A high-fidelity finite element optimization method for thermal conductivity modeling of dock folded structures

Abstract

The present invention discloses a high-fidelity finite element optimization method and device, including: establishing a non-local heat conduction model based on a three-dimensional homogenization problem with a temperature gradient only in the x-direction; converting the non-local homogenization term of the temperature gradient in the x-direction into the form of the temperature difference between two surfaces obtained by a finite element tool to obtain a simplified model under a uniform temperature field condition; considering the influence of width and height, obtaining a heat conduction model of a three-dimensional microstructure effect; obtaining an effective thermal conductivity calculation formula based on a metamaterial structure with infinite size in three directions, obtaining an effective thermal conductivity standard value according to the heat conduction model of the three-dimensional microstructure effect through a high-fidelity finite element method, optimizing the effective thermal conductivity calculation formula, and obtaining an optimized effective thermal conductivity calculation model. The method can more accurately simulate and predict the thermal performance of complex materials at the microstructure scale, especially when considering non-local effects, and improve the accuracy and practicality of the heat transfer model.

Description

Technical Field

[0001] The invention relates to the field of heat conduction of dock folding device structures, and in particular to a high-fidelity finite element optimization method for thermal conductivity modeling of dock folding structural parts. Background Art

[0002] With the development of shipbuilding and marine engineering technology, dock folding devices are located in docks. As important facilities for the manufacture, maintenance and overhaul of marine engineering equipment such as ships, dock folding devices generate a lot of heat during operation, which is mainly caused by mechanical movement and friction between metal parts. If the heat cannot be effectively dissipated, it may cause overheating of the structural parts, thereby affecting their performance and life, and may even cause safety accidents. In order to improve the heat dissipation performance of the dock folding device structural parts, filling them with complex lattice microstructures is one of the effective means. However, traditional heat transfer models often ignore the influence of the internal microstructure of the dock folding device structural parts on the macroscopic thermal performance, resulting in the inability to accurately describe key parameters such as temperature gradients. Although the existing homogenization method has solved this problem to some extent, it still fails to fully consider the non-local effect, that is, the influence of changes in material properties at a small scale on the macroscopic performance.

[0003] Therefore, how to conduct thermodynamic modeling of the dock folding structure and optimize the model, accurately simulate and predict the thermal properties of complex materials at the microstructure scale, optimize their heat transfer performance and thus improve the heat transfer performance is an urgent problem to be solved. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a high-fidelity finite element optimization method and device for thermal conductivity modeling of dock folded structures, which can optimize the thermal conductivity model. The optimized model can more accurately simulate and predict the thermal properties of complex materials at the microstructure scale, especially when considering non-local effects, thereby improving the accuracy and practicality of the heat transfer model.

[0005] To achieve the above purpose, the present invention adopts the following technical solution.

[0006] In some embodiments, a high-fidelity finite element optimization method for thermal conductivity modeling of a dock folded structure is provided, wherein the dock folded structure includes a metamaterial structure, and the high-fidelity finite element optimization method includes the following steps:

[0007] S1: A nonlocal heat conduction model is established based on a three-dimensional homogenization problem with temperature gradient only in the x-direction.

[0008] The non-local heat conduction model in step S1 is:

[0009]

[0010] in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, represents the nonlocal homogenization term of the heat flux in the x direction;

[0011] S2: Define non-local homogenization terms, including the non-local homogenization term of the temperature gradient in the x-direction and the non-local homogenization term of the heat flux in the x-direction, and express the mathematical form of the volume homogenization operator and the temperature gradient;

[0012] The volume homogenization operator <·> V in step S2 is defined as follows:

[0013]

[0014] Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x-direction, y-direction and z-direction, respectively;

[0015] S3: Using the method of integration by parts, the non-local homogenization term of the temperature gradient in the x direction is converted into the temperature difference between the two surfaces obtained by the finite element tool, and a simplified model under the condition of uniform temperature field is obtained;

[0016] Among them, the simplified model under the uniform temperature field condition in step S3 is:

[0017]

[0018] in,

[0019] S4: Combining the nonlocal heat conduction model, the nonlocal homogenization term of the heat flux in the x-direction and the simplified model under the condition of uniform temperature field, the heat conduction model of the three-dimensional microstructure effect is obtained by considering the temperature gradient in the x-direction and the influence of width and height;

[0020] The thermal conductivity model of the three-dimensional microstructure effect in step S4 is:

[0021]

[0022] where ξ is the contribution fraction of the nonlocal phase with size-dependent effect, k x , k y , k z are the thermal conductivities in the x, y, and z directions, respectively, and K is the thermal conductivity;

[0023] S5: Based on the infinite metamaterial structure in three directions, a multi-scale method and periodic boundary conditions are used to obtain a calculation formula for effective thermal conductivity; the three directions include the x direction, the y direction, and the z direction based on an orthogonal coordinate system;

[0024] The effective thermal conductivity calculation formula in step S5 is:

[0025]

[0026] Where l is the intrinsic length;

[0027] S6: Obtain the standard value of effective thermal conductivity based on the thermal conductivity model of the three-dimensional microstructure effect by high-fidelity finite element method

[0028] S7: According to the standard value of effective thermal conductivity The effective thermal conductivity calculation formula is optimized to obtain an optimized effective thermal conductivity calculation model.

[0029] In some embodiments, the simplified model under the uniform temperature field condition in step S3 is derived using the method of integration by parts, and setting the surfaces z=0.5L and z=-0.5L to be under the condition of a uniform temperature field.

[0030] In some embodiments, the non-local homogenization term of the temperature gradient within the volume in step S3 is The calculation is evaluated by the temperature difference on the surfaces perpendicular to the x-direction at the two ends of the volume.

[0031] In some embodiments, the extrinsic length of the metamaterial structure is compared to the intrinsic length

[0032] In some embodiments, the effective thermal conductivity in step S4 depends not only on the temperature gradient in the x direction, but also on the y and z directions; the effective thermal conductivity in step S5 depends not only on the temperature gradient in the x direction, but also on the width and height.

[0033] In some embodiments, a high-fidelity finite element optimization device for thermal conductivity modeling of a dock folded structure is also provided, wherein the dock folded structure includes a metamaterial structure, and the dock folded structure optimization device includes the following modules:

[0034] Non-local heat conduction model building module: Based on the three-dimensional homogenization problem with temperature gradient only in the x-direction, a non-local heat conduction model is built;

[0035] Non-local homogenization term definition module: defines non-local homogenization terms, including the non-local homogenization term of the temperature gradient in the x-direction and the non-local homogenization term of the heat flux in the x-direction, and expresses the mathematical form of the volume homogenization operator and the temperature gradient;

[0036] Simplified model building module under uniform temperature field conditions: using the partial integration method, the non-local homogenization term of the temperature gradient in the x-direction is converted into the temperature difference between the two surfaces obtained by the finite element tool, and the simplified model under uniform temperature field conditions is obtained;

[0037] Thermal conductivity model building module for three-dimensional microstructure effect: Combine the non-local heat conduction model, the non-local homogenization term of the heat flux in the x-direction and the simplified model under the condition of uniform temperature field, consider the temperature gradient in the x-direction and the influence of width and height, and obtain the thermal conductivity model of the three-dimensional microstructure effect;

[0038] Effective thermal conductivity calculation formula acquisition module: Based on the infinite metamaterial structure in three directions, the effective thermal conductivity calculation formula is obtained using a multi-scale method and periodic boundary conditions; the three directions include the x direction, y direction, and z direction based on an orthogonal coordinate system;

[0039] Optimization module: obtaining an effective thermal conductivity standard value according to the thermal conductivity model of the three-dimensional microstructure effect through a high-fidelity finite element method; optimizing the effective thermal conductivity calculation formula according to the effective thermal conductivity standard value to obtain an optimized effective thermal conductivity calculation model;

[0040] in,

[0041] The non-local heat conduction model is:

[0042]

[0043] in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, represents the nonlocal homogenization term of the heat flux in the x direction;

[0044] The volume homogenization operator <·> V The definition is as follows:

[0045]

[0046] Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x-direction, y-direction and z-direction, respectively;

[0047] The simplified model under the uniform temperature field condition is:

[0048]

[0049] in,

[0050] The thermal conductivity model of the three-dimensional microstructure effect is:

[0051]

[0052] where ξ is the contribution fraction of the nonlocal phase with size-dependent effect, k x , k y , k z are the thermal conductivities in the x, y, and z directions, respectively, and κ is the thermal conductivity;

[0053] The effective thermal conductivity calculation formula is:

[0054]

[0055] where l is the intrinsic length.

[0056] In some embodiments, the effective thermal conductivity calculation formula is optimized according to the effective thermal conductivity standard value to obtain an optimized effective thermal conductivity calculation model, including:

[0057] According to the standard value of the effective thermal conductivity and the initial contribution fraction ξ, the intrinsic length l is obtained by inverse calculation according to the effective thermal conductivity calculation formula.

[0058] In some embodiments, an electronic device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements any of the above-described methods when executing the program.

[0059] In some embodiments, a computer-readable storage medium is further provided, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, any of the above-described methods is implemented.

[0060] Compared with the prior art, the beneficial effects of the present invention are:

[0061] The non-local homogenization method for calculating the heat conduction of the dock folding device structure disclosed in the present invention can more accurately simulate and predict the thermal performance of the dock folding device structure filled with complex microstructures, especially when considering the non-local effect, which improves the accuracy and practicality of the heat transfer model. And the thermal conductivity model is optimized by the high-fidelity finite element method, which further improves the accuracy of the heat transfer model. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The figure is a schematic diagram of the overall process of a high-fidelity finite element optimization method according to an embodiment of the present invention.

[0063] Figure 2 The figure is a schematic diagram of a dock folding device according to an embodiment of the present invention.

[0064] Figure 3 It is a schematic diagram of a dock folding structure according to an embodiment of the present invention.

[0065] Figure 4 A schematic diagram of a dock folded structural component model filled with complex microstructures according to an embodiment of the present invention.

[0066] Figure 5 The effective thermal conductivity of the porous titanium structure predicted by the nonlocal model, multiscale method, parallel model and high-fidelity finite element method (FEM) for microstructure enhancement according to an embodiment of the present invention.

[0067] Figure 6 FIG. 1 is a schematic diagram showing a comparison of effective thermal conductivities calculated by a high-fidelity finite element method (High-fidelity FEM) and a microstructure enhanced nonlocal model (Nonlocal model) according to an embodiment of the present invention.

[0068] Figure 7 A schematic diagram of a module of a high-fidelity finite element optimization device according to an embodiment of the present invention.

[0069] Figure 8 A schematic diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0071] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0072] Figure 1 The figure is a schematic diagram of the overall process of a high-fidelity finite element optimization method according to an embodiment of the present invention. Figure 4This is a schematic diagram of a dock folding structure model filled with complex microstructures according to an embodiment of the present invention. Figure 1 and Figure 4 In some embodiments, a high-fidelity finite element optimization method is provided, wherein the dock folding structure comprises a metamaterial structure filled with a complex microstructure, and the method comprises the following steps:

[0073] S1: A nonlocal heat conduction model is established based on a three-dimensional homogenization problem with temperature gradient only in the x-direction.

[0074] S2: Define non-local homogenization terms, including the non-local homogenization term of the temperature gradient in the x-direction and the non-local homogenization term of the heat flux in the x-direction, and express the mathematical form of the volume homogenization operator and the temperature gradient;

[0075] S3: Using the method of integration by parts, the non-local homogenization term of the temperature gradient in the x direction is converted into the temperature difference between the two surfaces obtained by the finite element tool, and a simplified model under the condition of uniform temperature field is obtained;

[0076] S4: Combining the nonlocal heat conduction model, the nonlocal homogenization term of the heat flux in the x-direction and the simplified model under the condition of uniform temperature field, the heat conduction model of the three-dimensional microstructure effect is obtained by considering the temperature gradient in the x-direction and the influence of width and height;

[0077] S5: Based on the infinite metamaterial structure in three directions, a multi-scale method and periodic boundary conditions are used to obtain a calculation formula for effective thermal conductivity; the three directions include the x direction, the y direction, and the z direction based on an orthogonal coordinate system;

[0078] S6: Obtain the standard value of effective thermal conductivity based on the thermal conductivity model of the three-dimensional microstructure effect by high-fidelity finite element method

[0079] S7: According to the standard value of effective thermal conductivity The effective thermal conductivity calculation formula is optimized to obtain an optimized effective thermal conductivity calculation model.

[0080] in,

[0081] The non-local heat conduction model in the S1 step is:

[0082]

[0083] in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, represents the nonlocal homogenization term of the heat flux in the x direction;

[0084] The volume homogenization operator in the S2 step <·> V The definition is as follows:

[0085]

[0086] Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x-direction, y-direction and z-direction, respectively;

[0087] The simplified model under the uniform temperature field condition in step S3 is:

[0088]

[0089] in,

[0090] The thermal conductivity model of the three-dimensional microstructure effect in step S4 is:

[0091]

[0092] where ξ is the contribution fraction of the nonlocal phase with size-dependent effect, k x , k y , k z are the thermal conductivities in the x, y, and z directions, respectively, and κ is the thermal conductivity;

[0093] The calculation formula for the effective thermal conductivity in step S5 is:

[0094]

[0095] where l is the intrinsic length.

[0096] In some embodiments of the present invention, the execution subject for implementing the above high-fidelity finite element optimization method may be an electronic device, such as a laptop computer, a desktop computer or other terminal device, and of course, may also be a host computer or a server, and the server may be a local or remote server.

[0097] Figure 2 The figure is a schematic diagram of a dock folding device according to an embodiment of the present invention. Figure 3 FIG. 1 is a schematic diagram of a dock folding structure according to an embodiment of the present invention. Figure 2 and Figure 3The dock folding device includes a folding mechanism, a mobile hydraulic oil station, a watertight junction box, etc. The folding mechanism is mainly a mechanical device to realize the erection and folding of the dock pier; the mobile hydraulic oil station is used to provide folding power, electrical and manual control of the device; the watertight junction box is used to collect the status signal of the outboard watertight travel switch of the folding mechanism, and transmit it to the mobile hydraulic oil station for status display and control. The folding mechanism includes a folding frame, a folding cylinder, a ballast, a pulley block, an outboard watertight travel switch, etc. In some embodiments, the dock folding structure can be a folding cylinder, a pulley block ( Figure 3 As shown) and other structural parts.

[0098] Specifically, the process of establishing a non-local heat conduction model is as follows:

[0099] For a three-dimensional homogenization problem with a temperature gradient only in the x-direction, the nonlocal homogenization model can be expressed as:

[0100]

[0101] in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, Represents the nonlocal homogenization term for the heat flux in the x-direction.

[0102] Specifically, they are in the following form:

[0103]

[0104] Among them, the volume homogenization operator <·> V and temperature gradient are defined as follows:

[0105]

[0106] Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x direction, y direction and z direction, respectively. Specifically, L, W and H are the length, width and height of the composite structure made of the metamaterial having a solid network gyroid unit cell.

[0107] Specifically, the simplified model derivation process under uniform temperature field conditions is as follows:

[0108] Using the method of integration by parts, the nonlocal homogenization term of the temperature gradient in equation (3) is It can also be expressed as:

[0109]

[0110] If the temperature field applied to the surfaces z = 0.5L and z = -0.5L is uniform, it can be further simplified as:

[0111]

[0112] in:

[0113]

[0114] Specifically, the derivation process of the thermal conductivity model of the three-dimensional microstructure effect is as follows:

[0115] Through equations (1), (2), and (7), the effective thermal conductivity can be solved by the following equation:

[0116]

[0117] The uniform constitutive relation for heat transfer is given by:

[0118]

[0119] Where κ is the thermal conductivity, l is the intrinsic length, and ξ is the contribution fraction of the size-dependent effect of the nonlocal phase. x, y, and z are the coordinate positions in the x, y, and z directions, respectively, and x', y', and z' are the coordinate positions of the points adjacent to the coordinate positions x, y, and z, respectively.

[0120] Substituting formula (10) into formula (9), we can get:

[0121]

[0122] It is able to capture three-dimensional microstructural effects. Among them:

[0123]

[0124] In some embodiments, the effective thermal conductivity depends not only on the temperature gradient in the x-direction, but also on the y-direction and the z-direction. The method based on non-local homogenization modeling proposed in the present application can capture the three-dimensional microstructure effect.

[0125] Specifically, the derivation process of the effective thermal conductivity calculation formula is as follows:

[0126] In some embodiments, the metamaterial structure is a composite structure, including a porous titanium structure and a titanium-aluminum composite structure. For the porous titanium structure, the filling material is air. For the titanium-aluminum composite structure, the filling material is aluminum. For an infinite metamaterial structure with infinite cells in all three directions, the intrinsic length is much smaller than the extrinsic length (infinity). In some embodiments, the extrinsic length of the metamaterial structure is much smaller than the intrinsic length. That is, the nonlocal contribution can be ignored. In this case, ξ = 0, and the size-free thermal conductivity κ can be calibrated. In order to obtain the size-free thermal conductivity, we impose periodic boundary conditions on a unit cell in all three directions for simulation. This method is called the multiscale method. Let us set a temperature difference of 0.1K on the two surfaces of a unit cell. Combining the multiscale method with the material properties, the size-free effective thermal conductivity is κ = 9.4062W / (m·K) for the porous titanium structure; and κ = 81.0510W / (m·K) for the titanium-aluminum composite structure. Since the size-free thermal conductivity κ is calibrated based on the multiscale method, where infinity is achieved by using periodic boundary conditions, the size-free thermal conductivity κ is size-free and cannot capture size-dependent heat transfer phenomena.

[0127] Integrate equations (13) and (14), k y and k z can be easily determined as:

[0128]

[0129] According to equation (7), k in equation (12) x can be rewritten as:

[0130]

[0131] Substituting equations (15) and (16) into equation (11), we obtain:

[0132]

[0133] In some embodiments, the effective thermal conductivity depends not only on the temperature gradient in the x-direction, but also on the width and height. In some embodiments, the height variation in the z-direction is selected to obtain a size-dependent thermal conductivity to calibrate the intrinsic length l and the non-local contribution fraction ξ.

[0134] In some embodiments, a high-fidelity finite element method is used to obtain a standard value of effective thermal conductivity based on the thermal conductivity model of the three-dimensional microstructure effect; based on the standard value of effective thermal conductivity, the effective thermal conductivity calculation formula is optimized to obtain an optimized effective thermal conductivity calculation model.

[0135] At the same time, this application proposes a microstructure enhanced non-local continuum model to simulate the ability of heat transfer in metamaterials.

[0136] Consider two composite structures made of metamaterials: a porous titanium structure and a titanium-aluminum composite structure. Solid network gyroid cells are used to represent these two structures, namely, the porous titanium structure and the titanium-aluminum composite structure. The level set approximation (geometric control equation) of the solid network gyroid cell is given by the following formula:

[0137] f(x,y,z) = sin(ωx)cos(ωy)

[0138] +sin(ωz)cos(ωx)+sin(ωy)cos(ωz)(19)

[0139] Here, ω = 2π / a, where a is the lattice constant, which is chosen as the characteristic length. The intrinsic length l = e0a, where e0 represents the strength of the nonlocal effect, which is an unknown parameter to be calibrated. The intrinsic length depends on the characteristic length and the strength of the nonlocal effect. The value of the parameter f(x,y,z) = c can be defined as a design variable to control the porosity volume fraction V p or relative density. For the solid gyroid unit cell, the solid volume is restricted by the minimum surface, i.e., f(x,y,z) < c or f(x,y,z) > c. The spatial volume V of the gyroid unit cell is a 3 , the volume of the matrix material (solid) is V m , and the porosity V p is defined as:

[0140]

[0141] The porosity V p can be filled with a filling material. For the porous titanium structure, the filling material is air; for the titanium-aluminum composite structure, the filling material is aluminum. In some embodiments of the present application, the porosity V p is 40% in all cases.

[0142] In some embodiments of the present application, the nonlocal parameters of the proposed model are calibrated using the high-fidelity finite element method (High-fidelity FEM). In some embodiments, the high-fidelity finite element method (FEM) can be some methods known in the prior art, and the high-fidelity finite element method (FEM) can consider all microstructural features. High-fidelity finite elements usually require a large amount of computing resources because fully resolved microstructures need to be considered. In high-fidelity finite elements, the classical Fourier model is adopted. However, for large engineering structures, high-fidelity finite elements require extremely large computing resources because fully resolved microstructures must be considered, and even multi-physics problems are often impossible to simulate. The microstructure-enhanced nonlocal model can solve the computational problem.

[0143] According to the multiscale theory, the microstructure of the representative volume element (RVE) can be equivalent to a linear isotropic homogeneous medium. In some embodiments, the nonlocal effect can transform the heterogeneous metamaterial into an equivalent homogeneous medium, thereby capturing the size-dependent thermodynamic behavior.

[0144] For the case of non-locally homogeneous media, the second-order tensor κ of thermal conductivity can be simplified to:

[0145]

[0146] where the thermal conductivity κ is now a scalar, e i and e j represents the unit basis vector, Represents a tensor product.

[0147] Without loss of generality, in some embodiments, a three-dimensional steady-state heat conduction problem with a temperature gradient only along the x-direction is considered. Within the framework of the microstructure-rich non-local model of the present application, the uniform constitutive relation for heat transfer can be written as:

[0148]

[0149] Wherein, L, W, and H represent the length, width, and height of the composite structure made of the metamaterial having the gyroid unit cell, respectively. In some embodiments, the effective thermal conductivity depends not only on the temperature gradient in the x direction, but also on the width and height. In some embodiments, the composite structure such as Figure 4 As shown. It has a composite structure of infinite length L and fixed width W=1a. The height H can be varied from 1a to 10a in order to characterize size-dependent heat transfer phenomena. In some embodiments, a=1m. Although the temperature gradient changes only in the x-direction, the non-local heat flux in the x-direction changes in all three directions. This is a major difference between the local (classical) model without microstructure and the microstructure-enhanced non-local model.

[0150] In some embodiments of the present application, the one-dimensional microstructure enhanced non-local continuous model can be expressed as:

[0151]

[0152] It can be verified that the heat fluxes in the local Fourier model and the microstructure-enhanced nonlocal continuum model are identical when considering a uniform temperature gradient field.

[0153] The cells in metamaterials are usually very complex and the structure is three-dimensional. For three-dimensional heat transfer problems, the one-dimensional microstructure enhanced non-local continuum model (Equation 22) can be expanded to the following form, namely the three-dimensional microstructure enhanced non-local continuum model:

[0154]

[0155] The above analysis shows that the microstructure-enhanced nonlocal continuum model is naturally suitable for constructing metamaterial structure models, because the local Fourier-like term can capture the pure microstructure effect, while the spatially varying exponent of the power-law kernel function in the nonlocal term captures the position-dependent strength of the coupling interaction between the microstructure effect and the nonlocal effect.

[0156] In the embodiment of the present application, although the high-fidelity finite element method is time-consuming, it can take into account all microstructural features and thus has high-precision results. Therefore, the homogenized model equation (1) based on the accurate results obtained by the high-fidelity finite element method can be used to calibrate the non-local parameters and intrinsic length of the proposed model. Through the high-fidelity finite element method, the effective thermal conductivity is obtained according to equation (11).

[0157] For comparison, a parallel model or Voigt-type thermal conductivity model is introduced. When the temperature gradient is considered to be constant, the effective thermal conductivity based on the classical Fourier model is It can be expressed as:

[0158]

[0159] Here V p is the volume fraction of the inclusion phase. In the embodiment of the present application, the inclusion phase is air or aluminum, and V p =40%. m and κ p denote the thermal conductivity of the matrix (titanium) and the inclusion phase (air or aluminum), respectively. The effective thermal conductivity in equation (26) is Same as in the parallel model or Voigt-type thermal conductivity model. Same as size-dependent thermal conductivity in the microstructure-enhanced nonlocal model Unlike (Equation 11), the parallel model is size-independent.

[0160] In the x-direction, the temperature difference between the two surfaces was set to 0.1 K. Two composite structures made of metamaterials composed of gyroid cells were used, namely a porous titanium structure and a titanium-aluminum composite structure. The characteristic length a (lattice constant) was fixed to 1 meter. The x-axis represents the length direction, which is infinite and modeled using periodic boundary conditions. The y-axis represents the width direction, which is fixed to 1a. The height is measured in the z-direction and can be varied to characterize size-dependent heat transfer phenomena.

[0161] Figure 5The effective thermal conductivity of porous titanium structures predicted by nonlocal model, multiscale method, parallel model and high-fidelity FEM for microstructure enhancement. Figure 5 It can be observed that the effective thermal conductivity evaluated by the high-fidelity finite element method Dependent on height size. Since the parallel model cannot take into account the microstructural effects and the multiscale method ignores the size-dependent effects, both methods fail to capture the highly dependent thermal conductivity predicted by the high-fidelity finite element method. For porous titanium structures, the error range of the parallel model is between 44.1% and 44.9% because it considers a constant temperature gradient and ignores the microstructural effects. Compared with the parallel model, the multiscale method has higher accuracy. This is because the multiscale method can take into account the microstructural effects but ignores the size-dependent effects characterized by the intrinsic length. For porous titanium structures, the intrinsic length is comparable to the extrinsic length (such as width). The error range of the multiscale method is reduced to between 7.2% and 1.4%. Unlike the parallel model without microstructure and the multiscale method without size dependence, the microstructure-enhanced nonlocal continuum model proposed in this application combines microstructural effects and size-dependent effects. Therefore, the nonlocal homogenized thermal conductivity can capture the highly size-dependent heat transfer behavior and is in good agreement with the results evaluated by the high-fidelity finite element method. In some embodiments, the nonlocal parameter e0 is calibrated to 0.2681, the nonlocal contribution fraction ξ is calibrated to 23.7%, and for V p =40% porous titanium metamaterial structure, k x =12.36W / (m·K). The effective thermal conductivity of various metamaterial structures can be stored in a database. By selecting the effective thermal conductivity in the database, the temperature distribution of the microstructure enhanced non-local model can be calculated using traditional heat transfer analysis, which is similar to the method commonly used in the classical Fourier model. Unlike the high-fidelity finite element method, the microstructure enhanced non-local continuum model does not consider the microstructure characteristics, and the method of optimizing the microstructure enhanced non-local continuum model is more efficient than the high-fidelity finite element method. In an embodiment of the present application, the microstructure enhanced non-local modeling optimization method is an efficient and accurate method.

[0162] In some embodiments of the present application, a microstructure enhanced non-local modeling optimization method for a dock folding structure is proposed, wherein the dock folding structure includes a metamaterial structure, and the microstructure enhanced non-local modeling optimization method includes the following steps:

[0163] S1: Based on the heat flow and thermal resistance of the metamaterial structure in one dimension, a discrete variable model is introduced to construct a non-classical heat transfer continuum model; the discrete variable model includes discrete units and discrete parameters, and the metamaterial structure is a porous metamaterial;

[0164] S2: Using the lumped element method and combining the non-local effect, the porous metamaterial is divided into multiple discrete elements, and the one-dimensional lumped element model of the metamaterial structure is obtained by combining the microstructure effect and the size-dependent effect;

[0165] S3: replacing the discrete parameters with corresponding continuous medium form parameters, using integral form and integration by parts method to obtain a one-dimensional microstructure enhanced non-local continuous model of heat transfer of metamaterial structure; wherein the length of the metamaterial structure on a macroscopic scale is much smaller than the intrinsic length;

[0166] S4: Ignoring the size dependence effect, the one-dimensional microstructure enhanced non-local continuous model of heat transfer in metamaterial structure is simplified to a multi-scale method model, and combined with the normalization condition, a three-dimensional microstructure enhanced non-local continuous model of metamaterial structure is obtained; in which the external length of the metamaterial structure is much larger than the intrinsic length;

[0167] S5: calculating the temperature distribution of the metamaterial structure based on the three-dimensional microstructure enhanced non-local continuous model of the metamaterial structure, and optimizing the metamaterial structure based on the temperature distribution;

[0168] The non-classical heat transfer continuum model in step S1 is:

[0169]

[0170] Where Q represents thermal energy, t represents time, is the internal heat flow of the discrete unit, T1 and T2 represent the temperatures of two adjacent lumped units, and k is the thermal conductivity, which is defined as follows:

[0171]

[0172] Where R is the thermal resistance, L e represents the total length of the lumped element, A represents the cross-sectional area, and κ represents the thermal conductivity;

[0173] The one-dimensional lumped unit model of the metamaterial structure in step S2 is:

[0174]

[0175] in, represents the internal heat flow of the i-th cell, i and j represent the i-th and j-th cells respectively, and x i and x jThey represent the coordinate positions of the i-th cell and the j-th cell respectively, Δx is the distance between two adjacent lumped cells, i.e., the length on the macroscopic scale, l is the intrinsic length, i.e., the intrinsic length. is the coefficient determined according to the normalization condition, ξ is the contribution fraction of the non-local phase considering the size dependence effect, T i and T j are the temperatures of the ith and jth cells, respectively;

[0176] The one-dimensional microstructure enhanced non-local continuous model in step S3 is:

[0177]

[0178] Wherein, the independent variable x is the coordinate position, x' is the coordinate position of the point adjacent to the coordinate position x after replacing the discrete parameter with the corresponding continuous medium form, T(x) is the temperature at the coordinate position x, T(x') is the temperature at the coordinate position x', and q x is the heat flux:

[0179]

[0180] The three-dimensional microstructure enhanced non-local continuous model in step S4 is:

[0181]

[0182] in, is the Hamiltonian operator, T is the temperature, x, y, z are the coordinate positions in the x, y, and z directions respectively, x', y', z' are the coordinate positions of the points adjacent to the coordinate positions x, y, and z after the discrete parameters are replaced by the corresponding continuous medium forms, and κ is the thermal conductivity in vector form.

[0183] like Figure 6 The effective thermal conductivity of the titanium-aluminum composite structure evaluated by the high-fidelity finite element method is shown in Figure 2. It is also highly size-dependent. The effective thermal conductivities of the titanium-aluminum composite structure predicted by the parallel model and the multiscale method are 107.94 W / (m·K) and 81.0510 W / (m·K), respectively. These two effective thermal conductivities are much larger than the values ​​predicted by the high-fidelity finite element method. Since the proposed microstructure-enhanced nonlocal model combines the microstructure effect and the size-dependent effect, the nonlocal homogenized thermal conductivity is able to capture the highly size-dependent heat transfer behavior and shows good consistency with the results evaluated by the high-fidelity finite element method, such as Figure 7 As shown. The nonlocal parameter e0 is calibrated to 0.2661, the nonlocal contribution fraction ξ is calibrated to 26.61%, and the k of the titanium-aluminum composite structure is x= 100.3 W / (m·K). The proposed model can achieve prediction accuracy consistent with the high-fidelity finite element model of the titanium-aluminum composite structure.

[0184] Figure 7 A schematic diagram of a module of a high-fidelity finite element optimization device for modeling thermal conductivity of a dock folded structure according to an embodiment of the present invention. Figure 7 In some embodiments of the present application, a high-fidelity finite element optimization device is further provided, wherein the dock folding structure comprises a metamaterial structure, and the dock folding structure optimization device comprises the following modules:

[0185] Non-local heat conduction model building module: Based on the three-dimensional homogenization problem with temperature gradient only in the x-direction, a non-local heat conduction model is built;

[0186] Non-local homogenization term definition module: defines non-local homogenization terms, including the non-local homogenization term of the temperature gradient in the x-direction and the non-local homogenization term of the heat flux in the x-direction, and expresses the mathematical form of the volume homogenization operator and the temperature gradient;

[0187] Simplified model building module under uniform temperature field conditions: using the partial integration method, the non-local homogenization term of the temperature gradient in the x-direction is converted into the temperature difference between the two surfaces obtained by the finite element tool, and the simplified model under uniform temperature field conditions is obtained;

[0188] Thermal conductivity model building module for three-dimensional microstructure effect: Combine the non-local heat conduction model, the non-local homogenization term of the heat flux in the x-direction and the simplified model under the condition of uniform temperature field, consider the temperature gradient in the x-direction and the influence of width and height, and obtain the thermal conductivity model of the three-dimensional microstructure effect;

[0189] Effective thermal conductivity calculation formula acquisition module: Based on the infinite metamaterial structure in three directions, the effective thermal conductivity calculation formula is obtained using a multi-scale method and periodic boundary conditions; the three directions include the x direction, y direction, and z direction based on an orthogonal coordinate system;

[0190] Optimization module: obtaining an effective thermal conductivity standard value according to the thermal conductivity model of the three-dimensional microstructure effect through a high-fidelity finite element method; optimizing the effective thermal conductivity calculation formula according to the effective thermal conductivity standard value to obtain an optimized effective thermal conductivity calculation model;

[0191] in,

[0192] The non-local heat conduction model is:

[0193]

[0194] in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, represents the nonlocal homogenization term of the heat flux in the x direction;

[0195] The volume homogenization operator <·> V The definition is as follows:

[0196]

[0197] Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x-direction, y-direction and z-direction, respectively;

[0198] The simplified model under the uniform temperature field condition is:

[0199]

[0200] in,

[0201] The thermal conductivity model of the three-dimensional microstructure effect is:

[0202]

[0203] where ξ is the contribution fraction of the nonlocal phase with size-dependent effect, k x , k y , k z are the thermal conductivities in the x, y, and z directions, respectively, and κ is the thermal conductivity;

[0204] The effective thermal conductivity calculation formula is:

[0205]

[0206] where l is the intrinsic length.

[0207] In some embodiments, the simplified model under the uniform temperature field condition is derived using the method of integration by parts, and setting the surfaces z=0.5L and z=-0.5L to be under the condition of a uniform temperature field.

[0208] In some embodiments, the high-fidelity finite element optimization device corresponds to the high-fidelity finite element optimization method, and each module has the function of implementing the high-fidelity finite element optimization method.

[0209] In some embodiments, a dock folding structure optimization system is also provided, which is optimized based on a thermal conductivity model of the dock folding structure. The dock folding structure optimization system includes the above-mentioned high-fidelity finite element optimization device based on the thermal conductivity model of the dock folding structure, and calculates the temperature distribution of the metamaterial structure based on the optimized effective thermal conductivity calculation model, and optimizes the metamaterial structure based on the temperature distribution.

[0210] In some embodiments, a dock folding structure optimization method is also provided, and the dock folding structure optimization method is optimized based on a thermal conductivity model of the dock folding structure. The dock folding structure optimization method includes the high-fidelity finite element optimization method based on the thermal conductivity model of the dock folding structure described in any of the above embodiments, and based on the optimized effective thermal conductivity calculation model, the temperature distribution of the metamaterial structure is calculated, and the metamaterial structure is optimized based on the temperature distribution.

[0211] Figure 8 FIG. 1 is a schematic diagram of an electronic device according to an embodiment of the present invention. Figure 8 In some embodiments, an electronic device is also provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements any of the above-described methods when executing the program.

[0212] At the hardware level, the electronic device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory, and may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 1 The high-fidelity finite element optimization method described above. Of course, in addition to the software implementation, this specification does not exclude other implementation methods, such as logic devices or a combination of software and hardware, etc., that is, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices. It can be understood that the method flow only needs to be slightly logically programmed in a hardware description language and programmed into an integrated circuit to obtain a hardware circuit that implements the logical method flow.

[0213] The above method can be implemented by a controller in any appropriate manner. For example, the controller can take the form of a microprocessor or processor and a computer-readable medium storing a computer-readable program code (such as software or firmware) that can be executed by the (micro)processor, a logic gate, a switch, an application-specific integrated circuit (ASIC), a programmable logic controller, and an embedded microcontroller. Examples of controllers include but are not limited to microcontrollers. The memory controller can also be implemented as part of the control logic of the memory. It is understandable that in addition to implementing the controller in a purely computer-readable program code manner, the controller can be implemented in the form of a logic gate, a switch, an application-specific integrated circuit, a programmable logic controller, and an embedded microcontroller by logically programming the method steps. Therefore, this controller can be considered as a hardware component, and the devices included therein for implementing various functions can also be regarded as structures within the hardware component. Or even, the devices for implementing various functions can be regarded as both software modules for implementing the method and structures within the hardware component.

[0214] The systems, devices, modules or units in the above embodiments may be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0215] For the convenience of description, the above device is described by dividing it into various modules according to its functions. Of course, when implementing this specification, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0216] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, this specification may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0217] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present specification. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0218] In some embodiments, a computer-readable storage medium is further provided, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, any of the above-described methods is implemented.

[0219] In some embodiments, these computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0220] In some embodiments, these computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0221] In some embodiments, the computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0222] In some embodiments, the memory may include non-permanent storage in a computer-readable medium, in the form of random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0223] In some embodiments, computer-readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, modules of programs or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0224] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions 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. A high-fidelity finite element optimization method for thermal conductivity modeling of dock folded structural parts, characterized in that: The dock folding structure comprises a metamaterial structure, and the high-fidelity finite element optimization method comprises the following steps: S1: A nonlocal heat conduction model is established based on a three-dimensional homogenization problem with temperature gradient only in the x-direction. The non-local heat conduction model in step S1 is: in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, represents the nonlocal homogenization term of the heat flux in the x direction; S2: Define non-local homogenization terms, including the non-local homogenization term of the temperature gradient in the x-direction and the non-local homogenization term of the heat flux in the x-direction, and express the mathematical form of the volume homogenization operator and the temperature gradient; Wherein, the volume homogenization operator in step S2 is V The definition is as follows: Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x-direction, y-direction and z-direction, respectively; S3: Using the method of integration by parts, the non-local homogenization term of the temperature gradient in the x direction is converted into the temperature difference between the two surfaces obtained by the finite element tool, and a simplified model under the condition of uniform temperature field is obtained; Among them, the simplified model under the uniform temperature field condition in step S3 is: in, S4: Combining the nonlocal heat conduction model, the nonlocal homogenization term of the heat flux in the x-direction and the simplified model under the condition of uniform temperature field, the heat conduction model of the three-dimensional microstructure effect is obtained by considering the temperature gradient in the x-direction and the influence of width and height; The thermal conductivity model of the three-dimensional microstructure effect in step S4 is: where ξ is the contribution fraction of the nonlocal phase with size-dependent effect, k x , k y , k z are the thermal conductivities in the x, y, and z directions, respectively, and κ is the thermal conductivity; S5: Based on the infinite metamaterial structure in three directions, a multi-scale method and periodic boundary conditions are used to obtain a calculation formula for effective thermal conductivity; the three directions include the x direction, the y direction, and the z direction based on an orthogonal coordinate system; The effective thermal conductivity calculation formula in step S5 is: Where l is the intrinsic length; S6: Obtain the standard value of effective thermal conductivity based on the thermal conductivity model of the three-dimensional microstructure effect by high-fidelity finite element method S7: According to the standard value of effective thermal conductivity The effective thermal conductivity calculation formula is optimized to obtain an optimized effective thermal conductivity calculation model.

2. The high-fidelity finite element optimization method according to claim 1, characterized in that: In the step S7, according to the effective thermal conductivity standard value The effective thermal conductivity calculation formula is optimized to obtain an optimized effective thermal conductivity calculation model, including: According to the standard value of effective thermal conductivity and the initial contribution fraction ξ, and the intrinsic length l is obtained by inverse calculation according to the effective thermal conductivity calculation formula.

3. The high-fidelity finite element optimization method according to claim 2, characterized in that: The simplified model under the uniform temperature field condition in step S3 is derived by using the method of integration by parts and setting the surfaces z=0.5L and z=-0.5L to be under the condition of a uniform temperature field.

4. The high-fidelity finite element optimization method according to claim 3, characterized in that: The nonlocal homogenization term of the temperature gradient within the volume in the S3 step The calculation is evaluated by the temperature difference on the surfaces perpendicular to the x-direction at the two ends of the volume.

5. The high-fidelity finite element optimization method according to claim 4, characterized in that: The extrinsic length of a metamaterial structure compared to its intrinsic length 6. The high-fidelity finite element optimization method according to claim 5, characterized in that: The effective thermal conductivity in the step S4 depends not only on the temperature gradient in the x direction, but also on the y direction and the z direction; the effective thermal conductivity in the step S5 depends not only on the temperature gradient in the x direction, but also on the width and the height.

7. A high-fidelity finite element optimization device for thermal conductivity modeling of dock folded structural parts, characterized in that: The dock folding structure comprises a metamaterial structure, and the dock folding structure optimization device comprises the following modules: Non-local heat conduction model building module: Based on the three-dimensional homogenization problem with temperature gradient only in the x-direction, a non-local heat conduction model is built; Non-local homogenization term definition module: defines non-local homogenization terms, including the non-local homogenization term of the temperature gradient in the x-direction and the non-local homogenization term of the heat flux in the x-direction, and expresses the mathematical form of the volume homogenization operator and the temperature gradient; Simplified model building module under uniform temperature field conditions: using the partial integration method, the non-local homogenization term of the temperature gradient in the x-direction is converted into the temperature difference between the two surfaces obtained by the finite element tool, and the simplified model under uniform temperature field conditions is obtained; Thermal conductivity model building module for three-dimensional microstructure effect: Combine the non-local heat conduction model, the non-local homogenization term of the heat flux in the x-direction and the simplified model under the condition of uniform temperature field, consider the temperature gradient in the x-direction and the influence of width and height, and obtain the thermal conductivity model of the three-dimensional microstructure effect; Effective thermal conductivity calculation formula acquisition module: Based on the infinite metamaterial structure in three directions, the effective thermal conductivity calculation formula is obtained using a multi-scale method and periodic boundary conditions; the three directions include the x direction, y direction, and z direction based on an orthogonal coordinate system; Optimization module: obtaining an effective thermal conductivity standard value according to the thermal conductivity model of the three-dimensional microstructure effect through a high-fidelity finite element method; optimizing the effective thermal conductivity calculation formula according to the effective thermal conductivity standard value to obtain an optimized effective thermal conductivity calculation model; in, The non-local heat conduction model is: in, represents the nonlocal homogenization term of the temperature gradient in the x direction, is the effective thermal conductivity, represents the nonlocal homogenization term of the heat flux in the x direction; The volume homogenization operator <·> V The definition is as follows: Wherein, L, W and H represent the length, width and height of the metamaterial structure, respectively, and the length, width and height directions correspond to the x-direction, y-direction and z-direction, respectively; The simplified model under the uniform temperature field condition is: in, The thermal conductivity model of the three-dimensional microstructure effect is: where ξ is the contribution fraction of the nonlocal phase with size-dependent effect, k x , k y , k z are the thermal conductivities in the x, y, and z directions, respectively, and κ is the thermal conductivity; The effective thermal conductivity calculation formula is: where l is the intrinsic length.

8. The high-fidelity finite element optimization device according to claim 7, characterized in that: The step of optimizing the effective thermal conductivity calculation formula according to the effective thermal conductivity standard value to obtain an optimized effective thermal conductivity calculation model comprises: According to the standard value of the effective thermal conductivity and the initial contribution fraction ξ, the intrinsic length l is obtained by inverse calculation according to the effective thermal conductivity calculation formula.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the method described in any one of claims 1 to 6 is implemented.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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