Composite reticulated curved rib structure and optimization design method thereof

Abstract

The application provides a composite reticulated curve stiffened structure and an optimization design method thereof, and the method comprises the following steps: defining the reticulated curve stiffened structure and constructing an optimization mathematical model; determining the geometric size, composite material fixed parameters, composite material design parameters, and load and displacement boundary conditions of the reticulated curve stiffened structure; constructing a geometric model and a material model of the reticulated curve stiffened structure based on the geometric size, the composite material fixed parameters, and the composite material design parameters; carrying out load analysis and mass calculation under the load and displacement boundary conditions based on the geometric model and the material model, obtaining the buckling load and the total mass of the reticulated curve stiffened structure, and then obtaining the buckling load to weight ratio based on the optimization mathematical model; obtaining a plurality of groups of composite material design parameters based on a global search algorithm; and obtaining the composite material design parameters under the target of the maximum buckling load to weight ratio based on the plurality of groups of composite material design parameters and the optimization iteration, so as to complete the optimization design.

Description

Technical Field

[0001] This application belongs to the field of composite materials, and specifically relates to a composite material mesh curve stiffened structure and its optimization design method. Background Technology

[0002] Composite stiffened plates are widely used in the aerospace field due to their excellent mechanical properties. However, due to limitations in the manufacturing technology of composite structures, the girder axis of traditional composite stiffened plates is usually straight, which reduces design flexibility. Straight-line composite stiffened plates have lower yield strength, resulting in a smaller buckling load weight and lower load-bearing efficiency of the stiffened structure. Summary of the Invention

[0003] The purpose of this application is to provide a composite material mesh-curved stiffened structure and its optimized design method to solve or alleviate at least one problem in the prior art.

[0004] The technical solution of this application is: a method for optimizing the design of a composite material mesh-curved stiffened structure, the method comprising:

[0005] Define a mesh curve stiffening structure and construct an optimized mathematical model of the mesh curve stiffening structure;

[0006] Determine the geometric dimensions, composite material fixing parameters, composite material design parameters, and load and displacement boundary conditions of the mesh-curved stiffened structure;

[0007] Based on the geometric dimensions of the mesh-curved stiffened structure, the fixed parameters of the composite material, and the design parameters of the composite material, a geometric model and a material model of the mesh-curved stiffened structure are constructed. Based on the geometric model and the material model, load analysis and mass calculation of the mesh-curved stiffened structure under load and displacement boundary conditions are carried out to obtain the buckling load and total mass of the mesh-curved stiffened structure, and then the buckling load-to-weight ratio of the mesh-curved stiffened structure based on the optimized mathematical model is obtained.

[0008] Multiple sets of composite material design parameters are obtained based on a global search algorithm. Based on these multiple sets of composite material design parameters, and with the goal of maximizing the buckling load-to-weight ratio of the mesh-curved stiffened structure, the composite material design parameters under this goal are obtained through optimization iteration, thereby completing the optimized design of the composite material mesh-curved stiffened structure.

[0009] In a preferred embodiment of this application, the mesh-curve stiffened structure is as follows:

[0010] The skin covering the first and second curved stringers is used to establish a rectangular coordinate system xoy at the center of the skin. The x-axis is parallel to the length of the skin, and the y-axis is parallel to the width of the skin. The overall length of the mesh-curved stiffened structure is L and the width is W.

[0011] Several first curved stringers at acute angles to the x-axis and several second curved stringers at obtuse angles to the x-axis are arranged in an alternating network. The central stringer axis of the first curved stringers is a linearly varying curve, which is symmetrical about the origin. At x = 0, the tangent direction makes an angle T0 with the x-axis, and at x = L / 2, the tangent direction makes an angle T1 with the x-axis. Therefore, at any point on the curved stringer, the tangent direction makes an angle α(x) with the x-axis.

[0012]

[0013] Therefore, when T0≠T1, the axis of the central truss has a curve equation:

[0014]

[0015] When T0 = T1, the axis of the central girder is a straight line: y = x · tanT0,

[0016] The axes of the remaining first curved trusses are translated from the axis of the central truss along the y-axis, and the translation distance between adjacent first curved trusses is D;

[0017] The axis of the second curved stringer is symmetrical to the axis of the corresponding first curved stringer about the x-axis;

[0018] When printing curved stringers, the fiber direction is along the axis of the curved stringers;

[0019] The first and second curved stringers have I-shaped cross sections with upper and lower edge widths of W1 and W2, respectively, and a web height of H. The thickness of both the edge and web is h1, which is determined by the printing layer thickness t1 and the number of printing layers N1, i.e., h1 = t1N1. The thickness of the skin is h2, which is determined by the ply thickness t2 and the number of ply layers N2, i.e., h2 = t2N2.

[0020] In a preferred embodiment of this application, the optimized mathematical model of the mesh curve stiffened structure is as follows:

[0021]

[0022] In the formula, f([θ i [,D,<T0|T1>) represents the buckling load-to-weight ratio, i.e., the optimization objective function;

[0023] P cr ([θ i [,D,<T0|T1>) represents the structural buckling load;

[0024] m(D, <T0|T1>) represents the total mass of the structure;

[0025] [θi [] represents the skin ply sequence, where i indicates the ply number;

[0026] D is the translation distance of the curved stringer;

[0027] <T0|T1> are the configuration parameters of the curved stringer axis;

[0028] g is the acceleration due to gravity;

[0029] T min T max These are the minimum and maximum included angles, respectively.

[0030] D min D max These are the minimum translation distance and the maximum translation distance, respectively.

[0031] In a preferred embodiment of this application, the geometric dimensions of the mesh-curved stiffened structure include: skin length L, skin width W, widths W1 and W2 of the upper and lower edge strips of the curved stringer, and web height H;

[0032] The fixed parameters of the composite material include: the number of printed layers of the curved stringer N1, the number of skin layers N2, and material properties;

[0033] The composite material design parameters include: skin layup sequence [θ] i The translation distance D of the curved stringer and the configuration parameters of the curved stringer axis <T0|T1>.

[0034] In a preferred embodiment of this application, the global search algorithm includes the Hawke-Kevis direct search algorithm and the multi-island genetic algorithm.

[0035] In a preferred embodiment of this application, the optimization iteration has a maximum number of optimizations. When the number of iterations reaches the maximum or the optimization target is reached, the iteration calculation ends.

[0036] In addition, this application also provides a composite material mesh curve stiffened structure, which is designed according to any of the above-described composite material mesh curve stiffened structure optimization design methods.

[0037] Compared with traditional linear reinforced mesh structures, the optimization method for composite material mesh-curved stiffened structures provided in this application significantly improves the buckling load-to-weight ratio and significantly enhances the buckling resistance capacity. Attached Figure Description

[0038] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0039] Figure 1This is a schematic diagram of the composite material mesh curve reinforcement structure optimization method of this application.

[0040] Figure 2 This is a schematic diagram of the composite material mesh-curved stiffened structure in this application.

[0041] Figure 3 This is a schematic diagram of the cross-section of the stringer and part of the skin in this application.

[0042] Figure 4 This is a schematic diagram of the finite element model and load boundary conditions of an embodiment of this application.

[0043] Figure 5 This is a schematic diagram of an optimized mesh curve stiffened structure according to an embodiment of this application.

[0044] Figure 6 This is a waveform diagram of buckling load of a mesh-curved stiffened structure according to an embodiment of this application. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0046] The development of continuous fiber 3D printing technology has made curved stiffened structures possible. For mesh-like curved stiffened structures, the skin is still manufactured using traditional fiber layup processes, while the curved girder is 3D printed. To fully utilize the designability advantages of composite materials to improve structural load-bearing efficiency, this application provides an optimized design method for composite mesh-like curved stiffened structures. By optimizing the skin layup, girder translation distance, and girder center curve form of the mesh-like stiffened structure, the load-to-weight ratio of the stiffened structure is maximized, thereby improving the load-bearing efficiency and achieving weight reduction.

[0047] like Figure 1 As shown, the composite material mesh curve stiffened structure optimization design method provided in this application includes the following process:

[0048] Step 1: Construct a mesh curve stiffened structure model and optimize the mathematical model.

[0049] 1.1, such as Figure 2 The diagram shows a composite material mesh-curved stiffened structure, where the blank area is the skin. The overall length of the mesh-curved stiffened structure is L and the width is W. A rectangular coordinate system xoy is established at the center of the skin, with the x-axis parallel to the length direction of the skin and the y-axis parallel to the width direction of the skin.

[0050] The first curved stringer 1 (at an acute angle to the x-axis) and the second curved stringer 2 (at an obtuse angle to the x-axis) are arranged in an alternating network. The axis of the central stringer 11 of the first curved stringer 1 is a linear angle-changing curve. This curve is symmetrical about the origin o. The angle between the tangent direction and the x-axis is T0 at x = 0 and T1 at x = L / 2. Therefore, the angle between the tangent direction and the x-axis at any point on the curved stringer is α(x).

[0051]

[0052] Therefore, when T0≠T1, the axis of the central girder 11 has a curve equation:

[0053]

[0054] When T0 = T1, the axis of the central girder is a straight line:

[0055]

[0056] The axes of the remaining first curved stringers 1 are derived from the axis of the central stringer 11 by translation along the y-axis, with the translation distance of adjacent first curved stringers being D. The axis of the second curved stringer 2 is symmetrical to the axis of the corresponding first curved stringer about the x-axis.

[0057] When printing curved stringers, the fiber direction is along the axis of the curved stringer.

[0058] A schematic diagram of the curved stringer and part of the skin section is shown below. Figure 3 As shown, the cross-section of the curved stringer is I-shaped, with the widths of the upper and lower flanges being W1 and W2 respectively, the web height being H, and the thickness of both the flanges and the web being h1, which is determined by the thickness of the printed layer t1 and the number of printed layers N1, i.e., h1 = t1N1; the thickness of the skin is h2, which is determined by the ply thickness t2 and the number of ply layers N2, i.e., h2 = t2N2.

[0059] 1.2, Based on the skin layering sequence [θ] i (i represents the ply number), the translation distance D of the curved girder, and the configuration parameters of the curved girder axis <T0|T1> are used as design variables, with the structural buckling load weight ratio f([θ]) as the basis. i The mathematical model for the optimization design of composite material mesh curve stiffened structures is shown below, where D, <T0|T1>, is the objective function.

[0060]

[0061] In the formula, P cr ([θ i [,D,<T0|T1>) represents the structural buckling load, m(D,<T0|T1>) represents the total mass of the structure, g represents the gravitational acceleration, and T represents the total mass of the structure. min Tmax These are the minimum and maximum included angles, D. min D max These are the minimum translation distance and the maximum translation distance, respectively.

[0062] Step 2: Determine the geometric dimensions, composite material fixing parameters, composite material design parameters, and load and displacement boundary conditions of the mesh-curved stiffened structure;

[0063] The geometric dimensions of the mesh-curved stiffened structure include: skin length L, skin width W, widths of the upper and lower edge strips of the curved stringer W1 and W2, and web height H;

[0064] The fixed parameters of composite materials include: the number of printed layers of curved stringers N1, the number of skin layers N2, and material properties (transverse and longitudinal modulus, shear modulus, in-plane Poisson's ratio, and material density, etc.).

[0065] The composite material design parameters are the skin layup sequence [θ] i [i represents the i-th ply], the translation distance D of the curved stringer and the configuration parameters of the curved stringer axis <T0|T1>, and the skin ply sequence for the k-th (k=0,1,2…N) calculation is [θ i ] k The translation distance of the curved stringer is D. k The configuration parameters of the curved stringer axis are <T0|T1>. k ,in:

[0066] When k=0, the initial skin layering order is given [θ] i ] 0 Translation distance D of the curved stringer 0 Curved stringer axis configuration parameters <T0|T1> 0 ;

[0067] When k≠0, the skin layering order is determined by direct search algorithms such as Hawke-Kevis search (HJ) or global search methods such as multi-island genetic algorithm (MIGA) [θ]. i ] k Translation distance D of the curved stringer k Curved stringer axis configuration parameters <T0|T1> k .

[0068] Step 3: Based on the geometric dimensions of the mesh-curved stiffened structure, the fixed parameters of the composite material, and the design parameters of the composite material, construct the geometric model and material model of the composite mesh-curved stiffened structure. Based on the geometric model and material model of the mesh-curved stiffened structure, conduct load analysis and mass calculation of the mesh-curved stiffened structure under load and displacement boundary conditions to obtain the buckling load and total mass of the mesh-curved stiffened structure. Then, based on the optimized mathematical model, obtain the buckling load-to-weight ratio of the mesh-curved stiffened structure.

[0069] Establish a rectangular coordinate system xoy at the center of the skin, with the x-axis parallel to the length of the skin and the y-axis parallel to the width of the skin.

[0070] Based on the dimensions and material properties of the stiffening plate structure, create the geometric and material models of the composite material mesh curve stiffening structure; the number of skin layers and angles are determined according to the given number of layers N2 and layer sequence [θ]. i ] k Settings: Set the number of printing layers for the curved stringer to N1, with the fiber direction along the axis of the curved stringer; set the global mesh size, set the cell type, and generate the mesh.

[0071] Buckling analysis was performed by setting loads and boundary conditions for the mesh-reinforced structure, and the buckling load P of the mesh-reinforced structure under different load conditions (tension, compression, shear, and combined compression and shear) was obtained. cr ([θ i ] k D k <T0|T1> k Simultaneously, calculate the total mass m(D) of the mesh-reinforced structure. k <T0|T1> k Thus, the structural buckling load-to-weight ratio f([θ) is determined. i ] k D k <T0|T1> k ).

[0072] Step 4: Based on the global search algorithm, obtain multiple sets of composite material design parameters. Repeat step 3 and obtain the composite material design parameters under the objective of maximizing the buckling load-to-weight ratio of the mesh-curved stiffened structure, thereby completing the optimized design of the composite material mesh-curved stiffened structure.

[0073] To prevent excessive computation time, this application limits the maximum number of optimization iterations; for example, the maximum number of optimization iterations N can be limited to no more than 1000. The iterative computation ends when the maximum number of iterations is reached or the optimization objective is achieved.

[0074] To make this application clearer, this application provides an example of optimizing the design by maximizing the buckling load-to-weight ratio of a composite mesh-curved stiffened structure under uniaxial compressive loading conditions.

[0075] The geometric dimensions of the mesh-like curved stiffened structure are L = 600 mm, W = 600 mm, W1 = 40 mm, W2 = 20 mm, and H = 20 mm. The number of printed layers for the curved stringer is N1 = 8, the number of skin layers is N2 = 8, and the single-layer thickness of the wire layup and 3D printing processes is t1 = t2 = 0.19 mm. The composite material performance parameters are as follows: longitudinal modulus 118 GPa, transverse modulus 8.98 GPa, shear modulus 4.21 GPa, in-plane Poisson's ratio 0.306, and material density 1600 kg / m³. 3 The gravitational acceleration is assumed to be 10 m / s² in the design. 2 The load boundary conditions are as follows: the top and bottom sides are set as simply supported boundary conditions, the left and right sides are set as fixed support boundary conditions, and a 1000N compressive load is applied to the right side.

[0076] The initial skin ply angle sequence is [45 / -45 / 0 / 90]. S The initial translation distance of the curved stringer is D = 250 mm, and the configuration parameters of the curved stringer axis are <45|45>.

[0077] A Cartesian coordinate system xoy is established with the skin center as the origin. Based on the dimensions and material properties of the mesh-curved stiffened structure, a geometric and material model of the composite material mesh-curved stiffened structure is created. The global mesh size is set to 10 mm, with S4R as the primary element type, and then the mesh is generated. Buckling analysis is performed by setting loads and boundary conditions to obtain the first-order buckling load. The finite element model and boundary conditions are as follows: Figure 4 As shown. Subsequently, the weight of the mesh-curved stiffened structure is calculated to obtain the buckling load-to-weight ratio. Based on the Python language, the entire process of modeling, buckling analysis, structural weight calculation, and buckling load-to-weight ratio calculation is formed into a parametric analysis script, which facilitates the analysis of the buckling load-to-weight ratio of the structure under different stringer translation distances and stringer axis configuration parameters.

[0078] In this embodiment of the application, in order to obtain optimization results more quickly, only the translation distance of the curved stringer and the configuration parameters of the curved stringer axis are optimized, and the parameter range is set as follows: skin ply sequence [θ i ]≡[45 / -45 / 0 / 90] SThe translation distance of the curved girder is D∈[150,300], and the configuration parameters of the curved girder axis are T0,T1∈[10,80]. The translation distance D is limited to multiples of 10, and the included angles T0,T1 are multiples of 5. The maximum number of optimization iterations is N=100. The Hawke-Kives search algorithm provided by the optimization software Isight is used to solve the optimization mathematical model. The optimization results are: translation distance of the curved girder D=210, configuration parameters of the curved girder axis <T0|T1>=<30|65>, and buckling load-to-weight ratio f=7361.87. The optimized mesh-curved stiffened structure and buckling waveform are shown below. Figure 5 , Figure 6 As shown, compared with the initial straight stringer structure, the buckling load-to-weight ratio increased by 118%, and the buckling resistance capacity was significantly enhanced.

[0079] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for optimizing the design of a composite material mesh-curved stiffened structure, characterized in that, The method includes: Define a mesh curve stiffening structure and construct an optimized mathematical model of the mesh curve stiffening structure; Determine the geometric dimensions, composite material fixing parameters, composite material design parameters, and load and displacement boundary conditions of the mesh-curved stiffened structure; Based on the geometric dimensions of the mesh-curved stiffened structure, the fixed parameters of the composite material, and the design parameters of the composite material, a geometric model and a material model of the mesh-curved stiffened structure are constructed. Based on the geometric model and the material model, load analysis and mass calculation of the mesh-curved stiffened structure under load and displacement boundary conditions are carried out to obtain the buckling load and total mass of the mesh-curved stiffened structure, and then the buckling load-to-weight ratio of the mesh-curved stiffened structure based on the optimized mathematical model is obtained. Multiple sets of composite material design parameters are obtained based on a global search algorithm. Based on these multiple sets of composite material design parameters, and with the goal of maximizing the buckling load-to-weight ratio of the mesh-curved stiffened structure, the composite material design parameters under this goal are obtained through optimization iteration, thereby completing the optimized design of the composite material mesh-curved stiffened structure.

2. The method for optimizing the design of composite material mesh-curved stiffened structures as described in claim 1, characterized in that, The mesh-curved stiffened structure is as follows: The skin covering the first and second curved stringers is used to establish a rectangular coordinate system xoy at the center of the skin. The x-axis is parallel to the length of the skin, and the y-axis is parallel to the width of the skin. The overall length of the mesh-curved stiffened structure is L and the width is W. Several first curved stringers at acute angles to the x-axis and several second curved stringers at obtuse angles to the x-axis are arranged in an alternating network. The central stringer axis of the first curved stringers is a linearly varying curve, which is symmetrical about the origin. At x = 0, the tangent direction makes an angle T0 with the x-axis, and at x = L / 2, the tangent direction makes an angle T1 with the x-axis. Therefore, at any point on the curved stringer, the tangent direction makes an angle α(x) with the x-axis. Therefore, when T0≠T1, the axis of the central truss has a curve equation: When T0 = T1, the axis of the central girder is a straight line: y = x · tanT0, The axes of the remaining first curved trusses are translated from the axis of the central truss along the y-axis, and the translation distance between adjacent first curved trusses is: The axis of the second curved stringer is symmetrical to the axis of the corresponding first curved stringer about the x-axis; When printing curved stringers, the fiber direction is along the axis of the curved stringers; The first and second curved stringers have I-shaped cross sections with upper and lower edge widths of W1 and W2, respectively, and a web height of H. The thickness of both the edge and web is h1, which is determined by the printing layer thickness t1 and the number of printing layers N1, i.e., h1 = t1N1. The thickness of the skin is h2, which is determined by the ply thickness t2 and the number of ply layers N2, i.e., h2 = t2N2.

3. The composite material mesh curve stiffened structure optimization design method as described in claim 2, characterized in that, The optimized mathematical model for the mesh-curve stiffened structure is as follows: In the formula, f([θ i [,D,<T0|T1>) is the objective function for optimizing the buckling load-to-weight ratio; P cr ([θ i [,D,<T0|T1>) represents the structural buckling load; m(D, <T0|T1>) represents the total mass of the structure; [θ i [] represents the skin ply sequence, where i indicates the ply number; D is the translation distance of the curved stringer; <T0|T1> are the configuration parameters of the curved stringer axis; g is the acceleration due to gravity; T min T max These are the minimum and maximum included angles, respectively. D min D max These are the minimum translation distance and the maximum translation distance, respectively.

4. The method for optimizing the design of composite material mesh-curved stiffened structures as described in claim 3, characterized in that, The geometric dimensions of the mesh-curved stiffened structure include: skin length L, skin width W, widths of the upper and lower edges of the curved stringer W1 and W2, and web height H. The fixed parameters of the composite material include: the number of printed layers of the curved stringer N1, the number of skin layers N2, and material properties; The composite material design parameters include: skin layup sequence [θ] i The translation distance D of the curved stringer and the configuration parameters of the curved stringer axis <T0|T1>.

5. The method for optimizing the design of composite material mesh-curved stiffened structures as described in claim 3, characterized in that, The global search algorithm includes the Hawke-Kevis direct search algorithm and the multi-island genetic algorithm.

6. The method for optimizing the design of composite material mesh-curved stiffened structures as described in claim 1, characterized in that, The optimization iteration has a maximum number of optimizations. When the number of iterations reaches the maximum or the optimization target is reached, the iteration calculation ends.

7. A composite material mesh-curved stiffened structure, characterized in that, The composite material mesh curve reinforced structure is designed using the composite material mesh curve reinforced structure optimization design method according to any one of claims 1 to 6.

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