CN113806982B - Variable structure wearable flexible thermoelectric device substrate topology optimization method - Google Patents
Variable structure wearable flexible thermoelectric device substrate topology optimization method Download PDFInfo
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Abstract
The application relates to a topological optimization method of 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 ribbon 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; wherein the structural topology is such that the substrate, when subjected to a load, drives deformation of the ribbon thermoelectric material to produce maximum out-of-plane displacement. When the optimized substrate structure is acted by a 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 application 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 electricity by means of temperature difference, and has a huge application prospect in the aspects of energy supply of wearable equipment and the Internet of things. The structural topology optimization method has the characteristics of high design freedom and large design space, and is a powerful design tool for improving the temperature difference of the flexible thermoelectric device, thereby improving energy output and ensuring wearing comfort.
In the related art, the conventional in-plane structure flexible thermoelectric device has the defect that a large temperature difference between a cold end and a 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 application aims to overcome the defects of the prior art, and provides a topology optimization method for a substrate of a variable-structure wearable flexible thermoelectric device, so as to solve the problem that the conventional in-plane structure flexible thermoelectric device in the prior art has the defects that a large temperature difference between a cold end and a hot end is difficult to establish, and the energy output voltage capability of the thermoelectric device is low.
In order to achieve the above purpose, the application adopts the following technical scheme: a method of topological optimization of a variable structure wearable flexible thermoelectric device substrate, comprising:
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 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;
wherein the structural topology is such that the substrate, when subjected to a load, drives deformation of the ribbon thermoelectric material to produce a maximum out-of-plane displacement.
Further, the selecting a physical model, constructing a finite element model according to the physical model, includes:
selecting a substrate structure shape according to an application scene;
selecting a loading point position 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 part of the substrate and other thermoelectric devices;
setting finite element model parameters and carrying out grid division on the finite element model parameters to obtain finite element grids;
and constructing a finite element model according to the shape of the base structure, the loading point position, the period boundary condition and the finite element grid.
Further, the formula of the optimization model is as follows:
s.t.R(u(η))＝0
V(ρ(η))≤V pre
η T W i η≤1,(i＝1,2,…,N P )；
wherein η= { η 1 η 2 … η M } T The design variable is an optimization problem and is also a control variable of a field function form;the relative density of the finite element mesh mapped based on the field function; />Is the average out-of-plane displacement at the thermoelectric material intermediate electrode; r (u) =0 is the equilibrium equation for the geometric nonlinearity finite problem; v is the volume of the structure during optimization; v (V) pre Is a volume constraint specified before optimization; η (eta) T W i η.ltoreq.1 is a bounded constraint of the field function; n (N) P The number of observation points;
the optimization model is a band-shaped thermoelectric material out-of-plane displacement maximization model which meets the volume constraint requirement and the field function bounded requirement under the condition of large mechanical deformation.
Further, the field function has the formula:
wherein x is any point coordinate in space;expressing the correlation of any point in space with each observation point, x j (j＝1,2…N p ) For the viewpoint coordinates, the elements in the vector are expressed asl c Is the correlation length, is the 2-norm; Λ and ψ are the relative moments composed of the observation points, respectivelyAnd decomposing the matrix eigenvalue to obtain an eigenvalue matrix and an eigenvector matrix.
Further, the solving the optimization model to obtain a topology structure includes:
smoothing the field function by using a smoothing function;
substituting the field function after the smoothing treatment into an optimization model, and calculating to obtain the structural topological configuration.
Further, the smoothing of the field function using the smoothing function includes:
wherein, beta is a smoothing parameter, and is continuously increased from 0 to 30 in the optimization process;
substituting the field function after the smoothing treatment into an optimization model comprises the following steps:
wherein E is 0 An elastic modulus that is the base structure; p is penalty factor; e (x) characterizes the modulus of elasticity at a point in space when it is less than 0.01E 0 It is considered that there is no material.
Further, the method further comprises the following steps:
and obtaining the optimized temperature difference gradient and the optimized electric energy voltage output value of the single thermoelectric device through multi-field coupling finite element analysis.
Further, a non-design domain is disposed on the periphery of the substrate for ensuring connection with other thermoelectric devices.
By adopting the technical scheme, the application has the following beneficial effects:
the application provides a topological optimization method of 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 ribbon 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; wherein the structural topology is such that the substrate when subjected to a load drives the ribbon thermoelectric material to deform resulting in maximum out-of-plane displacement. When the optimized substrate structure is acted by the appointed load, the thermoelectric material can be driven to generate the maximized 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 technical scheme provided by the application can greatly improve the temperature difference of the cold and hot ends of the device, thereby improving the output voltage of the thermoelectric device and supplying energy to the wearable equipment. By applying the technology, the structure form of the thermoelectric device can be changed when a human body moves, so that the power generation capacity of the thermoelectric device is increased, and energy is better provided for intelligent monitoring equipment.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to the drawings without giving inventive effort to those skilled in the art.
FIG. 1 is a schematic diagram of the steps of a method for topology optimization of a variable structure wearable flexible thermoelectric device substrate of the present application;
fig. 2 is a schematic structural view of a variable structure wearable flexible thermoelectric device substrate of the present application;
FIG. 3 is a schematic illustration of another construction of a variable structure wearable flexible thermoelectric device substrate of the present application;
fig. 4 is a schematic illustration of another construction of a variable structure wearable flexible thermoelectric device substrate of the present application;
FIG. 5 is a schematic diagram of the topology of the optimized structure of the present application;
FIG. 6 is a schematic diagram of the temperature differential of the thermoelectric device after optimization in accordance with the present application;
FIG. 7 is a schematic diagram of the voltage profile of an optimized thermoelectric device according to the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail below. It will be apparent that the described embodiments are only some, but not all, embodiments of the application. All other embodiments, based on the examples herein, which are within the scope of the application as defined by the claims, will be within the skill of those in the art without undue burden.
A specific method for optimizing the topology of a variable structure wearable flexible thermoelectric device substrate provided in an embodiment of the present application is described below with reference to the accompanying drawings.
As shown in fig. 1, the variable structure wearable flexible thermoelectric device substrate topology optimization method provided in the embodiment of the 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 a deformable strip thermoelectric material;
s102, constructing a field function, wherein the field function is used for describing the material distribution of a 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 such that the substrate, when subjected to a load, drives deformation of the ribbon thermoelectric material to produce a maximum out-of-plane displacement.
The working principle of the topological optimization method of the substrate of the variable structure wearable flexible thermoelectric device is as follows: first, a physical model is constructed, as shown in fig. 2, which includes a substrate to which a deformable ribbon thermoelectric material is connected at both ends. The deformable ribbon thermoelectric material includes P-type thermoelectric material and N-type thermoelectric material. Then constructing an optimization model based on finite element analysis according to the physical model; solving the optimization model by utilizing a pre-constructed field function to obtain a structural topological configuration; the structural topology is the structure topology that drives the ribbon thermoelectric material to deform when the substrate is subjected to a load, resulting in maximum out-of-plane displacement.
It will be appreciated that the greater the distance between the apex of the deformable ribbon thermoelectric material and the substrate, the greater the out-of-plane displacement of the ribbon thermoelectric material, the greater the power generation capacity of the thermoelectric device. The plurality of thermoelectric devices are periodically arranged to form a complete wearable device.
The application provides a topological optimization design method for a variable structure wearable flexible thermoelectric device substrate, 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 maximum out-of-plane displacement under the action of external load, and therefore the temperature difference between the cold end and the hot end of the device is improved, the power generation capacity is increased, and the wearable intelligent device is powered.
As shown in fig. 3, the topology optimization method of the variable structure wearable flexible thermoelectric device substrate 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. By utilizing the technical scheme provided by the application, the structure form of the thermoelectric device can be changed when a human body moves, so that the power generation capacity of the thermoelectric device is increased, and energy is better provided for intelligent monitoring equipment. The application can greatly improve the temperature difference between the cold end and the hot end of the device, thereby improving the output voltage of the thermoelectric device and supplying energy to the wearable equipment.
In some embodiments, the selecting a physical model, constructing a finite element model from the physical model, includes:
selecting a substrate structure shape according to an application scene;
selecting a loading point position 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 part of the substrate and other thermoelectric devices;
setting finite element model parameters and carrying out grid division on the finite element model parameters to obtain finite element grids;
and constructing a finite element model according to the shape of the base structure, the loading point position, the period boundary condition and the finite element grid.
Specifically, the shape of the substrate structure is selected according to the application scene, and the substrate can take various shapes such as rectangle, circle and the like. Taking fig. 2 as an example, the substrate is selected to be rectangular, and deformable strip thermoelectric materials are connected at both ends of the outer side of the substrate. As shown in fig. 4, since the substrate is required to deform when being loaded so as to drive the thermoelectric material to generate out-of-plane displacement, the loading point position is selected according to the connection relation between the application scene and the plurality of devices, and a period boundary condition is set at the connection position of the plurality of devices, in this embodiment, the loading point is set at the midpoint of the long side and stretched by 2mm. Periodic boundary conditions are set at four corner points of the rectangle. The substrate provided by the application is rectangular with the design domain length of 40mm and the width of 20 mm. Consider a structure with a non-engineered area of one millimeter width around the structure with an overall structure of 42mm 22mm. The thermoelectric material is in the shape of a 4mm wide strip in the middle of the design area. Setting finite element model parameters and carrying out grid division on the finite element model parameters to obtain finite element grids; 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 grid number in a design domain is 200×100=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 of the optimization model based on the characterization is as follows:
s.t.R(u(η))＝0
V(ρ(η))≤V pre
η T W i η≤1,(i＝1,2,…,N P )；
wherein η= { η 1 η 2 … η M } T The design variable is an optimization problem and is also a control variable of a field function form;the relative density of the finite element mesh mapped based on the field function; />Is the average out-of-plane displacement at the thermoelectric material intermediate electrode; r (u) =0 is the equilibrium equation for the geometric nonlinearity finite problem; v is the volume of the structure during optimization; v (V) pre Is a volume constraint specified before optimization; η (eta) T W i η.ltoreq.1 is a bounded constraint of the field function; n (N) P The number of observation points.
The optimization model is a band-shaped thermoelectric material out-of-plane displacement maximization model which meets the volume constraint requirement and the field function bounded requirement under the condition of large mechanical deformation.
V is also described as pre Is the volume constraint specified before optimization, and is set to 30%; n (N) P For the number of observation points, the observation points are uniformly distributed in the design domain, and 80×40=3200 observation points are designed.
Preferably, the method adopts an optimization algorithm to solve the optimization model to obtain a structural topology, and comprises the following steps:
smoothing the field function by using a smoothing function;
substituting the field function after the smoothing treatment into an 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 follows:where x is any point coordinate in space, η is a design variable, and also controls the morphology of the field function. />Expressing the correlation of any point of the space with each observation point, x j (j＝1,2…N p ) For the viewpoint coordinates, the elements in the vector are specifically expressed as +.>l c For the relevant length to be equal to 6mm in this example, the term "I" refers to a 2-norm. Λ and ψ are respectively a eigenvalue matrix and an eigenvector matrix obtained by decomposing eigenvalues of a correlation matrix composed of observation points
The field function is then smoothed using a smoothing function according to the field function mapping structure, the smoothing process function expressed asWhere β is a smoothing parameter, which is continuously incremented from 0 to 30 during the optimization process. Substituting the field function after smoothing into an optimization model, wherein the specific formula is +.>Wherein E is 0 For the elastic modulus of the base structure, P is typically 3 for the penalty factor. This modulus of elasticity 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 0.01E 0 It is considered that there is no material.
Other finite element model parameter settings and grid division, and adding non-design domain at the periphery of the substrate ensures structural connectivity, as shown in fig. 4. And setting material parameters such as elastic modulus, seebeck coefficient and the like, and dividing a finite element model grid of the whole device.
As a preferred embodiment, the application uses a proxy model optimization algorithm based on a Kriging model to solve the optimization model, so as to obtain the structural topological configuration shown in FIG. 5.
As a preferred embodiment, the temperature gradient and the voltage output value of the single thermoelectric device after optimization are obtained through multi-field coupling finite element analysis. Fig. 6 shows the temperature difference of the thermoelectric device after optimization, and fig. 7 shows the voltage output of the thermoelectric device after optimization.
The topological optimization method for the substrate of the variable structure wearable flexible thermoelectric device provided by the application gives consideration to wearing comfort and energy output requirements, and has feasibility for avoiding and reducing the charging times of intelligent equipment. In addition, the application is not only suitable for supplying power to wearable equipment, but also can be applied to the application of the hardware of the Internet of things depending on waste heat power generation and waste heat recovery
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 embodiment;
the processor is used to call and execute the computer program in the memory.
In summary, the application provides a variable structure wearable flexible thermoelectric device substrate topology optimization method, which comprises 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 ribbon thermoelectric materials; constructing a field function 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; wherein the structural topology is such that the substrate, when subjected to a load, drives deformation of the ribbon thermoelectric material to produce maximum out-of-plane displacement. When the optimized substrate structure is acted by a 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 is characterized in 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, so that the output voltage of the device is improved. Modifications to the thermoelectric device substrate geometry, thermoelectric material shape, optimization columns and solutions described in the various embodiments, or equivalent substitutions of some or all of the method features therein (e.g., using other shaped substrates and optimization solutions) do not depart from the essence of the corresponding methods and solutions from the scope of the methods and solutions of the various embodiments of the application.
It may be understood that the method embodiment provided above corresponds to the device embodiment, and the corresponding specific contents may be referred to each other and will not be described herein.
It will be appreciated by those skilled in the art that 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, magnetic 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 flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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 foregoing is merely illustrative of the present application, and the present application is not limited to the above embodiments, and any person skilled in the art can easily think about the changes and substitutions within the technical scope of the present application, and the changes and substitutions are intended to be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (3)
1. A method for topology optimization of a variable structure wearable flexible thermoelectric device substrate, comprising:
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 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;
wherein the structural topology is a structural topology that drives the ribbon thermoelectric material to deform to produce maximum out-of-plane displacement when the substrate is loaded;
the selecting a physical model, constructing a finite element model according to the physical model, and comprises the following steps:
selecting a substrate structure shape according to an application scene;
selecting a loading point position 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 part of the substrate and other thermoelectric devices;
setting finite element model parameters and carrying out grid division on the finite element model parameters to obtain finite element grids;
constructing a finite element model according to the shape of the base structure, the position of the loading point, the period boundary condition and the finite element grid;
the formula of the optimization model is as follows:
s.t.R(u(η))＝0
V(ρ(η))≤V pre
η T W i η≤1,(i＝1,2,…,N P )；
wherein η= { η 1 η 2 …η M } T The method is a design variable of an optimization problem and is also a control variable of a field function form;the relative density of the finite element mesh mapped based on the field function; u (u) Z Is the average out-of-plane displacement at the thermoelectric material intermediate electrode; r (u) =0 is the equilibrium equation for the geometric nonlinearity finite problem; v is the volume of the structure during optimization; v (V) pre Is a volume constraint specified before optimization; η (eta) T W i η.ltoreq.1 is a bounded constraint of the field function; n (N) P The number of observation points;
the optimization model is a band-shaped thermoelectric material out-of-plane displacement maximization model which meets the volume constraint requirement and the field function bounded requirement under the condition of large mechanical deformation;
the formula of the field function is:
wherein x is any point coordinate in space;expressing the correlation of any point of the space with each observation point, x j (j＝1,2…N p ) For the viewpoint coordinates, the elements in the vector are expressed asl c Is the correlation length, is the 2-norm; Λ and ψ are respectively a eigenvalue matrix and an eigenvector matrix which are obtained after eigenvalue decomposition of a correlation matrix formed by observation points;
solving the optimization model to obtain a structural topological configuration, wherein the method comprises the following steps:
smoothing the field function by using a smoothing function;
substituting the field function after the smoothing treatment into an optimization model, and calculating to obtain a structural topological configuration;
the smoothing of the field function using a smoothing function includes:
wherein, beta is a smoothing parameter, and is continuously increased from 0 to 30 in the optimization process;
substituting the field function after the smoothing treatment into an optimization model comprises the following steps:
wherein E is 0 An elastic modulus that is the base structure; p is penalty factor; e (x) characterizes the modulus of elasticity at a point in space when it is less than 0.01E 0 It is considered that there is no material.
2. The method as recited in claim 1, further comprising:
and obtaining the optimized temperature difference gradient and the optimized electric energy voltage output value of the single thermoelectric device through multi-field coupling finite element analysis.
3. The method of claim 2, wherein the step of determining the position of the substrate comprises,
and a non-design domain is arranged on the periphery of the substrate and used for ensuring connection with other thermoelectric devices.
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