the first rear wing spar: ; Second rear wing spar upper flange area: , the lower flange area of ​​the second rear wing spar: ; Rear wing rib thickness: ; Rear wing skin thickness: ; Structural layout parameters include: First front spar position: , second front spar position: ; Front wing rib spacing: ; First rear spar position: , second rear spar position: ; Rear wing rib spacing: ; Material property parameters include: Young's modulus of the reference material: ; Shear modulus of the reference material: .

3. The structural characteristics rapid equivalent analysis method for integrated connecting wing configuration design according to claim 1 is characterized by: In step 3, the specific steps for establishing a cross-section centroid coordinate system are as follows: Step 3.1: Calculate the total structural area of ​​the section ; In the formula, is the reduction factor; is the skin thickness of the section corresponding area, is the arc length of the skin; is the beam web thickness in the section corresponding area, is the arc length of the beam web; is the flange area of ​​the kth type spar in the corresponding area of ​​the section; Step 3.2: Calculate the total static moment of the section on the X-axis of the global coordinate system Total static moment of Z axis In the formula, is the Z-coordinate of the arc length element of the skin in the corresponding area of ​​the cross section in the global coordinate system, is the Z-coordinate of the arc length of the beam web in the corresponding area of ​​the section in the global coordinate system, is the Z-coordinate of the k-th wing spar flange in the corresponding area of ​​the cross section in the global coordinate system; is the X-coordinate of the skin arc length element in the corresponding area of ​​the cross section in the global coordinate system, is the X-coordinate of the arc length of the beam web in the corresponding area of ​​the section in the global coordinate system, is the X-coordinate of the k-th wing spar flange in the corresponding area of ​​the cross section in the global coordinate system; Step 3.3: Calculate the centroid coordinates of the section ; Move the origin of the global coordinate system to the centroid coordinates , and obtain the centroid coordinate system corresponding to the section.

4. The structural characteristics rapid equivalent analysis method for integrated joint wing configuration design according to claim 3 is characterized by: In step 4, the X-axis moment of inertia of a section in its centroid coordinate system is and the Z-axis moment of inertia Calculated by the following formula:

5. The structural characteristics rapid equivalent analysis method for integrated joint wing configuration design according to claim 4 is characterized by: In step 5, the coordinates of the rigid center of a section It is obtained by the following calculation formula: in, is the total static moment of the section on the X-axis of the centroid coordinate system, is the total static moment of the section on the Z axis of the centroid coordinate system, is the vertical distance from the shear force of the skin arc length element in the corresponding area of ​​the section to the reference point of the set moment, is the vertical distance from the shear force of the beam web arc length microelement in the corresponding area of ​​the section to the reference point of the set moment, It is twice the area contained by the closed curve of the single closed chamber corresponding to the skin arc length microelement of the section. It is twice the area contained by the arc length of the beam web in the corresponding area of ​​the section corresponding to the closed curve of the single closed chamber. is the shear modulus of the reference material.

6. The structural characteristics rapid equivalent analysis method for integrated joint wing configuration design according to claim 5 is characterized by: In step 6, according to the formula Calculate the rigid center coordinate system The X-axis moment of inertia and the Z-axis moment of inertia ; According to the formula Obtain the torsional stiffness per unit length of the equivalent beam .

7. The structural characteristics rapid equivalent analysis method for integrated joint wing configuration design according to claim 6 is characterized by: The step 7 comprises the following sub-steps: Step 7.1: Treat each section as a node. The location of the node is the rigid center of the section. and nodes The local coordinate system of the unit is based on the node is the origin, Axis as Node and nodes Connection, Axis and Node The coordinate system of the rigid center of the section Axis coincidence, Axis and Axis and The axes form a right-handed coordinate system; According to the inertia moment and torsional stiffness of each section in its own rigid center coordinate system obtained in step 6, the local stiffness matrix in the unit local coordinate system is established : In the formula, For Node The total structural area, For Node The total structural area, and For Node X-axis moment of inertia in its rigid center coordinate system and the Z-axis moment of inertia, , and For Node X-axis moment of inertia in its rigid center coordinate system and the Z-axis moment of inertia, , is the unit length, i.e. the distance between the two sections; Step 7.2: According to the formula The local stiffness matrix of the element in the local coordinate system is The element global stiffness matrix converted to the global coordinate system ,in in is the coordinate transformation matrix, is the Euler transformation matrix, is the unit global stiffness matrix, It is the unit local coordinate system to the global coordinate system Euler angles of three-axis rotation; Step 7.3: Assemble the unit global stiffness matrix of each unit to obtain the structural global stiffness matrix .

8. The structural characteristics rapid equivalent analysis method for integrated joint wing configuration design according to claim 1 is characterized by: The step 8 comprises the following sub-steps: Step 8.1: Establish the structural equation, specifically: 1) Load handling: Get Node Load , the node Load It is expressed as: In the formula, For Node Force loads in three directions in the global coordinate system, For Node Moment loads in three directions in the global coordinate system; Assembling load vectors , expressed as: For the number of nodes The configuration of which the load vector is a size of The column vector of is composed of the loads at each node; Assemble to obtain load vector Then, combined with the overall stiffness matrix obtained in step 7 , the structural equation is established ,in is the displacement vector to be solved; 2) Boundary condition processing: The displacement vector The positions of the nodes corresponding to the wing roots of the front and rear wings are limited to 0; and the displacement vectors of the nodes corresponding to the connecting end plates are limited to 0; Step 8.2: Solve the structural equations, specifically: 1) By structural equation Available , get the deflection and rotation of each node; The deflection and rotation of each node include the following six parameters: Direction displacement: , Direction displacement: , Direction displacement: ; Direction Angle: , Direction Angle: , Direction Angle: ; 2) Based on the deflection and rotation of each node, the shape function of the deflection and rotation is interpolated for each element to obtain the deflection and rotation of any point in the element, as follows: X-direction displacement shape function: In the formula Is the unit in position The displacement along the X direction, is the unknown coefficient, obtained by interpolation; Y-direction displacement shape function: In the formula Is the unit in position The displacement along the Y direction, is the unknown coefficient, obtained by interpolation; Z-direction displacement shape function: In the formula Is the unit in position The displacement along the Z direction, is the unknown coefficient, obtained by interpolation; Shape function of rotation around the X axis: In the formula Is the unit in position The rotation angle around the X axis, is the unknown coefficient, obtained by interpolation; Shape function of rotation around the Y axis: In the formula Is the unit in position The rotation angle around the Y axis, is the unknown coefficient, obtained by interpolation; Shape function of rotation around the Z axis: In the formula Is the unit in position The rotation angle around the Z axis, is the unknown coefficient, obtained by interpolation; 3) Based on the obtained displacement shape functions in the X, Y, and Z directions, the stress on the unit is calculated as follows: According to the displacement shape function, the linear strain along the X-axis, Y-axis, and Z-axis is obtained: In the formula is the linear strain along the X-axis, is the linear strain along the Y-axis, is the linear strain along the Z axis; According to the displacement shape function, the shear strain along the XY plane, YZ plane, and ZX plane is obtained: In the formula is the shear strain in the XY plane, is the shear strain in the YZ plane, is the shear strain in the ZX plane; Based on the obtained linear strain, the normal stress is calculated as follows: In the formula, is the Poisson's ratio of the material; Based on the obtained shear strain, the shear stress is calculated as follows: Based on the obtained normal stress and shear stress, the stress state tensor is obtained: Solve its characteristic equation: ; Get the eigenvalue , that is, the three principal stresses of the element , , , is the identity matrix; Based on the three principal stresses , , , the equivalent stress is obtained by using the fourth strength theory : ; 4) Calculate the mass of the entire connecting wing configuration based on the parameters of each section , the specific calculation formula is as follows: In the formula, , Node The total structural area of ​​the section, For Node The distance, n is the number of nodes, is the average density of the cross section.

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