A Topology Optimization Method for Electrothermal Driven Compliant Mechanisms Based on Minimum Size Control

Abstract

This invention discloses a topology optimization method for an electrothermal driven compliant mechanism based on minimum size control. It defines the design domain and boundary conditions of the electrothermal driven compliant mechanism, initializes design parameters, and uses a sequential coupling method to solve the multi-physics structural response of the electrothermal-structural fields. The optimization objective is to maximize the output displacement of the mechanism. By introducing a structural indicator function, minimum size constraint functions for real and empty phase material structures are constructed, establishing a topology optimization model for the electrothermal driven compliant mechanism based on minimum size control. The moving asymptotic algorithm is used to solve the topology optimization problem, determining whether the convergence criterion is met, and finally outputting the optimal topology configuration of the electrothermal driven compliant mechanism. This method effectively suppresses the occurrence of small-sized structures, facilitating processing and manufacturing.

Description

Technical Field

[0001] This invention relates to the technical field of compliant topology optimization design, and in particular to a topology optimization method for an electrothermal driven compliant mechanism based on minimum size control. Background Technology

[0002] A compliant mechanism is a mechanism that utilizes its own elastic deformation to achieve the transfer and conversion of motion, force, and energy. The main driving methods for compliant mechanisms include electrostatic, electromagnetic, piezoelectric, and electrothermal actuation. Compared with other actuation methods, electrothermal driven compliant mechanisms can generate larger output displacement and output force under low voltage, and have advantages such as ease of control, integration, and manufacturing. Therefore, electrothermal driven compliant mechanisms are used for micromanipulation such as cell clamping, puncture, and release, and have broad application prospects in the field of bioengineering micromanipulation.

[0003] Currently, the design of electrothermal driven compliant mechanisms is mostly based on the designer's intuition and experience, making it difficult to obtain the optimal performance of such mechanisms. Using topology optimization for electrothermal driven compliant mechanism design only requires specifying the design domain and input / output actions, and seeking the optimal mechanism topology configuration under constraints to achieve optimal mechanism performance. However, the topology configuration of electrothermal driven compliant mechanisms designed through topology optimization is prone to contain single-node hinge-like structures, which poses certain difficulties in manufacturing. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a topology optimization method for an electrothermal driven compliant mechanism based on minimum size control. The method uses a structure indicator function to construct minimum size constraints for the real and empty phase material structures. The minimum characteristic dimensions of the real and empty phases of the topology configuration of the electrothermal driven compliant mechanism designed by topology optimization can meet the specified size constraints, effectively suppressing the occurrence of small-sized structures and facilitating processing and manufacturing.

[0005] To achieve the above technical objectives, this invention provides a topology optimization method for an electrothermal driven compliant mechanism based on minimum size control, comprising:

[0006] S1, set the design domain and boundary conditions of the electrothermal driven compliant mechanism, discretize the design domain into N finite elements, and define material parameters, applied load magnitude, output spring stiffness, minimum size control parameters and initial values ​​of design variables;

[0007] S2, the finite element density is filtered by the element density filtering method, and then the filtered element density is filtered again by the Heaviside mapping function to obtain the element material density;

[0008] S3, a solid isotropic material penalty model is used to describe the relationship between the dielectric constant, thermal conductivity and elastic modulus of the material and the density of the unit material. The electro-thermal-structural multi-physics finite element equilibrium equations are solved by sequential coupling method to obtain the displacement response of the mechanism structure.

[0009] S4, taking the output displacement of the electrothermal driven compliant mechanism as the optimization target, by introducing a structural indicator function, constructing a geometric constraint function for the minimum size of the real phase and empty phase material structure, and establishing a topology optimization model of the electrothermal driven compliant mechanism based on minimum size control;

[0010] S5. Based on the topology optimization model of the electrothermal driven compliant mechanism, calculate the optimization objective function and constraint values ​​to obtain the output displacement and sensitivity of the minimum characteristic size of the real phase and empty phase structures and the structural volume constraint of the electrothermal driven compliant mechanism.

[0011] S6. The moving asymptotic optimization algorithm is used to design variables and solve the topology optimization problem of the electrothermal driven compliant mechanism based on minimum size control. It is determined whether the convergence criterion is met. If not, the process is transferred to step S2. If it is met, the topology optimization process of the electrothermal driven compliant mechanism ends and the optimal topology configuration of the electrothermal driven compliant mechanism is output.

[0012] Optionally, step S2 includes the following steps:

[0013] S21, the finite element density is filtered using an element density filtering method. The filtered element density is obtained by weighted averaging of adjacent element densities.

[0014]

[0015] In the formula, ρ represents the unit density after filtering unit i; j The density of element j; v j Ω represents the volume of element j. i The distance between the centroid of element i and the centroid of element i does not exceed the minimum filtration radius R. min The set of all units; x j Let ω(x) be the coordinates of the center of element j; j ) is the weighting function:

[0016]

[0017] In the formula, x i The coordinates of the center of element i;

[0018] S22, The filtered unit density is further filtered using the Heaviside mapping function to obtain the unit material density:

[0019]

[0020] η is the unit material density of unit i; i β is the threshold; β is a parameter that controls the approximation degree of the Heaviside mapping function.

[0021] Optionally, S3 includes the following steps:

[0022] S31, a solid isotropic material penalty model is used to describe the relationship between the material's dielectric constant, thermal conductivity, elastic modulus, and the density of the unit material:

[0023]

[0024]

[0025]

[0026] σ is the unit mass density of unit e; E σ T E and E represent the dielectric constant, thermal conductivity, and elastic modulus of unit e, respectively; σ E0 σ T0 E0 and E0 are the unit dielectric constant, thermal conductivity and elastic modulus of the solid material, respectively; P1, P2 and P3 are penalty values, all of which are 3.

[0027] S32, Considering the linear elastic deformation range, the sequential coupling method is used to solve the multi-physics finite element equilibrium equations of the electric-thermal-structural fields. The finite element equilibrium equations for the electric field, thermal field, and structural field are respectively expressed as:

[0028]

[0029]

[0030]

[0031] In the formula, the subscripts E, T, and S represent the electric field, thermal field, and structural field, respectively; K E K T and K s These represent the overall electrical conduction matrix, overall thermal conduction matrix, and overall stiffness matrix of the structure, respectively; U E U T and U s These represent the voltage array, temperature array, and displacement array of the node, respectively; F E F T and F s These are voltage load arrays, temperature load arrays, and force load arrays, respectively. This represents the unit density of the material.

[0032] Optionally, S4 includes the following steps:

[0033] S41, control the minimum dimensions of the real and unreal phase material structures of the compliant mechanism, satisfying the following sufficient condition:

[0034]

[0035]

[0036] In the formula, Ω1 represents the filtered unit density; Ω2 represents the empty phase material region; η represents the unfiltered phase material region. e η i and η d These are all threshold values, with values ​​of 0.75, 0.5, and 0.25 respectively. The unit density after filtration The spatial gradient; x represents the coordinates of the element;

[0037] S42, Introduce the structural indicator function to describe the real phase material region Ω1 and the empty phase material region Ω2 in the compliant mechanism configuration:

[0038]

[0039]

[0040] In the formula, the superscripts s and v represent the real phase and the empty phase, respectively; I s and I v These are respectively represented as structure indicator functions for the real and empty phase material regions; when I s When I = 1, it indicates that the unit cell is located inside the real material region Ω1; when I s When I = 1, it indicates that the unit cell is located outside the real phase material region Ω1; for the empty phase material region, the structure indicator function I... v They exhibit the same pattern; λ takes a value of 10. -4 ;R min Minimum filtration radius;

[0041] S43, using the aforementioned structural indicator function, construct geometric constraint functions for the minimum dimensions of the real and empty phase material structures:

[0042]

[0043]

[0044] In the formula, G s and G vLet N and i represent the geometric constraint functions of the real and empty phase material regions, respectively; N represents the number of finite elements; and i represents the i-th element. η is the unit density after filtering unit i; e η d Both are threshold values, taken as 0.75 and 0.25 respectively;

[0045] S44, Relax the geometric constraint function:

[0046]

[0047]

[0048] In the formula, It is a very small positive value;

[0049] S45, Establish a topology optimization model for an electrothermal driven compliant mechanism based on minimum size control:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In the formula, U out Let L be the output displacement of the mechanism; L is a unit vector, with 1 degree of freedom in the output displacement direction and 0 degrees of freedom in all other directions. The unit cell density represents the density of the material in the cell; V0 and V represent the volume of the structure before and after optimization, respectively, and v0 is the volume of the cell filled with material; f * The permissible number of volume fractions; K E K T and K s These represent the overall electrical conduction matrix, overall thermal conduction matrix, and overall stiffness matrix of the structure, respectively; U E U T and U s These represent the voltage array, temperature array, and displacement array of the node, respectively; F E F T and Fs These are voltage load arrays, temperature load arrays, and force load arrays, respectively. unit material density The minimum value is set to 10 to prevent the stiffness matrix from being non-positive definite. -4 .

[0059] Optionally, S5 includes the following steps:

[0060] S51, Solve for the sensitivity of the output displacement of the electrothermal driven compliant mechanism to the design variables;

[0061] S52. Sensitivity to solve the minimum characteristic size constraint of real and empty phase structures;

[0062] S53. Sensitivity to solve structural volume constraints.

[0063] Optionally, the sensitivity of the output displacement of the electrothermal driven compliant mechanism in S51 to the design variable is:

[0064]

[0065] in:

[0066]

[0067]

[0068]

[0069] In the formula, λ E , λ T and λ S These are the adjoint matrix vectors; U out v is the output displacement of the mechanism; j ρ is the volume of element j; i K represents the density of element i; E K T and K s These represent the overall electrical conduction matrix, overall thermal conduction matrix, and overall stiffness matrix of the structure, respectively; U E U T and U s These represent the voltage array, temperature array, and displacement array of the node, respectively; F E F T and F s These are the voltage load array, temperature load array, and force load array, respectively; ω j Let j be the weight of cell j;

[0070] Since the adjoint matrix vector can be any vector, in order to eliminate and Item, λS , λ T and λ E They respectively satisfy the following equations:

[0071] K s λ s =L

[0072]

[0073]

[0074] The partial derivative of the output displacement with respect to the unit material density is obtained as follows:

[0075]

[0076] Optionally, the sensitivity of the minimum characteristic size constraint of the real and empty phase structures in S52 is:

[0077]

[0078]

[0079] in:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] The derivatives of the structure indicator functions of real and unused phase materials with respect to the density of the unit cell are as follows:

[0087]

[0088]

[0089] in:

[0090]

[0091]

[0092] In the formula, λ takes the value of 10. -4 ;R min This is the minimum filtration radius.

[0093] Optionally, the sensitivity of the structural volume constraint in S53 is:

[0094]

[0095] The present invention has the following technical effects:

[0096] By using structural indicator functions to construct minimum size constraints for real and empty phase material structures, the minimum characteristic dimensions of the real and empty phases of the topology configuration of the electrothermal driven compliant mechanism designed by topology optimization can meet the specified size constraints, effectively suppressing the occurrence of small-sized structures and facilitating processing and manufacturing. Attached Figure Description

[0097] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0098] Figure 1 This is a flowchart of the topology optimization method for an electrothermal driven compliant mechanism based on minimum size control, according to an embodiment of the present invention.

[0099] Figure 2 This is a schematic diagram of the design domain, applied load, and boundary conditions of the electrothermal driven compliant mechanism in an embodiment of the present invention;

[0100] Figure 3 The topological configuration of the electrothermal driven compliant mechanism obtained in the embodiments of the present invention;

[0101] Figure 4 The spatial gradient of the electrothermal driven compliant mechanism obtained in the embodiments of the present invention;

[0102] Figure 5 This refers to the solid-phase inflection point region of the electrothermal driven compliant mechanism obtained in the embodiments of the present invention;

[0103] Figure 6 This refers to the empty phase inflection point region of the electrothermal driven compliant mechanism obtained in the embodiments of the present invention. Detailed Implementation

[0104] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0105] like Figure 1As shown, this invention discloses a topology optimization method for an electrothermal driven compliant mechanism based on minimum size control, comprising:

[0106] S1 sets the design domain and boundary conditions for the electrothermal driven compliant mechanism, discretizes the design domain into N finite elements, and defines material parameters, applied load magnitude, output spring stiffness, minimum size control parameters, and initial values ​​of design variables.

[0107] S2, the unit density filtering method is used to filter the structural unit density of the finite element, and then the Heaviside mapping function is used to filter the filtered unit density a second time to obtain the unit material density;

[0108] S21, the element density filtering method is used to filter the structural element density of the finite elements. The filtered element density is obtained by weighted averaging of the densities of adjacent elements.

[0109]

[0110] In the formula, ρ represents the unit density after filtering unit i; j The density of element j; v j Ω represents the volume of element j. i The distance between the centroid of element i and the centroid of element i does not exceed the minimum filtration radius R. min The set of all units; x j Let ω(x) be the coordinates of the center of element j; j ) is the weighting function:

[0111]

[0112] In the formula, x i The coordinates of the center of element i;

[0113] S22, In order to concentrate the cell density values ​​towards the 0 and 1 extremes, the Heaviside mapping function is used to filter the cell density. Secondary filtration is performed to obtain the unit material density. The calculation formula is:

[0114]

[0115] In the formula, η is the unit material density of unit i; i β is the threshold; β is a parameter that controls the approximation degree of the Heaviside mapping function.

[0116] S3 uses a solid isotropic material penalty model to describe the relationship between the material's dielectric constant, thermal conductivity, elastic modulus and unit material density. The sequential coupling method is used to solve the electro-thermal-structural multi-physics finite element equilibrium equations to obtain the displacement response of the mechanism structure.

[0117] S31, a solid isotropic material penalty model is used to describe the relationship between the material's dielectric constant, thermal conductivity, elastic modulus, and the density of the unit material:

[0118]

[0119]

[0120]

[0121] σ is the unit mass density of unit e; E σ T E and E represent the dielectric constant, thermal conductivity, and elastic modulus of unit e, respectively; σ E0 σ T0 E0 and E0 are the unit dielectric constant, thermal conductivity and elastic modulus of the solid material, respectively; P1, P2 and P3 are penalty values, all of which are 3.

[0122] S32, Considering the linear elastic deformation range, the sequential coupling method is used to solve the multi-physics finite element equilibrium equations of the electric-thermal-structural fields. The finite element equilibrium equations for the electric field, thermal field, and structural field are respectively expressed as:

[0123]

[0124]

[0125]

[0126] In the formula, the subscripts E, T, and S represent the electric field, thermal field, and structural field, respectively; K E K T and K s These represent the overall electrical conduction matrix, overall thermal conduction matrix, and overall stiffness matrix of the structure, respectively; U E U T and U s These represent the voltage array, temperature array, and displacement array of the node, respectively; F E F T and F s These are voltage load arrays, temperature load arrays, and force load arrays, respectively. This represents the unit density of the material.

[0127] S4. Taking the output displacement of the electrothermal driven compliant mechanism as the optimization objective, by introducing the structural indicator function, the geometric constraint function of the minimum size of the real phase and empty phase material structure is constructed, and a topology optimization model of the electrothermal driven compliant mechanism based on minimum size control is established.

[0128] For S41, the minimum dimensions of the real and unreal phase material structures of the compliant mechanism are controlled to satisfy the following sufficient conditions:

[0129]

[0130]

[0131] In the formula, Ω1 represents the filtered unit density; Ω3 represents the empty phase material region; η represents the unused phase material region. e η i and η d These are all threshold values, with values ​​of 0.75, 0.5, and 0.25 respectively. The unit density after filtration The spatial gradient; x represents the coordinates of the element.

[0132] S42 introduces two structural indicator functions to describe the real material region Ω1 and the empty material region Ω2 in the compliant mechanism configuration:

[0133]

[0134]

[0135] In the formula, the superscripts s and v represent the real phase and the empty phase, respectively; I s and I v These are respectively represented as structure indicator functions for the real and empty phase material regions; when I s When I = 1, it indicates that the unit cell is located inside the real material region Ω1; when I s When I = 1, it indicates that the unit cell is located outside the real phase material region Ω1; for the empty phase material region, the structure indicator function I... v They exhibit the same pattern; λ takes a value of 10. -4 ;R min This is the minimum filtration radius.

[0136] S43, In order to satisfy the above sufficient conditions, geometric constraint functions for the minimum dimensions of the real and empty phase material structures are constructed using the above two structural indicator functions:

[0137]

[0138]

[0139] In the formula, Gs and G v Let N and i represent the geometric constraint functions of the real and empty phase material regions, respectively; N represents the number of finite elements; and i represents the i-th element. η is the unit density after filtering unit i; e η d Both are threshold values, taken as 0.75 and 0.25 respectively;

[0140] By satisfying the above geometric constraint functions, the filtered cell density is greater than the threshold η. e The cells are located within the inflection point region Ω1, and the filtered cell density is less than the threshold η. d The unit is located within the inflection point region Ω2, thereby achieving minimum size control of the real and empty phase material structures of the electrothermal driven compliant mechanism.

[0141] S44, due to the structural indicator function I in the non-inflection point region s and I v The value is non-zero, resulting in the geometric constraint function G. s and G v It is also a non-zero value, and cannot strictly satisfy the above geometric constraint equation. Therefore, for the geometric constraint function G... s and G v Perform relaxation treatment:

[0142]

[0143]

[0144] In the formula, It is a very small positive value.

[0145] S45, the topology optimization model of the electrothermal driven compliant mechanism based on minimum size control is established as follows:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] In the formula, Uout Let L be the output displacement of the mechanism; L is a unit vector, with 1 degree of freedom in the output displacement direction and 0 degrees of freedom in all other directions. The unit cell density represents the density of the material in the cell; V0 and V represent the volume of the structure before and after optimization, respectively, and v0 is the volume of the cell filled with material; f * The permissible number of volume fractions; K E K T and K s These represent the overall electrical conduction matrix, overall thermal conduction matrix, and overall stiffness matrix of the structure, respectively; U E U T and U s These represent the voltage array, temperature array, and displacement array of the node, respectively; F E F T and F s These are voltage load arrays, temperature load arrays, and force load arrays, respectively. unit material density The minimum value is set to 10 to prevent the stiffness matrix from being non-positive definite. -4 .

[0155] S5. Based on the topology optimization model of the electrothermal driven compliant mechanism, calculate the optimization objective function and constraint values ​​to obtain the output displacement and sensitivity of the minimum characteristic size of the real phase and empty phase structures and the structural volume constraint of the electrothermal driven compliant mechanism.

[0156] S51, Solve for the sensitivity of the output displacement of the electrothermal driven compliant mechanism to the design variables;

[0157]

[0158] in:

[0159]

[0160]

[0161]

[0162] In the formula, λ E , λ T and λ S These are the adjoint matrix vectors; U out v is the output displacement of the mechanism; j ρ is the volume of element j; i K represents the density of element i; E K T and K s These represent the overall electrical conduction matrix, overall thermal conduction matrix, and overall stiffness matrix of the structure, respectively; U E UT and U s These represent the voltage array, temperature array, and displacement array of the node, respectively; F E F T and F s These are the voltage load array, temperature load array, and force load array, respectively; ω j Let j be the weight of cell j;

[0163] Since the adjoint matrix vector can be any vector, in order to eliminate and Item, λ S , λ T and λ E They respectively satisfy the following equations:

[0164] K s λ s =L

[0165]

[0166]

[0167] The partial derivative of the output displacement with respect to the unit material density is obtained as follows:

[0168]

[0169] S52. Sensitivity to solving the minimum characteristic size constraint of real and empty phase structures:

[0170]

[0171]

[0172] in:

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179] The derivatives of the structure indicator functions of real and unused phase materials with respect to the density of the unit cell are as follows:

[0180]

[0181]

[0182] in:

[0183]

[0184]

[0185] In the formula, λ takes the value of 10. -4 ;R min This is the minimum filtration radius.

[0186] S53. Sensitivity to solving structural volume constraints:

[0187]

[0188] S6. The moving asymptotic optimization algorithm is used to design variables and solve the topology optimization problem of the electrothermal driven compliant mechanism based on minimum size control. It is determined whether the convergence criterion is met. If not, the process is transferred to step S2. If it is met, the topology optimization process of the electrothermal driven compliant mechanism ends and the optimal topology configuration of the electrothermal driven compliant mechanism is output.

[0189] To further verify the effectiveness of the topology optimization method for the electrothermal driven compliant mechanism based on minimum size control in the embodiments of the present invention, a two-dimensional electrothermal driven compliant mechanism is used as an example to further illustrate the present invention. The design domain, boundary conditions, and input and output terminals of the electrothermal driven compliant mechanism are as follows: Figure 2 As shown, the design domain has dimensions of 160μm × 86μm. The left and right edges of the design domain are fixed, and a voltage of 7.5V is applied at both ends. The spring stiffness k at the output end is... out The strength is 5 μN / μm, and the design domain is discretized into 160 × 86 planar four-node elements. The material's elastic modulus E is 1 GPa, Poisson's ratio μ is 0.3, electrical conductivity q is 1, thermal conductivity c is 1, and coefficient of thermal expansion α is 1 × 10⁻⁶. -4 Permissible volume fractions f * The value is 0.25, and the minimum filtration radius is R. min =6.

[0190] Figures 3-6 The diagrams show the topology, spatial gradient, solid-phase inflection point domain, and open-phase inflection point domain of the electrothermal driven compliant mechanism obtained from topology optimization design based on minimum size control. Figure 3 It can be seen that the minimum characteristic size of the real phase and empty phase material structure can meet the specified size constraints, so that the minimum characteristic size of the electrothermal driven compliant mechanism can be effectively controlled, and the appearance of hinge-like structures can be effectively avoided.

[0191] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A topology optimization method of electro-thermal driven compliant mechanisms based on minimum size control, characterized in that, The method comprises the following steps: S1, set the electric heating driven compliant mechanism design domain, boundary conditions, discretize the design domain into a plurality of finite elements, define material parameters, action load size, output spring stiffness, minimum size control parameters and initial values of design variables; N S1, set the electric heating driven compliant mechanism design domain, boundary conditions, discretize the design domain into a plurality of finite elements, define material parameters, action load size, output spring stiffness, minimum size control parameters and initial values of design variables; S2, filtering the limited unit by using a unit density filtering method, and then filtering the filtered unit density by using a Heaviside mapping function to obtain a unit material density; S3, using a solid isotropic material with penalization model to describe the relationship between the material dielectric constant, thermal conductivity and elastic modulus and the unit material density, and using a sequential coupling method to solve the electric-thermal-structure multi-physical finite element balance equation to obtain the displacement response of the mechanism structure; S4, taking the output displacement of the electro-thermal driving flexible mechanism as an optimization target, introducing a structure indicator function to construct a geometric constraint function of the minimum size of the real phase and the empty phase material structure, and establishing an electro-thermal driving flexible mechanism topology optimization model based on minimum size control; S5, calculating the optimization objective function and the constraint value according to the electro-thermal driving flexible mechanism topology optimization model to obtain the sensitivity of the output displacement of the electro-thermal driving flexible mechanism and the minimum feature size of the real phase and the empty phase structure and the volume constraint of the structure; S6, using a moving asymptotic optimization algorithm to solve the electro-thermal driving flexible mechanism topology optimization problem based on minimum size control, and judging whether the convergence criterion is met; if not, going to step S2; if yes, the electro-thermal driving flexible mechanism topology optimization process is ended, and the optimal electro-thermal driving flexible mechanism topology is output; The S4 comprises the following steps: S41, controlling the minimum size of the real phase and the empty phase material structure of the flexible mechanism to meet the following sufficient conditions: ； ； wherein, is the filtered cell density; represents the solid material region; represents the void material region; , and are threshold values, respectively taking the values 0.75, 0.5 and 0.25; is the filtered cell density of the spatial gradient; x represents the coordinates of the cell; S42, introducing the structure indicating function, describing the real phase material region in the compliant mechanism configuration and the void phase material region : ； ； wherein the superscripts s and v denote the real and void phases, respectively; and denote the structure indicator functions for the real and void material regions, respectively; when = 1, it indicates that the cell is inside the real material region ; when = 1, it indicates that the cell is outside the real material region ; the structure indicator functions for the void material region have the same rule; takes the value of 10 -4; is the minimum filtering radius; S43, using the structure indicator function to construct a geometric constraint function of the minimum size of the real phase and the empty phase material structure: ； ； wherein, and are the geometric constraint functions for the real and void material regions, respectively; N is the number of finite elements; is the element ; is the element density after filtering; are the threshold values, taken as 0.75 and 0.25, respectively. S44, relaxing the geometric constraint function: ； ； wherein is a very small positive value; S45, establishing an electro-thermal driving flexible mechanism topology optimization model based on minimum size control: ； where, is the output displacement of the mechanism; is the unit vector, which is 0 in all directions except the direction of the output displacement, which is 1; represents the unit material density of the element; and are the volume of the mechanism before and after optimization, respectively, is the volume of the element filled with material; is the allowed volume fraction; , and represent the global electrical conductance matrix, the global thermal conductance matrix, and the global stiffness matrix of the structure, respectively; , and represent the voltage array, the temperature array, and the displacement array of the nodes, respectively; , and are the voltage load array, the temperature load array, and the force load array, respectively; is the minimum value of the unit material density to prevent the stiffness matrix from being non-positive definite, which is 10-4.

2. The minimum size control based topology optimization method of electrothermal driven compliant mechanisms according to claim 1, wherein, The S2 comprises the following steps: S21, filtering the limited unit by using a unit density filtering method, and obtaining the filtered unit density by using a weighted average method of adjacent unit densities: ； wherein is a cell density after filtering; is a cell density; is a cell volume; is a set of all cells whose distance between the cell center and the cell center is not more than the minimum filtering radius is a coordinate of the cell center; is a weight function: ； In the formula, unit coordinates of the center; S22, filtering the filtered unit density by using a Heaviside mapping function to obtain a unit material density: ； unit unit substance density; threshold value; is a parameter controlling the degree of approximation of the approximate Heaviside mapping function.

3. The topology optimization method of electrothermal-driven compliant mechanisms based on minimum size control according to claim 1, wherein, The S3 comprises the following steps: S31, using a solid isotropic material with penalization model to describe the relationship between the material dielectric constant, thermal conductivity and elastic modulus and the unit material density: ； ； ； is the density of the unit material; , , are the dielectric constant, the thermal conductivity and the elastic modulus of the unit, respectively; , , are the dielectric constant, the thermal conductivity and the elastic modulus of the unit filled with the solid material, respectively; is the penalty value, which is 3.​​ S32, considering the linear elastic deformation range, using a sequential coupling method to solve the electric-thermal-structure multi-physical finite element balance equation, wherein the electric field, thermal field and structure field finite element balance equations are respectively represented as: ； ； ； where the subscripts , and denote the electric, thermal and structural fields, respectively; , and denote the overall electric, thermal and stiffness conductance matrices of the structure, respectively; , and denote the voltage, temperature and displacement column arrays of the nodes, respectively; , and are the voltage, temperature and force load column arrays, respectively; denotes the cell material density of the cell.

4. The minimum size controlled electrothermal driven compliant mechanism topology optimization method of claim 1, wherein, The S5 comprises the following steps: S51, solving the sensitivity of the output displacement of the electro-thermal driving flexible mechanism to the design variable; S52, solving the sensitivity of the minimum feature size constraint of the real phase and the empty phase structure; S53, solving the sensitivity of the volume constraint of the structure.

5. The minimum size control based topology optimization method of electrothermal driven compliant mechanisms according to claim 4, wherein, The sensitivity of the output displacement of the electro-thermal driving flexible mechanism to the design variable in the S51 is: ； Wherein: ； ； ； wherein, , and are the companion matrix vectors; is the output displacement of the mechanism; is the volume of the element j ; is the density of the element ; , and denote the overall electrical conductance matrix, overall thermal conductance matrix and overall stiffness matrix of the structure, respectively; , and denote the voltage array, temperature array and displacement array of the nodes, respectively; , and are the voltage load array, temperature load array and force load array, respectively; is the weight of the element j ; Since the accompanying matrix vector can be any vector, to eliminate , and terms, , and respectively satisfy the following equations: ； ； ； The partial derivative of the output displacement to the unit material density is obtained as: 。 6. The topology optimization method of an electrothermal-driven compliant mechanism based on minimum size control according to claim 4, wherein, The sensitivity of the minimum feature size constraint of the real phase and the empty phase structure in the S52 is: ； ； Wherein: ； ； ； ； ； ； The derivatives of the real and imaginary material structure indicator functions with respect to the unit substance density are: ； ； where: ； ； In the formula, takes the value 10-4; is the minimum filtering radius.

7. The topology optimization method of claim 4, wherein, The sensitivity of the structure volume constraint in S53 is: 。

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