CN113806982A - Substrate topology optimization method for variable-structure wearable flexible thermoelectric device - Google Patents
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Abstract
The invention relates to a variable structure wearable flexible thermoelectric device substrate topology optimization method, which comprises the steps of selecting a physical model, and constructing a finite element model according to the physical model; the physical model comprises a substrate, wherein two ends of the substrate are connected with deformable strip-shaped thermoelectric materials; constructing a field function, wherein the field function is used for describing the material distribution of the substrate; constructing an optimization model according to the finite element model and the field function; solving the optimization model to obtain a structural topological configuration; the structural topological configuration is that the substrate drives the strip-shaped thermoelectric material to deform to generate the maximum out-of-plane displacement when being loaded. When the optimized substrate structure is subjected to the action of specified load, the thermoelectric material can be driven to generate maximum out-of-plane displacement, so that the temperature difference between the cold end and the hot end of the thermoelectric device is increased, and the energy output capacity of the device is increased.
Description
Technical Field
The invention belongs to the technical field of flexible electronic devices, and particularly relates to a topological optimization method for a variable-structure wearable flexible thermoelectric device substrate.
Background
The flexible thermoelectric device has the capability of generating power by depending on temperature difference, and has huge application prospect in the aspect of energy supply of wearable equipment and the Internet of things. The structural topology optimization method has the characteristics of high design freedom degree and large design space, and is a powerful design tool for improving the temperature difference of the flexible thermoelectric device, thereby improving the energy output and ensuring the wearing comfort.
In the related art, the traditional flexible thermoelectric device with the in-plane structure has the defect that the large temperature difference between the cold end and the hot end is difficult to establish, so that the energy output voltage capability of the thermoelectric device is low.
Disclosure of Invention
In view of the above, the present invention provides a topology optimization method for a substrate of a variable-structure wearable flexible thermoelectric device, so as to solve the problem that the traditional in-plane structure flexible thermoelectric device in the prior art is difficult to establish a large temperature difference between a cold end and a hot end, which results in a low energy output voltage capability of the thermoelectric device.
In order to achieve the purpose, the invention adopts the following technical scheme: a topology optimization method for a variable-structure wearable flexible thermoelectric device substrate comprises the following steps:
selecting a physical model, and constructing a finite element model according to the physical model; wherein the physical model comprises a substrate, and the two ends of the substrate are connected with deformable strip-shaped thermoelectric materials;
constructing a field function describing a material distribution of the substrate;
constructing an optimization model according to the finite element model and the field function;
solving the optimization model to obtain a structural topological configuration;
wherein the structural topology is a structural topology in which the substrate drives the deformation of the ribbon thermoelectric material to generate maximum out-of-plane displacement when subjected to a load.
Further, the selecting a physical model and constructing a finite element model according to the physical model includes:
selecting a base structure shape according to an application scene;
selecting the position of a loading point of the substrate according to an application scene and the connection relation between the substrate and other thermoelectric devices, and setting a periodic boundary condition at the connection position between the substrate and other thermoelectric devices;
setting parameters of a finite element model and carrying out meshing division on the parameters of the finite element model to obtain a finite element mesh;
and constructing a finite element model according to the substrate structure shape, the loading point position, the periodic boundary condition and the finite element mesh.
Further, the formula of the optimization model is as follows:
s.t.R(u(η))＝0
V(ρ(η))≤Vpre
ηTWiη≤1,(i＝1,2,…,NP)；
wherein η ═ η1 η2 … ηM}TIs a design variable of an optimization problem and is also a control variable of a field function form;
is based on the relative density of the finite element mesh mapped by the field function;
is the average out-of-plane displacement at the middle electrode of the thermoelectric material; r (u) ═ 0 is the equilibrium equation for the finite problem of geometric nonlinearity; v is the volume of the structure during optimization; vpreIs a volume constraint specified before optimization; etaTWiEta ≦ 1 is a bounded constraint requirement for the field function; n is a radical ofPThe number of observation points;
the optimization model is a strip-shaped thermoelectric material out-of-plane displacement maximization model meeting the volume constraint requirement and the field function bounded requirement under the condition of large mechanical deformation.
Further, the formula of the field function is:
wherein x is the coordinate of any point in space;
correlation of any point in the expression space with each observation point, xj(j＝1,2…Np) For viewpoint coordinates, the elements in the vector are embodied as
lcFor correlation length, | | | | is 2-norm; and Λ and ψ are an eigenvalue matrix and an eigenvector matrix obtained after eigenvalue decomposition of the correlation matrix composed of the observation points, respectively.
Further, solving the optimization model to obtain a topological structure includes:
smoothing the field function by using a smoothing function;
and substituting the smoothed field function into the optimization model, and calculating to obtain the structural topological configuration.
Further, the smoothing the field function by using the smoothing function includes:
wherein beta is a smooth parameter and is continuously increased from 0 to 30 in the optimization process;
substituting the smoothed field function into the optimization model includes:
wherein E is0Is the modulus of elasticity of the base structure; p is a penalty factor; e (x) characterizes the elastic modulus at a point in space when it is less than 0.01E0It is assumed that there is no material present here。
Further, the method also comprises the following steps:
and obtaining the optimized temperature difference gradient and electric energy voltage output value of the single thermoelectric device through multi-field coupling finite element analysis.
Further, a non-design region is arranged on the periphery of the substrate and used for ensuring connection with other thermoelectric devices.
By adopting the technical scheme, the invention can achieve the following beneficial effects:
the invention provides a variable-structure wearable flexible thermoelectric device substrate topology optimization method, which comprises the steps of selecting a physical model, and constructing a finite element model according to the physical model; the physical model comprises a substrate, wherein two ends of the substrate are connected with deformable strip-shaped thermoelectric materials; constructing a field function, wherein the field function is used for describing the material distribution of the substrate; constructing an optimization model according to the finite element model and the field function; solving the optimization model to obtain a structural topological configuration; the structural topological configuration is that the substrate drives the strip-shaped thermoelectric material to deform to generate maximum out-of-plane displacement when being loaded. When the optimized substrate structure is subjected to the action of specified load, the thermoelectric material can be driven to generate maximum out-of-plane displacement, so that the temperature difference between the cold end and the hot end of the thermoelectric device is increased, and the energy output capacity of the device is increased.
The application provides a technical scheme can promote the cold and hot end difference in temperature of device by a wide margin to improve thermoelectric device output voltage, for the energy supply of wearable equipment. By applying the technology, the structural form of the thermoelectric device can be changed when a human body moves, so that the power generation capacity of the thermoelectric device is improved, and the energy is better supplied to intelligent monitoring equipment.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without any creative effort.
FIG. 1 is a schematic diagram of the steps of the topology optimization method for the substrate of the variable-structure wearable flexible thermoelectric device;
FIG. 2 is a schematic structural diagram of a variable-structure wearable flexible thermoelectric device substrate according to the present invention;
FIG. 3 is another structural schematic diagram of the variable-structure wearable flexible thermoelectric device substrate of the invention;
FIG. 4 is another structural schematic diagram of the variable-structure wearable flexible thermoelectric device substrate of the invention;
FIG. 5 is a schematic diagram of the optimized structural topology of the present invention;
FIG. 6 is a schematic diagram of the temperature difference of the thermoelectric device after the optimization of the present invention;
FIG. 7 is a schematic diagram of the voltage condition of the thermoelectric device optimized according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without making any creative effort, shall fall within the protection scope of the present invention.
A specific method for optimizing the topology of the variable-structure wearable flexible thermoelectric device substrate provided in the embodiment of the present application is described below with reference to the accompanying drawings.
As shown in fig. 1, a method for optimizing a topology of a variable-structure wearable flexible thermoelectric device substrate provided in an embodiment of the present application includes:
s101, selecting a physical model, and constructing a finite element model according to the physical model; the physical model comprises a substrate, wherein two ends of the substrate are connected with deformable strip-shaped thermoelectric materials;
s102, constructing a field function, wherein the field function is used for describing the material distribution of the substrate;
s103, constructing an optimization model according to the finite element model and the field function;
s104, solving the optimization model to obtain a structural topological configuration;
wherein the structural topology is a structural topology in which the substrate drives the deformation of the ribbon thermoelectric material to generate maximum out-of-plane displacement when subjected to a load.
The working principle of the variable-structure wearable flexible thermoelectric device substrate topology optimization method is as follows: first, a physical model is constructed, as shown in fig. 2, the physical model includes a substrate with a deformable strip-shaped thermoelectric material connected to both ends of the substrate. The deformable strip thermoelectric material comprises a P-type thermoelectric material and an N-type thermoelectric material. Then, an optimization model based on finite element analysis is constructed according to the physical model; solving the optimization model by using a pre-constructed field function to obtain a structural topological configuration; the structural topological configuration is the structural topological configuration which drives the strip-shaped thermoelectric material to deform to generate the maximum out-of-plane displacement when the substrate is loaded.
It will be appreciated that the deformable strip of thermoelectric material deforms to a curved shape when subjected to an external load, the further the apex is from the substrate, i.e. the greater the out-of-plane displacement of the strip of thermoelectric material the greater the power generation capability of the thermoelectric device. In the application, a plurality of thermoelectric devices are periodically arranged to form a complete wearable device.
The application provides a variable-structure wearable flexible thermoelectric device substrate topology optimization design method, which is used for constructing an optimization model based on finite elements and corresponding mathematical relations and solving the optimization problem through a field function mapping structure and an optimization algorithm. The optimal substrate material distribution can be obtained through solving, so that the flexible thermoelectric device obtains the maximum out-of-plane displacement under the action of external load, the cold-hot end temperature difference of the device is improved, the power generation capacity is improved, and the wearable intelligent equipment is supplied with energy.
As shown in fig. 3, the variable structure wearable flexible thermoelectric device substrate topology optimization method provided by the application can increase the output voltage of the device while considering wearing comfort. The application scene is that the in-plane flexible thermoelectric device can drive the thermoelectric device to generate out-of-plane displacement when bearing in-plane load, and the temperature difference between a skin end (hot end) and an environment end (cold end) is increased, so that the power generation capacity is improved. The technical scheme who utilizes this application to provide can make the thermoelectric device change structural morphology when human motion and increase the generating capacity of thermoelectric device to better provide the energy for intelligent monitoring equipment. This application can promote the device cold and hot end difference in temperature by a wide margin to improve thermoelectric device output voltage, for wearable equipment energy supply.
In some embodiments, the selecting a physical model from which to construct a finite element model includes:
selecting a base structure shape according to an application scene;
selecting the position of a loading point of the substrate according to an application scene and the connection relation between the substrate and other thermoelectric devices, and setting a periodic boundary condition at the connection position between the substrate and other thermoelectric devices;
setting parameters of a finite element model and carrying out meshing division on the parameters of the finite element model to obtain a finite element mesh;
and constructing a finite element model according to the substrate structure shape, the loading point position, the periodic boundary condition and the finite element mesh.
Specifically, the shape of the substrate structure is selected according to the application scenario, and the substrate can be in various shapes such as a rectangle, a circle and the like. Taking fig. 2 as an example, the substrate is rectangular, and the deformable strip thermoelectric material is connected at two ends of the outer side of the substrate. As shown in fig. 4, since the substrate needs to be deformed to drive the pyroelectric material to generate out-of-plane displacement when receiving a load, the position of the loading point is selected according to an application scene and the connection relationship of a plurality of devices, and a period boundary condition is set at the connection of the plurality of devices, in this embodiment, the loading point is set at the middle point of the long side and is stretched by 2 mm. Periodic boundary conditions are set at the four corner points of the rectangle. The substrate design domain provided by the application is a rectangle with the length of 40mm and the width of 20 mm. Consider a non-design domain one millimeter wide around the structure that is 42mm by 22mm across the structure. The thermoelectric material was in the form of a 4mm wide strip in the middle of the design area. Then setting finite element model parameters and carrying out meshing on the finite element model parameters to obtain finite element meshes; the finite element model parameters are parameters for setting specific material properties such as elastic modulus, seebeck coefficient and the like, the finite element model grids of the whole device are divided, and the number of the grids in the design domain is 200 multiplied by 100 which is 20000. Finally, an optimization model is constructed, the material distribution in the substrate design domain is characterized by a field function, and the mathematical expression based on the characterization of the optimization model is as follows:
s.t.R(u(η))＝0
V(ρ(η))≤Vpre
ηTWiη≤1,(i＝1,2,…,NP)；
wherein η ═ η1 η2 … ηM}TIs a design variable of an optimization problem and is also a control variable of a field function form;
is based on the relative density of the finite element mesh mapped by the field function;
is the average out-of-plane displacement at the middle electrode of the thermoelectric material; r (u) ═ 0 is the equilibrium equation for the finite problem of geometric nonlinearity; v is the volume of the structure during optimization; vpreIs a volume constraint specified before optimization; etaTWiEta ≦ 1 is a bounded constraint requirement for the field function; n is a radical ofPThe number of observation points.
The optimization model is a strip-shaped thermoelectric material out-of-plane displacement maximization model meeting the volume constraint requirement and the field function bounded requirement under the condition of large mechanical deformation.
In addition, V ispreIs a specified volume constraint before optimization, set to 30%; n is a radical ofPThe observation points are uniformly distributed in the design domain for the number of observation points, and the number of observation points is 80 multiplied by 40 to 3200.
Preferably, the optimization model is solved by using an optimization algorithm to obtain a structural topology, including:
smoothing the field function by using a smoothing function;
and substituting the smoothed field function into the optimization model, and calculating to obtain the structural topological configuration.
In some embodiments, the solution process for the optimization model is: establishing a field function model, wherein the field function is specifically expressed as:
where x is the coordinate of any point in space and η is the design variable, which also controls the shape of the landing function.
Correlation of any point in the expression space with each observation point, xj(j＝1,2…Np) For viewpoint coordinates, the elements in the vector are embodied as
lcTo the correlation length in this example equal 6mm, | | | | is a 2-norm. Lambda and psi are respectively an eigenvalue matrix and an eigenvector matrix obtained after eigenvalue decomposition of a correlation matrix consisting of observation points
The field function is then smoothed using a smoothing function, expressed as a smoothing procedure function, according to the field function mapping structure
Where β is a smoothing parameter that is continuously incremented from 0 to 30 during the optimization. Substituting the smoothed field function into an optimization model, wherein the specific formula is
Wherein E0For the elastic modulus of the substrate structure, P is a penalty factor, typically taken as 3. This elastic modulus is incorporated into the optimization model in step 1.4). In fact, E (x) characterizes the elastic modulus at a point in space, when it is less than 0.01E0It is considered that there is no material here.
And (3) setting parameters of other finite element models and dividing meshes, and adding a non-design domain at the periphery of the substrate to ensure the structural connectivity, as shown in FIG. 4. And setting material parameters such as elastic modulus, Seebeck coefficient and the like, and dividing the finite element model mesh of the whole device.
As a preferred implementation mode, the application uses a Kriging model-based agent model optimization algorithm to solve the optimization model, and obtains the structural topological configuration shown in FIG. 5.
In a preferred embodiment, the optimized temperature gradient and voltage output value of the single thermoelectric device are obtained through multi-field coupling finite element analysis. Fig. 6 shows the temperature difference of the optimized thermoelectric device, and fig. 7 shows the voltage output of the optimized thermoelectric device.
The variable-structure wearable flexible thermoelectric device substrate topology optimization method provided by the application considers wearing comfort and energy output requirements, and has feasibility for avoiding and reducing charging times of intelligent equipment. In addition, the invention is not only suitable for power supply of wearable equipment, but also can be applied to the application of generating power by waste heat and recovering waste heat of Internet of things hardware
The embodiment of the application provides computer equipment, which comprises a processor and a memory connected with the processor;
the memory is used for storing a computer program, and the computer program is used for executing the variable-structure wearable flexible thermoelectric device substrate topology optimization method provided by any one of the above embodiments;
the processor is used to call and execute the computer program in the memory.
In summary, the invention provides a topology optimization method for a variable-structure wearable flexible thermoelectric device substrate, which comprises the steps of selecting a physical model, and constructing a finite element model according to the physical model; the physical model comprises a substrate, wherein two ends of the substrate are connected with deformable strip-shaped thermoelectric materials; constructing a field function, wherein the field function is used for describing the material distribution of the substrate; constructing an optimization model according to the finite element model and the field function; solving the optimization model to obtain a structural topological configuration; the structural topological configuration is that the substrate drives the strip-shaped thermoelectric material to deform to generate the maximum out-of-plane displacement when being loaded. When the optimized substrate structure is subjected to the action of specified load, the thermoelectric material can be driven to generate maximum out-of-plane displacement, so that the temperature difference between the cold end and the hot end of the thermoelectric device is increased, and the energy output capacity of the device is increased.
The essence of the invention is that the out-of-plane displacement of the thermoelectric material in the device is maximized by the variable structure design, and the temperature difference gradient of the cold end and the hot end of the flexible thermoelectric device is increased, thereby improving the output voltage of the device. Modifications to the geometry of the thermoelectric device substrate, the shape of the thermoelectric material, the optimization columns and solutions described in the embodiments or equivalent substitutions of some or all of the method features (e.g., the use of other shapes of the substrate and optimization solution algorithms) may be made without departing from the spirit and scope of the methods and solutions of the embodiments of the present invention.
It is to be understood that the method embodiments provided above correspond to the apparatus embodiments, and corresponding specific contents may be referred to each other, which is not described herein again.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (8)
1. A topology optimization method for a variable-structure wearable flexible thermoelectric device substrate is characterized by comprising the following steps:
selecting a physical model, and constructing a finite element model according to the physical model; wherein the physical model comprises a substrate, and the two ends of the substrate are connected with deformable strip-shaped thermoelectric materials;
constructing a field function describing a material distribution of the substrate;
constructing an optimization model according to the finite element model and the field function;
solving the optimization model to obtain a structural topological configuration;
wherein the structural topology is a structural topology in which the substrate drives the strip-shaped thermoelectric material to deform to generate maximum out-of-plane displacement when the substrate is subjected to a load.
2. The method of claim 1, wherein selecting the physical model from which to build the finite element model comprises:
selecting a base structure shape according to an application scene;
selecting the position of a loading point of the substrate according to an application scene and the connection relation between the substrate and other thermoelectric devices, and setting a periodic boundary condition at the connection position between the substrate and other thermoelectric devices;
setting parameters of a finite element model and carrying out meshing division on the parameters of the finite element model to obtain a finite element mesh;
and constructing a finite element model according to the substrate structure shape, the loading point position, the periodic boundary condition and the finite element mesh.
3. The method of claim 2, wherein the optimization model is formulated as:
s.t.R(u(η))＝0
V(ρ(η))≤Vpre
ηTWiη≤1,(i＝1,2,…,NP)；
wherein η ═ η1 η2…ηM}TIs a design variable of an optimization problem and is also a control variable of a field function form;
is based onRelative density of finite element mesh mapped by the field function;
is the average out-of-plane displacement at the middle electrode of the thermoelectric material; r (u) ═ 0 is the equilibrium equation for the finite problem of geometric nonlinearity; v is the volume of the structure during optimization; vpreIs a volume constraint specified before optimization; etaTWiEta ≦ 1 is a bounded constraint requirement for the field function; n is a radical ofPThe number of observation points;
the optimization model is a strip-shaped thermoelectric material out-of-plane displacement maximization model meeting the volume constraint requirement and the field function bounded requirement under the condition of large mechanical deformation.
4. The method of claim 1, wherein the field function is formulated as:
wherein x is the coordinate of any point in space;
correlation of any point in the expression space with each observation point, xj(j＝1,2…Np) For viewpoint coordinates, the elements in the vector are embodied as
lcFor correlation length, | | | | is 2-norm; and Λ and ψ are an eigenvalue matrix and an eigenvector matrix obtained after eigenvalue decomposition of the correlation matrix composed of the observation points, respectively.
5. The method of claim 2, wherein solving the optimization model to obtain a structural topology comprises:
smoothing the field function by using a smoothing function;
and substituting the smoothed field function into the optimization model, and calculating to obtain the structural topological configuration.
6. The method of claim 5,
the smoothing of the field function by using the smoothing function comprises:
wherein beta is a smooth parameter and is continuously increased from 0 to 30 in the optimization process;
substituting the smoothed field function into the optimization model includes:
wherein E is0Is the modulus of elasticity of the base structure; p is a penalty factor; e (x) characterizes the elastic modulus at a point in space when it is less than 0.01E0It is considered that there is no material here.
7. The method of any of claims 1 to 6, further comprising:
and obtaining the optimized temperature difference gradient and electric energy voltage output value of the single thermoelectric device through multi-field coupling finite element analysis.
8. The method of claim 7,
and arranging a non-design area on the periphery of the substrate for ensuring the connection with other thermoelectric devices.
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| 邢健: "航天薄膜结构褶皱不确定性分析与抗褶皱优化设计", 《中国博士学位论文全文数据库 (工程科技Ⅰ辑)》, no. 7 * |
| 陈玉丽;马勇;潘飞;王升涛;: "多尺度复合材料力学研究进展", 固体力学学报, no. 01 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115659690A (en) * | 2022-11-08 | 2023-01-31 | 哈尔滨工业大学 | Curved surface near-zero stress acquisition method and device, computer and storage medium |
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