Three-dimensional curved shell structure generation method and device, electronic equipment and storage medium

Abstract

The invention relates to a three-dimensional curved shell structure generation method and device, electronic equipment and a storage medium. The method comprises the steps of obtaining target mechanical properties specified by a user; at least one target implicit equation is selected from a preset equation library, the implicit equation in the preset equation library is obtained by combining at least one basic monomial expression and at least one variable parameter, and the basic monomial expression is obtained by randomly combining at least one basic trigonometric function based on a three-dimensional variable; based on the target mechanical property, determining a target parameter value of a variable parameter when the three-dimensional curved shell structure corresponding to each target implicit equation has the target mechanical property in the feasible region of each target implicit equation; and on the basis of the target parameter values of the variable parameters in the at least one target implicit equation, at least one target three-dimensional curved shell structure is generated, and the target three-dimensional curved shell structure has the target mechanical property. Therefore, the target three-dimensional curved shell structure with the target mechanical property specified by the user can be efficiently and automatically generated.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the field of material structures, and particularly relates to a three-dimensional curved shell structure generation method and device, an electronic device and a storage medium. BACKGROUND

[0002] Porous materials have excellent performance in lightweight, high strength and multifunctionality. Lattice structures are a special class of porous materials formed by the periodic arrangement of basic units in three-dimensional space, which are usually superior to random porous materials at the same density, exhibiting more excellent mechanical properties, such as higher stiffness, higher strength, etc. According to the different geometric shapes of the basic units, lattice structures can be divided into three categories: truss, plate and curved shell. Curved shell structures have many advantages over truss or plate structures in terms of performance and manufacturing. First, curved shell structures effectively disperse stress and improve mechanical transmission efficiency through smooth geometric transitions, which can significantly reduce stress concentration and make the material less likely to be damaged due to excessive stress in certain areas, thereby improving the durability of the overall structure. Second, curved shell structures divide the overall space into two independent and separately connected regions, allowing for easy removal of uncured residual materials after additive manufacturing, which can affect the performance and service life of the material, and the design of curved shell structures reduces the presence of these residual materials.

[0003] In addition, curved shell structures exhibit excellent mechanical properties at low relative densities. Document 1 “Achieving the theoretical limit of strength in shell-based carbon nanolattices” (Li et al., PNAS, Vol. 119, 2022) discloses an optimized I-WP curved shell structure that is superior to optimized cubic, octahedral lattice and truss lattice structures in terms of modulus and strength. When the density exceeds 0.53 g·cm -3 , the strength of pyrolytic carbon I-WP nanostructures reaches the theoretical limit. Document 2 “Smooth-shell metamaterials of cubic symmetry: Anisotropic elasticity, yield strength and specific energy absorption” (Dirk et al., Acta Materialia, Vol. 164, pp. 301-321, 2019) found that for three types of curved shell structures designed based on simple cubic (SC), face-centered cubic (FCC) and body-centered cubic (BCC) lattices, when reaching isotropy, the stiffness and strength provided by the three types of structures are higher than those of isotropic truss lattice structures at the same density.

[0004] However, the types of curved shell structures researched and applied are relatively single, which cannot meet the needs of users who want to efficiently generate curved shell structures with specific mechanical properties. SUMMARY

[0005] Therefore, the present disclosure provides a three-dimensional curved shell structure generation method and device, electronic equipment and storage medium, which can efficiently and automatically generate a target three-dimensional curved shell structure with a user-specified target mechanical property.

[0006] According to an aspect of the present disclosure, a three-dimensional curved shell structure generation method is provided, including: obtaining a user-specified target mechanical property; selecting at least one target implicit equation from a preset equation library based on the target mechanical property, wherein the implicit equations in the preset equation library are obtained by combining at least one basic monomial with at least one variable parameter, and the basic monomial is obtained by randomly combining at least one basic trigonometric function based on three-dimensional variables; determining a target parameter value of the variable parameter when each target implicit equation corresponds to a three-dimensional curved shell structure with the target mechanical property in the feasible region of each target implicit equation based on the target mechanical property; wherein the feasible region of any implicit equation represents the value range of the variable parameter when the three-dimensional curved shell structure corresponding to the implicit equation is of the same type and is a single whole; and generating at least one target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the at least one target implicit equation, wherein the target three-dimensional curved shell structure has the target mechanical property.

[0007] In a possible implementation, the determining of the target parameter value of the variable parameter when each target implicit equation corresponds to a three-dimensional curved shell structure with the target mechanical property in the feasible region of each target implicit equation based on the target mechanical property includes: predicting the target parameter value of the variable parameter of each target implicit equation in the feasible region of each target implicit equation based on each target implicit equation and the target mechanical property by using a parameter prediction model; wherein the parameter prediction model is obtained by training a generative adversarial network using a data set, and the data set includes a plurality of real parameter values sampled in the feasible region of the variable parameter of each implicit equation in a plurality of implicit equations, and a real mechanical property corresponding to each real parameter value.

[0008] In a possible implementation, the generative adversarial network comprises a generator and a discriminator, and the training process of the parameter prediction model comprises: inputting, for any implicit equation in the data set and a real mechanical property corresponding to any real parameter value of the implicit equation, the implicit equation, the corresponding real mechanical property and random noise into the generator to obtain a predicted parameter value output by the generator; inputting the predicted parameter value and the corresponding real mechanical property into the discriminator to obtain a first discrimination result output by the discriminator, the first discrimination result representing a probability that the input predicted parameter value is a real parameter value; inputting the real parameter value of the implicit equation and the corresponding real mechanical property into the discriminator to obtain a second discrimination result output by the discriminator, the second discrimination result representing a probability that the input real parameter value is a real parameter value; optimizing model parameters of the discriminator based on a difference between the first discrimination result and the second discrimination result, and optimizing model parameters of the generator based on the first discrimination result to obtain a trained generator and discriminator; and the parameter prediction model is the trained generator.

[0009] In a possible implementation, the determining, based on the target mechanical property, a target parameter value of the variable parameter when each target implicit equation is used to make the three-dimensional curved shell structure have the target mechanical property, in a feasible region of each target implicit equation, comprises: randomly selecting, for any target implicit equation, a parameter value of the variable parameter in the target implicit equation from the feasible region of the target implicit equation; determining a simulation mechanical property of the three-dimensional curved shell structure corresponding to the target implicit equation with the randomly selected parameter value by using a finite element simulation analysis technology; in a case where the simulation mechanical property does not reach the target mechanical property, randomly selecting again a parameter value of the variable parameter of the target implicit equation from the feasible region of the target implicit equation until the simulation mechanical property reaches the target mechanical property; and in a case where the simulation mechanical property reaches the target mechanical property, determining the randomly selected parameter value as the target parameter value.

[0010] In a possible implementation, the preset equation library further comprises a mechanical property range corresponding to each implicit equation, and the mechanical property range corresponding to any implicit equation represents a range of mechanical properties of a three-dimensional curved shell structure generated based on the implicit equation in a feasible region of the implicit equation; and the selecting, based on the target mechanical property, at least one target implicit equation from the preset equation library comprises: selecting at least one target implicit equation whose mechanical property range contains the target mechanical property from the preset equation library; or obtaining a structure quantity specified by a user and selecting a target implicit equation whose mechanical property range contains the target mechanical property from the preset equation library, the mechanical property range corresponding to the structure quantity.

[0011] In a possible implementation, the generating the at least one target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the at least one target implicit equation comprises: for any target implicit equation, generating a target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the target implicit equation by using a finite element simulation analysis technology, and calculating the real mechanical performance of the target three-dimensional curved shell structure to verify whether the real mechanical performance of the target three-dimensional curved shell structure reaches the target mechanical performance.

[0012] In a possible implementation, the method further comprises: for any target three-dimensional curved shell structure, periodically arranging the target three-dimensional curved shell structure as a basic unit to obtain a three-dimensional curved shell periodic structure.

[0013] According to another aspect of the present disclosure, a three-dimensional curved shell structure generation apparatus is provided, comprising: an acquisition module configured to acquire a target mechanical performance specified by a user; a selection module configured to select at least one target implicit equation from a preset equation library based on the target mechanical performance, wherein the implicit equations in the preset equation library are obtained by combining at least one basic monomial with at least one variable parameter, and the basic monomial is obtained by randomly combining at least one basic trigonometric function with three-dimensional variables; a determination module configured to determine a target parameter value of a variable parameter when a three-dimensional curved shell structure corresponding to each target implicit equation has the target mechanical performance within a feasible region of each target implicit equation based on the target mechanical performance; wherein the feasible region of any implicit equation represents a range of values of the variable parameter when the three-dimensional curved shell structure corresponding to the implicit equation is of the same type and is a single whole; and a generation module configured to generate at least one target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the at least one target implicit equation, wherein the target three-dimensional curved shell structure has the target mechanical performance.

[0014] According to another aspect of the present disclosure, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0015] According to another aspect of the present disclosure, a non-volatile computer readable storage medium is provided, which stores a computer program, wherein the computer program is executed by a processor to implement the steps of the above method.

[0016] According to another aspect of the present disclosure, a computer program product is provided, comprising a computer program, or a non-volatile computer readable storage medium carrying the computer program, wherein the computer program is executed by a processor to implement the steps of the above method.

[0017] According to the aspects of the present disclosure, by acquiring the target mechanical property specified by the user, selecting the target implicit equation generated based on the three-dimensional function from the preset equation library, and then determining the target parameter value in the feasible region of each target implicit equation, the target three-dimensional curved shell structure with the target mechanical property is generated, which can automatically generate the implicit equation parameter combination meeting the performance requirements in the feasible region according to the target mechanical property required by the user, thereby realizing the automatic, efficient and systematic generation of the target three-dimensional curved shell structure with the target mechanical property, and realizing the generation automation and higher freedom of the three-dimensional curved shell structure, and meeting the personalized performance requirements of the user on the three-dimensional curved shell structure.

[0018] Other features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0019] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the present disclosure and serve to explain the principles of the present disclosure.

[0020] Figure 1 A flow chart of a three-dimensional curved shell structure generation method according to an embodiment of the present disclosure is shown.

[0021] Figure 2 A schematic diagram of an implicit equation construction process according to an embodiment of the present disclosure is shown.

[0022] Figure 3 Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown.

[0023] Figure 4 Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown.

[0024] Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Figure 5 Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown.

[0025] Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Figure 6 Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown.

[0026] Shape schematic diagrams of three-dimensional curved shell structures generated by 15 implicit equations respectively under a certain set of specific parameter values according to an embodiment of the present disclosure are shown. Figure 7A schematic diagram showing a training process of a generative adversarial network according to an embodiment of the present disclosure.

[0027] Figure 8 A schematic diagram showing shapes of four target three-dimensional curved shell structures according to an embodiment of the present disclosure.

[0028] Figure 9 A schematic diagram showing structures ③, ④, -1, ⑤, -2 and ⑥, A schematic diagram showing comparison of curved shell structures with other existing curved shell structures and isotropic lattice structures at different relative densities when reaching isotropy.

[0029] Figure 10 A schematic diagram showing structures ③, ④, -1, ⑤, -2 and ⑥, A schematic diagram showing comparison of yield strength and Young's modulus of other existing curved shell structures and isotropic lattice structures at different relative densities when reaching isotropy.

[0030] Figure 11 A schematic diagram showing structures ③, ④, -1, ⑤, -2 and ⑥, A schematic diagram showing stress-strain curve of isotropic structure under uniaxial compression when the relative density is about 15%.

[0031] Figure 12 A block diagram showing a three-dimensional curved shell structure generation apparatus according to an embodiment of the present disclosure.

[0032] Figure 13 A block diagram showing an electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0033] Various exemplary embodiments, features and aspects of the present disclosure will be explained in detail below with reference to the accompanying drawings. Like reference numerals in the drawings denote like elements or components having a substantially the same function. Although various aspects of embodiments are illustrated in the drawings, the drawings are not necessarily drawn to scale unless specifically noted.

[0034] As used herein, the terms "include", "comprise", "have", or their variants, are open-ended, and include one or more stated features, integers, elements, steps, components or functions but do not preclude the presence or addition of one or more other features, integers, elements, steps, components, functions or groups thereof.

[0035] When an element is referred to as being "connected", "coupled", "responsive", or "in communication" with, to another element, it can be directly connected, coupled, responsive, or in communication with the other element or intervening elements can be present.

[0036] Although the terms first, second, third, etc. can be used herein to describe various elements / operations, these elements / operations should not be limited by these terms. These terms are only used to distinguish one element / operation from another. Thus, a first element / operation in some embodiments could be termed a second element / operation in other embodiments without departing from the teachings of the present inventive concept.

[0037] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations.

[0038] In addition, for the purpose of convenience and brevity, detailed descriptions of well-known functions and structures incorporated in the present disclosure can be omitted. It will be appreciated that those skilled in the art will be able to devise various modes of implementing the advantageous aspects of the present disclosure without the exercise of inventive faculty and without the aid of further experimentation.

[0039] As described above, the types of curved shell structures currently being researched and applied are relatively single, and most of the existing curved shell structures have significant mechanical performance anisotropy, and their responses strongly depend on the load direction. It is unable to meet the needs of users who want to generate curved shell structures with specific mechanical properties. Therefore, it is urgently needed to explore new types of curved shell structures with more abundant geometric shapes and the ability to automatically generate more optimal or specific (such as isotropic, specific strength, high specific surface area, etc.) mechanical properties, in order to break through the above bottleneck.

[0040] Therefore, the embodiments of the present disclosure aim to provide a three-dimensional curved shell structure generation method with adjustable mechanical properties. The method establishes an inverse design model from mechanical properties to structure parameters based on a generative adversarial network, determines the implicit equation parameters of the curved shell structure through a machine learning method, and thus precisely regulates the geometric shape of the three-dimensional curved shell structure to realize directional adjustment of its mechanical properties, and can generate design parameters meeting the requirements according to target properties. The three-dimensional curved shell structure obtained through the method can have specific mechanical properties, such as mechanical isotropy, specified stiffness or strength, etc. Moreover, the generated three-dimensional curved shell structure can also be used as a basic unit to construct a three-dimensional curved shell periodic structure through periodic arrangement, and is widely applied in the fields of lightweight design, aerospace, etc.

[0041] Figure 1 A flowchart of a three-dimensional curved shell structure generation method according to an embodiment of the present disclosure is shown. As shown in FIG. 1, the method comprises the following steps. Figure 1As shown, the method includes steps S11 to S14.

[0042] In step S11, the target mechanical properties specified by the user are obtained.

[0043] In practical applications, for example, an interactive interface can be provided to the user so that the user can input or set the target mechanical properties of the three-dimensional curved shell structure to be generated. The embodiments of this disclosure do not limit the method of obtaining the target mechanical properties.

[0044] The mechanical properties of the three-dimensional curved shell structure may include, but are not limited to, anisotropy, strength, stiffness, high specific surface area, and relative density. It should be understood that users can set the specific content of the target mechanical properties according to actual needs, and this disclosure does not limit this. The target mechanical properties specified by the user may include one or more of the above-mentioned mechanical properties. For example, the target mechanical properties specified by the user may include isotropy (i.e., anisotropy of 1) and a relative density of 10%. That is, the user needs to generate a three-dimensional curved shell structure with isotropy and a relative density of 10%.

[0045] In step S12, based on the target mechanical properties, at least one target implicit equation is selected from the preset equation library. The implicit equation in the preset equation library is obtained by combining at least one basic monomial with at least one variable parameter. The basic monomial is obtained by randomly combining at least one basic trigonometric function based on three-dimensional variables.

[0046] The basic trigonometric functions used in this disclosure include sine and cosine functions, to determine the form of implicit equations that can be used to generate three-dimensional curved shell structures based on these basic sine and cosine functions. A basic trigonometric function can be either a sine function or a cosine function; for example, a sine function could be... , ... Any of the expressions, a cosine function can be, for example, , ... Any of the following expressions, and All are positive integers; three-dimensional variables are also three-dimensional spatial coordinate variables. By using three-dimensional variables to randomly combine at least one basic trigonometric function in any way through multiplication, addition, or subtraction, various basic monomials can be formed, for example, , , , , And so on. It can be seen that each basic monomial has a different form, but all contain three-dimensional variables. , so as to generate a three-dimensional curved shell structure with structural symmetry. It should be understood that there are various basic trigonometric functions and various ways of random combination, so various basic monomials can be generated, and the number and type of basic monomials generated by the embodiments of the present disclosure are not limited.

[0047] After generating various basic monomials, the basic monomials can be multiplied by variable parameters and combined by addition and subtraction to obtain various implicit equations of the three-dimensional curved shell structure. If n basic monomials are generated, n+1 variable parameters can be used, n variable parameters can be multiplied by n basic monomials respectively to serve as coefficient terms before the n basic monomials, and the remaining variable parameter can serve as a bias term in the implicit equation. Then, the basic monomials with the coefficient terms can be arranged and combined to obtain a plurality of implicit equations, and a large number of pre-constructed implicit equations can be included in the preset equation library.

[0048] Exemplarily, as shown in Figure 2 , various basic trigonometric functions are randomly combined based on three-dimensional variables, that is, the basic trigonometric functions of , , , , , are randomly combined, and n basic monomials are obtained as , , …, ; n+1 variable parameters, that is, , , …, and are used; and , , …, are multiplied by , , …, , and , , …, are arranged and combined, and serves as a bias term to obtain a plurality of implicit equations, such as = , = , …, = . It should be understood that each implicit equation shown in Figure 2 is only some exemplary embodiments, and actually, more implicit equations can be generated, such as = , = .However, this disclosure does not limit the scope of the embodiments.

[0049] For example, the following are 15 implicit equations generated in the manner described above:

[0050] Equation ①: ;

[0051] Equation ②: ;

[0052] Equation ③: ;

[0053] Equation ④: ;

[0054] Equation ⑤: ;

[0055] Equation ⑥: ;

[0056] Equation ⑦: ;

[0057] Equation ⑧: ;

[0058] Equation 9: ;

[0059] Equation 10: ;

[0060] equation : ;

[0061] equation : =0;

[0062] equation : ;

[0063] equation : ;

[0064] equation : .

[0065] Figure 3 The diagram shows the shape of the three-dimensional curved shell structure generated by each of the above 15 implicit equations under a specific set of parameter values, such as... Figure 3 As shown, for equation ①, when , , The three-dimensional curved shell structure at that time is structure ①; for equation ②, when , The three-dimensional curved shell structure of time is structure ②; and the like, Table 1 shows a list of mechanical properties of 15 three-dimensional curved shell structures generated by using the above 15 implicit equations and two existing three-dimensional curved shell structures (namely I-WP and Schwarz P), and it can be seen from Table 1 that the mechanical properties of the three-dimensional curved shell structures generated by different implicit equations are different. Among them, the implicit equation of I-WP is represented as: , and the implicit equation of Schwarz P is represented as: .

[0066] Table 1 List of mechanical properties

[0067]

[0068] Wherein, the material parameters are taken as Young's modulus of 2.1 GPa, yield strength of 7.2 MPa, and Poisson's ratio of 0.3; the side length of the basic unit is 2 mm, and the surface area is the single-sided surface area of the curved shell structure.

[0069] It should be understood that the preset equation library can include but is not limited to the above 15 implicit equations, and the number and type of implicit equations included in the preset equation library are not limited in the embodiments of the present disclosure. In actual application, at least one implicit equation can be randomly selected from the preset equation library as a target implicit equation, of course, all implicit equations in the preset equation library can also be used as target implicit equations to generate a target three-dimensional curved shell structure with target mechanical properties.

[0070] It should be understood that the three-dimensional curved shell structure generated by different implicit equations is usually different, and for the same implicit equation, adjusting its parameter value will often lead to changes in structure morphology and mechanical properties. In order to improve the generation efficiency of the target three-dimensional curved shell structure, the mechanical property range of each implicit equation can be obtained in advance by finite element simulation analysis technology, and it is judged that the target mechanical property required by the user is located in the mechanical property range of which implicit equation, and then the parameter value of the variable parameter that meets the target mechanical property is determined according to these implicit equations falling into the mechanical property range. Therefore, the above preset equation library can also include the mechanical property range corresponding to each implicit equation, and then in the above step S12, selecting at least one target implicit equation from the preset equation library based on the target mechanical property can include: selecting at least one target implicit equation from the preset equation library whose mechanical property range contains the target mechanical property.

[0071] Here, the range of mechanical properties corresponding to any implicit equation represents the range of mechanical properties of the three-dimensional curved shell structure generated based on the implicit equation within the feasible region of the implicit equation. The feasible region of any implicit equation represents the range of values ​​of the variable parameters that make the three-dimensional curved shell structures corresponding to the implicit equation of the same type and a single entity. The process of determining the feasible region may include: within a given parameter range, adjusting the parameter values ​​of the variable parameters in the implicit equation; as long as the generated three-dimensional curved shell structures belong to the same type and are a single entity, outputting their parameter values; summing up the parameter values ​​of all three-dimensional curved shell structures that can generate the same type and are a single entity, obtaining the feasible region. Here, three-dimensional curved shell structures belonging to the same type means that the implicit equations of the three-dimensional curved shell structures have the same form, or that the shapes of the three-dimensional curved shell structures are similar; three-dimensional curved shell structures being a single entity means that the three-dimensional curved shell structures are continuous structures, or that they are a single entity.

[0072] For example, Figure 4 Equation ③ and equation ④ are shown above. and equations Two-dimensional feasible region with some variable parameters, such as Figure 4 As shown in (a), (b) and (c), the colored region is the feasible region. The parameter values ​​within the colored region make the three-dimensional curved shell structure corresponding to the implicit equation the same type and a single whole. However, when the parameter values ​​fall in the gray region, the generated three-dimensional curved shell structure will be discontinuous, that is, the three-dimensional curved shell structure contains multiple discrete parts, and may not be of the same type.

[0073] In practical applications, given the feasible region of any implicit equation, open-source finite element simulation analysis techniques (such as open-source finite element analysis software) can be used to generate the corresponding three-dimensional curved shell structure based on the feasible region of the implicit equation and calculate various mechanical properties of the three-dimensional curved shell structure. This allows us to obtain the range of mechanical properties of the three-dimensional curved shell structure corresponding to each implicit equation within the feasible region. This disclosure does not limit the specific implementation method of generating the three-dimensional curved shell structure and analyzing its mechanical properties using finite element analysis software, as long as the range of mechanical properties of any three-dimensional curved shell structure within the feasible region can be obtained.

[0074] Optionally, the implicit equation in the preset equation library, which has a mechanical property range containing the target mechanical property (i.e., the target mechanical property falls within the mechanical property range), can be taken as the target implicit equation, or one or more implicit equations can be randomly selected from the implicit equations with the mechanical property range containing the target mechanical property as the target implicit equation. Alternatively, the user can also propose a quantity requirement, such as hoping to obtain three three-dimensional curved shell structures with the target mechanical property, and then three implicit equations with the mechanical property range containing the target mechanical property can be selected from the preset equation library as the target implicit equation. Thus, in the step S12, based on the target mechanical property, selecting at least one target implicit equation from the preset equation library can further include: obtaining the structure quantity specified by the user, and selecting the target implicit equation with the mechanical property range containing the target mechanical property corresponding to the structure quantity from the preset equation library. In this way, the target three-dimensional curved shell structure satisfying the quantity requirement of the user can be generated.

[0075] As described above, the user can be provided with an interactive interface to facilitate the user to input or set the target mechanical property, and the interactive interface can also provide a functional control for setting the structure quantity, so as to facilitate the user to set the quantity of the three-dimensional curved shell structure to be generated, and the embodiments of the present disclosure do not limit this.

[0076] In the step S13, based on the target mechanical property, the target parameter value of the variable parameter is determined in the feasible region of each target implicit equation, so that the three-dimensional curved shell structure corresponding to each target implicit equation has the target mechanical property.

[0077] As described above, the feasible region of any implicit equation represents the value range of the variable parameter that makes the three-dimensional curved shell structure corresponding to the implicit equation the same type and a single whole. Optionally, for any target implicit equation, the parameter value of the variable parameter in the target implicit equation can be randomly adjusted in the feasible region of the target implicit equation, so that the three-dimensional curved shell structure of the same type but with different mechanical properties can be formed under the condition that the relative density of the structure is unchanged, until the mechanical property of the three-dimensional curved shell structure corresponding to the target implicit equation reaches the target mechanical property, and the target parameter value is obtained. Thus, in one possible implementation, in the step S13, based on the target mechanical property, the target parameter value of the variable parameter is determined in the feasible region of each target implicit equation, so that the three-dimensional curved shell structure corresponding to each target implicit equation has the target mechanical property, which can include:

[0078] For any target implicit equation, the parameter value of the variable parameter in the target implicit equation is randomly selected in the feasible region of the target implicit equation;

[0079] The simulation mechanical property of the three-dimensional curved shell structure corresponding to the target implicit equation with the randomly selected parameter value is determined by using the finite element simulation analysis technology;

[0080] In a case where the simulated mechanical property does not reach the target mechanical property, the parameter value of the variable parameter of the target implicit equation is randomly selected again from the feasible region of the target implicit equation until the simulated mechanical property reaches the target mechanical property.

[0081] In a case where the simulated mechanical property reaches the target mechanical property, the randomly selected parameter value is determined as the target parameter value.

[0082] As described above, the three-dimensional curved shell structure corresponding to the target implicit equation at any parameter value can be generated and the mechanical property of the three-dimensional curved shell structure can be calculated by using any open-source finite element analysis software in the field, that is, the finite element simulation and the mechanical property analysis of the three-dimensional curved shell structure can be implemented, and the embodiments of the present disclosure do not limit this.

[0083] The above-described manner of determining the target parameter value by randomly selecting the parameter value of the variable parameter of the target implicit equation from the feasible region of the target implicit equation can be understood as a manner of traversing the parameter value in the feasible region to obtain the target parameter value satisfying the target mechanical property. For example, it is assumed that the above-described equation ③, equation and equation are target implicit equations, Figure 5 the (a), (b) and (c) in the equations respectively show the shape of the three-dimensional curved shell structure generated by randomly selecting four groups of parameter values in the feasible region of the three equations, as shown in Figure 5 the shape of the three-dimensional curved shell structure generated by the different parameter values of the variable parameter in the same equation is different, so that the mechanical property is different, but the shape remains similar (that is, all are of the same type); further, the mechanical property of the three-dimensional curved shell structure at different parameter values can be obtained by performing finite element simulation and analysis on the three-dimensional curved shell structure at different parameter values of each target implicit equation, so as to select the parameter value at which the simulated mechanical property reaches the target mechanical property as the target parameter value.

[0084] Alternatively, the embodiments of the present disclosure also provide an implementation manner of predicting the target parameter value by using a model, by which the determination efficiency of the target parameter value can be improved, and further the generation efficiency of the target three-dimensional curved shell structure can be improved. Specifically, in a possible implementation manner, in the step S13, the target parameter value of the variable parameter of each target implicit equation when the three-dimensional curved shell structure corresponding to each target implicit equation has the target mechanical property can be determined in the feasible region of each target implicit equation based on the target mechanical property, which can include:

[0085] predicting the target parameter value of the variable parameter of each target implicit equation in the feasible region of each target implicit equation by using a parameter prediction model based on each target implicit equation and the target mechanical property;

[0086] The parameter prediction model is obtained by training a generative adversarial network using a dataset, which includes multiple real parameter values ​​of the variable parameters of each implicit equation in multiple implicit equations within the feasible region, as well as the real mechanical properties corresponding to each real parameter value.

[0087] It should be understood that the parameter prediction model is trained on a dataset constructed using real parameter values ​​sampled within the feasible region of the implicit equation. Therefore, the parameter prediction model must predict the target parameter values ​​of the variable parameters for each target implicit equation within the feasible region of each target implicit equation. Specifically, for any target implicit equation, the target implicit equation and the target mechanical properties can be input into the parameter prediction model to obtain the target parameter values ​​of the variable parameters predicted by the parameter prediction model that enable the three-dimensional curved shell structure corresponding to the target implicit equation to possess the target mechanical properties.

[0088] In practical applications, within the feasible region of any implicit equation, parameter values ​​of variable parameters can be sampled, for example, with a step size of 0.5, and finite element analysis software can be used to calculate the actual mechanical properties (e.g., anisotropy) corresponding to the sampled true parameter values, thereby constructing a dataset containing parameter-performance pairs. For example, Figure 6 (a), (b), and (c) in the figure respectively show equation ③ and equation ④ above. and equations A schematic diagram showing different true parameter values ​​sampled in 0.5 increments within their respective feasible regions and their corresponding anisotropy degrees. It should be understood that... Figure 6 We can obtain equation ③ above, equation ④ and equations The dataset consists of the true parameter values ​​and the corresponding anisotropy degrees. The data in the dataset can then be standardized and preprocessed, and a parameter prediction model can be trained based on a generative adversarial network. It should be understood that the dataset may include various true parameter values ​​sampled from all or part of the implicit equations in the aforementioned preset equation library within the feasible region, as well as the true mechanical properties corresponding to each true parameter value. This disclosure embodiment does not limit the method of acquiring the data in the aforementioned dataset or the amount of data.

[0089] The generative adversarial network (GAN) includes a generator and a discriminator. This disclosure does not limit the network type or structure of the GAN; for example, a Conditional Generative Adversarial Network (CGAN) can be specifically used, and this disclosure does not limit this approach. Therefore, in one possible implementation, the training process of the above parameter prediction model may include:

[0090] Step S21, inputting the implicit equation, the corresponding real mechanical property and random noise into the generator to obtain a predicted parameter value output by the generator, for any implicit equation in the data set and the real mechanical property corresponding to any real parameter value of the implicit equation;

[0091] Step S22, inputting the predicted parameter value and the corresponding real mechanical property into the discriminator to obtain a first discrimination result output by the discriminator, the first discrimination result representing the probability that the input predicted parameter value is a real parameter value;

[0092] Step S23, inputting the real parameter value of the implicit equation and the corresponding real mechanical property into the discriminator to obtain a second discrimination result output by the discriminator, the second discrimination result representing the probability that the input real parameter value is a real parameter value;

[0093] Step S24, optimizing the model parameters of the discriminator based on the difference between the first discrimination result and the second discrimination result, and optimizing the model parameters of the generator based on the first discrimination result to obtain trained generator and discriminator; wherein the parameter prediction model is the trained generator.

[0094] In step S21, a certain implicit equation and the real mechanical property of the implicit parameter under a certain real parameter value can be randomly selected from the data set, for example, based on Table 1 above, equation ③ can be selected, and the real parameter value is selected as The real mechanical property of "anisotropy degree of 1.79 and relative density of 15.93%" can be input into the generator, and the predicted parameter value output by the generator can be obtained, wherein more training data can be generated by adding multiple groups of random noise and input groups of the same real mechanical property to make the generator generate multiple different predicted parameter value output groups that meet the same mechanical property requirements, which is beneficial to improve the reliability and robustness of the model prediction after training.

[0095] The random noise is a parameter for controlling the data quality (or accuracy) of the generator output. The random noise can be multi-dimensional noise data. A random noise with a moderate dimension can be used as input. A random noise with a too low dimension (e.g., 2 dimensions) can express very limited variations. A moderate dimension (e.g., 100 dimensions) can combine extremely rich and diverse results. The noise dimension determines how many different variations the generator can produce, that is, how many buttons are used to control the quality of the parameter values of the output. It should be noted that the random noise is not related to the number of sample groups of the output. The generator can be used for single generation, that is, 1 group of random noise + conditions (i.e., real mechanical properties and implicit equations) → 1 sample (i.e., a group of predicted parameter values). For example, in the case of single generation, the input noise shape can be represented as [1, 100], that is, 1 group of 100-dimensional noise, the condition input shape can be represented as [1, condition dimension], and the output result shape can be represented as [1, output dimension] 1 sample. Alternatively, the generator can be used for batch generation, that is, N groups of noise + conditions → N samples. For example, in the case of batch generation, if 8 samples are expected to be generated, the input noise shape can be represented as [8, 100], that is, 8 groups of 100-dimensional noise, the condition input shape can be represented as [8, condition dimension], and the output result shape can be represented as [8, output dimension], that is, 8 samples.

[0096] It should be understood that the model training can be performed in multiple batches. For each batch, a batch of training data can be randomly extracted from the data set. The batch of training data can include at least one implicit equation and the real mechanical properties corresponding to each real parameter value of each implicit equation. Then, the predicted parameter values corresponding to each real mechanical property of each implicit equation in a batch can be obtained by using the generator according to the implementation manner of step S21. For the same implicit equation and the same real mechanical property, the number of groups of input random noise determines the number of groups of output predicted parameter values. The number of groups of input during training can be determined according to personal needs, and the present embodiment does not limit this.

[0097] In step S22, the real mechanical property corresponding to the predicted parameter value is the real mechanical property based on which the predicted parameter value is generated by the generator. For example, if the equation ③, “the anisotropy degree is 1.79 and the relative density is 15.93%”, and the random noise are input into the generator in step S21, the predicted parameter value output by the generator is In step S22, the predicted parameter value is and the real mechanical property "anisotropy degree of 1.79 and relative density of 15.93%" are input into the discriminator, to obtain a first discrimination result output by the discriminator, which is equivalent to scoring the predicted parameter value by using the discriminator. The discrimination result output by the discriminator can be represented as a score value or a probability value. If the first discrimination result is larger (i.e., the score value or the probability value is higher), it means that the discriminator considers the predicted parameter value to be more real. Conversely, if the first discrimination result is smaller (i.e., the score value or the probability value is lower), it means that the discriminator considers the predicted parameter value to be less real.

[0098] In step S23, the real parameter value corresponding to the implicit equation input into the generator in step S21 and the corresponding real mechanical property are input into the discriminator. For example, if the equation ③ and "anisotropy degree of 1.79 and relative density of 15.93%" and random noise are input into the generator in step S21, the real parameter value and the corresponding real mechanical property "anisotropy degree of 1.79 and relative density of 15.93%" are input into the discriminator in step S23, to obtain a second discrimination result output by the discriminator, which is equivalent to scoring the real predicted value by using the discriminator. Correspondingly, if the second discrimination result is larger (i.e., the score value or the probability value is higher), it means that the discriminator considers the real parameter value to be more real. Conversely, if the second discrimination result is smaller (i.e., the score value or the probability value is lower), it means that the discriminator considers the real parameter value to be less real.

[0099] In step S24, the training target of the discriminator is to give high scores (i.e., output high probabilities) to real data (i.e., real parameter values and real mechanical properties) and low scores (i.e., output low probabilities) to predicted data (i.e., predicted parameter values and real mechanical properties). Thus, the first discrimination result represents the score of the discriminator on the predicted data, and it is desired that the first discrimination result output by the discriminator be small. The second discrimination result represents the score of the discriminator on the real data, and it is desired that the second discrimination result output by the discriminator be large. Thus, the difference or absolute difference or mean square error between the first discrimination result and the second discrimination result can be used as the loss of the discriminator to optimize the model parameters of the discriminator. For example, the loss function of the discriminator can be represented as: Loss_D = [D(Fake_Pairs)] - [D(Real_Pairs)], D(Fake_Pairs) represents the first discrimination result, and [D(Real_Pairs)] represents the second discrimination result. The smaller the Loss_D, the better the performance of the discriminator (i.e., giving high scores to real data and low scores to predicted data). After the loss Loss_D of the discriminator is calculated, the parameters of the generator can be fixed, and the model parameters of the discriminator are updated by calculating the gradient through back propagation to achieve the optimization of the parameters of the discriminator, so that the discriminator becomes more intelligent.

[0100] In step S24, the training target of the generator is opposite to the discriminator, that is, the training target of the generator is to strive to let the discriminator give high scores to the predicted parameter values generated by itself. Therefore, the loss of the generator can be determined directly based on the second discrimination result output by the discriminator, for example, the loss function of the generator can be represented as Loss G = - [D (Fake Pairs)], then the model parameters of the generator can be optimized with the goal of minimizing Loss G, which is equivalent to maximizing D (Fake Pairs). In this way, the model parameters of the generator are optimized through the loss Loss G, and the purpose is to make the discriminator think that the predicted parameter values generated by the generator are “true”. Thus, after obtaining the loss Loss G of the generator by using the first discrimination result, the parameters of the discriminator can be fixed, and the model parameters of the generator can be updated by calculating the gradient through back propagation with the goal of minimizing the loss of the generator, so that the fake ability of the generator is stronger, that is, the predicted parameter values generated by the generator are more true.

[0101] As can be seen from the above, since the real parameter values in the data set do not appear in the loss Loss G of the generator. The generator does not care whether the predicted parameter values generated by itself are the same as a certain real parameter value, but only cares whether the predicted parameter values generated by itself can be judged as true by the current discriminator. The essence of the whole training process is that the discriminator strives to expand the score gap between the true and false samples by minimizing Loss D = [D (Fake Pairs)] - [D (Real Pairs)]. The generator strives to narrow this gap by minimizing Loss G = - [D (Fake Pairs)], so that the score of the false sample (i.e. the predicted parameter value) approaches the true sample (i.e. the real parameter value). In this training process, the game of “you chase me” between the generator and the discriminator continues until the predicted parameter values generated by the generator cannot be distinguished from the real parameter values by the discriminator. At this time, a high-quality generator is obtained, and then the trained high-quality generator can be used as a parameter prediction model to predict the target parameter values under the target implicit equation and the target mechanical performance, so as to quickly and efficiently generate a target three-dimensional curved shell structure with target mechanical performance.

[0102] In practical applications, the above generator and discriminator can be trained in stages, for example, a batch of data can be extracted from the data set "real parameter value-mechanical property" (i.e. real data Real Pairs). At the same time, the generator is used to obtain the "predicted parameter value-mechanical property" of the batch of data (i.e. predicted data Fake Pairs). The two batches of data are input into the discriminator, and the discriminator outputs a discrimination result for each pair of data in the two batches of data. Then the loss of the discriminator is calculated, the parameters of the generator are fixed, the gradient is calculated by back propagation and the parameters of the discriminator are updated. Then the generator G is used again to generate a new batch of predicted data (new Fake Pairs) based on the implicit equation, random noise and real mechanical property. The new batch of predicted data is input into the discriminator whose parameters have been fixed, and the discriminator scores. Then the loss of the discriminator is calculated, the parameters of the discriminator D are fixed, the gradient is calculated by back propagation and the model parameters of the generator G are updated. It should be understood that the above training of the generator and the discriminator can be iterated multiple times until the loss converges or is zero, and the trained generator is used as a parameter prediction model.

[0103] Exemplarily, Figure 7 A schematic diagram showing the training process of a generative adversarial network is shown as follows: Figure 7 As shown, the generator G takes random noise and implicit equation and real mechanical property sampled from the data set as input, and outputs the predicted parameter value of the variable parameter; then the discriminator D can take the predicted parameter value and the corresponding real mechanical property as input, and take the real parameter value and the corresponding real mechanical property as input, to judge whether the input parameter value and mechanical property conform to the real distribution (i.e. to judge the probability that the input parameter value is the real parameter value), if it is judged as false, output "0" and feedback to the generator to regenerate, if it is judged as true, output "1". By alternately training the generator and the discriminator, the trained generator can accurately generate parameter values that meet the target mechanical property; finally, the trained generator is used as a parameter prediction model to generate the parameter value of the variable parameter according to the required target mechanical property, and the mechanical property and reliability of the predicted parameter value of the model can also be verified by finite element simulation, so as to obtain a three-dimensional curved shell structure design that meets the target mechanical property. That is, by inputting the target implicit equation and target mechanical property into the trained generator (i.e. parameter prediction model), the target parameter value of the three-dimensional curved shell structure with the target mechanical property can be generated. It is equivalent to adjusting the parameter value of the implicit equation through the parameter prediction model to make the mechanical property close to the target mechanical property, and the three-dimensional curved shell structure that meets the performance requirement can be obtained by finite element simulation verification.

[0104] It should be understood that, regardless of whether the target parameter value is predicted by using the parameter prediction model or determined by traversing the parameter values in the feasible region, for each target implicit equation, one or more sets of target parameter values that satisfy the target mechanical property can be determined, and the number of target parameter values determined by each target implicit equation of the embodiments of the present disclosure is not limited. For example, assuming that the target mechanical property is isotropic and the relative density is 15%, for the above equation ③, equation and equation , respectively, equation ③, equation and equation and the target mechanical property are input into the parameter prediction model, for equation ③, the parameter prediction model outputs the target parameter value that realizes isotropy and a relative density of 15% as ; for equation , the parameter prediction model outputs two effective parameter value combinations, which are and , that is, for equation , two sets of target parameter value combinations can make the generated target three-dimensional curved shell structure have isotropy and a relative density of 15%; for equation , the parameter prediction model outputs the target parameter value that realizes isotropy and a relative density of 15% as .

[0105] In step S14, at least one target three-dimensional curved shell structure is generated based on the target parameter value of the variable parameter in at least one target implicit equation, and the target three-dimensional curved shell structure has the target mechanical property.

[0106] In practical applications, given the target parameter value of the variable parameter in any target implicit equation, the corresponding target three-dimensional curved shell structure can be generated by using finite element analysis software or other modeling software, and the generation process of the three-dimensional curved shell structure is not limited in the embodiments of the present disclosure. Therefore, based on the target parameter value of the variable parameter in the at least one target implicit equation, generating at least one target three-dimensional curved shell structure includes: for any target implicit equation, using finite element simulation analysis technology to generate a target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the target implicit equation, and calculating the real mechanical property of the target three-dimensional curved shell structure to verify whether the real mechanical property of the target three-dimensional curved shell structure reaches the target mechanical property.

[0107] In practical applications, the real mechanical property of the target three-dimensional curved shell structure reaching the target mechanical property can be that the error between the real mechanical property and the target mechanical property of the target three-dimensional curved shell structure is within a specified error range, and of course, the real mechanical property can be the same as the target mechanical property. If the real mechanical property of the target three-dimensional curved shell structure under a target parameter value of a variable parameter of a target implicit equation does not reach the target mechanical property (for example, the error between the real mechanical property and the target mechanical property of the target three-dimensional curved shell structure exceeds the specified error range), the above step S13 can be re-executed to re-generate the target parameter value of the variable parameter of the target implicit equation, or the above steps S12 and S13 can be re-executed to re-select a new target implicit equation from the preset equation library and determine the target parameter value for the new target implicit equation, or the target three-dimensional curved shell structure whose real mechanical property does not reach the target mechanical property can be directly discarded, and the embodiments of the present disclosure do not make any limitation.

[0108] Exemplarily, it is assumed that the above equation ③, equation and equation are target implicit equations, the target parameter value of equation ③ is , that is, the implicit equation of the target three-dimensional curved shell structure with isotropy and a relative density of 15% includes: ; the two groups of target parameter values and of equation , the implicit equation of the target three-dimensional curved shell structure with isotropy and a relative density of 15% further includes: , ; the target parameter value of equation is , and the implicit equation of the target three-dimensional curved shell structure with isotropy and a relative density of 15% further includes: .

[0109] Based on the four implicit equations of the above target three-dimensional curved shell structure, Figure 8 (a), (b), (c) and (d) respectively show the shape schematic diagrams of the four target three-dimensional curved shell structures, that is, Figure 8 (a) in the structure ③ shown in is generated based on Figure 8 (b) in the structure -1 shown in is generated based on Figure 8 (c) in the structure -2 shown in is generated based on Figure 8 (d) in the structure shown in is generated based on

[0110] Table 2 shows the mechanical property list obtained by performing finite element simulation on the above-mentioned Figure 8 structures ③, structures -1, structures -2 and structures As can be seen from Table 2, the anisotropy degrees of the four structures are close to 1, which means that the four structures are isotropic, and the relative densities are all close to 15%. Although there is an error between the mechanical properties of the four structures and the target mechanical properties, within the error range, it can be considered that the four structures all meet the target mechanical property requirements of isotropy and a relative density of 15%, and the four structures are all fed back to the user. Of course, the target three-dimensional curved shell structure closest to the target mechanical properties (for example, structure ) can be selected to feed back to the user, and the embodiments of the present disclosure do not make any limitation in this regard.

[0111] Table 2 Mechanical property list

[0112]

[0113] Figure 9 structures ③, structures -1, structures -2 and structures reach isotropy, and the comparison between the curved shell structures and other existing curved shell structures and lattice structures reaching isotropy under different relative densities is shown. Figure 10 structures ③, structures -1, structures -2 and structures reach isotropy, and the comparison between the curved shell structures and other existing curved shell structures and lattice structures reaching isotropy under different relative densities is shown. Figure 11 structures ③, structures -1, structures -2 and structures reach isotropy, and the comparison between the curved shell structures and other existing curved shell structures and lattice structures reaching isotropy under different relative densities is shown. Figure 9 As shown in FIG. 8, the four three-dimensional curved shell structures generated by the method of the embodiments of the present disclosure have a relatively low relative density while having isotropy (i.e., the anisotropy degree is close to 1), and the anisotropy degrees of the other existing curved shell structures (“Schwarz P shell”, “I-WP shell”, “Neovius shell”) are relatively large. As shown in FIG. 9, the stress-strain curves of the isotropic structures under uniaxial compression when the relative density is about 15% are shown. As shown in FIG. 9, the four three-dimensional curved shell structures generated by the method of the embodiments of the present disclosure have a relatively low relative density while having isotropy (i.e., the anisotropy degree is close to 1), and the anisotropy degrees of the other existing curved shell structures (“Schwarz P shell”, “I-WP shell”, “Neovius shell”) are relatively large. Figure 10As shown in (a) and (b) in the table, the four three-dimensional curved shell structures generated by the method of the embodiments of the present disclosure have higher Young's modulus and higher yield strength at a lower relative density and isotropy compared to most of the existing isotropic structures ("isotropic truss", "ISO-COP", "OCT-COP"). Only one isotropic structure ("cubic+octet plate") has better mechanical properties than the isotropic curved shell structures generated by the embodiments of the present disclosure, which means that the target three-dimensional curved shell structures generated by the method of the embodiments of the present disclosure have better mechanical properties. As shown in the table, Figure 11 As shown in the table, the four three-dimensional curved shell structures generated by the method of the embodiments of the present disclosure have better strength than the structures -2.

[0114] In practical applications, after generating the target three-dimensional curved shell structure with the target mechanical properties, any one of the target three-dimensional curved shell structures can be periodically arranged as a basic unit to obtain a three-dimensional curved shell periodic structure. For example, the structure ③ shown in (a) in the table can be periodically arranged in three-dimensional space to obtain a three-dimensional curved shell periodic structure, which can also be referred to as a three-dimensional curved shell type periodic lattice structure, which is equivalent to generating a structure of a porous material. Figure 8

[0115] According to the method of the embodiments of the present disclosure, by obtaining the target mechanical properties specified by the user, selecting the target implicit equation generated based on the three-dimensional function from the preset equation library, and then determining the target parameter value in the feasible region of each target implicit equation, the target three-dimensional curved shell structure with the target mechanical properties can be generated. The method can automatically generate the implicit equation parameter combination that meets the performance requirements in the feasible region according to the target mechanical properties required by the user, thereby automatically and efficiently and systematically generating the target three-dimensional curved shell structure with the target mechanical properties, realizing the automation and high degree of freedom of the generation of the three-dimensional curved shell structure, and meeting the performance requirements of the user on the individualization of the three-dimensional curved shell structure.

[0116] The method of the embodiments of the present disclosure learns from the design idea of biological porous structure and combines the reverse design mode driven by the generative adversarial network to realize the three-dimensional curved shell structure with significant advantages: on the one hand, the generator can directly output the isotropic configuration parameters that meet the requirement of extremely low relative density, significantly improve the porosity while ensuring the performance, and have lower density than the traditional design under the same material, which is more in line with the lightweight demand; on the other hand, the curved shell structure generated by the method of the embodiments of the present disclosure effectively relieves the stress concentration problem in the traditional isotropic truss or plate structure, and its continuous and smooth geometric shape is more conducive to the removal of the unsolidified material in the additive manufacturing process, thereby improving the manufacturing feasibility.

[0117] ​The method of the embodiments of the present disclosure realizes high design automation and freedom by generating a generative adversarial network trained parameter prediction model. The parameter prediction model can automatically generate a large number of parameter combinations of implicit equations that meet the requirements in the feasible region according to the input stiffness, strength, anisotropy and other performance targets, thereby efficiently and systematically designing a three-dimensional curved shell structure with target mechanical properties, and further generating a three-dimensional curved shell type periodic lattice structure with target mechanical properties through periodic arrangement.

[0118] Figure 12 A block diagram of a three-dimensional curved shell structure generation device according to an embodiment of the present disclosure is shown, as shown in the figure, the device comprises: Figure 12

[0119] The acquisition module 121 is configured to acquire target mechanical properties specified by a user.

[0120] The selection module 122 is configured to select at least one target implicit equation from a preset equation library based on the target mechanical properties, wherein the implicit equations in the preset equation library are obtained by combining at least one basic monomial with at least one variable parameter, and the basic monomial is obtained by randomly combining at least one basic trigonometric function with three-dimensional variables.

[0121] The determination module 123 is configured to determine target parameter values of the variable parameters when each target implicit equation corresponds to a three-dimensional curved shell structure with the target mechanical properties in the feasible region of each target implicit equation based on the target mechanical properties. The feasible region of any implicit equation represents the value range of the variable parameters of the three-dimensional curved shell structure corresponding to the implicit equation which is of the same type and a single whole.

[0122] The generation module 124 is configured to generate at least one target three-dimensional curved shell structure based on the target parameter values of the variable parameters in the at least one target implicit equation, and the target three-dimensional curved shell structure has the target mechanical properties.

[0123] In a possible implementation, the determination of the target parameter values of the variable parameters when each target implicit equation corresponds to a three-dimensional curved shell structure with the target mechanical properties in the feasible region of each target implicit equation based on the target mechanical properties comprises: predicting the target parameter values of the variable parameters of each target implicit equation in the feasible region of each target implicit equation based on each target implicit equation and the target mechanical properties by using a parameter prediction model; wherein the parameter prediction model is obtained by training a generative adversarial network using a data set, and the data set includes multiple real parameter values sampled in the feasible region of the variable parameters of each implicit equation in multiple implicit equations, and a real mechanical property corresponding to each real parameter value.

[0124] ​In a possible implementation, the generative adversarial network comprises a generator and a discriminator, and the training process of the parameter prediction model comprises: inputting, for any implicit equation in the data set and a real mechanical property corresponding to any real parameter value of the implicit equation, the implicit equation, the corresponding real mechanical property and random noise into the generator to obtain a predicted parameter value output by the generator; inputting the predicted parameter value and the corresponding real mechanical property into the discriminator to obtain a first discrimination result output by the discriminator, the first discrimination result representing a probability that the input predicted parameter value is a real parameter value; inputting the real parameter value of the implicit equation and the corresponding real mechanical property into the discriminator to obtain a second discrimination result output by the discriminator, the second discrimination result representing a probability that the input real parameter value is a real parameter value; optimizing model parameters of the discriminator based on a difference between the first discrimination result and the second discrimination result, and optimizing model parameters of the generator based on the first discrimination result to obtain a trained generator and discriminator; and the parameter prediction model is the trained generator.

[0125] In a possible implementation, the determining, based on the target mechanical property, a target parameter value of the variable parameter when each target implicit equation is used to make the three-dimensional curved shell structure have the target mechanical property, in a feasible region of each target implicit equation, comprises: randomly selecting, for any target implicit equation, a parameter value of the variable parameter in the target implicit equation from the feasible region of the target implicit equation; determining a simulation mechanical property of the three-dimensional curved shell structure corresponding to the target implicit equation with the randomly selected parameter value by using a finite element simulation analysis technology; in a case where the simulation mechanical property does not reach the target mechanical property, randomly selecting again a parameter value of the variable parameter of the target implicit equation from the feasible region of the target implicit equation until the simulation mechanical property reaches the target mechanical property; and in a case where the simulation mechanical property reaches the target mechanical property, determining the randomly selected parameter value as the target parameter value.

[0126] In a possible implementation, the preset equation library further comprises a mechanical property range corresponding to each implicit equation, and the mechanical property range corresponding to any implicit equation represents a range of mechanical properties of a three-dimensional curved shell structure generated based on the implicit equation in a feasible region of the implicit equation; and the selecting, based on the target mechanical property, at least one target implicit equation from the preset equation library comprises: selecting at least one target implicit equation whose mechanical property range contains the target mechanical property from the preset equation library; or obtaining a structure quantity specified by a user and selecting a target implicit equation whose mechanical property range contains the target mechanical property from the preset equation library, the mechanical property range corresponding to the structure quantity.

[0127] In a possible implementation, the generating the at least one target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the at least one target implicit equation comprises: for any target implicit equation, generating a target three-dimensional curved shell structure based on the target parameter value of the variable parameter in the target implicit equation by using a finite element simulation analysis technology, and calculating the real mechanical performance of the target three-dimensional curved shell structure to verify whether the real mechanical performance of the target three-dimensional curved shell structure reaches the target mechanical performance.

[0128] In a possible implementation, the apparatus further includes a periodic structure generation module configured to, for any target three-dimensional curved shell structure, periodically arrange the target three-dimensional curved shell structure as a basic unit to obtain a three-dimensional curved shell periodic structure.

[0129] In some embodiments, the apparatus provided by the embodiments of the present disclosure has functions or includes modules that can be used to perform the methods described in the above method embodiments, and the specific implementation can be referred to the description of the above method embodiments. For brevity, details are not described here.

[0130] The embodiments of the present disclosure further provide an electronic device, including a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to implement the steps of the above method.

[0131] The embodiments of the present disclosure further provide a non-volatile computer readable storage medium having a computer program stored thereon, and the computer program is executed by a processor to implement the steps of the above method.

[0132] The embodiments of the present disclosure further provide a computer program product, including a computer program or a non-volatile computer readable storage medium carrying the computer program, and the computer program is executed by a processor to implement the steps of the above method.

[0133] Figure 13 A block diagram of an electronic device 1900 according to an embodiment of the present disclosure is shown. For example, the electronic device 1900 can be provided as a server or a terminal device. Referring to Figure 13 , the electronic device 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932, for storing instructions executable by the processing component 1922, such as an application program. The application program stored in the memory 1932 can include one or more than one module each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute the instructions to perform the above method.

[0134] The electronic device 1900 can further include a power supply component 1926 configured to perform power management of the electronic device 1900, a wired or wireless network interface 1950 configured to connect the electronic device 1900 to a network, and an input / output interface 1958 (I / O interface). The electronic device 1900 can operate based on an operating system stored in the memory 1932, such as Windows Server TM , Mac OS X TM , Unix TM , Linux TM , FreeBSD TM or the like.

[0135] In exemplary embodiments, there is also provided a non-transitory computer readable storage medium, such as the memory 1932 including computer program instructions, which can be executed by the processing component 1922 of the electronic device 1900 to perform the above method.

[0136] The computer readable storage medium can be a tangible device that can retain and store instructions for execution by a processor. The computer readable storage medium can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or punched tape, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0137] The computer program (or computer readable program instructions) described herein can be downloaded from a computer readable storage medium to various computing / processing devices by way of a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0138] Computer readable program instructions for carrying out operations of the present disclosure can be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions can execute entirely on the user's computing / processing device, partly on the user's computing / processing device, as a stand-alone software package, partly on the user's computing / processing device and partly on a remote computing / processing device or entirely on the remote computing / processing device or server. In the latter scenario, the remote computing / processing device can be connected to the user's computing / processing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computing / processing device, for example, through the Internet using an Internet Service Provider. In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate array (FPGA), or programmable logic array (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0139] The computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0140] These computer readable program instructions can be provided to a processor of a general purpose computer, special purpose computer, 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, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can include a non-transitory computer readable storage medium that can be a computer- readable storage medium having no data storage cycles that change state. The instructions can be executed by one or more processors of a computer, to cause a series of operational steps to be performed on the computer to produce a computer-implemented process. The instructions can also cause one or more processors of a computer or other programmable data processing apparatus to

[0141] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0142] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0143] Embodiments of the present disclosure have been described above, and the description is intended to be illustrative of the embodiments and not restrictive of the disclosure. Many modifications and variations of the described embodiments are possible in light of this disclosure without departing from the scope and spirit of the described embodiments. The choice of words in this document is intended to best explain the principles of the embodiments, the practical application, or technical improvement over prior art, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for generating a three-dimensional curved shell structure, characterized in that, include: Obtain the target mechanical properties specified by the user; Based on the target mechanical properties, at least one target implicit equation is selected from a preset equation library. The implicit equation in the preset equation library is obtained by combining at least one basic monomial with at least one variable parameter. The basic monomial is obtained by randomly combining at least one basic trigonometric function based on three-dimensional variables. Based on the target mechanical properties, within the feasible domain of each target implicit equation, the target parameter values ​​of the variable parameters that enable the three-dimensional curved shell structure corresponding to each target implicit equation to possess the target mechanical properties are determined; wherein, the feasible domain of any implicit equation represents the range of values ​​of the variable parameters that make the three-dimensional curved shell structure corresponding to the implicit equation the same type and a single whole. Based on the target parameter values ​​of the variable parameters in the at least one target implicit equation, at least one target three-dimensional curved shell structure is generated, and the target three-dimensional curved shell structure possesses the target mechanical properties.

2. The method according to claim 1, characterized in that, The step of determining the target parameter values ​​for the variable parameters that enable the three-dimensional curved shell structure corresponding to each target implicit equation to possess the target mechanical properties within the feasible region of each target implicit equation, based on the target mechanical properties, includes: Using a parametric prediction model, based on each target implicit equation and the target mechanical properties, the target parameter values ​​of the variable parameters of each target implicit equation are predicted within the feasible region of each target implicit equation. The parameter prediction model is obtained by training a generative adversarial network using a dataset. The dataset includes multiple real parameter values ​​of the variable parameters of each implicit equation in multiple implicit equations within the feasible region, as well as the real mechanical properties corresponding to each real parameter value.

3. The method according to claim 2, characterized in that, The generative adversarial network includes a generator and a discriminator, and the training process of the parameter prediction model includes: For any implicit equation in the dataset and the actual mechanical properties corresponding to any true parameter value of the implicit equation, the implicit equation, the corresponding actual mechanical properties, and random noise are input into the generator to obtain the predicted parameter values ​​output by the generator. The predicted parameter values ​​and the corresponding actual mechanical properties are input into the discriminator to obtain the first discrimination result output by the discriminator. The first discrimination result represents the probability that the input predicted parameter value is the actual parameter value. The true parameter values ​​of the implicit equation and the corresponding true mechanical properties are input into the discriminator to obtain a second discrimination result output by the discriminator. The second discrimination result represents the probability that the input true parameter value is the true parameter value. Based on the difference between the first discrimination result and the second discrimination result, the model parameters of the discriminator are optimized, and the model parameters of the generator are optimized based on the first discrimination result, so as to obtain a trained generator and discriminator; The parameter prediction model is a pre-trained generator.

4. The method according to claim 1, characterized in that, The step of determining the target parameter values ​​for the variable parameters that enable the three-dimensional curved shell structure corresponding to each target implicit equation to possess the target mechanical properties within the feasible region of each target implicit equation, based on the target mechanical properties, includes: For any target implicit equation, randomly select parameter values ​​for the variable parameters in the target implicit equation from within the feasible region of the target implicit equation. The simulated mechanical properties of a three-dimensional curved shell structure corresponding to a target implicit equation with randomly selected parameter values ​​were determined using finite element simulation analysis technology. If the simulated mechanical performance does not reach the target mechanical performance, the parameter values ​​of the variable parameters of the target implicit equation are randomly selected again from the feasible region of the target implicit equation until the simulated mechanical performance reaches the target mechanical performance. When the simulated mechanical properties have reached the target mechanical properties, the randomly selected parameter values ​​are determined as the target parameter values.

5. The method according to any one of claims 1 to 4, characterized in that, The preset equation library also includes the mechanical performance range corresponding to each implicit equation. The mechanical performance range corresponding to any implicit equation represents the range of mechanical performance of the three-dimensional curved shell structure generated based on the implicit equation within the feasible domain of the implicit equation. The step of selecting at least one target implicit equation from a preset equation library based on the target mechanical properties includes: Select at least one target implicit equation from the preset equation library that includes the target mechanical properties within a specific mechanical property range; or... Obtain the number of structures specified by the user, and select from the preset equation library the target implicit equations whose mechanical performance range corresponds to the number of structures and includes the target mechanical performance.

6. The method according to any one of claims 1 to 4, characterized in that, The generation of at least one target three-dimensional curved shell structure based on the target parameter values ​​of the variable parameters in the at least one target implicit equation includes: For any target implicit equation, the finite element simulation analysis technique is used to generate a target three-dimensional curved shell structure based on the target parameter values ​​of the variable parameters in the target implicit equation, and the actual mechanical properties of the target three-dimensional curved shell structure are calculated to verify whether the actual mechanical properties of the target three-dimensional curved shell structure reach the target mechanical properties.

7. The method according to any one of claims 1 to 4, characterized in that, The method further includes: For any target three-dimensional curved shell structure, the target three-dimensional curved shell structure is used as a basic unit and arranged periodically to obtain a three-dimensional curved shell periodic structure.

8. A three-dimensional curved shell structure generation device, characterized in that, include: The acquisition module is used to acquire the target mechanical properties specified by the user. The selection module is used to select at least one target implicit equation from a preset equation library based on the target mechanical properties. The implicit equation in the preset equation library is obtained by combining at least one basic monomial with at least one variable parameter. The basic monomial is obtained by randomly combining at least one basic trigonometric function using three-dimensional variables. The determination module is used to determine, based on the target mechanical properties, the target parameter values ​​of the variable parameters that enable the three-dimensional curved shell structure corresponding to each target implicit equation to possess the target mechanical properties within the feasible domain of each target implicit equation; wherein, the feasible domain of any implicit equation represents the range of values ​​of the variable parameters that make the three-dimensional curved shell structure corresponding to the implicit equation the same type and a single whole. A generation module is used to generate at least one target three-dimensional curved shell structure based on the target parameter values ​​of the variable parameters in the at least one target implicit equation, wherein the target three-dimensional curved shell structure possesses the target mechanical properties.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A non-volatile computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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