Plastic deformation-based bistable thin-wall shell design method for supersonic civil aircraft

Abstract

The invention belongs to the field of supersonic civil aircraft structure design, and particularly relates to a plastic deformation-based bistable thin-wall shell design method for a supersonic civil aircraft. The method comprises the following steps: step 1, constructing a non-prestressed cylindrical shell with an initial curvature; 2, the cylindrical shell is flattened; thirdly, the flattened cylindrical shell is bent, so that the cylindrical shell is partially yielded; fourthly, the cylindrical shell is unloaded, and a first stable state of the cylindrical shell is obtained; 5, the cylindrical shell is flattened again; and 6, the cylindrical shell flattened again is bent, and a second stable state of the cylindrical shell is obtained after the cylindrical shell is unloaded. According to the method, the bistable thin-wall shell structure can be rapidly designed, and the form of the bistable thin-wall shell structure can be designed according to the analytical solution of the curvature of the bistable cylindrical shell after plastic deformation.

Description

Technical Field

[0001] The present application belongs to the field of supersonic civil aircraft structure design, and in particular relates to a bistable thin-walled shell design method for a supersonic civil aircraft based on plastic deformation. Background Art

[0002] The bistable thin-walled structure is a special structural form with two stable states, which can independently complete deformation according to external forces. Due to its unique performance, the application prospects of the bistable thin-walled structure in aerospace, automobile, electronics and other fields will become more and more broad.

[0003] At present, a large number of studies have explored the formation mechanism of bistable thin-walled structures by changing the material layer and geometric shape. Simulation and experimental verification are important means to study bistable thin-walled structures. However, due to factors such as material nonlinearity and geometric complexity, there may be certain differences between simulation results and experimental results.

[0004] Therefore, it is desired to have a technical solution to overcome or at least alleviate at least one of the above-mentioned defects of the prior art. Summary of the invention

[0005] The purpose of the present application is to provide a bistable thin-walled shell design method for a supersonic civil aircraft based on plastic deformation to solve at least one problem existing in the prior art.

[0006] The technical solution of this application is:

[0007] The first aspect of the present application provides a bistable thin-walled shell design method for a supersonic civil aircraft based on plastic deformation, comprising:

[0008] Step 1: construct a non-prestressed column shell with an initial curvature;

[0009] Step 2: Flatten the column shell;

[0010] Step 3, bending the flattened column shell to make the column shell partially yield;

[0011] Step 4: Unload the column shell to obtain the first stable state of the column shell;

[0012] Step 5: Flatten the column shell again;

[0013] Step six, bend the flattened column shell again, and unload the column shell to obtain the second stable state of the column shell.

[0014] In at least one embodiment of the present application, in step 1, constructing a non-prestressed column shell with an initial curvature includes:

[0015] The column shell has the following characteristics:

[0016] The cylindrical shell is a thin shell that satisfies the straight normal assumption;

[0017] The cylindrical shell is in a plane stress state, the mid-surface has no strain, and the curvature of each point in the mid-surface is the same at any time, and the curvature direction of the cylindrical shell is the same as the bending moment direction, and the initial curvature κ 0x =0,κ 0y >0;

[0018] The material of the column shell is an ideal elastic-plastic material;

[0019] A three-dimensional coordinate system is constructed at any point in the mid-plane of the cylindrical shell, where the x-axis is the longitudinal direction of the cylindrical shell, the y-axis is the transverse direction of the cylindrical shell, the z-axis is the thickness direction of the cylindrical shell, and the thickness of the cylindrical shell is t.

[0020] In at least one embodiment of the present application, the column shell is made of 304 stainless steel.

[0021] In at least one embodiment of the present application, in step 2, flattening the column shell comprises:

[0022] A symmetrical bending moment M is applied along the straight side of the cylindrical shell. 1y , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 1x , flatten the cylindrical shell.

[0023] In at least one embodiment of the present application,

[0024] Bending moment M 1y for:

[0025]

[0026] Bending moment M 1x for:

[0027] M 1x =v×M 1y

[0028] Among them, σ 1y is the stress in the y direction when the cylindrical shell is flattened, E is the elastic modulus, v is the deformation rate, k 0y is the initial curvature in the y direction.

[0029] In at least one embodiment of the present application, in step three, bending the flattened column shell to partially yield the column shell includes:

[0030] Maintain bending moment M 1y No change, continue to increase the bending moment M 1x , causing the cylindrical shell to undergo plastic deformation, the cylindrical shell to bend, and the cylindrical shell to partially yield.

[0031] In at least one embodiment of the present application,

[0032] The yield depth z of the cylindrical shell cr for:

[0033]

[0034] The bending moment M when the cylindrical shell yields 2x for:

[0035]

[0036] Among them, σ 0 is the yield stress of the cylindrical shell under uniaxial tension, k 2x is the curvature in the x direction when the cylindrical shell is bent, σ 2x is the stress in the x direction when the cylindrical shell is bent.

[0037] In at least one embodiment of the present application, in step five, flattening the column shell again comprises:

[0038] A symmetrical bending moment M is applied along the straight side of the cylindrical shell. 4x , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 4y , flatten the cylindrical shell again.

[0039] In at least one embodiment of the present application,

[0040] Bending moment M 4y =M 1y ;

[0041] Bending moment M 4x for:

[0042]

[0043] Among them, σ 4x is the stress in the x direction when the cylindrical shell is flattened again.

[0044] The second aspect of the present application provides a bistable thin-walled shell design device based on plastic deformation for a supersonic civil aircraft, comprising:

[0045] The non-prestressed column shell construction module is used to construct the non-prestressed column shell with initial curvature;

[0046] A column shell flattening module, used for flattening the column shell;

[0047] The column shell bending module is used to bend the flattened column shell to make the column shell partially yield;

[0048] A column shell unloading module is used to unload the column shell and obtain the first stable state of the column shell;

[0049] A column shell flattening module is used to flatten the column shell again;

[0050] The stable state acquisition module is used to bend the cylindrical shell after being flattened again, and obtain the second stable state of the cylindrical shell after unloading the cylindrical shell.

[0051] The invention has at least the following beneficial technical effects:

[0052] The supersonic civil aircraft bistable thin-walled shell design method based on plastic deformation of the present application can quickly design a bistable thin-walled shell structure, and the morphology of the bistable thin-walled shell structure can be designed according to the analytical solution of the curvature of the bistable cylindrical shell after plastic deformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a schematic diagram of an initial state of a column housing according to an embodiment of the present application;

[0054] Figure 2 is a flattened schematic diagram of a column shell of an embodiment of the present application;

[0055] Figure 3 is a schematic diagram of column shell yielding of a column shell according to an embodiment of the present application;

[0056] Figure 4 It is a schematic diagram of column shell unloading of a column shell according to one embodiment of the present application;

[0057] Figure 5 It is a schematic diagram of a column shell of an embodiment of the present application being flattened again;

[0058] Figure 6 is a schematic diagram of a second stable state of a column housing according to an embodiment of the present application;

[0059] Figure 7 It is a schematic diagram of a semicircular thin-walled column shell structure according to an embodiment of the present application;

[0060] Figure 8 It is a cloud diagram of column shell deformation and stress distribution according to one embodiment of the present application. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical scheme and advantages of the implementation of this application clearer, the technical scheme in the embodiment of this application will be described in more detail below in conjunction with the drawings in the embodiment of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of this application, not all of them. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain this application, and should not be construed as limitations on this application. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The embodiments of this application are described in detail below in conjunction with the drawings.

[0062] In the description of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the scope of protection of the present application.

[0063] The following is combined with Figures 1 to 8 This application is described in further detail.

[0064] The first aspect of the present application provides a bistable thin-walled shell design method for a supersonic civil aircraft based on plastic deformation, comprising the following steps:

[0065] Step 1: construct a non-prestressed column shell with an initial curvature;

[0066] Step 2: Flatten the column shell;

[0067] Step 3, bending the flattened column shell to make the column shell partially yield;

[0068] Step 4: Unload the column shell to obtain the first stable state of the column shell;

[0069] Step 5: Flatten the column shell again;

[0070] Step six, bend the flattened column shell again, and unload the column shell to obtain the second stable state of the column shell.

[0071] The bistable thin-walled shell design method based on plastic deformation of the supersonic civil aircraft of the present application, in step 1, constructs a non-prestressed cylindrical shell with an initial curvature, including:

[0072] The cylindrical shell satisfies the following assumptions:

[0073] (1) The cylindrical shell is a thin shell that satisfies the straight normal assumption;

[0074] (2) The cylindrical shell is in a plane stress state, there is no strain on the mid-surface, and the curvature of each point in the mid-surface is the same at any time, and the direction of the curvature of the cylindrical shell is the same as the direction of the bending moment;

[0075] (3) The material of the cylindrical shell is an ideal elastic-plastic material;

[0076] like Figure 1 As shown, a three-dimensional coordinate system is constructed at any point in the mid-plane of the cylindrical shell, wherein the x-axis is the longitudinal direction of the cylindrical shell, the y-axis is the transverse direction of the cylindrical shell, the z-axis is the thickness direction of the cylindrical shell, and the thickness of the cylindrical shell is t.

[0077] Assumption (2) shows that: since the curvature of each point in the mid-plane is the same at any time, the coordinate system can be established at any point in the mid-plane. Assuming that the curvature direction of the cylindrical shell structure is the same as the bending moment direction, that is, positive bending moment corresponds to positive curvature, based on this assumption, the initial curvature κ of the cylindrical shell can be obtained: 0x =0,κ 0y >0.

[0078] In at least one embodiment of the present application, the column shell is made of 304 stainless steel.

[0079] The bistable thin-walled shell design method based on plastic deformation of the supersonic civil aircraft of the present application, in step 2, flattening the cylindrical shell, includes:

[0080] A symmetrical bending moment M is applied along the straight side of the cylindrical shell. 1y , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 1x , flatten the cylindrical shell.

[0081] in,

[0082] Bending moment M 1y for:

[0083]

[0084] Bending moment M 1x for:

[0085] M 1x =v×M 1y

[0086] Among them, σ 1y is the stress in the y direction when the cylindrical shell is flattened, t is the thickness of the cylindrical shell, E is the elastic modulus, v is the deformation rate, k 0y is the initial curvature in the y direction.

[0087] The bistable thin-walled shell design method based on plastic deformation of the supersonic civil aircraft of the present application, in step 3, is to bend the flattened cylindrical shell to make the cylindrical shell part yield, including:

[0088] Maintain bending moment M 1y No change, continue to increase the bending moment M 1x , causing the cylindrical shell to undergo plastic deformation, the cylindrical shell to bend, and the cylindrical shell to partially yield.

[0089] in,

[0090] The yield depth z of the cylindrical shell cr for:

[0091]

[0092] The bending moment M when the cylindrical shell yields 2x for:

[0093]

[0094] Among them, σ 0 is the yield stress of the cylindrical shell under uniaxial tension, k 2x is the curvature in the x direction when the cylindrical shell is bent, σ 2x is the stress in the x direction when the cylindrical shell is bent.

[0095] The bistable thin-walled shell design method based on plastic deformation of the supersonic civil aircraft of the present application, in step 5, flattens the cylindrical shell again, including:

[0096] A symmetrical bending moment M is applied along the straight side of the cylindrical shell. 4x , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 4y , flatten the cylindrical shell again.

[0097] in,

[0098] Bending moment M 4y =M 1y ;

[0099] Bending moment M 4x for:

[0100]

[0101] Among them, σ 4x is the stress in the x direction when the cylindrical shell is flattened again.

[0102] In a preferred embodiment of the present application, in step 2, as Figure 2 As shown, a uniform bending moment M is applied to the boundary of the cylindrical shell. 1x 、M 1y , so that the cylindrical shell is completely flattened, that is, κ 0x =0,κ 0y = 0, assuming that this process is completely in the elastic deformation stage, then the stress distribution along the shell thickness direction is linear. 1y is directly caused by the change in curvature of the shell along the y direction, and the stress σ 1x It is caused by Poisson's ratio v. According to the basic knowledge of elastic mechanics:

[0103]

[0104] In step 3, the flattened cylindrical shell is bent to make the cylindrical shell partially yield, and the curvature of the cylindrical shell is changed from κ 1x =0 becomes κ 2x <0, and keep κ 2y = 0 remains unchanged, assuming that the distance between the yield point of the cylindrical shell and the mid-surface of the cylindrical shell is z cr At this time, the boundary bending moment My The membrane force is balanced, and the membrane force is very small compared to the bending stress of the cylindrical shell and can be ignored. cr When , the stress distribution of the cylindrical shell is linear elastic, and its stress magnitude is:

[0105]

[0106] By the von Mises yield criterion:

[0107]

[0108] Among them, σ 0 is the yield stress of the cylindrical shell under uniaxial tension. Substituting the above formula into the equation, we get:

[0109]

[0110] Since the cylindrical shell material is assumed to be an ideal elastic-plastic material, we have:

[0111]

[0112] At this time, the shape and stress distribution of the cylindrical shell are as follows Figure 3 shown.

[0113] In step 4, the cylindrical shell is slowly unloaded so that the curvature changes from κ 2x <0 becomes κ 3x <0, and keep κ 3y =0 remains unchanged, and the stress magnitude is:

[0114]

[0115] At this time, the shape and stress distribution of the cylindrical shell are as follows Figure 4 shown.

[0116] The stable state of the cylindrical shell is the first stable state of the cylindrical shell. x By integrating z along the thickness direction, we can get M 3x , then let M 3x = 0, we can calculate the curvature κ corresponding to the first steady state of the cylindrical shell. 3x size.

[0117]

[0118] In step 5, the cylindrical shell is flattened again so that the curvature changes from κ 3x <0 becomes κ 3x = 0, and keep κ 3y =0 remains unchanged, assuming that the deformation of the cylindrical shell is linear elastic, and its stress magnitude is:

[0119]

[0120] At this time, the shape and stress distribution of the cylindrical shell are as follows Figure 5 shown.

[0121] In step 6, the cylindrical shell is bent so that the curvature changes from κ 4y =0 becomes κ 5y >0, and keep κ 5x =0 remains unchanged. This process is the elastic unloading process of the cylindrical shell. At this time, the state corresponding to the cylindrical shell is the second steady state of the cylindrical shell, and the corresponding stress is:

[0122]

[0123] At this time, the shape and stress distribution of the cylindrical shell are as follows Figure 6 shown.

[0124] Following the steps in step 4, y By integrating z along the thickness direction, we can get M 5y , then let M 5y = 0, we can calculate the curvature κ corresponding to the second steady state of the cylindrical shell. 5y size:

[0125]

[0126] In a specific embodiment of the present application, a semicircular cylindrical shell structure without prestress is established using finite element software ABAQUS, the length of the cylindrical shell L = 1351 mm, the radius of the cylindrical shell R = 430 mm, the thickness t = 0.8 mm, and the shape of the cylindrical shell is as follows: Figure 7 As shown, the parameters selected for the column shell material are 304 stainless steel.

[0127] Similar to the theoretical derivation in the previous section, by applying symmetrical bending moments on the boundaries of the cylindrical shell to deform the cylindrical shell, the bending moment value required for the cylindrical shell in each state can be roughly calculated based on the stress distribution of the cylindrical shell. A total of 5 analysis steps are set to complete the entire deformation process, such as Figure 8 The figure shows the entire deformation process and stress distribution cloud diagram of the cylindrical shell. The loading and unloading conditions of the entire deformation process of the cylindrical shell are as follows:

[0128] first step: Figure 8 (a) is the initial state of the cylindrical shell. At this time, the cylindrical shell has no prestress and the stress at each point is 0. A symmetrical bending moment M is applied along the straight edge of the cylindrical shell. 1y , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 1x , where M 1y The size of M can be obtained by integrating formula (2). 1x The size of M is due to Poisson's ratio 1x =v×M 1y , where the initial curvature of the cylindrical shell κ0y =1 / 430mm -1 , after the cylindrical shell is flattened Figure 8 (b) as shown.

[0129]

[0130] Step 2: Keep M 1y No change, continue to increase M 1x , causing the cylindrical shell to undergo plastic deformation, at which point the cylindrical shell partially yields, such as Figure 8 (c) The yield curvature of the cylindrical shell is taken as κ 2x =-1 / 150mm -1 , the yield depth z of the cylindrical shell can be calculated by formula (6): cr The bending moment M when the cylindrical shell yields can be calculated by formula (7) 2x The size of is calculated as follows:

[0131]

[0132] Step 3: Remove all external loads. At this time, the column shell maintains equilibrium under its own stress, such as Figure 8 (d) shows the first stable state of the cylindrical shell. The curvature of the cylindrical shell in the x direction is denoted by κ. 3x .

[0133] Step 4: Apply symmetrical bending moment M again on the boundary of the cylindrical shell 4x and M 4y , so that the cylindrical shell is flattened again, such as Figure 8 (e) as shown, where M 4y =M 1y , the bending moment M can be calculated from equations (15) and (17): 4x The size of is calculated as follows:

[0134]

[0135] Step 5: Bend the flattened column shell again to make M 5y >0, then remove all external loads of the cylindrical shell. At this time, the stable shape of the cylindrical shell is the second stable state of the cylindrical shell. The curvature of the cylindrical shell in the y direction is recorded as κ 5y ,like Figure 8 As shown in (f), compared with the initial state of the column shell, the column shell is now a prestressed structure.

[0136] The bistable thin-walled shell design method based on plastic deformation of the supersonic civil aircraft of the present application has a simple and clear idea and sufficient theoretical basis, and obtains an analytical solution to the curvature of the bistable cylindrical shell after plastic deformation, providing a new design idea for deformable wings.

[0137] The second aspect of the present application provides a bistable thin-walled shell design device based on plastic deformation for a supersonic civil aircraft, comprising:

[0138] The non-prestressed column shell construction module is used to construct the non-prestressed column shell with initial curvature;

[0139] A column shell flattening module, used for flattening the column shell;

[0140] The column shell bending module is used to bend the flattened column shell to make the column shell partially yield;

[0141] A column shell unloading module is used to unload the column shell and obtain the first stable state of the column shell;

[0142] A column shell flattening module is used to flatten the column shell again;

[0143] The stable state acquisition module is used to bend the cylindrical shell after being flattened again, and obtain the second stable state of the cylindrical shell after unloading the cylindrical shell.

[0144] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A bistable thin-walled shell design method for supersonic civil aircraft based on plastic deformation, characterized in that: include: Step 1: construct a non-prestressed column shell with an initial curvature; Step 2: Flatten the column shell; Step 3, bending the flattened column shell to make the column shell partially yield; Step 4: Unload the column shell to obtain the first stable state of the column shell; Step 5: Flatten the column shell again; Step six, bend the flattened column shell again, and unload the column shell to obtain the second stable state of the column shell.

2. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 1, characterized in that: In step 1, a non-prestressed cylindrical shell with initial curvature is constructed, including: The column shell has the following characteristics: The cylindrical shell is a thin shell that satisfies the straight normal assumption; The cylindrical shell is in a plane stress state, the mid-surface has no strain, and the curvature of each point in the mid-surface is the same at any time, and the curvature direction of the cylindrical shell is the same as the bending moment direction, and the initial curvature κ 0x =0,κ 0y >0; The material of the column shell is an ideal elastic-plastic material; A three-dimensional coordinate system is constructed at any point in the mid-plane of the cylindrical shell, where the x-axis is the longitudinal direction of the cylindrical shell, the y-axis is the transverse direction of the cylindrical shell, the z-axis is the thickness direction of the cylindrical shell, and the thickness of the cylindrical shell is t.

3. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 2, characterized in that: The column shell is made of 304 stainless steel.

4. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 3 is characterized in that: In step 2, the column shell is flattened, including: A symmetrical bending moment M is applied along the straight side of the cylindrical shell. 1y , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 1x , flatten the cylindrical shell.

5. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 4, characterized in that: Bending moment M 1y for: Bending moment M 1x for: M 1x =v×M 1y Among them, σ 1y is the stress in the y direction when the cylindrical shell is flattened, E is the elastic modulus, v is the deformation rate, k 0y is the initial curvature in the y direction.

6. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 5, characterized in that: In step 3, the flattened column shell is bent to yield the column shell part, including: Maintain bending moment M 1y No change, continue to increase the bending moment M 1x , causing the cylindrical shell to undergo plastic deformation, the cylindrical shell to bend, and the cylindrical shell to partially yield.

7. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 6, characterized in that: The yield depth z of the cylindrical shell cr for: The bending moment M when the cylindrical shell yields 2x for: Where σ0 is the yield stress of the cylindrical shell under uniaxial tension, k 2x is the curvature in the x direction when the cylindrical shell is bent, σ 2x is the stress in the x direction when the cylindrical shell is bent.

8. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 7, characterized in that: In step five, the column shell is flattened again, including: A symmetrical bending moment M is applied along the straight side of the cylindrical shell. 4x , and a symmetrical bending moment M is applied along the curved side of the cylindrical shell. 4y , flatten the cylindrical shell again.

9. The method for designing a bistable thin-walled shell of a supersonic civil aircraft based on plastic deformation according to claim 8, characterized in that: Bending moment M 4y =M 1y ; Bending moment M 4x for: Among them, σ 4x is the stress in the x direction when the cylindrical shell is flattened again.

10. A bistable thin-walled shell design device based on plastic deformation for supersonic civil aircraft, characterized in that: include: The non-prestressed column shell construction module is used to construct the non-prestressed column shell with initial curvature; A column shell flattening module, used for flattening the column shell; The column shell bending module is used to bend the flattened column shell to make the column shell partially yield; A column shell unloading module is used to unload the column shell and obtain the first stable state of the column shell; A column shell flattening module is used to flatten the column shell again; The stable state acquisition module is used to bend the cylindrical shell after being flattened again, and obtain the second stable state of the cylindrical shell after unloading the cylindrical shell.

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