Calculation method and medium for deformation in the width direction and three-dimensional deformation of a rectangular thin plate

Abstract

The present invention belongs to the technical field of the structural design of flexible-wall nozzles in wind tunnels, and discloses a calculation method and medium for the deformation of a rectangular thin plate in the width direction and three-dimensional deformation. The calculation method for the deformation of the rectangular thin plate in the width direction is as follows: First, calculate the structural strain #imgabs0# of the deformation of the rectangular thin plate in the main bending direction, and then calculate the deformation in the width direction according to the structural strain #imgabs1# of the deformation in the main bending direction. The deformation of the rectangular thin plate is represented by a beam function, and the beam function in the width direction v ( y ) is: #imgabs2#, where h is the thickness of the rectangular thin plate, μ is the Poisson's ratio of the rectangular thin plate, y is the coordinate length of the rectangular thin plate in the width direction, k 1 is the position influence coefficient, k 2 is the aspect ratio influence coefficient. The present invention realizes for the first time the calculation of the deformation of the flexible wall plate of the flexible-wall nozzle in the width direction, and provides a new calculation method for the structural design of the flexible-wall nozzle in the wind tunnel. The present invention combines the deformation in the width direction with the deformation in the main bending direction, and can realize the calculation of the three-dimensional deformation of the flexible wall plate.

Description

Technical Field

[0001] The present invention relates to the technical field of the structural design of a flexible-wall nozzle in a wind tunnel, and particularly to a calculation method and medium for the deformation in the width direction and three-dimensional deformation of a rectangular thin plate. Background Art

[0002] A flexible-wall nozzle is a core section in a transonic wind tunnel that affects the flow field quality and Mach number simulation accuracy of the transonic wind tunnel. The deformation of the flexible wall plate of the flexible-wall nozzle involves the deformation problem of a rectangular thin plate under multiple constraint conditions, and has the characteristics of large structural deformation scale, high positioning accuracy requirements, and complex motion relationships during the forming process, making it very difficult to solve the deformation. At present, the basic problems such as the deformation modeling and solution of a rectangular thin plate with a complex flexible structure have not been systematically solved, which greatly restricts the further improvement of the structural optimization design and operation and maintenance capabilities of a large flexible-wall nozzle.

[0003] The existing simulation or theoretical calculation methods for the deformation problem of a rectangular thin plate have problems such as low efficiency or low accuracy, which directly affect the uniformity of the air flow in the core area, and do not consider the deformation in the width direction and cannot calculate the three-dimensional deformation of the rectangular thin plate. Summary of the Invention

[0004] The purpose of the present invention is to solve at least one of the above technical problems, and provides a calculation method and medium for the deformation in the width direction and three-dimensional deformation of a rectangular thin plate.

[0005] To achieve the above purpose, the first aspect of the present invention provides:

[0006] A calculation method for the deformation in the width direction of a rectangular thin plate, with one end of the rectangular thin plate fixed and a forced displacement perpendicular to the plane of the rectangular thin plate applied at the other end. The method is as follows: first calculate the structural strain of the deformation in the main bending direction of the rectangular thin plate , and then calculate the deformation in the width direction according to the structural strain of the deformation in the main bending direction. Represent the deformation of the rectangular thin plate with a beam function, and the beam function v ( y ) is: ; where h is the thickness of the rectangular thin plate, μ is the Poisson's ratio of the rectangular thin plate, y is the coordinate length of the rectangular thin plate in the width direction, k 1 is the position influence coefficient, k 2 is the aspect ratio influence coefficient, and the calculation formula is , , l is the length of the rectangular thin plate in the main bending direction, b is the width of the rectangular thin plate, xis the coordinate length of the rectangular thin plate along the main bending direction.

[0007] Preferably, the deformation of the rectangular thin plate in the main bending direction is a small deflection deformation or a large deflection deformation in the main bending direction.

[0008] Preferably, the calculation method for the small deflection deformation of the rectangular thin plate in the main bending direction is as follows: taking the small deflection linear beam as the beam function in the main bending direction and solving it, and the solving methods include any one of the elastic beam calculation method, the difference method, the variational method, etc.; the calculation method for the large deflection deformation of the rectangular thin plate in the main bending direction is as follows: taking the large deflection elastic beam as the beam function in the main bending direction and solving it, and the solving methods include any one of the elliptic integral method, the polynomial method, the variational solution method, etc.

[0009] The second aspect of the present invention provides:

[0010] A method for calculating the three-dimensional deformation of a rectangular thin plate by using orthogonal beam functions, in which the beam function in the width direction in the calculation method for the deformation of the rectangular thin plate in the width direction in any one of the first technical solutions v ( y ) is superimposed with the beam function in the main bending direction of the rectangular thin plate to obtain the three-dimensional deformation, where the width direction is orthogonal to the main bending direction.

[0011] Preferably, the three-dimensional deformation of the rectangular thin plate is a small deflection three-dimensional deformation or a large deflection three-dimensional deformation of the rectangular thin plate. When calculating the small deflection three-dimensional deformation, the beam function in the width direction v ( y ) in the calculation formula, is the structural strain of the small deflection deformation in the main bending direction; when calculating the large deflection three-dimensional deformation, the beam function in the width direction v ( y ) in the calculation formula, is the structural strain of the large deflection deformation in the main bending direction.

[0012] Preferably, the structural strain of the deformation in the main bending direction is calculated from the beam function in the main bending direction.

[0013] The third aspect of the present invention provides:

[0014] A computer-readable storage medium, on which a computer program or instruction is stored, and when the computer program or instruction is executed by a processor, the method described in any one of the first aspect and the second aspect is implemented.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] The present invention realizes for the first time the calculation of the deformation of the flexible wall panel of a flexible nozzle in the width direction, provides a new calculation method for the structural design of the flexible nozzle in a wind tunnel, improves the calculation efficiency of the structural design, and ensures the accuracy of the calculation results. By combining the deformation in the width direction with the deformation in the main bending direction, the present invention can realize the calculation of the three-dimensional deformation of the flexible wall panel. Brief Description of the Drawings

[0017] Figure 1 It is a schematic diagram of the mechanism of the single-pivot semi-flexible nozzle profile assembly in a specific embodiment;

[0018] In the figure: 1, throat block; 2, crank arm; 3, connecting rod; 4, transmission guide rod; 5, rotation point; 6, flexible wall panel;

[0019] Figure 2 It is a beam model in the main bending direction in a specific embodiment of the present invention. Detailed Description of the Embodiments

[0020] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0021] The first embodiment of the present invention provides a calculation method for the deformation of a rectangular thin plate in the width direction. One end of the rectangular thin plate is fixed, and a forced displacement perpendicular to the plane of the rectangular thin plate is applied at the other end. The method is as follows: First, calculate the structural strain of the deformation of the rectangular thin plate in the main bending direction , and then calculate the deformation in the width direction according to the structural strain of the deformation in the main bending direction . Represent the deformation of the rectangular thin plate with a beam function. The beam function in the width direction v ( y ) is: ; where h is the thickness of the rectangular thin plate, μ is the Poisson's ratio of the rectangular thin plate, y is the coordinate length of the rectangular thin plate in the width direction, k 1 is the position influence coefficient, k 2 is the aspect ratio influence coefficient, and the calculation formula is , , l is the length of the rectangular thin plate in the main bending direction, b is the width of the rectangular thin plate, x is the coordinate length of the rectangular thin plate in the main bending direction.

[0022] It should be noted that the present invention is applicable to the three-dimensional deformation calculation of all rectangular thin plates with one end fixed and a forced displacement perpendicular to the plane of the rectangular thin plate applied at the other end, and is not limited to the deformation calculation of the flexible wall plate of a flexible wall nozzle.

[0023] The beam function in the width direction is calculated by the following method: The rectangular thin plate has a left-right symmetric structure. When calculating the deformation in the width direction, it is assumed that the displacement of the middle section is zero, and the strains at each point along the width direction are equal. Then the boundary conditions for the deformation in the width direction are:

[0024] (1);

[0025] (2);

[0026] (3);

[0027] Wherein, υ is the deformation amount of the rectangular thin plate along the width direction, y is the coordinate length of the rectangular thin plate along the width direction, y= 0 represents the position of the central axis, is the structural strain of the deformation in the main bending direction of the rectangular thin plate. Formula (1) indicates that the deflection on the central axis is 0, that is, the deflection value of the central axis of the rectangular thin plate is exactly the same as the deflection value of the beam function in the main bending direction. Formula (2) indicates that the rotation angle along the width direction on the central axis is 0, that is, symmetric constraints on both sides. Formula (3) indicates that the bending moment at any position along the width direction is a function of the principal strain in the main bending direction at this section (i.e., the structural strain of the deformation in the main bending direction).

[0028] From the boundary condition formulas (1)-(3), by solving the differential equation, the beam function in the width direction of the rectangular thin plate can be obtained: (4);

[0029] Wherein, k 1 is the position influence coefficient, k 2 is the aspect ratio influence coefficient, and the calculation formula is as follows:

[0030] (5);

[0031] (6).

[0032] Therefore, it can be seen from formula (4) that the beam function in the width direction of the rectangular thin plate is related to the structural strain of the deformation in the main bending direction of the rectangular thin plate. As long as the structural strain of the deformation in the main bending direction of the rectangular thin plate can be calculated, its deformation in the width direction can be obtained according to the above formula.

[0033] It should be noted that there is no special limitation on the calculation method of the deformation in the main bending direction. In the present invention, one end of the rectangular thin plate is fixed and a forced displacement perpendicular to the plane of the rectangular thin plate is applied at the other end. The calculation methods for the deformation in the main bending direction of the rectangular thin plate under this load condition in the art are all applicable to the present invention. The focus of the present invention lies in how to convert the calculation of the deformation in the width direction into the calculation of the relationship with the deformation in the main bending direction.

[0034] Understandably, the embodiments of the present invention are applicable to the calculation of both large deflection deformation and small deflection deformation. That is, when the main bending direction of the rectangular thin plate is small deflection deformation, the deformation in the width direction is calculated according to the calculation result of the small deflection deformation in the main bending direction; when the main bending direction of the rectangular thin plate is large deflection deformation, the deformation in the width direction is calculated according to the calculation result of the large deflection deformation in the main bending direction.

[0035] For example, for the calculation method of the small deflection deformation in the main bending direction of the rectangular thin plate, a small deflection linear beam is used as the beam function in the main bending direction and solved. The solving methods include any one of the elastic beam calculation method, the difference method, the variational method, etc.; the calculation method of the large deflection deformation in the main bending direction of the rectangular thin plate is: a large deflection elastic beam is used as the beam function in the main bending direction and solved. The solving methods include any one of the elliptic integral method, the polynomial method, the variational solution method, etc.

[0036] The second embodiment of the present invention provides a method for calculating the three-dimensional deformation of a rectangular thin plate using orthogonal beam functions, and the beam function in the width direction in the calculation method of the deformation in the width direction of any one of the rectangular thin plates in the first embodiment v ( y ) is superimposed with the beam function in the main bending direction of the rectangular thin plate to obtain the three-dimensional deformation, where the width direction is orthogonal to the main bending direction.

[0037] When the rectangular thin plate in the present invention is stressed, the deformation is divided into the deformation in the main bending direction and the deformation in the width direction. The deformations in the two directions are respectively represented by the beam functions in two orthogonal directions, and then superimposed to obtain the overall deformation. Let u ( x ) be the beam function in the main bending direction, v ( y ) be the beam function in the width direction, w be the orthogonal beam function of the three-dimensional deformation, then the orthogonal beam function of the three-dimensional deformation of the rectangular thin plate is specifically: w = u ( x )+ v ( y )。

[0038] The three-dimensional deformation of the rectangular thin plate is the small deflection three-dimensional deformation or the large deflection three-dimensional deformation of the rectangular thin plate. When calculating the small deflection three-dimensional deformation, the beam function in the width directionv ( y ) In the calculation formula, is the structural strain of the small deflection deformation in the main bending direction; when calculating the large deflection three-dimensional deformation, the beam function in the width direction v ( y ) In the calculation formula, is the structural strain of the large deflection deformation in the main bending direction.

[0039] It can be understood that the structural strain of the deformation in the main bending direction is calculated from the beam function in the main bending direction, that is, the beam function in the main bending direction has been obtained when calculating the beam function in the width direction. Therefore, the following can simultaneously illustrate the calculation methods of the deformation in the width direction and the three-dimensional deformation of the rectangular thin plate through multiple specific examples.

[0040] As a specific example, the calculation methods of the deformation in the width direction and the three-dimensional deformation under small deflection are as follows:

[0041] Taking the small deflection linear beam as the beam function in the main bending direction and using the elastic beam calculation method to solve this beam function. For the deformation in the main bending direction, it is regarded as an elastic beam model with one end fixed and the other end free (that is, the forced displacement and angle constraint end), and is subjected to the forced displacement and angle constraints in the direction perpendicular to the beam axis. The beam coordinate takes the fixed end as the origin O and is along the main bending direction as x direction, and the forced displacement direction is z direction;

[0042] The boundary conditions of this elastic beam can be obtained as:

[0043] (7);

[0044] (8);

[0045] (9);

[0046] (10);

[0047] Among them, u is the deflection deformation of the elastic beam, x is the coordinate length of the rectangular thin plate along the main bending direction, x=0 represents the position at the origin, x=l represents the position at the free end, δ is the forced displacement at the free end. Formulas (7) and (8) indicate that the deflection and rotation angle at the fixed end are 0, and formulas (9) and (10) indicate that the deflection at the free end is δ , and the bending moment is 0.

[0048] For the small deflection elastic beam, its curvature can be simplified as:

[0049] (11);

[0050] Wherein, is the coordinate length of the beam along the main bending direction x is the bending moment at E is the elastic modulus, I is the moment of inertia of the cross-section;

[0051] Without considering the deformation of the beam along the x direction after deformation, the bending moment is thus:

[0052] (12);

[0053] Wherein, P is the force at the free end;

[0054] From the boundary condition formulas (7) to (10), the beam function u ( x ) of the beam in the main bending direction and its first and second derivative equations can be solved. The beam function equation in the main bending direction is: (13);

[0055] Since the aspect ratio of the rectangular thin plate > 20 and the shear force effect is not considered, according to the geometric equation of the Euler beam, the structural strain of the deformation in the main bending direction, that is, the relationship between the main strain of the elastic beam and the curvature is: (14); wherein, h is the thickness of the rectangular thin plate;

[0056] Furthermore, it can be obtained: (15);

[0057] According to the relationship between the shear strain of the rectangular thin plate and the structural strain of the deformation in the main bending direction, it can be obtained: (16); wherein is the shear strain of the rectangular thin plate, µ is the Poisson's ratio of the rectangular thin plate.

[0058] Since the main bending direction is described by the beam function and the change of the main strain along the width direction is not considered, it can be assumed that the shear strain does not change along the width direction on the same cross-section.

[0059] Substituting the above formula (15) into the beam function in the width direction can obtain the deformation of the rectangular thin plate in the width direction. At this time, the orthogonal beam function representation of the three-dimensional deformation of the rectangular thin plate is: w = u ( x ) + v( y ).

[0060] As another specific example, the calculation methods for the deformation in the width direction and the three-dimensional deformation under large deflection are as follows:

[0061] Since the orthogonal beam function model is established based on the small deflection beam function in the main bending direction, it is difficult to accurately calculate the deformation in the main bending direction under large deflection. Therefore, to improve the accuracy of the calculation results of the large deflection deformation of rectangular thin plates, this example solves the large deflection main bending deformation of rectangular thin plates through the elliptic decomposition method. The results of the orthogonal beam model established under the above small deflection deformation conditions can simplify the large deflection deformation problem of rectangular thin plates into the large deflection deformation problem of beams, and then solve it accurately.

[0062] The large deflection deformation problem of the main bending direction of a rectangular thin plate can be simplified into the large deflection deformation problem of a beam and solved by the elliptic integral solution method. It is also assumed that the main bending direction is x direction, and the forced displacement direction is z direction. According to the Euler-Bernoulli beam hypothesis, when the beam is in plane bending, the relationship between the curvature and the bending moment is as follows:

[0063] (17);

[0064] where the rotation angle θ is the angle between the tangent of the beam and the horizontal axis, and the length s is the arc length along the neutral axis of the beam;

[0065] The bending moment received at the coordinate length x along the main bending direction of the beam on the rectangular thin plate is:

[0066] (18);

[0067] where M 0 is the bending moment received at the free end.

[0068] From formulas (17) and (18), we can obtain: (19);

[0069] Differentiating both ends of formula (19) with respect to s can obtain: (20);

[0070] For a micro-segment, the relationship between dx , dz and ds is as follows:

[0071] ;

[0072] ; (21)

[0073] Define the force load factor , then formula (20) can be written as: (22);

[0074] Multiply both sides of formula (22) by dθ to obtain: (23);

[0075] Integrate both sides of formula (23) to obtain:

[0076] ;

[0077] (24);

[0078] wherein, C is a constant term;

[0079] The boundary conditions at the free end (i.e., the forced displacement and angular constraint end) are:

[0080] ;

[0081] ;

[0082] (25); wherein, is the angle between the bent free end ( x=l ) and the horizontal direction, is the rotation angle of the beam at the free end.

[0083] Substitute the boundary conditions into formula (24) to obtain the constant term as follows: (26);

[0084] We can obtain ds the relationship between dθ and (27); wherein, the load ratio ;

[0085] Furthermore, integrate both sides of formula (27), s the upper and lower limits of integration are [0, l , θ the upper and lower limits of integration are [0, θ 0 , to obtain: (28);

[0086] Formula (28) is the relationship between the length and angle of the main bending direction of the rectangular thin plate. Considering z the maximum value of the deflection deformation in the z l, and within a micro-segment, it satisfies formula (21). Substitute formula (21) into formula (27) and integrate both ends to obtain z l and θ 0 the equation of: (29);

[0087] Furthermore, write formulas (28) and (29) as elliptic integral expressions as follows:

[0088] (30);

[0089] λ, f, e, t, γ 1 , γ 2 Solve the coefficients of the elliptic integral, , , , , , ; F（·） is the first kind of elliptic integral form, E（·） is the second kind of elliptic integral form.

[0090] Furthermore, solve formula (30) to obtain M 0 and P , and then obtain the implicit form of the elastic beam bending equation:

[0091] (31)

[0092] (32);

[0093] Among them, , , ;

[0094] The corresponding implicit equation is:

[0095] (33);

[0096] is the beam function of the large deflection beam, that is, the beam function in the main bending direction. Through formula (33), the structural strain of the large deflection deformation in the main bending direction of the rectangular thin plate can be calculated: (34);

[0097] Substitute it into formula (4) to calculate the deformation in the width direction of the rectangular thin plate. At this time, the orthogonal beam function of the three-dimensional deformation of the rectangular thin plate is : w = u ( x, z ) + v (y )。

[0098] To verify the accuracy and computational time consumption of the embodiments of the present invention, the present invention conducted experiments. The single-pivot semi-flexible wall nozzle model used in this experiment is as Figure 1 shown. The crank arm 2, connecting rod 3, and transmission guide rod 4 drive the throat block 1 to rotate around the rotation point 5 to adjust the deformation of the flexible wall panel 6. The front end of the flexible wall panel 6 is subjected to the forced displacement and rotation angle of the rigid rotation of the throat block 1, and the tail end is a one-way sliding constraint. In the wind tunnel body coordinate system, the origin of the coordinate system is set at the center point O of the nozzle outlet. The outlet of the flexible wall panel is point A (fixed end), and the coordinates are ( x 0 , 0), and the rotation angle is zero; the connection point between the throat block 1 and the flexible wall panel 6 is point B (free end, that is, the forced displacement and angle constraint end), and the coordinates are ( x l , y l ), and the rotation angle of the throat block 1 is θ 0. The throat block 1 exerts a concentrated force P and a bending moment M 0 on the flexible wall panel 6. Considering that the outlet end can slide freely along the axis of the wind tunnel, the force of the flexible wall panel 6 along the axis of the wind tunnel is zero. The beam model in the main bending direction is as Figure 2 shown, and the large deflection three-dimensional deformation of this model is calculated.

[0099] The embodiments of the present invention were compared with the finite element simulation results, and the deformation problems of the above single flexible wall panel were analyzed. The finite element simulation used ABAQUS software. The structural parameters of the flexible wall panel were a length of 1000 mm, a width of 200 mm, a thickness of 20 mm, an elastic modulus of 200 GPa, and a Poisson's ratio of 0.3. One end of the flexible wall panel was fixed, and a forced displacement of 100 mm was applied to the other end. The unit mesh type was S4R, which is applicable to both thick plates and thin plates. The mesh size was selected as 1 / 10 of the width direction, that is, 20 mm, and the geometric nonlinear calculation setting was enabled.

[0100] The comparison of the results of the finite element calculation method and the half-model calculation results of the beam function calculation method is shown in Tables 1 and 2. In Tables 1-2, "X (mm)", "Y (mm)", and "Z (mm)" respectively represent the coordinates in the X, Y, and Z directions, and the unit is "mm"; Table 1 shows the comparison results of the finite element and the calculation of the present invention for the deformation in the main bending direction (the central axis displacement curve). It can be seen that the two can fit well. Table 2 shows the comparison results of the finite element and the calculation of the present invention for the deformation in the width direction. It can be seen that the maximum deviation between the present invention and the finite element calculation results is about 0.03 mm, and this deviation (the calculation result of the beam function method - the calculation result of the finite element method) is only 0.15‰ of the beam width, indicating that the orthogonal beam function method can effectively describe the three-dimensional bending deformation problem of the flexible wall panel.

[0101] Table 1 Comparison of Results between the Finite Element Calculation Method for the Deformation in the Main Bending Direction of the Flexible Wall Panel and the Beam Function Calculation Method of the Present Invention

[0102] 。

[0103] Table 2 Comparison of Results between the Finite Element Calculation Method for the Deformation in the Width Direction of the Flexible Wall Panel and the Beam Function Calculation Method of the Present Invention

[0104] 。

[0105] In terms of computational efficiency, taking this experiment as an example, using an Intel i7-7500 dual-core 64-bit processor as the computing platform with a computer memory of 8.0 GB to solve the nozzle profile deformation, the solution times of the present invention and the finite element simulation are 3.3 s and 37 s respectively. The solution time of the present invention is about 8.9% of the finite element solution time, which can effectively improve the analysis efficiency of the single-pivot semi-flexible wall nozzle in the transonic wind tunnel.

[0106] From the above results, it can be seen that the present invention can achieve the calculation and solution of the large-deflection deformation of the flexible wall nozzle, and its calculation accuracy is equivalent to that of the finite element simulation, while the calculation efficiency of the present invention is higher. Based on the analytical solution of the present invention, rapid iteration can be carried out with the aerodynamic conditions in the preliminary design stage to achieve both aerodynamic performance and structural mechanics performance. Then, finite element analysis can be carried out for verification, thereby reducing the design time and improving the design efficiency.

[0107] Based on the above embodiments, the present invention also provides a computer program product, including a computer program, and the computer program realizes the calculation method for the deformation in the width direction of the rectangular thin plate and the method for calculating the three-dimensional deformation of the rectangular thin plate using orthogonal beam functions disclosed in the embodiments of the present invention when executed by a processor.

[0108] Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file or some intermediate forms, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0109] The various embodiments of the systems and techniques described above in this document can be implemented in digital electronic circuitry, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on a chip (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special-purpose or general-purpose programmable processor that receives data and instructions from a storage system, at least one input device, and at least one output device, and transmits the data and instructions to the storage system, the at least one input device, and the at least one output device.

[0110] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for calculating the deformation in the width direction of a rectangular thin plate, wherein one end of the rectangular thin plate is fixed and the other end is subjected to a forced displacement perpendicular to the plane of the rectangular thin plate, characterized in that: The method is: first calculate the structural strain of the rectangular thin plate in the main bending direction , and then according to the structural strain of the deformation in the main bending direction Calculate the deformation in the width direction and use the beam function to represent the deformation of the rectangular thin plate. The beam function in the width direction v ( y )for: ;in, h is the thickness of the rectangular plate, μ is the Poisson’s ratio of the rectangular plate, y is the coordinate length of the rectangular plate along the width direction, k 1 is the position influence coefficient, k 2 is the aspect ratio influence coefficient, and the calculation formula is: , , l is the length of the rectangular plate in the main bending direction, b is the width of the rectangular plate, x is the coordinate length of the rectangular plate along the main bending direction.

2. The method for calculating the widthwise deformation of a rectangular thin plate according to claim 1, characterized in that: The deformation of the rectangular thin plate in the main bending direction is a small deflection deformation or a large deflection deformation in the main bending direction.

3. The method for calculating the widthwise deformation of a rectangular thin plate as claimed in claim 2, characterized in that: The calculation method for the small deflection deformation in the main bending direction of the rectangular thin plate is: using a small deflection linear beam as the beam function in the main bending direction and solving it, and the solution method includes any one of the elastic beam calculation method, the difference method, and the variational method; the calculation method for the large deflection deformation in the main bending direction of the rectangular thin plate is: using a large deflection elastic beam as the beam function in the main bending direction and solving it, and the solution method includes any one of the elliptic integral method, the polynomial method, and the variational decomposition method.

4. A method for calculating the three-dimensional deformation of a rectangular thin plate using an orthogonal beam function, characterized in that: The beam function in the width direction in the calculation method of the width direction deformation of the rectangular thin plate described in any one of claims 1 to 3 is v ( y ) is superimposed with the beam function in the main bending direction of the rectangular thin plate to obtain the three-dimensional deformation, in which the width direction is orthogonal to the main bending direction.

5. The method for calculating the three-dimensional deformation of a rectangular thin plate using an orthogonal beam function as claimed in claim 4, characterized in that: The three-dimensional deformation of the rectangular thin plate is the small deflection three-dimensional deformation or large deflection three-dimensional deformation of the rectangular thin plate. When calculating the small deflection three-dimensional deformation, the beam function in the width direction v ( y ) calculation formula, The structural strain of small deflection in the main bending direction; When calculating large deflection three-dimensional deformation, the beam function in the width direction v ( y ) calculation formula, Structural strain for large deflection in the main bending direction.

6. The method for calculating the three-dimensional deformation of a rectangular thin plate using an orthogonal beam function according to claim 4, characterized in that: Structural strains due to deformation in the principal bending direction Calculated from the beam function in the principal bending directions.

7. The method for calculating the three-dimensional deformation of a rectangular thin plate using an orthogonal beam function as claimed in claim 5, characterized in that: Structural strains due to deformation in the principal bending direction Calculated from the beam function in the principal bending directions.

8. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed by a processor, the method described in any one of claims 1 to 7 is implemented.

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