Plate shell curve reinforced structure design method and plate shell curve reinforced structure

Abstract

The invention relates to the technical field of plate shell structures, in particular to a plate shell curve reinforced structure design method and a plate shell curve reinforced structure. According to the method, based on given design parameters, an implicit curved surface and a cross section of the curve reinforced structure are selected, then section parameters of the curve reinforced structure are optimized through layout optimization of the curve reinforced structure and establishment of an agent model, and finally the optimal curve reinforced structure design is obtained. The implicit curved surface in the method can be given by any general curved surface form, and has great degree of freedom. The application agent model is high in calculation efficiency and can explicitly process constraints, and the calculation amount is reduced. According to the design method, the E-AMS method is combined, high-precision reduction of the implicit curve can be achieved while explicit is achieved, and accurate modeling of the curve reinforcement structure is achieved. The plate shell curve reinforced structure provided by the invention is obtained by adopting the plate shell curve reinforced structure design method, the design cost is lower, the efficiency is higher, and the structure has better anti-buckling bearing capacity and bearing characteristic.

Description

Technical Field

[0001] The invention relates to the technical field of plate-shell structures, and in particular to a design method for a plate-shell curved reinforced structure and a plate-shell curved reinforced structure. Background Art

[0002] Plate-shell structure is one of the main load-bearing structural parts widely used in engineering structures, and is widely used in aerospace, energy wind power, communication and navigation. Its typical failure forms are stability failure (buckling) and strength failure, among which stability failure is dominant. Reinforcement design on plates and shells is a method that can significantly enhance the anti-buckling capacity of plates and shells, and is the main content of plate-shell structure design. In the design of reinforcement layout, the new curved layout has a wider design space and better anti-buckling bearing capacity and bearing characteristics than the traditional orthogonal, equal triangle and other uniformly configured reinforced structures. Therefore, the curved reinforcement design method of plate-shell structure has become an important research direction. However, compared with the traditional reinforced structure, the path characterization function of the curved reinforced structure is more complex, resulting in an explosive growth of design variables, which seriously restricts the optimization design of the curved reinforced structure layout.

[0003] In order to solve the above problems, some solutions have been proposed in the prior art, such as:

[0004] The Chinese patent application with application number 202010649313.5 and titled: A method for intelligent design of curved reinforced structure layout based on image feature learning discloses a scheme, which is essentially a method for realizing curved reinforcement layout design based on b-spline curve combined with image neural network, and its main steps are: 1. Select the curved reinforcement path function to generate an image set, input the autoencoder network for unsupervised learning training, and complete the extraction of curved reinforcement image structure features. 2. Establish an analysis model of the mechanical response of the curved reinforced structure to form a data set for supervised learning training, and further input the convolutional neural network model built by the decoding network model and the fully connected layer to complete the learning of the mechanical response of the curved reinforced structure. 3. Based on the convolutional neural network model of the mechanical response prediction of the curved reinforced structure, the evolutionary algorithm is used to complete the optimization design of the curved reinforced structure layout. The core part is the introduction of neural network technology to reduce the amount of calculation in structural design. However, since its curve definition uses the definition form of spline curve, a single spline curve has more than 8 design parameters, and the number of parameters will increase dramatically during multi-reinforcement optimization, making it difficult to obtain a configuration with good bearing capacity when faced with multi-reinforcement optimization. In addition, the image feature learning method it uses is highly dependent on the specific form of the problem, which limits its application to plate and shell structures of other geometric configurations (poor versatility).

[0005] The Chinese patent application with application number 202311358627.X and titled: A composite material mesh curved reinforced structure and its optimization design method provides a solution. Based on the uniform curved reinforcement layout, the curved reinforced structure is realized by improving the mathematical expression of the rib curve. The main steps of this method are 1. Define the mathematical model for optimizing the curved reinforced structure. 2. Determine the geometric dimensions, composite material design parameters, load and displacement boundary conditions of the mesh curved reinforced structure. 3. Construct an optimization model based on the above parameters and solve the obtained optimization design. Similarly, there is a Chinese patent application with application number 202311106128.1 and titled: A method for optimizing the multi-condition stability of a spiral composite material curved reinforced wall panel. The formula method is also used to directly give the layout form of the curved reinforcement. This method realizes the modeling of the curved reinforced structure. For application numbers 202311358627.X and 202311106128.1, both methods directly limit the form of the curve, and their configuration freedom is extremely limited. Summary of the invention

[0006] The first object of the present invention is to provide a design method for a plate-shell curved reinforced structure to solve the problems of low design freedom of the plate-shell curved reinforced structure and excessively high calculation load due to overly complex buckling mechanical response.

[0007] The second object of the present invention is to provide a plate-shell curved reinforced structure obtained based on the plate-shell curved reinforced structure design method.

[0008] In order to achieve the above first object, in a first aspect, the present invention provides a method for designing a plate-shell curved reinforced structure, comprising the following steps:

[0009] S100: Define the design problem, including:

[0010] S101: Determine the fixing method and force mode of the plate and shell;

[0011] S102: Determine the maximum mass allowed for plates and shells in a given structural design;

[0012] S103: Select the implicit surface of the curved reinforced structure and the cross section of the curved reinforced structure;

[0013] S200: Optimization design of curved reinforced structure layout, including:

[0014] S201: selecting relative stiffness parameters, fixing the geometric parameters of the cross section of the curved reinforced structure selected in S103, taking the parameters of the implicit surface in S103 as design parameters, and generating an initial sample set required by the evolutionary algorithm;

[0015] S202: geometrically modeling all sample points in the initial sample set using an E-AMS method according to implicit surfaces, and performing mechanical response analysis on the initial sample set;

[0016] S203: Evaluate the load-bearing efficiency of the initial sample set to determine whether the convergence requirement is met, and if the convergence requirement is met, output the curved reinforced structure layout;

[0017] If the convergence requirement is not met, the evolutionary algorithm iteratively generates a new sample set, geometrically models all sample points in the new sample set using the E-AMS method based on implicit surfaces, and performs mechanical response analysis and load-bearing efficiency evaluation on the new sample set to determine whether the convergence requirement is met, and repeats this process until the convergence requirement is met;

[0018] S300: Optimization design of curved reinforced structure section parameters, including:

[0019] S301: Sampling the sample space of the curved reinforcement structure layout outputted in step S203 to generate a parameter set of the sample;

[0020] S302: Modeling the parameter set of the sample generated in step S301 using the E-AMS method, and performing finite element buckling calculation on it using the finite element method to obtain the corresponding buckling load;

[0021] S303: Select and train a proxy model;

[0022] S304: Based on the proxy model trained in step S303, an optimization algorithm is used to calculate the maximized eigenvalue under equal quality constraints;

[0023] S305: After the results converge, the final cross-sectional parameters of the curved reinforced structure are output.

[0024] Optionally, the proxy model is trained based on the following buckling mode characteristic equation:

[0025]

[0026] Among them, λ and λ0 are the buckling characteristic values ​​of the plate shell after and before reinforcement, respectively, β i is the dimensionless parameter of tendon morphology;

[0027] is a dimensionless material constant, where E r 、E p , are the elastic moduli of the reinforcement and the plate and shell, respectively, and v is the Poisson’s ratio of the reinforcement;

[0028] is the area integral of the global buckling mode displacement field over the reinforcement layout;

[0029] is the dimensionless relative stiffness, S r , S p are the reinforcement layout and the area of ​​the plate and shell, I z is the section inertia moment of the cross section of the corresponding curved reinforced structure around the neutral axis of the plate, l1, l2 are the shape parameters of the cross section, t p is the thickness of the plate.

[0030] Optionally, the proxy model can be any generic proxy model, using β{β i}Two parameters as input, As the output, where β{β i The number of parameters is equal to the number of cross-section parameters of the curved reinforcement structure minus 2.

[0031] Optionally, in step S304, a direct search method is selected to calculate the maximized eigenvalue under equal quality constraints based on the following;

[0032] Objective function: Among them, β{β i The number of parameters is equal to the number of cross-sectional parameters of the curved reinforcement structure minus 2;

[0033] Constraint function: t p S p +A r L r = constant, where A r is the cross-sectional area of ​​the curved reinforced structure, L r is the total length of the reinforcement.

[0034] Optionally, the E-AMS method process is as follows:

[0035] Generate the initial background grid required by the marching grid method, and then model the first implicit curve by constructing an epsilon grid in the squares that capture the implicit curve. According to the curvature distribution information provided by the epsilon grid point set distribution, the grid is gradually encrypted to obtain an accurate implicit curve spline.

[0036] Optionally, the parameter expression of the implicit surface in step S103 is {S i (u j )}, where S i represents the ith implicit surface, u j represents the jth parameter, and the geometric parameters of the cross section of the curved reinforced structure are expressed as {t p ,l i}, where t p is the thickness of the plate shell, and the other parameters are the cross-sectional shape parameters of the curved reinforced structure.

[0037] The cross-sectional geometric parameters {t p ,l i}:

[0038]

[0039] Where S r , S p are the areas of the reinforced structure and the plate shell, I z is the section inertia moment of the cross section of the corresponding curved reinforced structure around the neutral axis of the plate, l1, l2 are the shape parameters of the cross section, t p is the thickness of the plate and C0 is a selected constant.

[0040] Optionally, in step S203, the carrying efficiency of the initial sample set and the new sample set is evaluated according to the following formula:

[0041]

[0042] Among them, λ and λ0 are the buckling characteristic values ​​of the plate and shell before and after reinforcement, respectively.

[0043] Optionally, the evolutionary algorithm in step S201 is any one of a genetic algorithm, a simulated annealing algorithm, a particle swarm algorithm, an artificial neural network algorithm and an ant colony algorithm.

[0044] Optionally, the mechanical response analysis in step S202 adopts a finite element method, a finite difference method or a boundary element method; and / or

[0045] The optimization algorithm in step S304 adopts a direct search method or a gradient descent method.

[0046] In a second aspect, the present invention further provides a plate-shell curved reinforced structure, which is obtained by the plate-shell curved reinforced structure design method of any implementation method in the first aspect.

[0047] The above technical solution of the present invention has the following advantages:

[0048] The plate-shell curved reinforced structure design method provided by the present invention determines the fixing method and force mode of the plate-shell around and the maximum mass allowed by the plate-shell in a given structural design, selects the implicit surface and section of the curved reinforced structure, then selects the relative stiffness parameter and fixes the geometric parameters of the selected section, uses the parameters of the selected implicit surface as design parameters, generates the initial sample set required by the evolutionary algorithm, performs geometric modeling on all sample points in the initial sample set through the E-AMS method based on the implicit surface, performs mechanical response analysis and load-bearing efficiency evaluation on the initial sample set, outputs the curved reinforced structure layout if the convergence requirement has been met, and iteratively generates a new sample set if the convergence requirement has not been met, and again performs geometric modeling on all sample points in the new sample set through the E-AMS method based on the implicit surface, performs mechanical response analysis and load-bearing efficiency evaluation until the convergence requirement is met. The sample space of the output curved reinforced structure layout is sampled to generate a parameter set of the sample. The parameter set of the sample is generated by the E-AMS method for modeling, and the finite element buckling calculation is performed on it using the finite element method to obtain the corresponding buckling load, and the proxy model is selected and trained. Based on the trained proxy model, the optimization algorithm is used to calculate the maximized eigenvalue under equal mass constraints, and the final curved reinforced structure section parameters are output after the results converge. In this method, the implicit surface can be given by any general surface form and has a large degree of freedom. Moreover, the application of the proxy model has high computational efficiency and can explicitly handle constraints, which can reduce the amount of calculation. In addition, the design method of the present invention combines the E-AMS method, which can achieve high-precision restoration of implicit curves while being explicit, and realize accurate modeling of curved reinforced structures.

[0049] The present invention provides a plate-shell curved reinforced structure design method, which trains a proxy model based on the buckling mode characteristic equation, solving the problem that the structural buckling mode cannot be predicted under a certain reinforcement layout. In addition, as part of the result analysis in the layout optimization, the parameters are decoupled to reduce the calculation cost.

[0050] The plate-shell curved reinforced structure provided by the present invention is obtained by adopting the plate-shell curved reinforced structure design method, which has lower design cost and higher efficiency, and the structure has better anti-buckling bearing capacity and bearing characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The drawings of the present invention are provided for illustrative purposes only, and the proportions and quantities of the components in the drawings may not necessarily be consistent with the actual products.

[0052] Figure 1 It is a schematic flow chart of a design method for a plate and shell curved reinforced structure in an embodiment of the present invention;

[0053] Figure 2is a flow chart of the E-AMS modeling method in an embodiment of the present invention;

[0054] Figure 3 It is a flow chart of layout design of plate and shell curved reinforcement structure and cross-section parameter design in an embodiment of the present invention;

[0055] Figure 4 It is a schematic diagram of the process of designing a sparse curved reinforced structure under a fixed support boundary condition in an embodiment of the present invention;

[0056] Figure 5 It is a schematic diagram of the process of designing a dense curved reinforced structure under fixed support boundary conditions in an embodiment of the present invention;

[0057] Figure 6 is a cross-sectional schematic diagram of a curved reinforcement structure in an embodiment of the present invention;

[0058] Figure 7 is a cross-sectional schematic diagram of another curved reinforcement structure in an embodiment of the present invention;

[0059] Figure 8 It is a cross-sectional schematic diagram of another curved reinforcement structure in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] like Figure 1 As shown, the plate and shell curved reinforced structure design method provided by the embodiment of the present invention comprises the following steps:

[0062] S100: Define the design problem.

[0063] S200: Optimization design of curved reinforced structure layout.

[0064] S300: Optimization design of section parameters of curved reinforced structures.

[0065] Wherein, step S100: defining the design problem includes:

[0066] S101: Determine the fixing method and force mode of the plate and shell.

[0067] S102: Determine the maximum mass of plates and shells allowed in a given structural design.

[0068] S103: Select the type of implicit surface of the curved reinforced structure and the cross section of the curved reinforced structure based on experience. It should be noted that the surface form can be any two-dimensional surface, such as isoparametric interpolation surface, Nurbs (non-uniform rational b-spline), polynomial surface, etc. The cross section can be any cross section, for example, Figure 6 The rectangular cross section shown, Figure 7 The T-shaped section shown, Figure 8 The I-shaped section shown, etc. In this embodiment, preferably, the implicit surface level set method is used when defining the curved reinforcement structure.

[0069] After the design problem is defined in step S100, the curved reinforced structure layout optimization design and the curved reinforced structure cross-sectional parameter optimization design are performed on this basis, thereby obtaining the final curved reinforced structure design.

[0070] In this embodiment, step S200: optimizing the layout of the curved reinforcement structure includes:

[0071] S201: Select relative stiffness parameters, and fix the geometric parameters of the cross section of the selected curved reinforcement structure in step S103 according to the selected relative stiffness parameters, use the parameters of the implicit surface in step S103 as design parameters, and generate the initial sample set required by the evolutionary algorithm. It should be noted that the term "relative stiffness" refers to the ratio of the stiffness of the rib to the stiffness of the plate shell. In this embodiment, preferably, the evolutionary algorithm can adopt any one of the algorithms such as genetic algorithm, simulated annealing algorithm, particle swarm algorithm, artificial neural network algorithm and ant colony algorithm.

[0072] S202: geometrically modeling all sample points in the initial sample set according to its implicit surface by using the E-AMS (Epsilon-net enhanced Adaptive Marching Squares) method, and then performing mechanical response analysis on the initial sample set. In this embodiment, the mechanical response analysis of the initial sample set can be performed by using a finite element method, a finite difference method, or a boundary element method.

[0073] S203: Evaluate the load-bearing efficiency of the initial sample set to determine whether the convergence requirement is met. If the convergence requirement is met, output the curved reinforced structure layout. If the convergence requirement is not met, the evolutionary algorithm iteratively generates a new sample set, and geometrically models all sample points in the new sample set using the E-AMS method based on its implicit surface, and conducts mechanical response analysis and load-bearing efficiency evaluation on the new sample set to determine whether the convergence requirement is met, and repeats until the convergence requirement is met.

[0074] S300: Optimization design of curved reinforced structure section parameters, including:

[0075] S301: Sampling the sample space of the curved reinforced structure layout outputted in step S203 to generate a parameter set of the sample.

[0076] S302: Modeling the parameter set of the sample generated in step S301 using the E-AMS method, and performing finite element buckling calculation on it using the finite element method to obtain the corresponding buckling load.

[0077] S303: Select and train a proxy model. It should be noted that, using the design method of the present invention, the proxy model can be any general proxy model such as a Gaussian regression model, an artificial neural network, a support vector machine, a polynomial surface response model, etc.

[0078] S304: Based on the proxy model trained in step S303, an optimization algorithm is used to calculate the maximized eigenvalue under equal quality constraints. In this embodiment, the optimization algorithm in step S304 can optionally use a direct search method or a gradient descent method.

[0079] S305: After the results converge, the final cross-sectional parameters of the curved reinforced structure are output.

[0080] In one example, the proxy model is trained based on the following buckling mode characteristic equation:

[0081]

[0082] Among them, λ and λ0 are the buckling characteristic values ​​of the plate shell after and before reinforcement, respectively, β i is the dimensionless parameter of tendon morphology;

[0083] is a dimensionless material constant, where E r 、E p , are the elastic moduli of the reinforcement and the plate and shell, respectively, and v is the Poisson’s ratio of the reinforcement;

[0084] is the area integral of the global buckling mode displacement field over the reinforcement layout;

[0085] is the dimensionless relative stiffness, S r , S p are the reinforcement layout and the area of ​​the plate and shell, I z is the section inertia moment of the cross section of the corresponding curved reinforced structure around the neutral axis of the plate, l1, l2 are the shape parameters of the cross section, and the ellipsis refers to the shape of the cross section (see Figure 6 to Figure 8 As shown in the figure, there may be more cross-sectional shape parameters, such as l3, l4, etc., tp is the thickness of the plate, h r is the height of the tendon.

[0086] In this example, the training of the proxy model based on the buckling mode characteristic equation solves the problem of being unable to predict the structural buckling mode under a certain reinforcement layout. And as part of the result analysis in the layout optimization, the parameters are decoupled to reduce the computational cost.

[0087] See also Figure 3 The basic principle of the buckling modal characteristic equation is shown. It is a dimensionless equation. From the figure, it can be seen that the modal characteristic equation is a binary function composed of two ridges. These two ridges divide the entire area into three parts, corresponding to the three possible buckling forms of the same reinforcement layout: local rib buckling, local shell buckling, and global buckling. The intersection of the two ridges is the strongest point of the structure's anti-buckling ability.

[0088] Based on the above function for agent model training, β{β i}Two parameters as input, As the output, where β{β i The number of parameters is equal to the number of cross-section parameters of the curved reinforcement structure minus 2.

[0089] On the basis of adopting the above function to train the proxy model, in step S304, a direct search method is selected to calculate the maximized eigenvalue under equal quality constraints based on the following.

[0090] Among them, the objective function is: The number of β parameters is equal to the number of reinforcement cross-section parameters minus 2. Constraint function: t p S p +A r L r = constant, A r is the cross-sectional area of ​​the curved reinforced structure, L r is the total length of the reinforcement.

[0091] See also Figure 2 As shown, in one example, the E-AMS method flow is as follows:

[0092] Generate the initial background grid required by the marching grid method, and then model the implicit curve for the first time. At this time, the captured curves are often not accurate enough. At this time, an epsilon grid is constructed in the squares where the implicit curve is captured. At this time, the discrete point set distribution of the epsilon grid represents the curvature distribution on the surface. Then, the grid is continuously iterated and gradually encrypted. The encrypted position is the position where the point set is dense in the epsilon grid. In this way, accurate implicit curve splines can be obtained. As the modeling part of the structural modeling-calculation-analysis process in the optimization design, the E-AMS method process solves the problem that the curve geometry spline cannot be accurately realized in the implicit curve reinforcement modeling.

[0093] Compared with Marching squares, which is a general implicit curve modeling method, this method cannot ensure the accuracy of the implicit curve modeled, and is prone to curve distortion. At the same time, epsilon mesh technology is one of the commonly used technologies for judging surface geometric information in computational geometry. It can give geometric information on the surface through a discrete point set, and then reflect the geometric information of the level set curve on the surface. By combining the episilon mesh with the marching squares method, the marching squares method can dynamically determine the required grid density while performing implicit surface modeling, thereby achieving accurate geometric modeling.

[0094] In one example, the parameters of the implicit surface in step S103 are expressed as {S i (u j )}, where S i represents the ith implicit surface, u j represents the jth parameter, and the geometric parameters of the cross section of the curved reinforced structure are expressed as {t p ,l i}, where t p is the thickness of the plate shell, and the remaining parameters are the cross-sectional parameters of the curved stiffener structure. Figure 6 to Figure 8 As shown, i Refers to the parameters needed to determine the cross-sectional geometry, which may be different for different cross-sections.

[0095] The cross-sectional geometric parameters {t p ,l i}:

[0096]

[0097] Where S r , S p are the areas of the reinforced structure and the plate shell, I zis the section inertia moment of the cross section of the corresponding curved reinforced structure around the neutral axis of the plate, l1, l2 are the shape parameters of the cross section, and the ellipsis refers to the shape of the cross section (see Figure 6 to Figure 8 As shown in the figure, there may be more cross-sectional shape parameters, such as l3, l4, etc., t p is the thickness of the plate, C0 is a selected constant;

[0098] In one example, in step S203, the carrying efficiency of the initial sample set and the new sample set is evaluated according to the following formula:

[0099]

[0100] Among them, λ and λ0 are the buckling characteristic values ​​of the plate and shell before and after reinforcement, respectively.

[0101] It should be noted that the formula in step S203 can evaluate the carrying efficiency of both the initial sample set and the new sample set.

[0102] See also Figure 4 and Figure 5 As shown, they are schematic diagrams of the process of designing a sparse curved reinforced structure and a dense curved reinforced structure under fixed support boundary conditions using a plate-shell curved reinforced structure design method of this embodiment. Figure 4 (a.1) and Figure 5 (b.1) in FIG. 2 shows the curved reinforcement layout obtained after optimization in step 200. Figure 4 (a.2) and Figure 5 (b.2) in the figure shows the load distribution diagram generated by the proxy model after the proxy model training in step 300. The four basic buckling modes of the corresponding curved reinforcement layout can be quickly divided by this equation ( Figure 4 (a.3) and Figure 5 (b.3) in . And the position corresponding to the maximum value of the equation is the optimal design point. It can be seen that this method provides a fast and efficient means for the buckling mechanics evaluation of complex curved reinforced structures.

[0103] This embodiment also discloses a plate-shell curved reinforced structure obtained based on any of the above-mentioned plate-shell curved reinforced structure design methods.

[0104] Any details not described in detail in the present invention are common knowledge or prior art.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that not every embodiment contains only one independent technical solution. In the absence of a conflict of solutions, the various technical features mentioned in each embodiment can be combined in any manner to form other implementation methods that can be understood by those skilled in the art.

[0106] In addition, without departing from the scope of the present invention, the technical solutions described in the aforementioned embodiments may be modified, or some of the technical features may be replaced by equivalents, without causing the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a plate and shell curved reinforced structure, characterized in that: The following steps are involved: S100: Define the design problem, including: S101: Determine the fixing method and force mode of the plate and shell; S102: Determine the maximum mass of plates and shells allowed in a given structural design; S103: Select implicit surfaces and cross sections of the curved reinforcement structure; S200: Optimization design of curved reinforced structure layout, including: S201: selecting relative stiffness parameters, fixing the geometric parameters of the cross section of the curved reinforced structure selected in S103, taking the parameters of the implicit surface in S103 as design parameters, and generating an initial sample set required by the evolutionary algorithm; S202: geometrically modeling all sample points in the initial sample set using an E-AMS method according to implicit surfaces, and performing mechanical response analysis on the initial sample set; S203: Evaluate the load-bearing efficiency of the initial sample set to determine whether the convergence requirement is met, and if the convergence requirement is met, output the curved reinforced structure layout; If the convergence requirement is not met, the evolutionary algorithm iteratively generates a new sample set, geometrically models all sample points in the new sample set using the E-AMS method based on implicit surfaces, and performs mechanical response analysis and load-bearing efficiency evaluation on the new sample set to determine whether the convergence requirement is met, and repeats this process until the convergence requirement is met; S300: Optimization design of curved reinforced structure section parameters, including: S301: Sampling the sample space of the curved reinforcement structure layout outputted in step S203 to generate a parameter set of the sample; S302: Modeling the parameter set of the sample generated in step S301 using the E-AMS method, and performing finite element buckling calculation on it using the finite element method to obtain the corresponding buckling load; S303: Select and train a proxy model; S304: Based on the proxy model trained in step S303, an optimization algorithm is used to calculate the maximized eigenvalue under equal quality constraints; S305: After the results converge, the final cross-sectional parameters of the curved reinforced structure are output.

2. The method for designing a plate and shell curved reinforced structure according to claim 1, characterized in that: The surrogate model is trained based on the following buckling mode characteristic equation: Among them, λ and λ0 are the buckling characteristic values ​​of the plate shell after and before reinforcement, respectively, β i is the dimensionless parameter of tendon morphology; is a dimensionless material constant, where E r 、E p , are the elastic moduli of the reinforcement and the plate and shell, respectively, and v is the Poisson’s ratio of the reinforcement; is the area integral of the global buckling mode displacement field over the reinforcement layout; is the dimensionless relative stiffness, S r , S p are the reinforcement layout and the area of ​​the plate and shell, I z is the section inertia moment of the cross section of the corresponding curved reinforced structure around the neutral axis of the plate, l1, l2 are the shape parameters of the cross section, t p is the thickness of the plate, h r is the height of the tendon.

3. The design method of plate and shell curved reinforced structure according to claim 2, characterized in that: The proxy model can be any common proxy model, using β{β i }Two parameters as input, As the output, where β{β i The number of parameters is equal to the number of cross-section parameters of the curved reinforcement structure minus 2.

4. The design method of plate and shell curved reinforced structure according to claim 2, characterized in that: In step S304, a direct search method is selected to calculate the maximum eigenvalue under equal quality constraints as follows; Objective function: Among them, β{β i The number of parameters is equal to the number of cross-sectional parameters of the curved reinforcement structure minus 2; Constraint function: t p S p +A r L r = constant, where A r is the cross-sectional area of ​​the curved reinforced structure, L r is the total length of the reinforcement.

5. The design method of plate and shell curved reinforced structure according to claim 1, characterized in that: The E-AMS method flow is as follows: Generate the initial background grid required by the marching grid method, and then model the first implicit curve by constructing an epsilon grid in the squares that capture the implicit curve. According to the curvature distribution information provided by the epsilon grid point set distribution, the grid is gradually encrypted to obtain an accurate implicit curve spline.

6. The design method of plate and shell curved reinforced structure according to claim 1, characterized in that: The parameter expression of the implicit surface in step S103 is {S i (u j )}, where S i represents the ith implicit surface, u j represents the jth parameter, and the geometric parameters of the cross section of the curved reinforced structure are expressed as {t p ,l i }, where t p is the thickness of the plate shell, and the remaining parameters are the cross-sectional shape parameters of the curved reinforced structure; The cross-sectional geometric parameters {t p ,l i }: Where S r , S p are the areas of the reinforced structure and the plate shell, I z is the section inertia moment of the cross section of the corresponding curved reinforced structure around the neutral axis of the plate, l1, l2 are the shape parameters of the cross section, t p is the thickness of the plate and C0 is a selected constant.

7. The design method of plate and shell curved reinforced structure according to claim 1, characterized in that: In step S203, the carrying efficiency of the initial sample set and the new sample set is evaluated according to the following formula: Among them, λ and λ0 are the buckling characteristic values ​​of the plate and shell before and after reinforcement, respectively.

8. The design method of plate and shell curved reinforced structure according to claim 1, characterized in that: The evolutionary algorithm in step S201 is any one of a genetic algorithm, a simulated annealing algorithm, a particle swarm algorithm, an artificial neural network algorithm and an ant colony algorithm.

9. The design method of plate and shell curved reinforced structure according to claim 1, characterized in that: The mechanical response analysis in step S202 adopts finite element method, finite difference method or boundary element method; and / or The optimization algorithm in step S304 adopts a direct search method or a gradient descent method.

10. A plate and shell curved reinforced structure, characterized in that: The method is obtained by the plate and shell curved reinforced structure design method as described in any one of claims 1 to 9.

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