Composite material C-shaped beam rotor wing type structural characteristic determination method, equipment, medium and product

Abstract

The invention discloses a composite material C-shaped beam rotor wing shape structure characteristic determination method and device, a medium and a product, and relates to the technical field of rotor wing aircrafts, the method comprises the following steps: generating a wing shape structure model; the airfoil structure model is a composite material C-shaped beam rotor airfoil structure model; the airfoil structure model comprises a skin structure model, a C-shaped beam structure model, a front edge counterweight structure model and a rear edge strip structure model; performing grid division on the airfoil profile structure model to obtain a grid-divided airfoil profile structure model; according to the airfoil profile structure model after grid division, airfoil profile structure characteristics are calculated by adopting a generalized Timoshenko beam theory; the wing-shaped structural characteristic is the wing-shaped structural characteristic of the composite material C-shaped beam rotor wing. According to the method, the wing type structural characteristics of the composite material C-shaped beam rotor wing can be rapidly calculated.

Description

Technical Field

[0001] The present application relates to the technical field of rotorcraft, and particularly to a method, device, medium and product for determining the structural characteristics of a composite C-beam rotor airfoil. Background Art

[0002] Blade design is a cyclic iterative process. Blade design includes not only airfoil structure design, but also dynamic design, calculating sectional characteristic parameters, and then calculating the dynamic characteristics of the blade to see if the requirements are met. If not, the airfoil structure needs to be adjusted and recalculated.

[0003] The blade sectional characteristics are the most basic original parameters for rotor dynamics calculation. When designing composite blades, it is first necessary to know the sectional characteristic parameters of the blades in order to carry out blade structure design and dynamic analysis later. At present, blade sectional characteristic calculation mainly relies on the finite element method and the Euler-Bernoulli beam theory. The finite element method can fully consider the complexity of the structure and can also consider the coupling among flapping, pitching and torsion, but the computer time it takes is unacceptable, and the result form cannot be corrected. The Euler-Bernoulli beam theory is mainly applicable to metal blades, and the calculation of torsional stiffness is inaccurate.

[0004] In summary, at present, the finite element method and the Euler-Bernoulli beam theory cannot achieve the rapid calculation of the structural characteristics of the composite C-beam rotor airfoil. How to quickly calculate the structural characteristics of the composite C-beam rotor airfoil has become an urgent problem for those skilled in the art. Summary of the Invention

[0005] The purpose of the present application is to provide a method, device, medium and product for determining the structural characteristics of a composite C-beam rotor airfoil, which can quickly calculate the structural characteristics of the composite C-beam rotor airfoil.

[0006] To achieve the above purpose, the present application provides the following solutions:

[0007] In the first aspect, the present application provides a method for determining the structural characteristics of a composite C-beam rotor airfoil, and the method for determining the structural characteristics of the composite C-beam rotor airfoil includes:

[0008] Generating an airfoil structure model; the airfoil structure model is a composite C-beam rotor airfoil structure model; the airfoil structure model includes the structural models of the skin, C-beam, leading edge counterweight and trailing edge strip;

[0009] Performing mesh division on the airfoil structure model to obtain the airfoil structure model after mesh division;

[0010] According to the airfoil structure model after grid division, the airfoil structure characteristics are calculated using the generalized Timoshenko beam theory; the airfoil structure characteristics are the composite C-beam rotary airfoil structure characteristics.

[0011] Optionally, the generation of the airfoil structure model specifically includes:

[0012] According to the C-beam rotary airfoil, the number of composite material plies, the single-layer thickness, and the ply angle, a structural model of the skin is generated at equal intervals.

[0013] According to the inner surface contour of the skin and the area of the C-beam, a structural model of the C-beam is generated according to the algorithm of constant area.

[0014] According to the center position and radius of the leading-edge weight, a structural model of the leading-edge weight is generated.

[0015] According to the chordwise distance from the trailing-edge starting position of the trailing-edge strip to the leading edge of the airfoil, a structural model of the trailing-edge strip is generated.

[0016] Optionally, the generation of the structural model of the C-beam according to the inner surface contour of the skin and the area of the C-beam according to the algorithm of constant area specifically includes:

[0017] According to the inner surface contour of the skin, the design positioning points on the upper chord, the design positioning points on the lower chord, and the design positioning points in the middle, a C-beam is initially generated. Two automatic adjustment points are respectively set between adjacent design positioning points. Area compensation is achieved by moving the automatic adjustment points along the normal direction. Calculate the current area of the C-beam component, find the area difference between the current area of the C-beam component and the sectional area of the input control parameter. Taking the automatic adjustment point as the moving point and the adjacent two control points as the base to form a triangle, the height of the triangle is directly calculated from the area that the control point needs to compensate, and the shape of the C-beam is obtained to generate the structural model of the C-beam.

[0018] Optionally, the grid division of the airfoil structure model to obtain the airfoil structure model after grid division specifically includes:

[0019] Quadrilateral grids are divided for the structural model of the skin, and triangular grids are divided for the structural models of the C-beam, the leading-edge weight, and the trailing-edge strip to obtain the airfoil structure model after grid division.

[0020] Optionally, the division of the quadrilateral grid for the structural model of the skin and the division of the triangular grid for the structural models of the C-beam, the leading-edge weight, and the trailing-edge strip to obtain the airfoil structure model after grid division specifically includes:

[0021] The structural model of the skin is divided into eight-node quadrilateral blocks. Within each eight-node quadrilateral block, isoparametric mapping is performed using shape functions to generate block meshes. The Delaunay triangulation method is used to divide the structural models of the C-beam, leading-edge counterweight, and trailing-edge strip into triangular meshes, obtaining the airfoil structural model after mesh division.

[0022] Optionally, based on the airfoil structural model after mesh division, the generalized Timoshenko beam theory is used to calculate the airfoil structural characteristics, specifically including:

[0023] Based on the airfoil structural model after mesh division, an elastic beam model with inhomogeneity, anisotropy, and torsional deformation is derived based on the variational asymptotic method. The local coordinate systems of the beam before and after deformation in the generalized Timoshenko beam theory are defined to describe the geometric deformation of the beam, obtaining the position vectors of the beam before and after deformation.

[0024] Based on the position vectors of the beam before and after deformation and the Timoshenko one-dimensional generalized strain, the sectional strain energy is obtained.

[0025] Based on the sectional strain energy and the variational asymptotic method, the sectional second-order asymptotically exact strain energy is obtained.

[0026] Based on the standard form of the generalized Timoshenko strain energy and the sectional second-order asymptotically exact strain energy, the constitutive relationship of the generalized Timoshenko strain energy is solved to obtain the airfoil structural characteristics; the airfoil structural characteristics only include the sectional stiffness matrix.

[0027] Optionally, the sectional stiffness matrix is composed of the stiffness coefficient for tension, the stiffness coefficient for torsion, the stiffness coefficient for shear in the X direction, the stiffness coefficient for shear in the Y direction, the stiffness coefficient for bending in the X direction, the stiffness coefficient for bending in the Y direction, and the coupling stiffness coefficients corresponding to any two different stiffness coefficients, forming a 6×6 matrix; the X direction is along the chord length direction; the Y direction is perpendicular to the chord length direction.

[0028] In a second aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the method for determining the composite C-beam rotary airfoil structural characteristics described in any one of the above.

[0029] In a third aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the method for determining the composite C-beam rotary airfoil structural characteristics described in any one of the above.

[0030] Fourthly, the present application provides a computer program product, including a computer program which, when executed by a processor, implements the method for determining the structural characteristics of a composite C-beam airfoil structure described in any one of the above.

[0031] According to the specific embodiments provided by the present application, the present application has the following technical effects:

[0032] The present application provides a method, device, medium and product for determining the structural characteristics of a composite C-beam airfoil structure. By generating structural models of the skin, C-beam, leading-edge counterweight and trailing-edge strip, meshing the structural models of the skin, C-beam, leading-edge counterweight and trailing-edge strip, and deriving the cross-section characteristic calculation method according to the generalized Timoshenko beam theory, an integrated process from the design of the composite C-beam airfoil structure model to meshing and then to the calculation of the structural characteristics of the composite C-beam airfoil structure is realized. The calculation speed is fast. Compared with the finite element method and the Euler-Bernoulli beam theory, the present application can achieve the effect of quickly calculating the structural characteristics of the composite C-beam airfoil structure. Description of the Drawings

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0034] Figure 1 It is a schematic flowchart of a method for determining the structural characteristics of a composite C-beam airfoil structure provided by an embodiment of the present application;

[0035] Figure 2 It is a flowchart of a fast calculation method for the structural characteristics of a composite C-beam airfoil structure of the present application;

[0036] Figure 3 It is a schematic diagram of the cross-section component description parameters in the parametric modeling of the airfoil structure of the present application;

[0037] Figure 4 It is a schematic diagram of the generation method for skin structure modeling of the present application;

[0038] Figure 5 It is a schematic diagram of the automatic algorithm for the constant area of the C-beam of the present application;

[0039] Figure 6 It is a schematic diagram of the triangular mesh generated for non-laminate structures of the present application;

[0040] Figure 7It is a schematic diagram of beam deformation in the generalized Timoshenko beam theory of this application;

[0041] Figure 8 It is a schematic diagram of the shear deformation coordinate system in the generalized Timoshenko beam theory of this application;

[0042] Figure 9 It is a schematic diagram of the structure of a computer device provided by an embodiment of this application. Detailed implementation manners

[0043] Next, the technical solutions in the embodiments of this application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this application.

[0044] The purpose of this application is to provide a method, device, medium and product for determining the structural characteristics of a composite C-beam rotary wing airfoil, which can quickly calculate the structural characteristics of the composite C-beam rotary wing airfoil.

[0045] To make the above objects, features and advantages of this application more obvious and understandable, the following further detailed description of this application will be given in conjunction with the accompanying drawings and specific implementation manners.

[0046] As Figure 1 shown, a method for determining the structural characteristics of a composite C-beam rotary wing airfoil provided by this application includes:

[0047] Step 101: Generate an airfoil structure model; the airfoil structure model is a composite C-beam rotary wing airfoil structure model; the airfoil structure model includes the structural models of the skin, C-beam, leading-edge weight and trailing-edge strip.

[0048] This step 101 specifically includes:

[0049] Generate the structural model of the skin at equal intervals according to the C-beam rotary wing airfoil, the number of composite material plies, the single-layer thickness and the ply angle.

[0050] Generate the structural model of the C-beam according to the inner surface contour of the skin and the area of the C-beam according to the algorithm of constant area.

[0051] Generate the structural model of the leading-edge weight according to the center position and radius of the leading-edge weight.

[0052] Generate the structural model of the trailing-edge strip according to the chordwise distance from the trailing-edge starting position of the trailing-edge strip to the leading edge of the airfoil.

[0053] Among them, a structural model of the C-beam is generated according to the inner surface profile of the skin and the area of the C-beam according to the algorithm of constant area, specifically including:

[0054] According to the inner surface profile of the skin, the design positioning points on the upper chord, the design positioning points on the lower chord, and the design positioning points in the middle, a C-beam is initially generated. Two automatic adjustment points are respectively set between adjacent design positioning points. Area compensation is achieved by moving the automatic adjustment points along the normal direction. Calculate the current area of the C-beam component, find the area difference between the current area of the C-beam component and the cross-sectional area of the input control parameter. Taking the automatic adjustment point as the moving point and the adjacent two control points as the base to form a triangle, the height of the triangle is directly calculated from the area that the control points need to compensate, and the shape of the C-beam is obtained, and the structural model of the C-beam is generated. Among them, the current area of the C-beam component is the area of the initially generated C-beam, and the cross-sectional area of the input control parameter is the area to be obtained.

[0055] Step 102: Perform mesh division on the airfoil structural model to obtain the airfoil structural model after mesh division.

[0056] This step 102 specifically includes:

[0057] Divide the structural model of the skin into quadrilateral meshes, and divide the structural models of the C-beam, the leading-edge weight, and the trailing-edge strip into triangular meshes to obtain the airfoil structural model after mesh division.

[0058] Among them, dividing the structural model of the skin into quadrilateral meshes and dividing the structural models of the C-beam, the leading-edge weight, and the trailing-edge strip into triangular meshes to obtain the airfoil structural model after mesh division specifically includes:

[0059] Divide the structural model of the skin into eight-node quadrilateral blocks, and use the shape function for isoparametric mapping to generate block meshes within each eight-node quadrilateral block. Use the Delaunay triangulation method to divide the structural models of the C-beam, the leading-edge weight, and the trailing-edge strip into triangular meshes to obtain the airfoil structural model after mesh division. Among them, the block mesh is further divided within the eight-node quadrilateral block. The block mesh can be an eight-node quadrilateral block mesh or a four-node quadrilateral block mesh.

[0060] Step 103: According to the airfoil structural model after mesh division, calculate the airfoil structural characteristics using the generalized Timoshenko beam theory; the airfoil structural characteristics are the composite C-beam rotary airfoil structural characteristics.

[0061] This step 103 specifically includes:

[0062] Based on the airfoil structure model after grid division, an elastic beam model with inhomogeneity, anisotropy, and torsional deformation is derived based on the variational asymptotic method. The local coordinate systems of the beam before and after deformation in the generalized Timoshenko beam theory are defined to describe the geometric deformation of the beam, and the position vectors of the beam before and after deformation are obtained.

[0063] Based on the position vectors of the beam before and after deformation and the Timoshenko one-dimensional generalized strain, the sectional strain energy is obtained.

[0064] Based on the sectional strain energy and the variational asymptotic method, the sectional second-order asymptotically exact strain energy is obtained.

[0065] Based on the standard form of the generalized Timoshenko strain energy and the sectional second-order asymptotically exact strain energy, the constitutive relationship of the generalized Timoshenko strain energy is solved to obtain the airfoil structure characteristics; the airfoil structure characteristics only include the sectional stiffness matrix.

[0066] Among them, the sectional stiffness matrix is composed of the stiffness coefficient of tension, the stiffness coefficient of torsion, the stiffness coefficient of shear in the X direction, the stiffness coefficient of shear in the Y direction, the stiffness coefficient of bending in the X direction, the stiffness coefficient of bending in the Y direction, and the coupling stiffness coefficients corresponding to any two different stiffness coefficients, forming a 6×6 matrix; the X direction is along the chord length direction; the Y direction is perpendicular to the chord length direction.

[0067] The following uses a specific embodiment to illustrate the technical solution of the present application:

[0068] The present application provides a method for determining the structural characteristics of a composite C-beam rotary wing airfoil, which is a method for quickly calculating the structural characteristics of a composite C-beam rotary wing airfoil (that is, a method for quickly calculating the static airfoil structural characteristics of a composite C-beam rotary wing), realizing an integrated process from airfoil structure design to grid division and then to structural characteristic calculation. The method for quickly calculating the structural characteristics of a composite C-beam rotary wing airfoil provided by the present application provides a method for parametric modeling of the airfoil structure and a method for calculating the airfoil structure characteristics using the generalized Timoshenko theory.

[0069] Among them, the method for parametric modeling of the airfoil structure includes:

[0070] According to the C-beam rotary wing airfoil, the number of composite material plies, the thickness of a single ply, and the ply angle, the structure of the skin (that is, the structural model of the skin) is generated at equal distances (that is, the thickness at any position in the same layer is equal).

[0071] According to the inner surface contour of the skin (that is, the skin generated in the previous step) and the area of the C-beam, the C-beam (that is, the structural model of the C-beam) is generated according to the algorithm of constant area.

[0072] Generate the leading-edge weight (i.e., the structural model of the leading-edge weight) according to the center position and radius of the leading-edge weight, and generate the trailing-edge strip (i.e., the structural model of the trailing-edge strip) according to the chordwise distance from the trailing-edge starting position of the trailing-edge strip to the leading-edge of the airfoil.

[0073] Among them, generate the C-beam according to the inner surface contour of the skin and the area of the C-beam according to the algorithm of constant area, specifically including:

[0074] According to the inner surface contour of the skin, the upper chordwise design positioning point X Ctop , the lower chordwise design positioning point X Cbot , the middle design positioning point (X Cmid , Y Cmid ) initially generate the C-beam, set two automatic adjustment points between adjacent design positioning points respectively, realize area compensation by moving the automatic adjustment points along the normal direction, calculate the current area S1 of the C-beam component, find out the area difference ΔS = S1 - S0 from the input control parameter cross-sectional area S0, form a triangle with the automatic adjustment point as the moving point and the adjacent two control points as the bottom edge, and directly calculate the height of the triangle from the area that the control point needs to compensate, so as to obtain the shape of the C-beam. Among them, X Cmid represents the X-direction coordinate of the middle design positioning point, and Y Cmid represents the Y-direction coordinate of the middle design positioning point. The X direction is along the chord length direction; the Y direction is perpendicular to the chord length direction.

[0075] The method for calculating the airfoil structural characteristics by using the generalized Timoshenko theory includes:

[0076] Obtain the sectional strain energy according to the position vectors before and after the beam deformation and the Timoshenko one-dimensional generalized strain.

[0077] Obtain the sectional second-order asymptotic exact strain energy according to the variational asymptotic method.

[0078] Solve the constitutive relationship according to the standard form of the generalized Timoshenko strain energy and the obtained sectional strain energy, and the structural characteristics can be obtained, that is, the sectional stiffness matrix (the structural characteristics calculated in this application only include the sectional stiffness matrix S).

[0079] Figure 2 Shows the flow of calculating the structural characteristics of the composite C-beam rotary airfoil, as Figure 2 shown, a method for quickly calculating the structural characteristics of the composite C-beam rotary airfoil provided by this application specifically includes the following steps:

[0080] Step 1: Parametrically model the airfoil structural components.

[0081] The composite blade with a C - type beam configuration usually consists of a leading - edge weight, a main beam, a skin, a trailing - edge strip, and a filling foam. According to the structural characteristics of the components, it can be divided into two categories: laminated and non - laminated. The laminated structure is usually stacked by composite material plies. With the changes in material, the number of plies, the thickness of a single ply, and the ply angle, the following changes occur: the greater the stiffness of the material, the greater the stiffness of the skin; the number of plies and the thickness of a single ply determine the overall thickness of the skin; the ply angle affects the stiffness of the skin. When the ply angle is 0°, the tensile, flapping, and lag stiffness are the largest. When the ply angle is 45°, the contribution to shear and torsion stiffness is the largest. For the non - laminated structure, its shape needs to be constrained by controlling parameters. The specific controlling parameters are as follows: trailing - edge strip: the chord - wise distance X from the leading - edge of the airfoil to the starting position of the trailing - edge T ; leading - edge weight: the center position and radius; C - type beam: the inner - surface contour of the skin, the upper - side chord - wise design positioning point X Ctop , the lower - side chord - wise design positioning point X Cbot , the middle design positioning point (X Cmid , Y Cmid ). Figure 3 The description parameters of the airfoil - section components are given. Among them, all the positioning parameters are dimensionless with respect to the chord length based on the leading - edge of the blade.

[0082] For the skin of the laminated component, its description parameters include the number of composite material plies, the thickness of a single ply, and the ply angle. Its structural modeling is generated at equal distances. The skin can be regarded as composed of a series of geometric parallel lines. As long as parallel lines with an equal number of points are generated according to the material thickness, a laminated structure is formed between every two parallel lines Figure 4 The generation method of the skin parallel lines (i.e., the broken - line parallel lines) is given Figure 4 Part (a) in it is the schematic diagram of the skin ply Figure 4 Part (b) in it is the schematic diagram of the equal - distance generation method. AB and AC intersect at point A. To form parallel lines with a spacing of h inward, the coordinates of A′ need to be calculated is and sum, and The coordinates of A′ are as follows:

[0083]

[0084] Performing the above calculations on each node at the contour control point (i.e., point A) of the laminated structure can obtain a single - layer laminate. By advancing inward in a loop, a multi - ply laminate structure can be obtained. Among them, points B and C are the two adjacent points on both sides of A, A′ is the point after the offset of point A, θ is the acute angle formed by the intersection of AB and AC, A′(x,y) represents the coordinates of point A′, and A(x,y) represents the coordinates of point A is the unit vector represents the unit vector of the AA′ side The unit vector representing side AC The unit vector representing side AB

[0085] For non-laminate structures, such as the leading-edge counterweight, its positioning parameters are mainly the position of the counterweight center (X M , Y M ) and the radius R M , X M represents the X-direction coordinate of the counterweight center position, and Y M represents the Y-direction coordinate of the counterweight center position. The X direction is along the chord length direction, and the Y direction is perpendicular to the chord length direction. The positioning parameter of the trailing-edge strip is mainly the chordwise distance X T from the leading edge of the airfoil to the starting position of the trailing edge. The positioning parameter of the C-beam is based on the area, forming a C-beam model with a constant area, Figure 5 which is a schematic diagram of the algorithm for keeping the area of the C-beam constant. The shape of the C-beam is controlled by the following parameters: the inner surface contour of the skin, the upper chordwise design positioning point X Ctop , the lower chordwise design positioning point X Cbot , and the middle design positioning point (X Cmid , Y Cmid ). Two automatic adjustment points are respectively set between adjacent design positioning points, and area compensation is achieved by moving the automatic adjustment points along the normal direction. The specific area adjustment steps are as follows:

[0086] Step 1.1: Calculate the current area S1 of the C-beam component, and find the area difference ΔS = S1 - S0 from the input control parameter cross-sectional area S0. The sign of ΔS determines the moving direction of the automatic control points.

[0087] Step 1.2: Take the automatic adjustment point as the moving point, and form a triangle with the adjacent two control points (as shown in Figure 5 ). The height of the triangle is directly calculated from the area that needs to be compensated by this control point, which is the adjustment amount of the automatic adjustment point.

[0088] Taking ΔS > 0 as an example, the area of the C-beam enclosed by the design positioning points is larger than the target cross-sectional area. To keep the area unchanged, the moving directions of each automatic control point are as shown in Figure 5 . Therefore, first calculate the area that each adjustment point C i needs to be compensated. The method adopted in this application is to use the normal distance from the adjustment point to the skin as the weight to distribute the compensated area, which can be specifically expressed as:

[0089]

[0090] where N is 4, S i is the area that C i needs to be compensated, and d i is the normal distance from the adjustment point C to the skin.i After obtaining the adjustment amount of the normal distance from the skin, the moving distances of each adjustment point are calculated using the triangle area formula. Taking C1 and C2 as examples, when calculating the movement amount of C1, the base is C2B1; when calculating the movement amount of C2, the base is AC′1, where C′1 is the point after the offset of point C1. By this method, the area of the C-beam can be ensured to be constant, and the shape of the C-beam can be automatically changed.

[0091] After the definition of the component geometry (i.e., the above-mentioned laminate and non-laminate structures) is completed, a material library for the cross-sectional components (i.e., the defined components) is established, material numbers are assigned to different materials, and the material numbers are bound to the description parameters of the corresponding components. For isotropic materials, its density ρ, Young's modulus E, and Poisson's ratio ν need to be given; for orthotropic composite materials, the density ρ, Young's moduli E 11 、E 22 and E 33 , the shear moduli G 12 、G 13 and G 23 , and the three Poisson's ratios ν 12 、ν 13 and ν 23 need to be given.

[0092] Step 2: Mesh the cross-sectional components.

[0093] For laminate components, due to their simple structure and regular regions, at the same calculation accuracy, the number of meshes required for quadrilateral meshes is less than that of triangular meshes; non-laminate components are composed of regions with complex shapes, and triangular meshes have better filling properties. The method for generating meshes for laminate structures is to divide the complex region (i.e., the structural model of the skin) into eight-node quadrilateral blocks, and use shape functions to perform isoparametric mapping within each block (i.e., each eight-node quadrilateral block) to generate block meshes. In the mesh generation of laminate components, since the component has multiple layers of plies, and the material properties, ply thicknesses, and ply angles of different plies can be different, dividing the blocks according to the plies and generating block meshes can endow the mesh elements within the entire ply with the same ply properties, reducing the modeling difficulty of composite components. The mesh generation of non-laminate structures uses the Delaunay triangulation method. As Figure 6 shown, Figure 6 part (a) in Figure 6 is a schematic diagram of generating C-beam and counterweight meshes by the Delaunay method,

[0094] Step 3: Calculate the airfoil structural characteristics using the generalized Timoshenko beam theory.

[0095] For a rotor blade, it can be treated as an elastic beam with a radial dimension significantly larger than its cross-sectional dimension. Based on the Variational Asymptotic Method (VAM), a non-homogeneous, anisotropic, and torsion-deformed elastic beam model is derived. The variational asymptotic method is based on tensor theory and obtains a finite element cross-section analysis method through geometrically non-linear three-dimensional elastic theory. The schematic diagram of the beam from the undeformed state to the deformed state is as shown in Figure 7 as follows. Figure 7 where u represents the displacement of any point on the beam axis. x1 represents the arc length coordinate along the axis r of the undeformed beam. The normal of the beam cross-section at any x1 is along the tangent direction of the axis r, and the coordinates of any point in the cross-section are represented by x2 and x3. A local undeformed coordinate system b i (b1, b2, b3) is introduced, where the base vector b1 is along the tangent direction of the axis r, b2 and b3 are along the coordinate axes x2 and x3 respectively, and s represents the arc length coordinate along the deformed beam axis R. The spatial position vector of any point on the cross-section can be expressed as: where the subscript α = 2, 3. When the beam deforms, the coordinate system b i rotates to a new position and defines a new coordinate system B i (B1, B2, B3). At this time, the base vector B1 does not point along the direction of x1. A local deformed coordinate system T i (T1, T2, T3) is introduced, where the base vector T1 is along the tangent direction of the axis R. The transverse shear deformation is incorporated into the warping, as shown in Figure 8 as follows. The relationship between the coordinate systems T i and B i is: where 2γ 12 and 2γ 13 are small angles caused by the shear deformation. The deformed position vector can be expressed as :

[0096]

[0097] where, represents the position vector of any point on the deformed cross-section, R(x1) represents the position vector of any point on the deformed beam axis, w i (x1, x2, x3) represents the warping component, T α (x1) is the base vector in the 2 and 3 directions, and T i (x1) is the base vector. The displacement field represented by the formula has 4 redundant degrees of freedom. To make the displacement field uniquely determined, four constraints are imposed on the cross-section warping: 《w i>= 0, <x2w3 - x3w2> = 0, where <<>> represents integration along the cross-sectional area, and this constraint indicates that the rigid body cross-sectional displacement has no relation with warping, w i is the warping component (w with a subscript i represents the component in a certain direction and is a scalar).

[0098] Timoshenko one-dimensional generalized strain: where represents the rotation tensor between coordinate system B i and b i , γ represents the sectional shear strain in coordinate system B i , κ represents the bending strain; R′ represents the derivative of R, r′ represents the derivative of r; k and K respectively represent the curvatures of the undeformed and deformed beams, k = k i b i , K = K i B i , k i represents the curvature in the i direction, K i represents the curvature in the i direction after deformation; γ 11 , 2γ 12 , 2γ 13 , κ1, κ2, κ3 respectively represent the Timoshenko one-dimensional generalized strains of the beam after deformation for tension, transverse shear in two directions (i.e., the X direction and the Y direction), torsion, and bending in two directions (i.e., the X direction and the Y direction). Let ε = {γ 11 , κ1, κ2, κ3} Trans , γ s = {2γ 12 , 2γ 13} Trans . The conversion relationship between the classical one-dimensional generalized strain ε and the Timoshenko one-dimensional generalized strains ε and γ s is:

[0099]

[0100] where ε and γ s are the Timoshenko one-dimensional generalized strains, Trans represents the transpose, and Q and P are conversion matrices, γ′ s represents the derivative of γ s .

[0101] The Jaumann - Biot - Cauchy strain at any point in the beam is calculated using the rotation tensor decomposition method and is expressed in coordinate system b i as follows: where Γ = {Γ 11 , 2Γ 12 , 2Γ 13, Γ 22 , 2Γ 23 , Γ 33} Trans The sectional strain energy U can be expressed as:

[0102]

[0103] where Γ represents the Jaumann - Biot - Cauchy strain, S represents the sectional area, Γ 11 , Γ 12 , Γ 13 , Γ 22 , Γ 23 , Γ 33 are the Jaumann - Biot - Cauchy strain components, w is the warping vector, w′ represents the derivative of w, k2 and k3 represent the bending curvatures, Γ α , Γ R , Γ l are operator matrices, represents the stiffness coefficient matrix of the material. In order to establish a beam model applicable to arbitrary sectional shapes and material distributions, the sectional warping is discretized using the shape function matrix N(x2, x3):

[0104] w(x1, x2, x3) = N(x2, x3)V(x1);

[0105] where w(x1, x2, x3) represents the sectional warping, and V(x1) is the vector composed of the unknown warping deformations of all nodes of the section. The variational asymptotic method is used to determine V(x1) so that the sectional strain energy reaches the minimum under the constraint equations. The strain energy of the beam can be expressed as: Substituting the formula into it, the quadratic asymptotically exact strain energy expressed by the Timoshenko one - dimensional generalized strain is obtained:

[0106]

[0107] where A, B, C, and D are characteristic matrices carrying material properties and geometric information, represents the derivative of , represents the derivative of , and ()' represents the derivative of the content in the parentheses.

[0108] The standard form of the generalized Timoshenko strain energy is:

[0109]

[0110] Simultaneously solve the non - linear equations for the unknown matrices X, Y, and G. The constitutive relation of the generalized Timoshenko strain energy is as follows:

[0111]

[0112] where X, Y, and G are sub - matrices of the stiffness coefficient matrix, and F Bi , M Bi represent the forces and moments on the cross - section in coordinate system B i . The 6×6 matrix composed of matrices X, Y, Y Trans and G is the stiffness matrix S of the cross - section, i.e.:

[0113]

[0114] where the diagonal elements S mm (m = 1, 2, 3, 4, 5, 6) represent the tensile stiffness coefficient, the shear stiffness coefficients in two directions (i.e., the X - direction and the Y - direction), the torsional stiffness coefficient, and the bending stiffness coefficients in two directions (i.e., the X - direction and the Y - direction) respectively; the non - diagonal elements S mn (m, n = 1, 2, 3, 4, 5, 6, m≠n) represent the corresponding coupling stiffness coefficients.

[0115] Briefly speaking, the steps to calculate the stiffness matrix S of the cross - section using the generalized Timoshenko beam theory include: (1) Establish the beam model and coordinate system: Simplify the beam into an elastic model, define the local coordinate systems before and after deformation, and describe the geometric deformation of the beam. (2) Define the displacement field and strain: Describe the tensile, shear, torsional, and bending strains of the beam through the Timoshenko one - dimensional generalized strain formula, and introduce constraint conditions to eliminate redundant degrees of freedom. (3) Calculate the strain energy: Calculate the strain energy of the cross - section based on the stiffness coefficients of the material and the strain components. (4) Discretize the warping deformation: Discretize the cross - section warping using the shape function matrix, and determine the warping deformation vector through the variational asymptotic method (i.e., the variational asymptotics method) to minimize the strain energy. (5) Establish the generalized strain energy: Substitute the Timoshenko strain into the strain energy formula to obtain the exact strain energy expression, and solve the non - linear equations to obtain the unknown matrices. (6) Solve the stiffness matrix: Finally, the stiffness matrix S of the cross - section is composed of the stiffness coefficients of tension, shear, torsion, and bending and their coupling effects, forming a 6×6 matrix.

[0116] The rapid calculation method for the structural characteristics of the composite C-beam rotary wing airfoil provided by the present application realizes an integrated process from airfoil structure design to mesh generation and then to structural characteristic calculation with high calculation speed. Through steps of obtaining the structural models of the skin, C-beam, trailing edge strip, and leading edge counterweight according to the sectional component description parameters, dividing quadrilateral meshes for the laminate structure (skin) and triangular meshes for the non-laminate structures (C-beam, leading edge counterweight, trailing edge strip), and deriving the sectional characteristic calculation method based on the generalized Timoshenko theory (i.e., the generalized Timoshenko beam theory). The rapid calculation method for the structural characteristics of the composite C-beam rotary wing airfoil of the present application adopts the generalized Timoshenko beam theory and can calculate the torsional stiffness (a value in the stiffness matrix S) more accurately, providing higher calculation accuracy compared with the Euler-Bernoulli beam theory. The rapid calculation method for the structural characteristics of the composite C-beam rotary wing airfoil of the present application adopts parametric modeling, improving the flexibility and accuracy of modeling.

[0117] In an exemplary embodiment, a computer device is provided. The computer device can be a server or a terminal, and its internal structure diagram can be as shown in Figure 9 Figure [not shown]. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the data for determining the structural characteristics of the composite C-beam rotary wing airfoil. The input / output interface of the computer device is used for the processor to exchange information with external devices. The communication interface of the computer device is used to communicate with external terminals through a network connection. When the computer program is executed by the processor, it realizes a method for determining the structural characteristics of a composite C-beam rotary wing airfoil.

[0118] Those skilled in the art can understand that Figure 9 the structure shown in [Figure not shown] is only a block diagram of some structures related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, it realizes the steps in the above method embodiments.

[0119] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program which, when executed by a processor, implements the steps in the above method embodiments.

[0120] In an exemplary embodiment, a computer program product is provided, including a computer program which, when executed by a processor, implements the steps in the above method embodiments.

[0121] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of relevant data need to comply with relevant regulations.

[0122] Those of ordinary skill in the art can understand that all or part of the processes in the above method embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above method embodiments. Among them, any reference to a memory, database, or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memories. Non-volatile memories can include read-only memory (ROM), magnetic tapes, floppy disks, flash memories, optical memories, high-density embedded non-volatile memories, resistive random-access memories (ReRAM), magnetoresistive random-access memories (MRAM), ferroelectric random-access memories (FRAM), phase change memories (PCM), graphene memories, etc. Volatile memories can include random access memory (RAM) or external cache memories, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0123] In each of the embodiments provided in this application, the database involved may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., without limitation. In each of the embodiments provided in this application, the processor may be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without limitation.

[0124] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0125] Specific examples are used in this article to elaborate on the principles and implementation manners of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A method for determining the structural characteristics of a composite C-beam rotary wing airfoil, characterized in that The method for determining the structural characteristics of the composite C-beam rotary wing airfoil includes: Generating an airfoil structural model; the airfoil structural model is a composite C-beam rotary wing airfoil structural model; the airfoil structural model includes the structural models of the skin, C-beam, leading-edge weight, and trailing-edge strip; Performing mesh division on the airfoil structural model to obtain the airfoil structural model after mesh division; According to the airfoil structural model after mesh division, using the generalized Timoshenko beam theory to calculate the airfoil structural characteristics; the airfoil structural characteristics are the composite C-beam rotary wing airfoil structural characteristics.

2. The method for determining the airfoil structural characteristics of the composite C-shaped beam rotor blade according to claim 1, characterized in that The generating of the airfoil structural model specifically includes: Generating the structural model of the skin at equal intervals according to the C-beam rotary wing airfoil, the number of composite material plies, the single-layer thickness, and the ply angle; Generating the structural model of the C-beam according to the inner surface contour of the skin and the area of the C-beam using an algorithm with a constant area; Generating the structural model of the leading-edge weight according to the center position and radius of the leading-edge weight; Generating the structural model of the trailing-edge strip according to the chordwise distance from the trailing-edge starting position of the trailing-edge strip to the leading edge of the airfoil.

3. The method for determining the structural characteristics of the composite C-type beam rotary wing airfoil according to claim 2, characterized in that, The generating of the structural model of the C-beam according to the inner surface contour of the skin and the area of the C-beam using an algorithm with a constant area specifically includes: Preliminarily generating the C-beam according to the inner surface contour of the skin, the design positioning points on the upper chord, the design positioning points on the lower chord, and the design positioning points in the middle, setting two automatic adjustment points between adjacent design positioning points respectively, realizing area compensation by moving the automatic adjustment points along the normal direction, calculating the current area of the C-beam component, finding the area difference between the current area of the C-beam component and the sectional area of the input control parameter, using the automatic adjustment points as moving points and the adjacent two control points as the base to form a triangle, directly calculating the height of the triangle from the area that the control points need to compensate, obtaining the shape of the C-beam, and generating the structural model of the C-beam.

4. The method for determining the airfoil structural characteristics of the composite C-shaped beam rotor blade according to claim 1, wherein Performing mesh division on the airfoil structural model to obtain the airfoil structural model after mesh division specifically includes: Dividing the structural model of the skin into quadrilateral meshes, and dividing the structural models of the C-beam, leading-edge weight, and trailing-edge strip into triangular meshes to obtain the airfoil structural model after mesh division.

5. The method for determining the structural characteristics of the composite C-type beam rotor airfoil according to claim 4, characterized in that The dividing of the structural model of the skin into quadrilateral meshes, and dividing the structural models of the C-beam, leading-edge weight, and trailing-edge strip into triangular meshes to obtain the airfoil structural model after mesh division specifically includes: Dividing the structural model of the skin into eight-node quadrilateral blocks, generating block meshes by using shape functions for isoparametric mapping within each eight-node quadrilateral block, and dividing the structural models of the C-beam, leading-edge weight, and trailing-edge strip into triangular meshes using the Delaunay triangulation method to obtain the airfoil structural model after mesh division.

6. The method for determining the structural characteristics of the composite C-shaped beam rotor airfoil according to claim 1, characterized in that, According to the airfoil structural model after mesh division, using the generalized Timoshenko beam theory to calculate the airfoil structural characteristics specifically includes: Based on the airfoil structural model after mesh division, deriving a non-homogeneous, anisotropic, and torsion-deformed elastic beam model with the variational asymptotic method, defining the local coordinate systems of the beam before and after deformation in the generalized Timoshenko beam theory, describing the geometric deformation of the beam, and obtaining the position vectors of the beam before and after deformation; Based on the position vectors before and after the beam deformation and the Timoshenko one-dimensional generalized strain, the sectional strain energy is obtained; Based on the sectional strain energy and the variational asymptotic method, the sectional second-order asymptotically exact strain energy is obtained; According to the standard form of the generalized Timoshenko strain energy and the sectional second-order asymptotically exact strain energy, the constitutive relationship of the generalized Timoshenko strain energy is solved to obtain the airfoil structural characteristics; the airfoil structural characteristics only include the sectional stiffness matrix.

7. The method for determining the structural characteristics of the composite C-shaped beam rotor airfoil according to claim 6, wherein The sectional stiffness matrix is composed of the stiffness coefficient for tension, the stiffness coefficient for torsion, the stiffness coefficient for shear in the X direction, the stiffness coefficient for shear in the Y direction, the stiffness coefficient for bending in the X direction, the stiffness coefficient for bending in the Y direction, and the coupling stiffness coefficients corresponding to any two different stiffness coefficients, forming a 6×6 matrix; the X direction is along the chord length direction; the Y direction is perpendicular to the chord length direction.

8. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the method for determining the composite C-beam rotating airfoil structural characteristics according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for determining the composite C-beam rotating airfoil structural characteristics according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for determining the composite C-beam rotating airfoil structural characteristics according to any one of claims 1-7.

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