Optimization design method, device and equipment of multi-dimensional functionally graded material and medium

Abstract

The invention provides an optimization design method, device, equipment and medium for a multi-dimensional functionally graded material, and belongs to the technical field of functionally graded material design, the method comprises the following steps: constructing the multi-dimensional functionally graded material based on a non-uniform rational B-spline basis function; the multi-dimensional functionally graded material comprises a plurality of control points; constructing a sample set, and training the initial material prediction model based on the sample set to obtain a completely trained material performance prediction model; constructing a multi-objective optimization function by taking the minimum total mass and the maximum free vibration fundamental frequency as objectives, and carrying out iterative solution on the multi-objective optimization function to obtain the volume fraction and the optimized thickness of a control point optimized material; wherein the prediction performance required in the iterative solving process of the multi-objective optimization function is determined based on the material performance prediction model. According to the method, the data volume in a multi-objective optimization algorithm is reduced, and rapid and reliable optimization design of the multi-dimensional functionally graded material with relatively high design dimension and relatively many design variables can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of functional gradient material design, and in particular to an optimization design method, device, equipment and medium for multi-dimensional functional gradient materials. Background Art

[0002] Functionally graded materials (FGMs) are a new type of inhomogeneous composite materials, usually composed of two or more materials, whose material composition gradually changes in space and has locally customized properties. They are widely used in aerospace, automotive, biomedical and military applications. In many complex service environments, unidirectional FGMs (1D-FGMs) often have difficulty meeting service requirements. For example, the propulsion systems and fuselages of modern aerospace aircraft usually operate in high-temperature environments that change in three directions. The unidirectional changes in the materials and properties of traditional 1D-FGMs can hardly meet these harsh service environments. To solve this problem, multidimensional functionally graded materials (3D-FGMs) are proposed, whose material properties change smoothly in predefined directions in the structural space. Specific properties can be achieved by specifying the material composition at specific locations within the structural domain.

[0003] In order to better design multidimensional functional gradient materials and obtain the best material and shape distribution according to application requirements, the use of optimization algorithms is an effective method. Multi-objective meta-heuristic optimization algorithms have recently been considered as robust and reliable methods to solve various complex optimization problems, such as non-dominated sorting genetic algorithm (NSGA-II, NSGA-Ⅲ), multi-objective particle swarm optimization (MOPSO), multi-objective evolutionary algorithm (MOEA) and multi-objective artificial bee colony algorithm (MOABC). Due to their superior performance, these algorithms have gradually been applied to the multi-objective optimization of MFGM. However, with the increase in the complexity of multi-field coupling performance analysis of multi-dimensional functional gradient materials and the accuracy requirements of numerical solutions, the required amount of calculation and calculation time have increased significantly, which seriously limits the multi-objective optimization of multi-dimensional functional gradient materials. Specifically, a large amount of performance calculations are required in the optimization algorithm, which will result in a very long optimization time and difficulty in actual operation. Therefore, the multi-objective optimization algorithm in the prior art can only optimize the design of functional gradient materials with low design dimensions and fewer design variables, and cannot achieve effective optimization design of multi-dimensional functional gradient materials.

[0004] Therefore, there is an urgent need to provide an optimization design method, device, equipment and medium for multidimensional functional gradient materials to reduce the amount of calculation and calculation time required for performance calculation in the optimization algorithm, and to achieve rapid and accurate optimization design of multidimensional functional gradient materials. Summary of the invention

[0005] In view of this, it is necessary to provide an optimization design method, device, equipment and medium for multi-dimensional functional gradient materials to solve the technical problems existing in the prior art that the multi-dimensional functional gradient materials cannot be effectively optimized or the optimization design efficiency is too low due to the excessive amount of calculation in the multi-objective optimization algorithm.

[0006] On the one hand, in order to solve the above technical problems, the present invention provides an optimization design method for a multi-dimensional functional gradient material, comprising: Constructing a multidimensional functional gradient material based on a non-uniform rational B-spline basis function; the multidimensional functional gradient material includes a plurality of control points; Constructing a sample set, and training an initial material prediction model based on the sample set to obtain a fully trained material performance prediction model; A multi-objective optimization function is constructed with the goal of minimizing the total mass and maximizing the fundamental frequency of free vibration, and the multi-objective optimization function is iteratively solved to obtain the optimized material volume fraction and optimized thickness of the control point; The prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material property prediction model.

[0007] In a possible implementation, the multidimensional functional gradient material is a composite material of a metal phase material and a ceramic phase material; the multi-objective optimization function is:

[0008]

[0009] In the formula, is the total mass; is the material volume fraction of the ceramic phase material at the jth control point; is the thickness of the jth control point; is the volume fraction of ceramic phase material at any point in space; is the density of the ceramic phase material; is the mass density of the metallic phase material at room temperature; is the total volume of the multi-dimensional functional gradient material, which is related to the thickness; is the dimensionless free vibration fundamental frequency; is the first-order natural frequency of free vibration; is the side length of the square multi-dimensional functional gradient material; is the elastic modulus of the metal phase material at room temperature; is the Poisson's ratio of the metallic phase material at room temperature; is the initial thickness of the square multi-dimensional functional gradient material; is the non-uniform rational B-spline basis function; n×m×l is the total number of control points.

[0010] In a possible implementation, the constraints of the multi-objective optimization function are:

[0011] In the formula, is the total material volume fraction of ceramic phase material; is the element stiffness matrix; is the temperature-dependent element thermal stiffness matrix; is the unit mass matrix; is the unit displacement vector.

[0012] In a possible implementation, the multidimensional functional gradient material includes a target sub-region and at least one mirror sub-region symmetrical to the target sub-region; the multi-objective optimization function is a function corresponding to the target sub-region, and the method includes: Determine the target material volume fraction and target thickness of each control point in the target sub-area based on the multi-objective optimization function and the material property prediction model; The target material volume fraction and the target thickness are mirror-symmetrically processed to obtain the mirror material volume fraction and the target thickness of each control point in the mirror sub-region.

[0013] In a possible implementation, the sample set includes a plurality of sample data, and the sample data includes a material volume fraction, a thickness, a total mass reference value, and a free vibration fundamental frequency reference value; The constructing of the sample set includes: Randomly initialize the material distribution and geometric model to obtain the material volume fraction and thickness of each control point; Determining the spatial thermal field of the multi-dimensional functional gradient material based on high-throughput parallel isogeometric analysis; A total mass reference value and a free vibration fundamental frequency reference value of the multi-dimensional functional gradient material are determined based on the spatial thermal field.

[0014] In a possible implementation, the training of the initial material prediction model based on the sample set to obtain a fully trained material property prediction model includes: Dividing the sample set into a training set and a validation set in a preset ratio; Training the initial material performance prediction model based on the training set to obtain a performance prediction model to be verified; The performance prediction model to be verified is verified based on the verification set, and when the verification passes, the performance prediction model to be verified is the material performance prediction model.

[0015] In one possible implementation, the material property prediction model includes a first three-dimensional convolution module, a first pooling layer, multiple second three-dimensional convolution modules, a flattening layer and a fully connected layer connected in sequence, and the first three-dimensional convolution module and each of the second three-dimensional convolution modules include a three-dimensional convolution layer, a batch normalization layer and an activation function layer.

[0016] On the other hand, the present invention also provides an optimization design device for a multi-dimensional functional gradient material, comprising: A multidimensional functional gradient material construction unit is used to construct a multidimensional functional gradient material based on a non-uniform rational B-spline basis function; the multidimensional functional gradient material includes a plurality of control points; A material property prediction model training unit is used to construct a sample set and train an initial material prediction model based on the sample set to obtain a fully trained material property prediction model; A material parameter optimization design unit is used to construct a multi-objective optimization function with the goal of minimizing the total mass and maximizing the fundamental frequency of free vibration, and iteratively solve the multi-objective optimization function to obtain the optimized material volume fraction and optimized thickness of the control point; The prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material property prediction model.

[0017] On the other hand, the present invention also provides an optimization design device, including a memory and a processor, wherein: The memory is used to store programs; The processor is coupled to the memory and is used to execute the program stored in the memory to implement the steps in the optimization design method of the multi-dimensional functional gradient material described in any one of the possible implementation methods mentioned above.

[0018] On the other hand, the present invention also provides a computer-readable storage medium for storing computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the optimization design method of multidimensional functional gradient materials described in any one of the above possible implementation methods.

[0019] The beneficial effects of the present invention are as follows: the optimization design method of the multidimensional functional gradient material provided by the present invention applies a well-trained material performance prediction model to the solution process of the multi-objective function, and does not require a multi-objective optimization algorithm to perform numerical solution on the total mass and the free vibration fundamental frequency, thereby improving the efficiency of determining the total mass and the free vibration fundamental frequency, reducing the amount of data in the multi-objective optimization algorithm, and accelerating the multi-objective optimization process, thereby realizing rapid and reliable optimization design of multidimensional functional gradient materials with higher design dimensions and more design variables, solving the current shortcomings of slow FGM performance prediction, low design dimensions, small design freedom, and performance limitations, and ensuring that the multidimensional functional gradient material meets the application needs of aerospace, automotive machinery, military defense and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 A schematic flow chart of an embodiment of the optimization design method of the multi-dimensional functional gradient material provided by the present invention; Figure 2 A schematic diagram of the structure of an embodiment of the multi-dimensional functional gradient material provided by the present invention; Figure 3 A schematic flow chart of another embodiment of the optimization design method of the multi-dimensional functional gradient material provided by the present invention; Figure 4 A schematic diagram of an embodiment of the process of constructing a sample set provided by the present invention; Figure 5 A schematic diagram of a flow chart of an embodiment of constructing a sample set provided by the present invention; Figure 6 A schematic diagram of the structure of an embodiment of the material property prediction model training and verification process provided by the present invention; Figure 7 A schematic diagram of simulation results of an embodiment of the optimized design structure provided by the present invention; Figure 8 A schematic structural diagram of an embodiment of an optimization design device for multi-dimensional functional gradient materials provided by the present invention; Fig. 9 A schematic structural diagram of an embodiment of the optimization design device provided by the present invention. DETAILED DESCRIPTION

[0022] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0023] It should be understood that the schematic drawings are not drawn to scale. The flowchart used in the present invention shows the operations implemented according to some embodiments of the present invention. It should be understood that the operations of the flowchart can be implemented out of order, and the steps without logical context can be reversed in order or implemented simultaneously. In addition, those skilled in the art, under the guidance of the content of the present invention, can add one or more other operations to the flowchart, and can also remove one or more operations from the flowchart. Some of the block diagrams shown in the accompanying drawings are functional entities, which do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor systems and / or microcontroller systems.

[0024] Reference to an "embodiment" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiment may be included in at least one embodiment of the present invention. The appearance of the phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0025] The present invention provides a method, device, equipment and medium for optimizing the design of a multi-dimensional functional gradient material, which are described below respectively.

[0026] Figure 1 A schematic flow chart of an embodiment of the optimization design method of the multi-dimensional functional gradient material provided by the present invention is as follows: Figure 1 As shown, the optimization design method of multi-dimensional functional gradient materials includes: S101. constructing a multidimensional functional gradient material based on a non-uniform rational B-spline (NURBS) basis function; the multidimensional functional gradient material includes a plurality of control points; S102, constructing a sample set, and training an initial material prediction model based on the sample set to obtain a fully trained material performance prediction model; S103, constructing a multi-objective optimization function with the goal of minimizing the total mass and maximizing the fundamental frequency of free vibration, iteratively solving the multi-objective optimization function, and obtaining the optimized material volume fraction and optimized thickness of the control point; Among them, the prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material performance prediction model.

[0027] Among them, based on the high-order continuity of NURBS basis functions, the continuous gradient distribution of materials in the structural domain can be smoothly represented, thereby enabling the construction of multidimensional functional gradient materials.

[0028] In a specific embodiment of the present invention, the multidimensional functional gradient material includes three spatial directions, namely, the length direction, the width direction and the height direction, and the NURBS basis function is:

[0029] In the formula, is the non-uniform rational B-spline basis function; p is the order of basis function in the length direction; n is the number of control points in the length direction; q is the order of basis function in the width direction; m is the number of control points in the width direction; r is the order of basis function in height direction; l is the number of control points in the height direction; is the B-spline basis function in the length direction; is the B-spline basis function in the width direction; is the B-spline basis function in the height direction; is the weight of the (i,j,k) control point.

[0030] For a one-dimensional B-spline basis function, it is usually composed of the node vector Composition, among which ,and and Typically repeated p+1 times. p is the interpolation basis function order; n is the number of control points and basis functions. B-spline basis functions It is defined by the Cox-de-Boor recursive formula: ; .

[0031] A one-dimensional NURBS basis function can be obtained by introducing weight values ​​under the premise of a one-dimensional B-spline basis function. The NURBS basis function in the embodiment of the present invention is a three-dimensional basis function, which can be constructed by the tensor product of a one-dimensional NURBS basis function.

[0032] Compared with the prior art, the optimization design method of the multidimensional functional gradient material provided in the embodiment of the present invention applies a well-trained material performance prediction model to the solution process of the multi-objective function. There is no need to use a multi-objective optimization algorithm to numerically solve the total mass and the free vibration fundamental frequency, thereby improving the efficiency of determining the total mass and the free vibration fundamental frequency, reducing the amount of data in the multi-objective optimization algorithm, and accelerating the multi-objective optimization process. Therefore, it is possible to achieve rapid and reliable optimization design of multidimensional functional gradient materials with higher design dimensions and more design variables, thereby solving the current shortcomings of slow FGM performance prediction, low design dimensions, small design freedom, and performance limitations, thereby ensuring that the multidimensional functional gradient material meets the application needs of aerospace, automotive machinery, military and national defense, and other fields.

[0033] In some embodiments of the present invention, the multidimensional functional gradient material is composed of two materials. Specifically, the multidimensional functional gradient material is composed of a metal phase material and a ceramic phase material. Then the multi-objective optimization function is:

[0034]

[0035] In the formula, is the total mass; is the material volume fraction of the ceramic phase material at the jth control point; is the thickness of the jth control point; is the volume fraction of ceramic phase material at any point in space; is the density of the ceramic phase material; is the mass density of the metallic phase material at room temperature; is the total volume of the multi-dimensional functional gradient material, which is related to the thickness; is the dimensionless free vibration fundamental frequency; is the first-order natural frequency of free vibration; is the side length of the square multi-dimensional functional gradient material; is the elastic modulus of the metal phase material at room temperature; is the Poisson's ratio of the metallic phase material at room temperature; is the initial thickness of the square multi-dimensional functional gradient material; is the non-uniform rational B-spline basis function; n×m×l is the total number of control points.

[0036] It should be noted that: , is the volume fraction of the metallic phase material at any point in space.

[0037] Specifically, the material volume fraction can be obtained by interpolation of NURBS basis functions.

[0038] In a specific embodiment of the present invention, the multi-dimensional functional gradient material is constructed based on the NURBS basis function. L = 1m square plate, the initial thickness of the plate h 0 is = 0.1m, such as Figure 2 (a) and Figure 2 (b) as shown.

[0039] In order to further improve the optimization efficiency of the multi-objective optimization function and the accuracy of the determined optimization parameters, in some embodiments of the present invention, at least one constraint condition is set to constrain the optimization process of the multi-objective optimization function. Specifically, the constraint condition of the multi-objective optimization function is:

[0040] In the formula, is the total material volume fraction of ceramic phase material; is the element stiffness matrix; is the temperature-dependent element thermal stiffness matrix; is the unit mass matrix; is the unit displacement vector.

[0041] In a specific embodiment of the present invention, the multi-objective optimization algorithm of the multi-objective optimization function is NSGA-III.

[0042] In some embodiments of the present invention, the multidimensional functional gradient material is a centrally symmetrical pattern, and the boundary conditions applied to the multidimensional functional gradient material are also centrally symmetrical, such as Figure 2 (a) and 2(b), the multidimensional functional gradient material is a square plate, the boundary conditions are that the four sides of the plate are fixed, and a uniform temperature is applied to the upper surface of the plate, and the lower surface is at a uniform room temperature, that is, the optimized material volume fraction and the optimized thickness are also symmetrical about the center.

[0043] If Figure 2 As shown in (c), the multidimensional functional gradient material can be divided into a target sub-area (Design Area) and three mirror sub-areas symmetrical to the target sub-area.

[0044] Under this premise, in order to further reduce the amount of calculation and improve the optimization design efficiency of multi-dimensional functional gradient materials, in some embodiments of the present invention, the multi-objective optimization function is a function corresponding to the target sub-region, such as Figure 3 As shown, the optimization design method of multi-dimensional functional gradient materials includes: S301, determining the target material volume fraction and target thickness of each control point in the target sub-region based on a multi-objective optimization function and a material property prediction model; S302 , performing mirror symmetry processing on the target material volume fraction and the target thickness to obtain the mirror material volume fraction and the target thickness of each control point in the mirror sub-region.

[0045] The embodiment of the present invention only needs to optimize the design of the target sub-region, and can reduce the amount of calculation in the optimization process by one-fourth or even one-eighth through the mirror material volume fraction and target thickness of the other three mirror sub-regions with three-mirror symmetry, thereby greatly reducing the amount of calculation and further improving the efficiency of the optimization design.

[0046] As can be seen from the above description, the input of the material performance prediction model is the material volume fraction and thickness of each control point, and the output is the total mass and the free vibration fundamental frequency. Therefore, the sample set includes a plurality of sample data, and the sample data includes the material volume fraction, thickness, total mass reference value and free vibration fundamental frequency reference value; in some embodiments of the present invention, such as Figure 4 As shown, the construction of the sample set in step S102 includes: S401, randomly initialize material distribution and geometric model to obtain material volume fraction and thickness of each control point; S402, determining the spatial thermal field of multi-dimensional functional gradient materials based on high-throughput parallel isogeometric analysis; S403. Determine a total mass reference value and a free vibration fundamental frequency reference value of the multi-dimensional functional gradient material based on the spatial thermal field.

[0047] Among them, the determination of the spatial thermal field in step S402 requires the use of equivalent material properties of the multi-dimensional functional gradient material. The specific equivalent material properties include but are not limited to elastic modulus, Poisson's ratio, thermal conductivity, and thermal expansion coefficient. Specifically:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] In the formula, E , v , k , 𝛼, They are elastic modulus, Poisson's ratio, thermal conductivity, thermal expansion coefficient and mass density of multi-dimensional functional gradient materials; is the bulk modulus; is the shear modulus; and are the bulk moduli of the metallic phase material and the ceramic phase, respectively; and are the bulk moduli of the metallic phase material and the ceramic phase, respectively; and are the elastic moduli of the metal phase material and the ceramic phase, respectively; and are the thermal conductivities of the metal phase material and the ceramic phase, respectively; and are the thermal expansion coefficients of the metal phase material and the ceramic phase, respectively; and are the mass densities of the metallic phase material and the ceramic phase, respectively.

[0060] It should be noted that the above-mentioned equivalent material properties are all related to temperature. The relationship between any equivalent material property and temperature is as follows: ; in, represents any of the equivalent material properties above. T is the temperature in Kelvin. is a constant determined from a cubic fit of material properties and temperature. , , , yes , , , The constant.

[0061] In a specific embodiment of the present invention, the ceramic phase material is ZrO2, the metal phase material is SUS304, and the above five temperature-related constants are shown in Table 1: Table 1 Material constants related to temperature

[0062] Among them, the determination process of the spatial thermal field is specifically as follows: The steady-state thermal field equation is shown below: ; The constitutive equation of isotropic material in three-dimensional elastic theory considering thermal-mechanical coupling can be written as: ； in and represents the stress and strain tensors, is the effective thermal expansion coefficient, ∆T is the temperature change, is the Kronecker operator, is the elastic constant matrix.

[0063] strain The displacement of the material point can be It is expressed as follows: ； For the bending problem of multidimensional functional gradient materials under thermal environment, according to the principle of virtual work, the control equation can be written as: ； Further expressed in matrix form: ; in, C is the elastic constant matrix, is the stress vector caused by temperature change, t is the boundary tension, is the volume domain; For the border.

[0064] Among them, stress ,strain , displacement , stress vector caused by temperature change , C The calculation formula is as follows: , , ,

[0065] .

[0066] For the free vibration problem under thermal environment, it is assumed that the temperature of each position of the multi-dimensional functional gradient material in the initial state is 300K, and the temperature boundary condition is applied. The heat transfer process will be carried out until equilibrium is reached. The increase in temperature will cause thermal expansion and initial internal stress in the multi-dimensional functional gradient material. The strain energy caused by the initial thermal stress can be written as: ; In the formula, and are the stress and strain under initial thermal stress, respectively.

[0067] The governing equation for free vibration in final matrix form can be written as:

[0068] In the formula, is the strain vector caused by temperature change.

[0069] The derived governing equations are discretized using isogeometric analysis numerical techniques and solved for the free vibration under thermomechanical coupling conditions.

[0070] Specifically, the temperature vector and displacement vector are obtained by NURBS basis function interpolation:

[0071]

[0072] in, and are the temperature vector and displacement vector at the control point.

[0073] Then the weak form governing equation for steady-state heat transfer in multidimensional functionally gradient materials can be written as:

[0074]

[0075]

[0076]

[0077] in, It is a multi-dimensional functional gradient material unit The vector of temperature variables for each control point in .

[0078] It is worth noting that the thermal conductivity in this equation is It is also a function of temperature. Changes in temperature will cause the thermal conductivity Therefore, an iterative method is needed to solve this equation.

[0079] The iterative process mainly includes: first initializing the temperature field, and then using the temperature field to calculate the thermal conductivity of the material , and solve the temperature field according to the control equation . Perform iterative calculation until the temperature vector and The convergence evaluation standard is less than the set tolerance, and the final temperature field vector is obtained. , that is: temperature thermal field distribution.

[0080] After obtaining the temperature field distribution, the unit The governing equation for the free vibration of can be written as: ; ; ; ; ; ; ;

[0081]

[0082]

[0083] In the formula, is the unit external force load vector; is the unit thermal load vector; is the non-uniform rational B-spline basis function.

[0084] in, To convert the volume After division, multiple units are obtained.

[0085] Solving the above equations gives the fundamental frequency of free vibration and the total mass.

[0086] The above process is repeated by changing the material volume fraction and plate thickness at the control point, boundary conditions, initial temperature field, and geometric model shape until the required number of training samples is obtained to generate a sample set.

[0087] In a specific embodiment of the present invention, the sample set includes 20,000 groups of data.

[0088] To further ensure the model performance of the material property prediction model, in some embodiments of the present invention, Figure 5 As shown, the process of determining the material property prediction model in step S102 is: S501, dividing the sample set into a training set and a validation set in a preset ratio; S502, training the initial material performance prediction model based on the training set to obtain a performance prediction model to be verified; S503 , verifying the performance prediction model to be verified based on the verification set. When the verification passes, the performance prediction model to be verified is a material performance prediction model.

[0089] Among them, the loss function used in the training process of the initial material property prediction model is the mean square error (MSE) function.

[0090] Specifically, the preset ratio is 8:2.

[0091] It should be noted that the indicator used in the verification process is the determination coefficient R 2 The specific expression is:

[0092] In the formula, is the predicted value of the material performance prediction model, the predicted value is the total mass and the fundamental frequency of free vibration; is the reference value in the sample set, the reference value is the total mass reference value and the free vibration fundamental frequency reference value; is the total number of data in the validation set.

[0093] It should be understood that: R 2 The closer it is to 1, the higher the prediction accuracy of the material properties prediction model.

[0094] In a specific embodiment of the present invention, Figure 6 As shown, the material property prediction model includes a first three-dimensional convolution module, a first pooling layer, multiple second three-dimensional convolution modules, a flattening layer and a fully connected layer connected in sequence, and the first three-dimensional convolution module and each second three-dimensional convolution module include a three-dimensional convolution layer, a batch normalization layer and an activation function layer.

[0095] Among them, the activation function of the activation function layer is the RELU function.

[0096] In a specific embodiment of the present invention, the Pareto front is obtained in step S103, and the representative elite solutions in the Pareto front can be uniformly selected for result visualization. From the drawn material distribution cloud map and the sample geometric model structure, the characteristics of the optimization results under different optimization objectives, constraints, boundary conditions, starting temperature fields, load conditions and other factors are extracted, and the influence of the material distribution mode and the sample geometric model on the macro performance of 3D-FGM is analyzed.

[0097] Specifically, taking a square plate with fixed boundary conditions on all sides and a uniform temperature of 500K on the upper surface as an example, the material volume fraction and thickness distribution visualization results of the ceramic phase material on the representative elite are shown in the figure below: Figure 7 As shown, there are 8 representative elites in total. Figure 7 (a) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 5.1080 and the total mass of 524.86 kg. Figure 7 (b) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.9901 and the total mass of 491.96 kg. Figure 7 (c) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.8921 and the total mass of 470.95 kg, Figure 7(d) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.7942 and the total mass of 460.16 kg, Figure 7 (e) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.7304 and the total mass of 451.97 kg, Figure 7 (f) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.6062 and the total mass of 440.25 kg, Figure 7 (g) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.5345 and the total mass of 434.41 kg, Figure 7 (h) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration fundamental frequency of 4.3768 and the total mass of 424.26 kg, Figure 7 The color changes from black to white, indicating that the thickness gradually decreases and the volume fraction of the ceramic phase decreases from more to less. Figure 7 It can be seen that the ceramic phase material is mainly located inside the plate area, and there are also some areas where the metal phase gathers in the inner area. For the plate thickness distribution, the plate is thicker in the middle and center of the four sides, while the other areas are thinner. In addition, with the decrease of mass and fundamental frequency, a significant decrease in plate thickness is observed.

[0098] In summary, the optimization design method of multidimensional functional gradient materials proposed in the embodiment of the present invention establishes a material performance prediction model for multidimensional functional gradient materials, improves the efficiency of determining the total mass and automatic vibration fundamental frequency of the multidimensional functional gradient materials required in the iterative solution process of the multi-objective optimization function, and improves the optimization design efficiency. At the same time, the optimal optimized material volume fraction and optimized thickness are obtained by combining the multi-objective optimization algorithm, which significantly improves the macroscopic mechanical properties of the multidimensional functional gradient materials and reduces the overall mass of the sample, solving the current FGM performance prediction problems such as slow speed, low design dimension, small design freedom, and performance limitations. It is of great significance to the development of multidimensional functional gradient materials in the fields of aerospace, automobile, biomedicine, and military applications.

[0099] In order to better implement the optimization design method of the multidimensional functional gradient material in the embodiment of the present invention, based on the optimization design method of the multidimensional functional gradient material, the embodiment of the present invention also provides an optimization design device for the multidimensional functional gradient material, such as Figure 8 As shown, the optimization design device 800 of the multi-dimensional functional gradient material includes: A multidimensional functional gradient material construction unit 801 is used to construct a multidimensional functional gradient material based on a non-uniform rational B-spline basis function; the multidimensional functional gradient material includes a plurality of control points; The material property prediction model training unit 802 is used to construct a sample set and train the initial material prediction model based on the sample set to obtain a fully trained material property prediction model; The material parameter optimization design unit 803 is used to construct a multi-objective optimization function with the minimum total mass and the maximum free vibration fundamental frequency as the objectives, iteratively solve the multi-objective optimization function, and obtain the control point optimized material volume fraction and optimized thickness; Among them, the prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material performance prediction model.

[0100] The multidimensional functional gradient material optimization design device 800 provided in the above embodiment can implement the technical solution described in the above embodiment of the multidimensional functional gradient material optimization design method. The specific implementation principles of the above modules or units can refer to the corresponding contents in the above embodiment of the multidimensional functional gradient material optimization design method, which will not be repeated here.

[0101] like Fig. 9 As shown, the present invention also provides an optimization design device 900. The optimization design device 900 includes a processor 901, a memory 902 and a display 903. Fig. 9 Only some components of the optimization design device 900 are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0102] In some embodiments, the processor 901 can be a central processing unit (CPU), a microprocessor or other data processing chip, which is used to run the program code or process data stored in the memory 902, such as the optimization design method of the multi-dimensional functional gradient material in the present invention.

[0103] In some embodiments of the present invention, the processor 901 may be a single server or a server group. The server group may be centralized or distributed. In some embodiments, the processor 901 may be local or remote. In some embodiments, the processor 901 may be implemented in a cloud platform. In one embodiment, the cloud platform may include a private cloud, a public cloud, a hybrid cloud, a community cloud, a distributed cloud, an internal cloud, a multi-cloud, etc., or any combination thereof.

[0104] In some embodiments, the memory 902 may be an internal storage unit of the optimization design device 900, such as a hard disk or memory of the optimization design device 900. In other embodiments, the memory 902 may also be an external storage device of the optimization design device 900, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the optimization design device 900.

[0105] Furthermore, the memory 902 may include both an internal storage unit of the optimization design device 900 and an external storage device. The memory 902 is used to store application software for installing the optimization design device 900 and various data.

[0106] In some embodiments, the display 903 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 903 is used to display information of the optimization design device 900 and to display a visual user interface. The components 901-903 of the optimization design device 900 communicate with each other through a system bus.

[0107] In some embodiments of the present invention, when the processor 901 executes the optimization design program of the multi-dimensional functional gradient material in the memory 902, the following steps may be implemented: Constructing a multidimensional functional gradient material based on non-uniform rational B-spline basis functions; the multidimensional functional gradient material includes multiple control points; Construct a sample set, and train the initial material prediction model based on the sample set to obtain a fully trained material performance prediction model; A multi-objective optimization function is constructed with the goal of minimizing the total mass and maximizing the fundamental frequency of free vibration. The multi-objective optimization function is iteratively solved to obtain the optimized material volume fraction and optimized thickness of the control point. Among them, the prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material performance prediction model.

[0108] It should be understood that: when the processor 901 executes the optimization design program of the multi-dimensional functional gradient material in the memory 902, in addition to the above functions, other functions can also be realized. For details, please refer to the description of the corresponding method embodiment above.

[0109] Furthermore, the embodiment of the present invention does not specifically limit the type of the optimization design device 900 mentioned. The optimization design device 900 may be a portable optimization design device such as a mobile phone, a tablet computer, a personal digital assistant (PDA), a wearable device, a laptop computer, etc. Exemplary embodiments of portable optimization design devices include but are not limited to portable optimization design devices equipped with IOS, Android, Microsoft or other operating systems. The above-mentioned portable optimization design device may also be other portable optimization design devices. It should also be understood that in some other embodiments of the present invention, the optimization design device 900 may not be a portable optimization design device, but a desktop computer with a touch-sensitive surface (such as a touch panel).

[0110] Correspondingly, an embodiment of the present invention also provides a computer-readable storage medium, which is used to store computer-readable programs or instructions. When the program or instructions are executed by a processor, it can implement the steps or functions in the optimization design method of multidimensional functional gradient materials provided in the above-mentioned method embodiments.

[0111] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware (such as a processor, a controller, etc.) through a computer program, and the computer program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0112] The above is a detailed introduction to the optimization design method, device, equipment and medium of a multidimensional functional gradient material provided by the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for technical personnel in this field, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A method for optimizing the design of multidimensional functional gradient materials, characterized in that: include: Constructing multidimensional functionally graded materials based on non-uniform rational B-spline basis functions; The multi-dimensional functional gradient material includes a plurality of control points; Constructing a sample set, and training an initial material prediction model based on the sample set to obtain a fully trained material performance prediction model; A multi-objective optimization function is constructed with the goal of minimizing the total mass and maximizing the fundamental frequency of free vibration, and the multi-objective optimization function is iteratively solved to obtain the optimized material volume fraction and optimized thickness of the control point; The prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material property prediction model.

2. The optimization design method of multidimensional functional gradient material according to claim 1, characterized in that: The multi-dimensional functional gradient material is a composite material of a metal phase material and a ceramic phase material; the multi-objective optimization function is: In the formula, is the total mass; is the material volume fraction of the ceramic phase material at the jth control point; is the thickness of the jth control point; is the volume fraction of ceramic phase material at any point in space; is the density of the ceramic phase material; is the mass density of the metallic phase material at room temperature; is the total volume of the multi-dimensional functional gradient material, which is related to the thickness; is the dimensionless free vibration fundamental frequency; is the first-order natural frequency of free vibration; is the side length of the square multi-dimensional functional gradient material; is the elastic modulus of the metal phase material at room temperature; is the Poisson's ratio of the metallic phase material at room temperature; is the initial thickness of the square multi-dimensional functional gradient material; is the non-uniform rational B-spline basis function; n×m×l is the total number of control points.

3. The optimization design method of multidimensional functional gradient material according to claim 2, characterized in that: The constraints of the multi-objective optimization function are: In the formula, is the total material volume fraction of ceramic phase material; is the element stiffness matrix; is the temperature-dependent element thermal stiffness matrix; is the unit mass matrix; is the unit displacement vector.

4. The optimization design method of multidimensional functional gradient material according to claim 1, characterized in that: The multi-dimensional functional gradient material comprises a target sub-region and at least one mirror sub-region symmetrical to the target sub-region; The multi-objective optimization function is a function corresponding to the target sub-region, and the method includes: Determine the target material volume fraction and target thickness of each control point in the target sub-area based on the multi-objective optimization function and the material property prediction model; The target material volume fraction and the target thickness are mirror-symmetrically processed to obtain the mirror material volume fraction and the target thickness of each control point in the mirror sub-region.

5. The optimization design method of multi-dimensional functional gradient material according to claim 1, characterized in that: The sample set includes a plurality of sample data, wherein the sample data includes a material volume fraction, a thickness, a total mass reference value, and a free vibration fundamental frequency reference value; The constructing of the sample set includes: Randomly initialize the material distribution and geometric model to obtain the material volume fraction and thickness of each control point; Determining the spatial thermal field of the multi-dimensional functional gradient material based on high-throughput parallel isogeometric analysis; A total mass reference value and a free vibration fundamental frequency reference value of the multi-dimensional functional gradient material are determined based on the spatial thermal field.

6. The optimization design method of multi-dimensional functional gradient material according to claim 5, characterized in that: The initial material prediction model is trained based on the sample set to obtain a fully trained material performance prediction model, including: Dividing the sample set into a training set and a validation set in a preset ratio; Training the initial material performance prediction model based on the training set to obtain a performance prediction model to be verified; The performance prediction model to be verified is verified based on the verification set, and when the verification passes, the performance prediction model to be verified is the material performance prediction model.

7. The optimization design method of multi-dimensional functional gradient material according to claim 1, characterized in that: The material property prediction model includes a first three-dimensional convolution module, a first pooling layer, multiple second three-dimensional convolution modules, a flattening layer and a fully connected layer connected in sequence, and the first three-dimensional convolution module and each of the second three-dimensional convolution modules include a three-dimensional convolution layer, a batch normalization layer and an activation function layer.

8. An optimization design device for multi-dimensional functional gradient materials, characterized in that: include: A multi-dimensional functional gradient material construction unit, used to construct a multi-dimensional functional gradient material based on a non-uniform rational B-spline basis function; The multi-dimensional functional gradient material includes a plurality of control points; A material property prediction model training unit is used to construct a sample set and train an initial material prediction model based on the sample set to obtain a fully trained material property prediction model; A material parameter optimization design unit is used to construct a multi-objective optimization function with the goal of minimizing the total mass and maximizing the fundamental frequency of free vibration, and iteratively solve the multi-objective optimization function to obtain the optimized material volume fraction and optimized thickness of the control point; The prediction performance required in the iterative solution process of the multi-objective optimization function is determined based on the material property prediction model.

9. An optimization design device, characterized in that: comprising a memory and a processor, wherein: The memory is used to store programs; The processor is coupled to the memory and is used to execute the program stored in the memory to implement the steps in the optimization design method of the multi-dimensional functional gradient material as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: Used to store computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the optimization design method of the multi-dimensional functional gradient material described in any one of claims 1 to 7.

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