Method and device for designing controllable curvature stiffening of a curved shell, equipment and storage medium

Abstract

The application discloses a curved shell controllable curvature stiffening design method, device, equipment and storage medium, and the method comprises the steps: S1, the thickness, curvature and periodic layout characteristics of the plane rod are controlled by setting the continuous variation of the implicit function control part parameters, the anti-chiral plane rod system grid is designed, and the spatial gradient change of the rod in the plane rod system grid is realized; S2, the plane rod system grid is mapped to the curved shell through coordinate mapping to generate a programmable gradient transition stiffening, and the stiffening design of the rotation body structure of the cylindrical shell is completed. The application describes the stiffening based on the analytical function and the coordinate function, can realize the stiffening of different thicknesses and curvatures through a small amount of parameter control of the function, controls the local mechanical performance strengthening, controls the continuous change of the stiffening curvature through the parameter distribution change, ensures the continuity of the stiffening grid of different curvatures through parameter filtering, ensures the freedom and reliability of the gradient stiffening design, and realizes the complex stiffening description and gradient stiffening design.

Description

Technical Field

[0001] This application relates to the field of aerospace equipment structural design technology, and in particular, to a method, apparatus, equipment and storage medium for designing a curved shell with controllable curvature stiffening. Background Technology

[0002] Stiffened plates, as a high-efficiency load-bearing structure, have been widely used in aerospace equipment, shipbuilding engineering, and the automotive industry due to their lightweight design, high rigidity, and superior mechanical properties. By rationally configuring the material properties, cross-sectional shape, arrangement density, and geometric parameters of the stiffeners, the bending performance of the structure can be significantly optimized with limited mass increment, thereby effectively improving the mechanical response characteristics and stability threshold of thin-walled components. Existing stiffened plate design methods include topology optimization methods and explicit stiffening design methods. Topology optimization optimizes the structure by defining the relative density distribution of spatial points, while explicit methods design stiffened structures using fixed geometric forms.

[0003] Existing topology optimization methods, by defining relative density at each spatial point, struggle to efficiently describe structural forms, such as stiffened structures, which are much smaller than macroscopic structural dimensions. Furthermore, traditional stiffening design methods based on explicit descriptions are limited by fixed forms such as orthogonal meshes, triangular frames, and hexagonal meshes, making it difficult to achieve complex stiffening descriptions and gradient stiffening designs. Summary of the Invention

[0004] This application provides a method for designing controllable curvature stiffening of curved shells to solve the technical problems of existing technologies, such as the difficulty in efficiently describing structural forms with stiffening that are much smaller than the macroscopic structural dimensions, and the difficulty in achieving complex stiffening descriptions and gradient stiffening designs.

[0005] This application is achieved through the following solution:

[0006] A method for designing stiffened curved shells with controllable curvature, including the following steps:

[0007] S1. By controlling the continuous change of parameters in the implicit function control section, the thickness, curvature and periodic layout characteristics of the planar rods are controlled, and a reciprocal planar rod grid is designed to realize the spatial gradient change of the rods in the planar rod grid.

[0008] S2. By mapping the planar bar grid to the curved shell through coordinate mapping, a programmable gradient transition stiffening is generated, thus completing the stiffening design of the cylindrical shell's rotating structure.

[0009] Further, step S1 specifically includes the following steps:

[0010] S11. For a reciprocal metamaterial cell structure composed of two sets of symmetrical curved rods, one set of symmetrical curved rods is configured as follows:

[0011] The mathematical expression for the curved rod along the entire vertical design direction is:

[0012] ;

[0013] ;

[0014] in,

[0015] ;

[0016] ;

[0017] The mathematical expression for the curved rod in the transverse design direction is defined using the cyclic symmetry of coordinates as follows:

[0018] ;

[0019] ;

[0020] in,

[0021] ;

[0022] in, c This represents the curvature parameter, used to control the curvature of the crank. l x and l y The extreme values ​​of the influence function are used to control the thickness of the curved rod in the x and y directions, respectively. r x and r y The phase of the influence function is used to control the spatial position of the crank in the x and y directions; p x and p y Control the number of curved rods in the x and y directions within a unit area; q x and q y The spatial position of the crank in the x and y directions is controlled, but the magnitude of its value has a significant impact on the specific position. r x and r y The opposite effect is... x and y It is the independent variable of the member generation function. , , and This represents the phase control function. The curvature along the y-direction is c The curve generating function, Indicates that the curvature along the y-direction is - c The curve generating function, Indicates that the curvature along the x-direction is c The curve generating function, Indicates that the curvature along the x-direction is - c The curve generating function, t x and t y The period of the phase control function affects the repetition frequency of the bending characteristics of the crankshaft. s x and s y Used to control the relative position of the crank within a single cell;

[0023] S12. After obtaining two sets of vertical symmetrical curved bar descriptions, the anti-handed curved bar grid structure is obtained through Boolean operations:

[0024] ;

[0025] Where H(•) is the Heaviside function, and • represents the independent variable mapped through the Heaviside function.

[0026] Furthermore, step S1 also includes the step of:

[0027] S13, By changing the curvature parameters of the anti-handed curved bar grid structure c and thickness parameters l The value of is used to obtain different shapes of reciprocal curved bar grid structures.

[0028] Furthermore, step S1 also includes the step of:

[0029] S14. For a periodically distributed reciprocal curved bar grid structure, the control curvature parameters are defined through density filtering to ensure continuous distribution. c A continuous transition is achieved, resulting in a reciprocal curved bar grid structure where grids of different curvatures transition continuously at the connection point.

[0030] Furthermore, step S2 specifically includes the following steps:

[0031] S21. First, complete the geometric modeling of the curved shell in the modeling software to obtain the parametric model of the cylindrical shell;

[0032] S22. Subsequently, the three-dimensional spatial position data of the nodes on the surface of the cylindrical shell are extracted through the format conversion interface to establish a spatial coordinate database that meets the requirements of parametric modeling.

[0033] S23. Extract three-dimensional spatial position data, and based on the coordinate mapping principle and the anti-handed curved bar grid structure, map the anti-handed curved bar grid structure onto the cylindrical shell to generate a curved shell anti-handed grid stiffened structure.

[0034] S24. The curvature parameter c of the control rod curvature is set to a continuously varying value to generate a surface gradient stiffening structure that varies continuously along the set direction.

[0035] Furthermore, step S23 specifically includes the following steps:

[0036] S231. Reconstruct the curvature parameter c as a continuous function of the cylindrical shell's axial coordinate z, assuming the minimum and maximum values ​​of the given cylindrical shell's axial coordinates are zmin and zmax, respectively. min and z max The axial coordinates z∈[z] are transformed by linear transformation. min , z max Mapped to the dimensionless parameter c∈[-1,1], its mathematical expression is:

[0037] ;

[0038] This generates a surface gradient stiffener structure that varies continuously along the axis of the cylinder.

[0039] Furthermore, step S23 also includes the step of:

[0040] S232, Curvature parameters c Reconstructed as a bilinear coupled function in the local coordinate system of the cylindrical shell, its mathematical expression is:

[0041] ;

[0042] In the formula, and These are the normalized coordinate components of points on the shell surface. R is the maximum radius of the cylindrical shell, and the denominator R 2 Used to eliminate size effects and ensure curvature parameters This generates a surface gradient stiffener structure that varies continuously along the circumference of the cylinder.

[0043] This application also provides a controllable curvature stiffening design device for curved shells, including:

[0044] The anti-handed planar bar grid design module is used to control the thickness, curvature, and periodic layout characteristics of planar bars by continuously changing the parameters set by implicit function control, and to design an anti-handed planar bar grid to realize the spatial gradient change of the bars in the planar bar grid.

[0045] The controllable curvature stiffening design module for curved shells is used to map planar bar grids onto curved shells through coordinate mapping to generate programmable gradient transition stiffening, thus completing the controllable curvature stiffening design of the cylindrical shell's rotating structure.

[0046] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the controllable curvature stiffening design method for the curved shell.

[0047] This application also provides a storage medium including a stored program that, when the program is executed, controls the device where the storage medium is located to perform the steps of the controlled curvature stiffening design method for the curved shell.

[0048] Compared with the prior art, this application has the following advantages:

[0049] This application describes stiffening based on analytical and coordinate functions, enabling the control of different thicknesses and curvatures through a small number of function parameters. This allows for control over local mechanical property enhancement, avoiding the problem of traditional topology-optimized density field-based stiffening design, which suffers from large parameters and difficulty in directly controlling stiffening geometric features (such as curvature and thickness). Furthermore, unlike traditional explicit stiffening based on spline curves, this application, based on implicit function description, can control the continuous change of stiffening curvature through parameter distribution variations. Parameter filtering ensures the continuity of stiffened grids with different curvatures, guaranteeing the freedom and reliability of gradient stiffening design, and realizing complex stiffening descriptions and gradient stiffening designs.

[0050] In addition to the purposes, features, and advantages described above, this application has other purposes, features, and advantages. A further detailed description of this application will be provided below with reference to the figures. Attached Figure Description

[0051] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0052] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0053] Figure 1 This is a schematic flowchart of a preferred embodiment of the curved shell controllable curvature stiffening design method of this application;

[0054] Figure 2This is a schematic diagram illustrating the generation principle of the straight bar grid structure;

[0055] Figure 3 Different parameters c Schematic diagram of straight and curved rods under control;

[0056] Figure 4 This is a schematic diagram of the design process for a chiral curved bar grid structure;

[0057] Figure 5 This is a schematic diagram of the design process for a reversible curved bar grid structure;

[0058] Figure 6 It is a parameter c and l Schematic diagram of the reciprocal curved bar grid structure with different values;

[0059] Figure 7 (a) is a continuously distributed curvature parameter c Schematic diagram;

[0060] Figure 7 (b) is a schematic diagram of a gradient-changing planar grid structure;

[0061] Figure 8 This is a schematic diagram of a planar curved bar grid structure mapped to a three-dimensional curved surface stiffened structure.

[0062] Figure 9 (a) is a front view schematic diagram of the reinforced curved shell structure;

[0063] Figure 9 (b) is a top view of the reinforced curved shell structure;

[0064] Figure 10 This is a schematic diagram illustrating the influence of parameters c and l on the reciprocal grid reinforcement structure of the curved shell;

[0065] Figure 11 This is a schematic diagram of a curved gradient stiffener structure that continuously varies along the axial direction of a cylinder.

[0066] Figure 12 It is a schematic diagram of a curved gradient stiffener structure that continuously varies along the circumference of a cylinder;

[0067] Figure 13 This is a schematic diagram of the curved shell controllable curvature stiffening design device module according to a preferred embodiment of this application;

[0068] Figure 14 This is a schematic block diagram of an electronic device according to a preferred embodiment of this application;

[0069] Figure 15 This is an internal structural diagram of a computer device according to a preferred embodiment of this application. Detailed Implementation

[0070] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0071] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0072] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or a curved shell controllable curvature stiffening design device capable of achieving the above functions. The following description uses a curved shell controllable curvature stiffening design device as the executing entity to illustrate this embodiment and the subsequent embodiments.

[0073] like Figure 1 As shown, a preferred embodiment of this application provides a method for designing a curved shell with controllable curvature stiffening, including the following steps:

[0074] S1. By controlling the continuous change of parameters in the implicit function control section, the thickness, curvature and periodic layout characteristics of the planar rods are controlled, and a reciprocal planar rod grid is designed to realize the spatial gradient change of the rods in the planar rod grid.

[0075] S2. By mapping the planar bar grid to the curved shell through coordinate mapping, a programmable gradient transition stiffening is generated, thus completing the stiffening design of the cylindrical shell's rotating structure.

[0076] This embodiment describes stiffening based on analytical and coordinate functions, enabling the control of different thicknesses and curvatures through a small number of function parameters. This allows for control over local mechanical property enhancement, avoiding the problem of traditional stiffening design based on topology optimization density fields, where the parameters are too large to directly control the stiffening geometry (such as curvature and thickness). Furthermore, unlike traditional explicit stiffening based on spline curves, this embodiment, based on implicit function description, can control the continuous change of stiffening curvature through parameter distribution variations. Parameter filtering ensures the continuity of stiffened grids with different curvatures, guaranteeing the freedom and reliability of gradient stiffening design, and realizing complex stiffening descriptions and gradient stiffening designs.

[0077] Preferably, step S1 specifically includes the following steps:

[0078] S11. For a reciprocal metamaterial cell structure composed of two sets of symmetrical curved rods, by using the phase function... Add symmetry parameter to the basis To control the degree of symmetry of the symmetrical curved rod, and also by controlling the phase function. The positive and negative signs yield a set of symmetrical curved rods. Furthermore, utilizing the cyclic symmetry of coordinates, a vertical curved rod is obtained. One set of symmetrical curved rods is defined as follows:

[0079] The mathematical expression for the curved rod along the entire vertical design direction is:

[0080] ;

[0081] ;

[0082] in,

[0083] ;

[0084] ;

[0085] The mathematical expression for the curved rod in the transverse design direction is defined using the cyclic symmetry of coordinates as follows:

[0086] ;

[0087] ;

[0088] in,

[0089] ;

[0090] in, c This represents the curvature parameter, used to control the curvature of the crank. l x and l y The extreme values ​​of the influence function are used to control the thickness of the curved rod in the x and y directions, respectively. r x and r y The phase of the influence function is used to control the spatial position of the crank in the x and y directions; p x and p y Control the number of curved rods in the x and y directions within a unit area; q x and q y The spatial position of the crank in the x and y directions is controlled, but the magnitude of its value has a significant impact on the specific position. r x and r y The opposite effect is... x and y It is the independent variable of the member generation function. , , and This represents the phase control function. The curvature along the y-direction is c The curve generating function, Indicates that the curvature along the y-direction is - c The curve generating function, Indicates that the curvature along the x-direction is c The curve generating function, Indicates that the curvature along the x-direction is - c The curve generating function, t x and t y The period of the phase control function affects the repetition frequency of the bending characteristics of the crankshaft. s x and s y Used to control the relative position of the crank within a single cell;

[0091] S12. After obtaining two sets of vertical symmetrical curved bar descriptions, the anti-handed curved bar grid structure is obtained through Boolean operations:

[0092] ;

[0093] Where H(•) is the Heaviside function, and • represents the independent variable mapped through the Heaviside function.

[0094] Specifically, step S1 further includes the following steps:

[0095] S13, By changing the curvature parameters of the anti-handed curved bar grid structure c and thickness parameters l The value of is used to obtain different shapes of reciprocal curved bar grid structures.

[0096] Specifically, step S1 further includes the following steps:

[0097] S14. For a periodically distributed reciprocal curved bar grid structure, the control curvature parameters are defined through density filtering to ensure continuous distribution. c A continuous transition is achieved, resulting in a reciprocal curved bar grid structure where grids of different curvatures transition continuously at the connection point.

[0098] Specifically, step S2 includes the following steps:

[0099] S21. First, complete the geometric modeling of the curved shell in the modeling software to obtain the parametric model of the cylindrical shell;

[0100] S22. Subsequently, the three-dimensional spatial position data of the nodes on the surface of the cylindrical shell are extracted through the format conversion interface to establish a spatial coordinate database that meets the requirements of parametric modeling.

[0101] S23. Extract three-dimensional spatial position data, and based on the coordinate mapping principle and the anti-handed curved bar grid structure, map the anti-handed curved bar grid structure onto the cylindrical shell to generate a curved shell anti-handed grid stiffened structure.

[0102] S24. The curvature parameter c of the control rod curvature is set to a continuously varying value to generate a surface gradient stiffening structure that varies continuously along the set direction.

[0103] Specifically, step S23 includes the following steps:

[0104] S231. Reconstruct the curvature parameter c as a continuous function of the cylindrical shell's axial coordinate z, assuming the minimum and maximum values ​​of the given cylindrical shell's axial coordinates are zmin and zmax, respectively. min and z max The axial coordinates z∈[z] are transformed by linear transformation. min , z max Mapped to the dimensionless parameter c∈[-1,1], its mathematical expression is:

[0105] ;

[0106] This generates a surface gradient stiffener structure that varies continuously along the axis of the cylinder.

[0107] Specifically, step S23 further includes the following steps:

[0108] S232, Curvature parameters c Reconstructed as a bilinear coupled function in the local coordinate system of the cylindrical shell, its mathematical expression is:

[0109] ;

[0110] In the formula, and These are the normalized coordinate components of points on the shell surface. R is the maximum radius of the cylindrical shell. 2 Used to eliminate size effects and ensure curvature parameters This generates a surface gradient stiffener structure that varies continuously along the circumference of the cylinder.

[0111] The basic principles of this application will be further explained below.

[0112] This application designs metamaterial cells of different forms using the open-source finite element analysis software FEniCS under Linux (Ubuntu system), and then exports the metamaterial cell design model as a PVD file. The PVD file is then imported into Paraview software for visualization. Finally, the metamaterial cell design model can be exported as an STL file from Paraview for post-processing and additive manufacturing. The technical optimization scheme of this application is as follows: This design method mainly uses the Python programming language to analyze and obtain the metamaterial design model in FEniCS, and calculates the macroscopic properties of the metamaterial cell using finite element analysis based on homogenization theory. Finally, numerical examples of metamaterial cell filling are given to verify the reliability of the results.

[0113] Straight bar grille design based on triangular periodic functions:

[0114] In implicit function modeling, the membership degree of a point is determined by the function value at that point. In structural mechanics, it is generally accepted that points with positive and zero function values ​​are included in the structure, and the level set of zero represents the boundary of the microstructure. The Heaviside function projects the trigonometric function values ​​onto 0 and 1, where 0 represents porous materials and 1 represents solid materials. The Heaviside function is expressed as:

[0115] ;

[0116] in, ξ This represents the independent variable mapped by the Heaviside function. The step size of the Heaviside function is controlled, and a fixed value is used throughout the entire technical solution. ,like >0, Return 1; if <0, Returns 0.

[0117] First, we present the use of trigonometric periodic functions and... The process for generating a planar straight bar grid structure using functions is shown below. Figure 2 The design space is selected as the Cartesian coordinate system. and Let X and Y be the coordinates of a point in space, respectively. Define the following trigonometric functions and Boolean operations:

[0118] ;

[0119] ;

[0120] ;

[0121] in, and Controlling the adjacent spacing between vertical and horizontal bars in a straight bar grid structure on a two-dimensional plane; and Used to control the relative position of the lever within a single cell; and For solid materials, a threshold is set for function values ​​greater than [a certain threshold]. and The function is mapped to 1 or solid material, thereby controlling the thickness of the straight bars in the grid.

[0122] Figure 2 middle, and This visualizes the trigonometric function values ​​in two mutually perpendicular directions (X and Y directions) in a two-dimensional plane, through... Function mapping maps negative values ​​to 0, ensuring a 0 / 1 distribution of function values, represented as holes and solids respectively. Boolean operations allow us to take the union of points in the function space. This yields an orthogonal straight bar grid structure.

[0123] After a simple parameterization of the periodic function, the structural characterization can be controlled by a small number of parameters, and these parameters are associated with the stiffened geometric features.

[0124] Curved bar grille design based on parametric periodic functions:

[0125] Adding a periodically varying phase along the vertical direction to the trigonometric functions describing a vertical bar grid can implicitly describe a curved bar. Figure 3 , Figure 3 The description function of the curved bar is as follows:

[0126] ;

[0127] ;

[0128] in:

[0129] ;

[0130] in, and The meaning remains unchanged. This represents the added phase. middle c Control the curvature of the crank (when parameter) hour, and (Equivalent effect) This represents the inherent period of the curved rod, that is, the period of the curved rod's shape. Used to control the relative position of the lever within a single cell.

[0131] Chiral crank bar grille design:

[0132] By adjusting the parameters, we can obtain... A single curved rod can be used to obtain a curved rod in the vertical direction by utilizing the cyclic symmetry of the X and Y coordinates. Boolean operations are then performed on the two rods. This leads to a chiral curved bar lattice structure. The term "chiral" refers to an object or structure whose mirror image cannot be perfectly superimposed through rotation or translation. The following is a schematic diagram illustrating the generation process of the chiral curved bar lattice structure. Figure 4 Its mathematical expression is as follows:

[0133] Horizontal design direction has

[0134] ;

[0135] in

[0136] ;

[0137] Vertical design direction has

[0138] ;

[0139] in

[0140] ;

[0141] ;

[0142] In the above formula ， and The physical meaning of the variable corresponding to the subscript x is the same, but it is used for control. y Geometric features of the steering column. Boolean operations can be used to take the union of points in the function space. U .

[0143] Reverse-hand curved bar grille design:

[0144] Antichirality can be composed of two sets of chiral lattices with a period of two times. For an antichiral metamaterial cell structure composed of two sets of symmetrical curved rods, through the function Add parameters based on This controls the degree of symmetry of the symmetrical curved rod. Additionally, it uses a control function... The positive and negative signs yield a set of symmetrical curved rods, and further, by utilizing the cyclic symmetry of the coordinates, a curved rod in the vertical direction can be obtained. Control function For a set of symmetrical curved rods, refer to step S11 above. After obtaining two sets of perpendicular symmetrical curved rod descriptions, merge them using Boolean operations, referring to step S12 above.

[0145] Boolean operations yield a reciprocal curved bar grid structure. A flowchart illustrating the process of generating reciprocal cells can be found here. Figure 5 By changing the curvature parameter in the parametric composite trigonometric function c and thickness parameters l The value of can be used to obtain reciprocal curved bar grid structures of different shapes, see Figure 6 .

[0146] A gradient grid can be implemented by controlling the parameters of a periodic function to describe the grid. For example... Figure 7 As shown, this paper defines density filtering. Figure 7 The curvature parameters in (a) are continuously distributed. c Then you can get the following Figure 7 (b) shows a gradient-varying planar grid structure. This is due to the curvature parameter... c Continuous transition: grilles with different curvatures can also transition continuously at the connection point.

[0147] Curved shell with reverse-handed grid reinforcement structure design:

[0148] A parametric model of a cylindrical shell with an inner diameter of 0.8m, an outer diameter of 1.0m, and a height of 3m was established based on the Gmsh finite element analysis platform. By performing a mesh data conversion from MSH format to XML format, the three-dimensional spatial position information of the shell surface nodes was accurately extracted. This data preprocessing workflow provides a key geometric foundation for the parametric reconstruction of the curved stiffened structure. The specific implementation process includes: first, completing the shell geometry model in Gmsh; then, extracting structured node data through the format conversion interface; and finally, establishing a spatial coordinate database that meets the requirements of parametric modeling. The specific mapping process is detailed in [link to documentation]. Figure 8 .

[0149] Analysis of the data characteristics reveals that the original coordinates output by the software are a discrete point set M(x, y, z) in a Cartesian coordinate system. To adapt to the geometric characteristics of the curved surface structure, a coordinate transformation operation was performed, converting it to a cylindrical coordinate system M'(r, z). The mathematical relationship between z and z' can be expressed as:

[0150]

[0151] The reinforcing rib layout area is confined within an annular region of the cylindrical shell, specifically within a radial range of radius R = 0.9 to R = 1.0. To achieve structural optimization on complex curved surfaces, this application proposes a mapping method based on surface unfolding: the three-dimensional surface is unfolded into a two-dimensional plane along the cylindrical generatrix direction, and the original cylindrical coordinate points M'(r, φ, z') are projected to the planar coordinate system M''(x', y') through coordinate mapping relationships. The transformation criterion is as follows:

[0152]

[0153] Based on the coordinate mapping principle and the design method of anti-handed curved bar grid structure, an anti-handed grid stiffened structure for curved shell was generated, as detailed in [link to details]. Figure 9 (a) and Figure 9 (b)

[0154] In the process of surface geometry parameterization, in order to obtain a more reasonable stiffener layout structure, the key parameters of the stiffener layout are... and Dynamic adjustments must be made according to curvature characteristics. For a rotating shell structure, the mathematical relationship between the stiffener distribution density parameter ω and the surface perimeter can be expressed as follows: Assuming the shell perimeter is L = 2πR (R is the radius), when the design requires stiffeners to be arranged for n complete cycles along the circumference, its angular frequency parameter must satisfy... , and then combine Calculated When the period parameter T is When approximately equal, to achieve a continuous distribution of n periods in the composite trigonometric function structure of the surface, its axial unfolded length must satisfy the geometric constraint L=nT. This leads to the following derivation. (n is an even number).

[0155] The stiffened configuration generated by this algorithm exhibits spatial continuity, and its rib distribution can be geometrically adjusted to meet mechanical performance requirements while maintaining the geometric compatibility of the curved surface. The innovation of this method lies in transforming the three-dimensional surface stiffening problem into a two-dimensional planar problem through differential geometric transformation, significantly reducing computational complexity.

[0156] In the parametric design of stiffened curved shell structures, parametric modeling methods enable high-precision control of the stiffener geometry. This is achieved by changing the curvature parameters. c The size of the rod can control the degree of bending, allowing the curved shell's reciprocal stiffened structure to take on different shapes. This is achieved through thickness parameters. l A reasonable configuration can achieve directional control of the stiffener thickness, and the resulting curved shell stiffener structure is shown in [reference needed]. Figure 10 .

[0157] To generate a structure with a surface gradient stiffener that varies continuously along the axial direction of the cylinder, this application controls the curvature parameter of the member curvature. c The curvature parameter is set to a continuously varying value to generate a surface gradient stiffening structure. c Reconstruct it as a continuous function of the axial coordinate z along the cylindrical shell. Assume the minimum and maximum values ​​of the given axial coordinates of the cylindrical shell are zmin and zmax, respectively. min and z max The axial coordinates z∈[z] are transformed by linear transformation. min , zmax The mapping to the dimensionless parameter c∈[-1,1] is expressed mathematically as described in step S231 above, and the generated result is shown in [see...]. Figure 11 .

[0158] To achieve a continuously varying surface gradient stiffener structure along the circumference of a cylindrical shell, the curvature parameter... c The function is reconstructed as a bilinear coupling function in the local coordinate system of the cylindrical shell, the mathematical expression of which is given in step S232 above, thereby generating a surface gradient stiffener structure with continuous variation along the circumference of the cylinder (see...). Figure 12 ).

[0159] This application's coordinate-standardized mapping method, while ensuring the standardization of parameter values, establishes an explicit relationship between spatial location and geometric features, providing a universal mathematical model for constructing complex gradient structures. The design of surface gradient stiffeners offers a new approach to stiffening layout development.

[0160] like Figure 13 As shown, another preferred embodiment of this application also provides a controllable curvature stiffening design device for curved shells, comprising:

[0161] The anti-handed planar bar grid design module is used to control the thickness, curvature, and periodic layout characteristics of planar bars by continuously changing the parameters set by implicit function control, and to design an anti-handed planar bar grid to realize the spatial gradient change of the bars in the planar bar grid.

[0162] The controllable curvature stiffening design module for curved shells is used to map planar bar grids onto curved shells through coordinate mapping to generate programmable gradient transition stiffening, thus completing the controllable curvature stiffening design of the cylindrical shell's rotating structure.

[0163] The controllable curvature stiffening design device for curved shells provided in this application adopts the controllable curvature stiffening design method for curved shells in the above embodiments, which can solve the technical problems of existing technologies that make it difficult to efficiently describe structural forms such as stiffeners that are much smaller than the macroscopic structural dimensions, and difficult to realize complex stiffening descriptions and gradient stiffening designs. Compared with the prior art, the beneficial effects of the controllable curvature stiffening design device for curved shells provided in this application are the same as the beneficial effects of the controllable curvature stiffening design method for curved shells provided in the above embodiments, and other technical features in the controllable curvature stiffening design device for curved shells are the same as the features disclosed in the methods of the above embodiments, and will not be repeated here.

[0164] like Figure 14 As shown, a preferred embodiment of this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the curved shell controllable curvature stiffening design method in the above embodiments.

[0165] The electronic device provided in this application employs the controllable curvature stiffening design method for curved shells described in the above embodiments. This method addresses the technical problems of existing technologies, such as the difficulty in efficiently describing stiffened structures much smaller than macroscopic structural dimensions and the difficulty in achieving complex stiffening descriptions and gradient stiffening designs. Compared with existing technologies, the beneficial effects of the electronic device provided in this application are the same as those of the controllable curvature stiffening design method for curved shells provided in the above embodiments. Furthermore, other technical features of the electronic device are the same as those disclosed in the methods of the above embodiments, and will not be elaborated upon here.

[0166] like Figure 15 As shown, a preferred embodiment of this application also provides a computer device, which may be a terminal or a liveness detection server, and its internal structure diagram may be as follows. Figure 15 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface is used to communicate with other external computer devices via a network connection. When the computer program is executed by the processor, it implements the steps of the aforementioned controlled curvature stiffening design method for curved shells.

[0167] Those skilled in the art will understand that Figure 15 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0168] The computer device provided in this application employs the controllable curvature stiffening design method for curved shells described in the above embodiments, which solves the technical problems of existing technologies, such as the difficulty in efficiently describing stiffened structures much smaller than macroscopic structural dimensions and the difficulty in achieving complex stiffening descriptions and gradient stiffening designs. Compared with the prior art, the beneficial effects of the computer device provided in this application are the same as those of the controllable curvature stiffening design method for curved shells provided in the above embodiments, and other technical features in the electronic device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0169] A preferred embodiment of this application also provides a storage medium, the storage medium including a stored program, which, when the program is executed, controls the device where the storage medium is located to perform the steps of the curved shell controllable curvature stiffening design method in the above embodiments.

[0170] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0171] If the functions described in this embodiment are implemented as software functional units and sold or used as independent products, they can be stored in one or more computing device-readable storage media. Based on this understanding, the parts of this application's embodiments that contribute to the prior art or the technical solutions can be embodied in the form of a software product. This software product is stored in a storage medium and includes several instructions to cause a computing device (which may be a personal computer, server, mobile computing device, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage media include: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0172] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language C++ and the embedded programming language C.

[0173] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0174] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0175] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0176] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described curved shell controllable curvature stiffening design method.

[0177] The computer program product provided in this application can solve the technical problems of existing technologies, such as the difficulty in efficiently describing structural forms much smaller than macroscopic structural dimensions, including stiffeners, and the difficulty in realizing complex stiffener descriptions and gradient stiffener designs. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the curved shell controllable curvature stiffening design method provided in the above embodiments, and will not be repeated here.

[0178] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0179] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for designing a curved shell with controllable curvature stiffeners, characterized in that, Including the following steps: S1. By continuously varying the parameters set in the implicit function control section, the thickness, curvature, and periodic layout characteristics of the planar rods are controlled to design a reciprocal planar rod grid, realizing the spatial gradient change of the rods in the planar rod grid. Specific steps include: S11. For a reciprocal metamaterial cell structure composed of two sets of symmetrical curved rods, one set of symmetrical curved rods is configured as follows: The mathematical expression for the curved rod along the entire vertical design direction is: ； ； in, ； ； The mathematical expression for the curved rod in the transverse design direction is defined using the cyclic symmetry of coordinates as follows: ； ； in, ； ； in, c This represents the curvature parameter, used to control the curvature of the crank. l x and l y The extreme values ​​of the influence function are used to control the thickness of the curved rod in the x and y directions, respectively. r x and r y The phase of the influence function is used to control the spatial position of the crank in the x and y directions; p x and p y Control the number of curved rods in the x and y directions within a unit area; q x and q y The spatial position of the crank in the x and y directions is controlled, but the magnitude of its value has a significant impact on the specific position. r x and r y The opposite effect is... x and y It is the independent variable of the member generation function. , , and This represents the phase control function. The curvature along the y-direction is c The curve generating function, Indicates that the curvature along the y-direction is - c The curve generating function, Indicates that the curvature along the x-direction is c The curve generating function, Indicates that the curvature along the x-direction is - c The curve generating function, t x and t y The period of the phase control function affects the repetition frequency of the bending characteristics of the crankshaft. s x and s y Used to control the relative position of the crank within a single cell; S12. After obtaining two sets of vertical symmetrical curved bar descriptions, the anti-handed curved bar grid structure is obtained through Boolean operations: ； Where H(•) is the Heaviside function, and • represents the independent variable mapped through the Heaviside function; S13, By changing the curvature parameters of the anti-handed curved bar grid structure c and thickness parameters l The value of is used to obtain different shapes of reciprocal curved bar grid structures; S14. For a periodically distributed reciprocal curved bar grid structure, the control curvature parameters are defined through density filtering to ensure continuous distribution. c A continuous transition is achieved, resulting in a reciprocal curved bar grid structure where grids of different curvatures transition continuously at the connection points. S2. By mapping the planar bar grid to the curved shell through coordinate mapping, a programmable gradient transition stiffening is generated, thus completing the stiffening design of the cylindrical shell's rotating structure.

2. The controllable curvature stiffening design method for curved shells according to claim 1, characterized in that, Step S2 specifically includes the following steps: S21. First, complete the geometric modeling of the curved shell in the modeling software to obtain the parametric model of the cylindrical shell; S22. Subsequently, the three-dimensional spatial position data of the nodes on the surface of the cylindrical shell are extracted through the format conversion interface to establish a spatial coordinate database that meets the requirements of parametric modeling. S23. Extract three-dimensional spatial position data, and based on the coordinate mapping principle and the anti-handed curved bar grid structure, map the anti-handed curved bar grid structure onto the cylindrical shell to generate a curved shell anti-handed grid stiffened structure. S24. The curvature parameter c of the control rod curvature is set to a continuously varying value to generate a surface gradient stiffening structure that varies continuously along the set direction.

3. The controllable curvature stiffening design method for curved shells according to claim 2, characterized in that, Step S23 specifically includes the following steps: S231. Reconstruct the curvature parameter c as a continuous function of the cylindrical shell's axial coordinate z, assuming the minimum and maximum values ​​of the given cylindrical shell's axial coordinates are zmin and zmax, respectively. min and z max The axial coordinates z∈[z] are transformed by linear transformation. min , z max Mapped to the dimensionless parameter c∈[-1,1], its mathematical expression is: ； This generates a surface gradient stiffener structure that varies continuously along the axis of the cylinder.

4. The controllable curvature stiffening design method for curved shells according to claim 3, characterized in that, Step S23 further includes the following steps: S232, Curvature parameters c Reconstructed as a bilinear coupled function in the local coordinate system of the cylindrical shell, its mathematical expression is: ； In the formula, and These are the normalized coordinate components of points on the shell surface. , ∈[−R,R], where R is the maximum radius of the cylindrical shell, and R is the denominator. 2 To eliminate size effects and ensure that the curvature parameter c∈[−1,1], a surface gradient stiffener structure with continuous variation along the circumference of the cylinder is generated.

5. A controllable curvature stiffening design device for curved shells, characterized in that, include: The anti-handed planar bar grid design module is used to control the thickness, curvature, and periodic layout characteristics of planar bars by continuously varying the parameters set by implicit function control, thereby designing an anti-handed planar bar grid and realizing the spatial gradient change of the bars in the planar bar grid. Specifically, it is used for: For a reciprocal metamaterial cell structure consisting of two sets of symmetrical curved rods, one set of symmetrical curved rods is set as follows: The mathematical expression for the curved rod along the entire vertical design direction is: ； ； in, ； ； The mathematical expression for the curved rod in the transverse design direction is defined using the cyclic symmetry of coordinates as follows: ； ； in, ； ； in, c This represents the curvature parameter, used to control the curvature of the crank. l x and l y The extreme values ​​of the influence function are used to control the thickness of the curved rod in the x and y directions, respectively. r x and r y The phase of the influence function is used to control the spatial position of the crank in the x and y directions; p x and p y Control the number of curved rods in the x and y directions within a unit area; q x and q y The spatial position of the crank in the x and y directions is controlled, but the magnitude of its value has a significant impact on the specific position. r x and r y The opposite effect is... x and y It is the independent variable of the member generation function. , , and This represents the phase control function. The curvature along the y-direction is c The curve generating function, Indicates that the curvature along the y-direction is - c The curve generating function, Indicates that the curvature along the x-direction is c The curve generating function, Indicates that the curvature along the x-direction is - c The curve generating function, t x and t y The period of the phase control function affects the repetition frequency of the bending characteristics of the crankshaft. s x and s y Used to control the relative position of the crank within a single cell; After obtaining two sets of vertical symmetrical curved bar descriptions, a reciprocal curved bar grid structure is obtained through Boolean operations: ； Where H(•) is the Heaviside function, and • represents the independent variable mapped through the Heaviside function; By changing the curvature parameters of the anti-handed curved bar grid structure c and thickness parameters l The value of is used to obtain different shapes of reciprocal curved bar grid structures; For a periodically distributed reciprocal curved bar grid structure, a continuously distributed control curvature parameter is defined by density filtering. c A continuous transition is achieved, resulting in a reciprocal curved bar grid structure where grids of different curvatures transition continuously at the connection points. The controllable curvature stiffening design module for curved shells is used to map planar bar grids onto curved shells through coordinate mapping to generate programmable gradient transition stiffening, thus completing the controllable curvature stiffening design of the cylindrical shell's rotating structure.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the controllable curvature stiffening design method for curved shells as described in any one of claims 1 to 4.

7. A storage medium comprising a stored program that, when the program is executed, controls a device in which the storage medium resides to perform the steps of the controllable curvature stiffening design method for curved shells as described in any one of claims 1 to 4.

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