Method for optimizing auxetic metamaterial filling curved surface structure and application thereof

Abstract

The invention discloses an auxetic metamaterial filling curved surface structure optimization method, which comprises the steps of selecting a curved surface parameterization model, dividing structured grids in a curved surface parameter domain, determining the type of a negative Poisson's ratio microstructure of a filling curved surface structure and volume fraction constraint, and optimizing the filling curved surface structure according to the type of the negative Poisson's ratio microstructure. Designing a plurality of negative Poisson's ratio microstructures in the volume fraction constraint by using a parameterized color level set method, uniformly filling the microstructures into the curved surface structure, simulating the relationship among the volume fractions of the microstructures, the level set function and various coefficients in the elastic matrix through an interpolation / fitting algorithm, establishing an optimized column formula of the volume fractions of the microstructures, and calculating the volume fractions of the microstructures according to the optimized column formula. And obtaining a microstructure level set function corresponding to the optimized volume fraction of each microstructure unit, and assembling and inversely mapping the microstructure level set function into a curved surface design domain to obtain a multi-scale curved surface component configuration subjected to gradient auxetic metamaterial filling optimization. The functional metamaterial can be effectively used in the structure of a complex curved surface structure, and the integrated design of the impact resistance function and the bearing performance is achieved.

Description

Technical Field

[0001] This application relates to the technical field of structural optimization design, and particularly to a method for optimizing a surface structure filled with auxetic metamaterials, a device for optimizing a surface structure filled with auxetic metamaterials, an electronic device, and a computer-readable storage medium. Background Art

[0002] As the core "skeleton" of equipment in fields such as aviation, aerospace, and navigation, surface structural components play a decisive role in the stable and effective operation of equipment in gaseous and flowing environments. Taking the fan blade of an aeroengine as an example, its working conditions are harsh. It not only bears huge centrifugal loads and alternating dynamic loads in a complex environment but also faces the threat of foreign object impact. This requires that the design of aviation blades needs to consider both the structural load-bearing requirements and the structural anti-impact functional requirements. Therefore, these large-scale and integral complex surface components begin to adopt multi-scale lattice / metamaterial filling configurations in order to achieve their integrated design of function and structure.

[0003] However, existing structural design means encounter difficulties in ensuring the comprehensive performance of structures: (1) There are cross-scale geometric matching problems between surface components with variable curvature shapes and regular-shaped filling microstructures; (2) There are also integration problems of functions and performances between metamaterial filling and integral surface structural components.

[0004] Therefore, how to combine the functional advantages of auxetic metamaterials with a multi-scale surface design method based on conformal geometry to form a set of optimization design methods for multi-scale surface structures filled with auxetic metamaterials, so as to effectively use functional metamaterials in the construction of complex surface structures and achieve the integrated design of anti-impact functions and load-bearing performances is an urgent problem to be solved currently. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art, the embodiments of the present invention provide a method for optimizing a surface structure filled with auxetic metamaterials and its application, which can effectively use functional metamaterials in the construction of complex surface structures and achieve the integrated design of anti-impact functions and load-bearing performances.

[0006] On the one hand, an embodiment of the present invention proposes a method for optimizing a surface structure filled with auxetic metamaterials, including: selecting a corresponding surface parameterization model according to the surface structure characteristics, and dividing a structured grid in the surface parameter domain according to the surface parameterization model; determining the type and volume fraction constraint of the negative Poisson's ratio microstructure to be filled into the surface structure, and generating a number of negative Poisson's ratio microstructures within the volume fraction constraint by using the parametric color level set method, and uniformly filling the negative Poisson's ratio microstructures into the surface structure to form an initial design; simulating the relationship between the microstructure volume fraction and the coefficients in the level set function and the elastic matrix through an interpolation algorithm and / or a fitting algorithm, so as to establish an optimization formulation of the microstructure volume fraction in the surface parameter domain; optimizing each microstructure unit in the initial design according to the optimization formulation, obtaining the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit, and assembling the level set function in the surface parameter domain; inversely mapping the assembled level set function into the surface design domain to obtain a multi-scale surface component configuration optimized by gradient auxetic metamaterial filling.

[0007] In an embodiment of the present invention, establishing an optimization formulation of the volume fraction in the surface parameter domain includes: taking the minimization of the compliance of the surface configuration under the volume fraction constraint under an external load as the design goal, and establishing an optimization design formulation of the multi-scale surface structure filled with gradient auxetic metamaterial microstructures as:

[0008]

[0009] Wherein, represents the pseudo-density field formed by the microstructure volume fraction in the parameter domain, C represents the compliance value of the overall structure, and are respectively the upper and lower bounds of the microstructure volume fraction, is the overall stiffness matrix assembled according to the gradient microstructure equivalent elastic coefficient matrix, U and F are respectively the displacement vector and the external load vector of the node, υ i is the volume or area of each microstructure design domain, is the volume or area of the overall macroscopic design domain, V is the overall volume fraction constraint of the optimization design, is the optimized volume fraction control function, represents the actual volume fraction within each microstructure unit, is the elastic matrix of the auxetic metamaterial microstructure after fitting operation, and ⊙ represents the Hadamard product.

[0010] In an embodiment of the present invention, the elastic matrix of the auxetic metamaterial microstructure The fitting process includes: obtaining the microstructural configurations of auxetic metamaterials with different volume fractions through topology optimization, and calculating the equivalent elastic matrix of each microstructure; wherein, the equivalent elastic matrix is obtained by performing a Hadamard product on the zero terms of the elastic matrix of the substrate being set to "1" and the coefficients in the elastic matrix of the auxetic metamaterial microstructure in which the coefficients in the elastic matrix of the auxetic metamaterial microstructure and the equivalent elastic tensor of the equivalent elastic matrix are both continuous functions of the volume fraction.

[0011] In an embodiment of the present invention, the obtaining of the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit according to the optimized formulation includes: refining all the nodes of the multiple microstructure level set functions generated by topology optimization onto the same set of grids to form a set of structured grid nodes x i，j , where i and j respectively represent the indices of the grid nodes; arranging the level set functions of the multiple microstructures in sequence according to the volume fraction to obtain their composition set, where K is the number of level set functions generated by topology optimization; for each node x i，j on the grid and its corresponding expansion coefficient α(x i，j ), interpolating the volume fraction of the corresponding microstructure with the expansion coefficient to obtain a continuous function of the expansion coefficient of the parameterized level set function corresponding to each microstructure with respect to the volume fraction; for each level set function node, after calculating the expansion coefficient and the corresponding continuous function based on the corresponding one, obtaining the level set function of the microstructure corresponding to the volume fraction constraint of each optimized microstructure.

[0012] On the other hand, an embodiment of the present invention also provides a device for optimizing a surface structure filled with auxetic metamaterials, including: a structured mesh generation module, configured to select a corresponding surface parameterization model according to the surface structure characteristics, and generate a structured mesh in the surface parameter domain according to the surface parameterization model; a microstructure filling module, configured to determine the type and volume fraction constraint of the negative Poisson's ratio microstructures to be filled into the surface structure, and generate a plurality of negative Poisson's ratio microstructures within the volume fraction constraint by using the parametric color level set method, and uniformly fill the negative Poisson's ratio microstructures into the surface structure to form an initial design; an optimization formulation establishment module, configured to simulate the relationship between the microstructure volume fraction and each coefficient in the level set function and the elastic matrix through an interpolation algorithm and / or a fitting algorithm, so as to establish an optimization formulation of the microstructure volume fraction in the surface parameter domain; a level set function assembly module, configured to optimize each microstructure unit in the initial design according to the optimization formulation, obtain the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit, and assemble the level set function in the surface parameter domain; a surface component configuration obtaining module, configured to inverse map the assembled level set function into the surface design domain to obtain a multi-scale surface component configuration optimized by gradient auxetic metamaterial filling.

[0013] In an embodiment of the present invention, the optimization formulation establishment module is specifically configured to: taking the minimization of the compliance of the surface configuration under the external load under the volume fraction constraint as the design goal, establish an optimization design formulation for the multi-scale surface structure filled with gradient auxetic metamaterial microstructures as:

[0014]

[0015] Wherein, represents the pseudo-density field formed by the microstructure volume fraction in the parameter domain, C represents the compliance value of the overall structure, and are respectively the upper and lower bounds of the microstructure volume fraction, is the overall stiffness matrix assembled according to the gradient microstructure equivalent elastic coefficient matrix, U and F are respectively the displacement vector and the external load vector of the nodes, υ i is the volume or area of each microstructure design domain, is the volume or area of the overall macroscopic design domain, V is the overall volume fraction constraint of the optimization design, is the optimized volume fraction control function, represents the actual volume fraction within each microstructure unit, is the elastic matrix of the auxetic metamaterial microstructure after fitting operation, and ⊙ represents the Hadamard product.

[0016] In one embodiment of the present invention, the optimized columnar establishment module is further configured to: obtain the auxetic metamaterial microstructure configurations with different volume fractions through topology optimization, and calculate the equivalent elastic matrix of each microstructure; wherein, the equivalent elastic matrix is obtained by performing a Hadamard product on the zero terms of the elastic matrix of the substrate set to "1" and the coefficients in the elastic matrix of the auxetic metamaterial microstructure The coefficients in the elastic matrix of the auxetic metamaterial microstructure And the equivalent elastic tensor of the equivalent elastic matrix Are all continuous functions of the volume fraction.

[0017] In one embodiment of the present invention, the level set function assembly module is specifically configured to: refine all the level set function nodes of the multiple microstructures generated by topology optimization onto the same set of grids to form a set of structured grid nodes x i，j , where i and j respectively represent the indices of the grid nodes; arrange the level set functions of the multiple microstructures in sequence according to the volume fraction to obtain their composition set Where K is the number of level set functions generated by topology optimization; for each node x on the grid i，j And its corresponding expansion coefficient α(x i，j ), interpolate the volume fraction of the microstructure corresponding to the expansion coefficient To obtain a continuous function of the expansion coefficient of the parameterized level set function corresponding to each microstructure with respect to the volume fraction; for each level set function node, based on the corresponding expansion coefficient and the corresponding continuous function, obtain the level set function corresponding to the volume fraction constraint of each microstructure.

[0018] On the other hand, an embodiment of the present invention also proposes an electronic device, including: a memory and one or more processors connected to the memory, the memory stores a computer program, and the processor is configured to execute the computer program to implement the auxetic metamaterial filled surface structure optimization method as described in any one of the above embodiments.

[0019] On the other hand, an embodiment of the present invention also proposes a computer-readable storage medium, the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to execute the auxetic metamaterial filled surface structure optimization method as described in any one of the above embodiments.

[0020] As can be seen from the above, compared with the prior art, the above embodiments of the present invention can at least have one or more of the following beneficial effects:

[0021] First, for the microstructure, the colored parametric level set method is used to describe the distribution of single-phase / multi-phase materials in the microstructure design domain, generating clear and smooth material boundaries. Combining with the numerical homogenization method, a topological optimization design model for the microstructure of auxetic metamaterials is established. The sensitivity formula of the optimization model is derived in detail, and various types of auxetic metamaterial microstructures are obtained. The performance and functions of the designed metamaterials are verified through simulation and experiment cross-validation. Secondly, for the parameterization of the microstructure geometry and physical properties, a continuous function of the volume fraction of the microstructure, the level set function, and the equivalent elastic tensor is established, realizing the continuous control of the geometry and physical properties of the microstructure by a single parameter, providing a basis for subsequent optimization. Finally, for the optimization design of the multi-scale surface construction filled with the gradient-distributed auxetic metamaterial microstructure, an optimization design model is established and solved, and the filling design schemes of the auxetic metamaterials with different types of surface structures are obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0023] Figure 1 is a flowchart of an optimization method for an auxetic metamaterial-filled surface structure provided by an embodiment of the present invention;

[0024] Figure 2 is a schematic diagram of the load conditions of a variable-curvature shell provided by an embodiment of the present invention;

[0025] Figure 3 is a schematic diagram of a continuously varying gradient-filled microstructure provided by an embodiment of the present invention;

[0026] Figure 4 is a schematic diagram of a uniformly filled microstructure before optimization and a gradient-filled microstructure after optimization provided by an embodiment of the present invention;

[0027] Figure 5 is an iterative curve graph of the optimization design of a lofting surface structure filled with a gradient auxetic metamaterial microstructure provided by an embodiment of the present invention;

[0028] Figure 6 is a schematic diagram of the optimization design result of a lofting surface structure filled with a gradient auxetic metamaterial microstructure provided by an embodiment of the present invention;

[0029] Figure 7 is a structural displacement nephogram before and after optimization provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described below with reference to the accompanying drawings and in combination with the embodiments.

[0031] In order to enable those of ordinary skill in the art to better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments, and all should fall within the protection scope of the present invention.

[0032] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that such terms can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0033] It should also be noted that the division of multiple embodiments in the present invention is only for the convenience of description and should not constitute a special limitation. The features in various embodiments can be combined and cross-referenced with each other without contradiction.

[0034] Such as Figure 1As shown in the figure, the first embodiment of the present invention proposes an optimization method for a surface structure filled with auxetic metamaterials, for example, including: Step S1, select a corresponding surface parameterization model according to the surface structure characteristics, and divide a structured grid in the surface parameter domain according to the surface parameterization model; Step S2, determine the type and volume fraction constraint of the negative Poisson's ratio microstructure to be filled into the surface structure, and use the parametric color level set method to generate a number of negative Poisson's ratio microstructures within the volume fraction constraint, and uniformly fill the negative Poisson's ratio microstructures into the surface structure to form an initial design; Step S3, simulate the relationship between the microstructure volume fraction and the level set function and each coefficient in the elastic matrix through an interpolation algorithm and / or a fitting algorithm, so as to establish an optimization formulation of the microstructure volume fraction in the surface parameter domain; Step S4, optimize each microstructure unit in the initial design according to the optimization formulation, obtain the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit, and assemble the level set function in the surface parameter domain; Step S5, inverse map the assembled level set function into the surface design domain to obtain a multi-scale surface component configuration optimized by gradient auxetic metamaterial filling.

[0035] Specifically, for example, taking the minimization of the compliance of a multi-scale surface structure under an external load with a total volume fraction constraint as the design goal, the optimization design formulation of a multi-scale surface structure filled with gradient auxetic metamaterial microstructures is established as follows:

[0036]

[0037] Among them, represents the pseudo-density field formed by the microstructure volume fraction in the parameter domain, C represents the compliance value of the overall structure, and are the upper and lower bounds of the microstructure volume fraction respectively, that is, the microstructure volume fraction filled in each unit is the overall stiffness matrix assembled according to the gradient microstructure equivalent elastic coefficient matrix, U and F are the displacement vector and external load vector of the nodes respectively. υ i is the volume or area of each microstructure design domain, is the volume or area of the overall macroscopic design domain, and satisfies V is the overall volume fraction constraint of the optimization design, and is the optimized volume fraction control function, that is, to ensure that the overall structure volume fraction is not greater than the specified overall volume fraction V.

[0038] Since the volume occupied by each grid in the lofted surface structure obtained by mapping is different, it is necessary to accumulate each microstructure when calculating the volume fraction of the overall structure. Represents the actual volume fraction within each microstructure unit, i.e., the unit pseudo-density. is the elastic matrix of the auxetic metamaterial microstructure after fitting operations, and ⊙ represents the Hadamard product.

[0039] Since the surface structure parameterization method determines the mesh division form and the geometry of the microstructure, in the optimization design method of this embodiment, the geometry of the microstructure filling unit does not change during the optimization process. Therefore, in the optimization design, the equivalent elastic matrix of the auxetic metamaterial microstructure is determined by the volume fraction solely. As mentioned before, the fitting of the microstructure geometry and physical properties with respect to the volume fraction can be achieved through polynomial functions, which facilitates the sensitivity analysis and the solution of the optimization formulation.

[0040] The fitting process is as follows: Obtain the auxetic metamaterial microstructure configurations with different volume fractions under the same type of geometric constraints through topology optimization, and calculate the equivalent elastic matrix of each microstructure. Similar to the previous text, the equivalent elastic matrix is obtained by setting the zero terms of the elastic matrix of the base material to "1" and then performing the Hadamard product with the coefficients. Therefore, there are coefficients and the equivalent elastic tensor are both continuous functions of the volume fraction.

[0041] For the mid-surface of the thin shell, there is:

[0042]

[0043] where T is a 6×6 diagonal matrix, and the last three terms in T are calculated from the thickness of the thin shell structure:

[0044] T = diag{1, 1, 1, t 2 / 12, t 2 / 12, t 2 / 12}.

[0045] Then is:

[0046]

[0047] where is the elastic matrix corresponding to the base material.

[0048] For the 3D microstructure, there is:

[0049]

[0050] For the generation of the level set function of the microstructure, it is necessary to first refine all the level set function nodes of the multiple microstructures generated by topology optimization onto the same set of grids to form a set of structured grid nodes x i，j, where \(i\) and \(j\) respectively represent the indices of the grid nodes; secondly, arrange the level set functions of multiple microstructures in sequence according to the volume fraction to obtain their composition set where \(K\) is the number of level set functions generated by topology optimization; then, for each node \(x\) on the grid i，j and its corresponding expansion coefficient \(\alpha(x\) i，j ), interpolate the volume fraction of the microstructure corresponding to the expansion coefficient to obtain a continuous function of the expansion coefficient of the parameterized level set function corresponding to each microstructure with respect to the volume fraction; finally, when solving the microstructure configuration with any volume fraction, the level set function corresponding to the volume fraction constraint of each microstructure can be obtained by calculating the expansion coefficient for each node, and then a clear geometric boundary of the microstructure can be obtained.

[0051] The following further illustrates the solution and effect of this embodiment in combination with an example calculation:

[0052] Regarding the optimal design of a thin-shell curved surface structure filled with auxetic metamaterials, as Figure 2 shown, the design domain is a variable-curvature shell rotating along the \(z\)-axis, with holes at the bottom. The volume fraction constraint of the variable-curvature shell is set to 45%, and the minimum volume fraction of the microstructure filled in the variable-curvature shell is and the maximum volume fraction is Conformally map the variable-curvature shell into a 2D rectangular parameter domain, and divide the rectangular domain into 48×80 (3840) square structured grids. In this example, the Young's modulus of the base material is 180 and the Poisson's ratio is 0.3. The stopping condition for the optimization iteration is: when the absolute value of the difference between the objective functions of two consecutive iterations is less than 10 -5 or the number of iterations is higher than 100 times.

[0053] As Figure 3 shown, the design domain of this example is a topological annulus. Figure 4 The following figure shows the design comparison before and after the optimization of the variable-curvature shell in this example. The optimization design results show that all the metamaterial microstructures automatically form an optimal gradient distribution form according to the load condition to increase the structural stiffness, and all the filled microstructures can conformally fit the variable-curved surface shell structure.

[0054] It should be noted that all the filled microstructures have a negative Poisson's ratio effect. Therefore, the optimal design can have good anti-impact functional characteristics while maintaining the stiffness performance. Before the optimization design, the maximum displacement of the structure is 0.115. After the optimization design, the maximum displacement of the structure is 0.068. The maximum displacement of the optimized structure is reduced by 40.87% compared with that before the optimization; the compliance value of the structure before the optimization is 0.04507, and the compliance value of the structure after the optimization is 0.02769. The stiffness of the optimized structure is increased by 38.56% compared with that before the optimization.

[0055] Regarding the optimal design of a lofted surface structure filled with 3D auxetic metamaterials, the design domain is a lofted surface structure with a trace line, and the trace line of the lofted surface structure is a cosine curve:

[0056]

[0057] In this example, each isoparametric surface of the lofted surface oscillates as the trace line bends, and each isoparametric surface is perpendicular to the trace line. Since the trace line is continuously differentiable and the isoparametric surface changes uniformly and smoothly, the resulting lofted surface body is also smooth.

[0058] In this example, the multi-scale surface structure is mapped to the normalized design domain through the proposed lofting parameterization method, and the parametric space is meshed into 16×10×20 (3200 elements), and the auxetic metamaterial microstructure filling elements are discretized into 30×30×30 (27000 elements). The entire optimal design problem has 8.64×10 7 design variables. In this example, the minimum volume fraction of the gradient auxetic metamaterial microstructure filled in the lofted surface body is The maximum volume fraction is Using non-dimensionalization, the load conditions for the optimal design are: all degrees of freedom in all directions at the four corner points at the bottom of the surface structure are constrained, and a vertical downward load of F = 1 is applied at the center of the top. The Young's modulus of the base material is 180 and the Poisson's ratio is 0.3. The goal of the optimal design is: under the premise that the volume fraction of the structure is constrained to 30%, minimize the compliance value of the structure under load. The stopping condition for the optimization iteration is: when the absolute value of the difference between the objective function values of two consecutive iterations is less than 10 -5 or the number of iterations is higher than 100 times, the optimization iteration stops.

[0059] Figure 5 Shows the changes in the compliance value and the overall volume fraction of the lofted surface structure filled with auxetic metamaterial microstructure during the optimal design as the number of iteration steps increases. Among them, the blue curve represents the change in the compliance value of the structure during the optimization process, and the red curve represents the change in the overall volume fraction of the structure during the optimization process. In the first 10 steps of iteration, the overall compliance of the structure decreases rapidly, and the change in the volume fraction of the microstructure in the parameter domain is also relatively obvious; after 10 steps of iteration, the gradient distribution change of the microstructure volume fraction tends to be stable, and the change in the overall compliance of the structure is small until convergence. Before optimization, when the auxetic metamaterial microstructure was uniformly filled in the surface design domain with a volume fraction of 30%, the compliance value of the structure under load was 40.21; after optimization, the auxetic metamaterial microstructure filled in the lofted surface structure shows a gradient distribution, and the compliance value under the same load and overall volume fraction is reduced to 19.89, and the stiffness performance is improved by 50.53% compared with that before optimization.

[0060] Figure 6 The optimized design results of the lofting surface filled with auxetic metamaterials are given. It can be noted that all the filled microstructures have smooth and complete geometric boundaries within the surface structure to ensure the function of the filled microstructures as much as possible, and the performance of the microstructures is ensured as much as possible by optimizing the gradient distribution of the microstructures. Figure 7 The overall structural displacement nephograms under load before and after the optimized design are plotted. Among them, the maximum displacement of the structure before optimization is 0.217, and the maximum displacement of the structure after optimization is reduced to 0.064. This further proves that the optimized design can well improve the stiffness performance of the multi-scale lofting surface structure. In addition, all the filled microstructures have the negative Poisson's ratio effect, indicating that the optimal design can also have good anti-impact functional characteristics while maintaining the stiffness performance.

[0061] In summary, the first embodiment of the present invention proposes an optimization method for the auxetic metamaterial-filled surface structure. By using the color parameterized level set method to describe the distribution of single-phase / multi-phase materials in the microstructure design domain, clear and smooth material boundaries are generated. Combining with the numerical homogenization method, a topology optimization design model of the auxetic metamaterial microstructure is established. The sensitivity formula of the optimization model is derived in detail, and various types of auxetic metamaterial microstructures are obtained. The performance and function of the designed metamaterials are verified by simulation and experiment cross-validation; a continuous function of the volume fraction of the microstructure, the level set function, and the equivalent elastic tensor is established, realizing the continuous control of the geometric and physical properties of the microstructure by a single parameter, providing a basis for subsequent optimization; an optimization design model is established and solved, and the auxetic metamaterial filling design schemes of different types of surface structures are obtained.

[0062] In addition, the second embodiment of the present invention also proposes an optimization device for the auxetic metamaterial-filled surface structure, including: a structured mesh generation module, a microstructure filling module, a volume fraction optimization formulation establishment module, a level set function assembly module, and a surface component configuration obtaining module.

[0063] Among them, the structured mesh generation module is used to select a corresponding surface parameterization model according to the surface configuration characteristics, and generate a structured mesh in the surface parameter domain according to the surface parameterization model; the microstructure filling module is used to determine the type, geometric constraints, and volume fraction range of the negative Poisson's ratio microstructures for filling the surface configuration, and use the parametric color level set method to design a number of negative Poisson's ratio microstructures within the volume fraction range, and uniformly fill the negative Poisson's ratio microstructures into the surface body to form an initial design; the optimization formulation establishment module is used to interpolate / fit to simulate the relationship between the microstructure volume fraction, the level set function, and the coefficients in the elastic matrix, so as to establish an optimization formulation of the volume fraction in the surface parameter domain; the level set function assembly module is used to obtain the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit according to the optimization formulation, and assemble the level set function in the surface parameter domain; the surface component configuration obtaining module is used to inversely map the assembled level set function to the surface design domain according to the surface parameterization method to obtain the multi-scale surface component configuration filled with the gradient auxetic metamaterial.

[0064] The method for optimizing the auxetic metamaterial-filled surface structure implemented by the auxetic metamaterial-filled surface structure optimization device disclosed in the second embodiment of the present invention is as described in the foregoing first embodiment, so details will not be repeated here. Optionally, each module in the second embodiment and the above other operations or functions are respectively for implementing the method described in the first embodiment, and the beneficial effects of the auxetic metamaterial-filled surface structure optimization device provided in this embodiment are the same as those of the auxetic metamaterial-filled surface structure optimization method provided in the foregoing first embodiment. For the sake of brevity, they will not be elaborated here.

[0065] The third embodiment of the present invention also proposes an electronic device, for example, including: at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the computer program is executed by the processing unit, the processing unit is enabled to execute the method described in the first embodiment, and the beneficial effects of the electronic device provided in this embodiment are the same as those of the auxetic metamaterial-filled surface structure optimization method provided in the first embodiment.

[0066] The fourth embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of the above method are implemented, and the beneficial effects of the computer-readable storage medium provided in this embodiment are the same as those of the auxetic metamaterial-filled surface structure optimization method provided in the first embodiment.

[0067] Among them, the computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, and magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0068] It should be noted that, for the foregoing method embodiments, for the sake of simple description, they are all expressed as a series of action combinations. However, those skilled in the art should know that this application is not limited by the described action sequence, because according to this application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0069] In the above embodiments, the descriptions of the respective embodiments have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0070] In several embodiments provided by this application, it should be understood that the disclosed device can be implemented in other ways. For example, the device embodiments described above are only illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some service interfaces. The indirect coupling or communication connection of the device or unit can be in an electrical or other form.

[0071] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place, or they can be distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0072] In addition, in each embodiment of this application, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0073] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes: various media such as USB flash drives, read-only memory (ROM), random access memory (RAM), external hard drives, magnetic disks, or optical discs that can store program codes.

[0074] Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program. This program can be stored in a computer-readable memory, and the memory can include: flash drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs, etc.

[0075] The above are only exemplary embodiments of the present disclosure, and the scope of the present disclosure cannot be limited thereby. That is, any equivalent changes and modifications made in accordance with the teachings of the present disclosure still fall within the scope covered by the present disclosure. Those skilled in the art will readily think of other embodiments of the present disclosure after considering the specification and practicing the present disclosure herein. This application aims to cover any variations, uses, or adaptive changes of the present disclosure, which follow the general principles of the present disclosure and include the common general knowledge or conventional technical means in the technical field not recorded in the present disclosure. The specification and embodiments are only regarded as exemplary, and the scope and spirit of the present disclosure are defined by the claims.

[0076] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as within the scope described in this specification.

[0077] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An optimization method for a surface structure filled with auxetic metamaterials, characterized in that Including: Select a corresponding surface parameterization model according to the surface structure characteristics, and divide a structured grid in the surface parameter domain according to the surface parameterization model; Determine the type and volume fraction constraint of the negative Poisson's ratio microstructure to be filled into the surface structure, and use the parametric color level set method to generate a number of negative Poisson's ratio microstructures within the volume fraction constraint, and uniformly fill the negative Poisson's ratio microstructures into the surface structure to form an initial design; Simulate the relationship between the microstructure volume fraction and the coefficients in the level set function and the elastic matrix through an interpolation algorithm and / or a fitting algorithm, so as to establish an optimization formulation of the microstructure volume fraction in the surface parameter domain; Optimize each microstructure unit in the initial design according to the optimization formulation, obtain the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit, and assemble the level set function in the surface parameter domain; Inverse map the assembled level set function into the surface design domain to obtain a multi-scale surface component configuration optimized by gradient auxetic metamaterial filling.

2. The optimization method of the auxetic metamaterial-filled curved surface structure according to claim 1, wherein, The establishment of the optimization formulation of the volume fraction in the surface parameter domain includes: Taking the minimization of the compliance of the surface configuration under the volume fraction constraint under an external load as the design goal, the optimization design formulation of the multi-scale surface structure filled with gradient auxetic metamaterial microstructure is: min: C = ∫ Ω ε T Dε dΩ Among them, represents the pseudo-density field formed by the volume fraction of the microstructure in the parameter domain, C represents the compliance value of the overall structure, and are the upper and lower bounds of the volume fraction of the microstructure, respectively, is the overall stiffness matrix assembled according to the gradient microstructure equivalent elastic coefficient matrix, U and F are the displacement vector and external load vector of the nodes, respectively, and v i is the volume or area of each microstructure design domain, is the volume or area of the overall macroscopic design domain, V is the overall volume fraction constraint of the optimal design, is the optimized volume fraction control function, represents the actual volume fraction within each microstructure unit, is the elastic matrix of the auxetic metamaterial microstructure after fitting operation, and ⊙ represents the Hadamard product.

3. The method for optimizing the surface structure filled with auxetic metamaterials according to claim 2, wherein The elastic matrix of the auxetic metamaterial microstructure The fitting process includes: Obtain the auxetic metamaterial microstructure configurations with different volume fractions through topology optimization, and calculate the equivalent elastic matrix of each microstructure; Among them, the equivalent elastic matrix is obtained by performing a Hadamard product on the elastic matrix of the substrate with zero terms set to "1" and the coefficients in the elastic matrix of the auxetic metamaterial microstructure. The coefficients in the elastic matrix of the auxetic metamaterial microstructure and the equivalent elastic tensor of the equivalent elastic matrix are both continuous functions of the volume fraction.

4. The optimization method of the auxetic metamaterial-filled curved surface structure according to claim 2, wherein The obtaining of the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit according to the optimization formulation includes: Refine all the nodes of the multiple microstructure level set functions generated by topology optimization onto the same set of grids to form a set of structured grid nodes \(x_{ij}\), where \(i\) and \(j\) respectively represent the indices of the grid nodes; i，j , where \(i\) and \(j\) respectively represent the indices of the grid nodes; Arrange the level set functions of multiple microstructures in order of volume fraction to obtain their composition set where K is the number of level set functions generated by topology optimization; For each node x on the grid i，j and its corresponding expansion coefficient α(x i，j ), interpolate the volume fraction of the microstructure corresponding to the expansion coefficient to obtain a continuous function of the expansion coefficient of the parameterized level set function corresponding to each microstructure with respect to the volume fraction; For each level set function node, based on the corresponding expansion coefficient and the corresponding continuous function, obtain the level set function corresponding to the volume fraction constraint of each microstructure.

5. A device for optimizing a surface structure filled with a auxetic metamaterial, characterized in that Including: A structured grid division module, configured to select a corresponding surface parameterization model according to the surface structure characteristics, and divide a structured grid in the surface parameter domain according to the surface parameterization model; A microstructure filling module, configured to determine the type and volume fraction constraint of the negative Poisson's ratio microstructure to be filled into the surface structure, and use the parametric color level set method to generate a number of negative Poisson's ratio microstructures within the volume fraction constraint, and uniformly fill the negative Poisson's ratio microstructures into the surface structure to form an initial design; An optimization formulation establishment module, which simulates the relationship between the microstructure volume fraction and the coefficients in the level set function and the elastic matrix through an interpolation algorithm and / or a fitting algorithm, so as to establish an optimization formulation of the microstructure volume fraction in the surface parameter domain; A level set function assembly module, configured to optimize each microstructure unit in the initial design according to the optimization formulation, obtain the microstructure level set function corresponding to the optimized volume fraction of each microstructure unit, and assemble the level set function in the surface parameter domain; A surface component configuration obtaining module, configured to inverse map the assembled level set function into the surface design domain to obtain a multi-scale surface component configuration optimized by gradient auxetic metamaterial filling.

6. The device for optimizing the surface structure filled with the auxetic metamaterial according to claim 5, characterized in that The optimization column - type establishment module is specifically used for: Taking the minimization of the compliance of the curved - surface configuration under the external load with the volume - fraction constraint as the design goal, establishing the optimization design column - type of the multi - scale curved - surface structure filled with the gradient auxetic metamaterial microstructure as: min: C = ∫ Ω ε T Dε dΩ Among them, represents the pseudo-density field formed by the volume fraction of the microstructure in the parameter domain, C represents the compliance value of the overall structure, and are the upper and lower bounds of the volume fraction of the microstructure respectively, is the overall stiffness matrix assembled according to the equivalent elastic coefficient matrix of the gradient microstructure, U and F are the displacement vector and external load vector of the nodes respectively, v i is the volume or area of each microstructure design domain, is the volume or area of the overall macroscopic design domain, V is the overall volume fraction constraint of the optimal design, is the optimized volume fraction control function, represents the actual volume fraction within each microstructure unit, is the elastic matrix of the auxetic metamaterial microstructure after fitting operation, and ⊙ represents the Hadamard product.

7. The device for optimizing the surface structure filled with the auxetic metamaterial according to claim 6, wherein The optimization column - type establishment module is also used for: Obtaining the auxetic metamaterial microstructure configurations with different volume fractions through topology optimization, and calculating the equivalent elastic matrix of each microstructure; Among them, the equivalent elastic matrix is obtained by setting the zero terms of the elastic matrix of the base material to "1" and then performing a Hadamard product with the coefficients in the elastic matrix of the auxetic metamaterial microstructure. The coefficients in the elastic matrix of the auxetic metamaterial microstructure and the equivalent elastic tensor of the equivalent elastic matrix are both continuous functions of the volume fraction.

8. The auxetic metamaterial-filled curved surface structure optimization device according to claim 6, characterized in that The level - set function assembly module is specifically used for: Refine all the nodes of the multiple microstructural level set functions generated by topology optimization onto the same set of meshes to form a set of structured mesh nodes \(x_{ij}\), where \(i\) and \(j\) respectively represent the indices of the mesh nodes; i，j , where \(i\) and \(j\) respectively represent the indices of the mesh nodes; Arrange the level set functions of multiple microstructures in order of volume fraction to obtain their composition set where K is the number of level set functions generated by topology optimization; For each node x on the grid i，j and its corresponding expansion coefficient α(x i，j ), interpolate the volume fraction of the microstructure corresponding to the expansion coefficient to obtain a continuous function of the expansion coefficient of the parameterized level set function corresponding to each microstructure with respect to the volume fraction; For each level - set function node, based on the corresponding expansion coefficient and the corresponding continuous function, obtaining the level - set function corresponding to the volume - fraction constraint of each microstructure.

9. An electronic device, characterized in that, Including: A memory and one or more processors connected to the memory, the memory stores a computer program, and the processor is used to execute the computer program to implement the auxetic metamaterial microstructure topology design method according to any one of claims 1 - 4.

10. A computer-readable storage medium, characterized in that, The computer - readable storage medium stores computer - executable instructions, and the computer - executable instructions are used to execute the optimization method of the auxetic - metamaterial - filled curved - surface structure according to any one of claims 1 - 4.

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