Thermally-driven micro-nano compliant mechanism topological optimization method considering scale effect

Abstract

The invention provides a thermally driven micro-nano compliant mechanism topological optimization method considering a scale effect. The method comprises the following steps: defining design conditions of a thermally driven micro-nano compliant mechanism, and setting material attribute indexes; establishing a finite element analysis model of the thermally driven micro-nano compliant mechanism; obtaining a structure displacement response; establishing a topological optimization model of the thermally driven micro-nano compliant mechanism; calculating and optimizing an objective function and constrained sensitivity information; performing smoothing processing on the sensitivity information; and solving the optimization problem of the thermally driven micro-nano compliant mechanism by adopting a moving progressive optimization algorithm, judging whether the convergence condition of the moving progressive algorithm is met or not, and if so, outputting the optimal topological configuration of the thermally driven micro-nano compliant mechanism considering the scale effect. The thermally-driven micro-nano compliant mechanism obtained through topological optimization has an obvious scale effect, the topological configuration of the thermally-driven micro-nano compliant mechanism is changed along with increasing of scale parameters related to the feature length, and it is indicated that the scale effect becomes more obvious.

Description

Technical Field

[0001] The present invention relates to the technical field of compliant mechanism optimization design, and particularly relates to a topology optimization method for thermally actuated micro-nano compliant mechanisms considering scale effects. Background Art

[0002] Thermally actuated compliant mechanisms utilize thermal expansion deformation to generate motion and force at the output end. Compared with other driving methods, thermally actuated compliant mechanisms can output larger forces and displacements, and have the advantages of easy control and easy integration. With the continuous development and application of micro-nano technology, the scale of thermal actuators has become smaller and smaller. When conducting topology optimization design of large-scale thermally actuated compliant mechanisms based on traditional medium theory, the obtained results cannot truly reflect the mechanical properties at the microscale. Therefore, it is necessary to consider scale effects for topology optimization design of thermally actuated compliant mechanisms.

[0003] In order to consider scale effects, most studies consider introducing higher-order elasticity theory, among which the couple stress theory is the most widely used. Although higher-order elasticity theory has been applied to many microstructural designs, its application in the field of topology optimization remains largely undeveloped. In addition, existing studies mainly focus on using compliance as the objective function. It is urgent to study the topology optimization design of thermally actuated micro-nano compliant mechanisms using the couple stress theory.

[0004] In summary, in the prior art, when conducting topology optimization design of large-scale thermally actuated compliant mechanisms based on traditional medium theory, the obtained results cannot truly reflect the mechanical properties at the microscale. Summary of the Invention

[0005] Based on this, the purpose of the present invention is to provide a topology optimization method for thermally actuated micro-nano compliant mechanisms considering scale effects to solve the deficiencies in the above prior art.

[0006] The present invention provides a topology optimization method for thermally actuated micro-nano compliant mechanisms, and the method includes: Defining the design conditions of the thermally actuated micro-nano compliant mechanism and setting various material property indexes of the thermally actuated micro-nano compliant mechanism; Based on the modified couple stress and introducing non-classical equivalent stress to establish a finite element analysis model of the thermally actuated micro-nano compliant mechanism; Based on the penalty model to represent the relationship between the design conditions and the material property indexes, deriving an equivalent nodal thermal load expression according to the relationship, and further solving the thermo-solid coupling finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism; Taking the maximization of the output displacement of the thermally actuated micro-nano compliant mechanism as the objective function and taking the volume of the thermally actuated micro-nano compliant mechanism as the constraint to establish a mathematical model for topology optimization of the thermally actuated micro-nano compliant mechanism; Calculate the output displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally actuated micro-nano compliant mechanism according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism; Use the sensitivity filtering technique to correct the optimization objective function and the sensitivity information, and smooth the sensitivity information using the Heaviside mapping function; Use the moving asymptote optimization algorithm to solve the optimization problem of the thermally actuated micro-nano compliant mechanism, and determine whether the convergence condition of the moving asymptote optimization algorithm is satisfied. If so, output the optimal topological configuration of the thermally actuated micro-nano compliant mechanism.

[0007] Compared with the prior art, the beneficial effects of the present invention are as follows: Based on the modified couple stress theory, a size-dependent non-classical equivalent stress is introduced to establish a finite element analysis model of the thermally actuated micro-nano compliant mechanism, and the structural displacement response of the thermally actuated micro-nano compliant mechanism is obtained by solving the thermo-solid coupling finite element equilibrium equation. By considering the scale effect of the topology optimization model of the thermally actuated micro-nano compliant mechanism, the sensitivity information of the optimization objective function and the constraints is calculated, and then it is determined whether the convergence condition is satisfied through the moving asymptote algorithm, so as to obtain the optimal topological configuration of the thermally actuated micro-nano compliant mechanism, and thus the scale effect of the thermally actuated micro-nano compliant mechanism can be effectively displayed.

[0008] Further, the steps of defining the design conditions of the thermally actuated micro-nano compliant mechanism and setting the material property indexes of the thermally actuated micro-nano compliant mechanism include: Define the design domain, boundary conditions, and applied load action of the thermally actuated micro-nano compliant mechanism; Set the material elastic modulus, Poisson's ratio, thermal expansion coefficient, finite element number, initial value of element density, sensitivity filtering radius, and scale parameter of the thermally actuated micro-nano compliant mechanism.

[0009] Further, the steps of establishing the finite element analysis model of the thermally actuated micro-nano compliant mechanism based on the modified couple stress and introducing the non-classical equivalent stress include: Based on the modified couple stress theory and the classical medium theory, describe the scale effect of the thermally actuated micro-nano compliant mechanism at the microscale; Introduce the non-classical equivalent stress, and characterize the strength of the scale effect of the thermally actuated micro-nano compliant mechanism with the scale parameter to obtain the finite element analysis model of the thermally actuated micro-nano compliant mechanism.

[0010] Further, the steps of representing the relationship between the design conditions and the material property indexes based on the penalty model, deriving the equivalent nodal thermal load expression according to the relationship, and further solving the thermo-solid coupling finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism include: An improved solid isotropic material penalty model is adopted to represent the relationship between the material elastic modulus and the initial value of the element density in the material property index, and the nodal load expression is derived based on this relationship; Solve the finite element equilibrium equation according to the nodal load expression, and perform finite element analysis on the structure of the thermally actuated micro-nano compliant mechanism based on the finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism.

[0011] Furthermore, the expression of the mathematical model for the topology optimization of the thermally actuated micro-nano compliant mechanism is: ; In the formula, represents the output displacement of the mechanism, represents a constant, where, , represents the number of elements, represents the th element density of the design variable of the , , represent displacement vector one, displacement vector two, and displacement vector three respectively, represents the overall stiffness matrix of the design domain, represents the equivalent nodal thermal load vector, represents the th element elastic modulus and the relationship function between the elastic modulus of the solid material , represents the temperature difference between a certain moment and the initial moment, represents the linear expansion coefficient of the material, represents the elastic modulus, represents the Poisson's ratio of the material, and the superscript represents the transpose symbol, is the transformation matrix for converting the element stiffness matrix into the global stiffness matrix, is the design domain, is the strain-displacement matrix of classical mechanics, is the strain-displacement matrix of the couple stress theory, is the classical theory element elastic matrix, is the couple stress theory element elastic matrix, is the constraint function, is the element volume, is the initial volume of the mechanism, is the mechanism volume constraint, represents the element design domain.

[0012] Further, the steps of calculating the output displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally actuated micro-nano compliant mechanism according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism include: Calculating the output displacement of the thermally actuated micro-nano compliant mechanism according to the mutual strain energy of the mechanism, and calculating the structural volume of the thermally actuated micro-nano compliant mechanism through the element density to obtain the optimization objective and volume constraint; Calculating the maximization of the output displacement of the objective function of the optimization objective and the sensitivity information of the volume constraint according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism.

[0013] Further, the steps of correcting the optimization objective function and the sensitivity information by using the sensitivity filtering technique and smoothing the sensitivity information by using the Heaviside mapping function include: Correcting the optimization objective function and the sensitivity information by using the sensitivity filtering technique; Smoothing the sensitivity information by using the Heaviside mapping function to concentrate the element density at both ends of the preset interval range, so as to reduce the appearance of intermediate gray-scale elements in the topological configuration.

[0014] Further, after the step of judging whether the convergence condition of the moving asymptote optimization algorithm is satisfied, the method further includes: If the convergence condition of the moving asymptote optimization algorithm is not satisfied, then repeatedly execute: establishing a finite element analysis model of the thermally actuated micro-nano compliant mechanism based on the modified couple stress and introducing non-classical equivalent stress; representing the relationship between the design conditions and the material property indexes based on the penalty model, deriving an equivalent nodal thermal load expression according to the relationship, and further solving the thermo-solid coupling finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism; taking the maximization of the output displacement of the thermally actuated micro-nano compliant mechanism as the objective function, and taking the volume of the thermally actuated micro-nano compliant mechanism as the constraint, establishing a mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism; calculating the output displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally actuated micro-nano compliant mechanism according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism; correcting the optimization objective function and the sensitivity information by using the sensitivity filtering technique and smoothing the sensitivity information by using the Heaviside mapping function; solving the optimization problem of the thermally actuated micro-nano compliant mechanism by using the moving asymptote optimization algorithm, and judging whether the convergence condition of the moving asymptote optimization algorithm is satisfied until the optimal topological configuration of the thermally actuated micro-nano compliant mechanism is output. Description of the Drawings

[0015] Figure 1Flow chart of the topology optimization method for a thermally - driven micro - nano compliant mechanism considering scale effect in the embodiments of the present invention; Figure 2 Schematic diagram of the design domain, load and boundary conditions of the thermally - driven micro - nano compliant mechanism in the embodiments of the present invention; Figure 3 Topology optimization result of the thermally - driven micro - nano compliant mechanism using classical theory without considering scale effect in the embodiments of the present invention; Figure 4 Topology optimization result of the thermally - driven micro - nano compliant mechanism using the modified couple stress theory considering scale effect in the embodiments of the present invention.

[0016] The following specific embodiments will further illustrate the present invention in conjunction with the above - mentioned drawings. Specific Embodiments

[0017] Please refer to Figure 1 , which shows the topology optimization method for a thermally - driven micro - nano compliant mechanism considering scale effect in the embodiments of the present invention. The method includes steps S1 to S7: S1. Define the design conditions of the thermally - driven micro - nano compliant mechanism and set various material property indexes of the thermally - driven micro - nano compliant mechanism; Specifically, step S1 includes steps S11 to S12: S11. Define the design domain, boundary conditions and applied load action of the thermally - driven micro - nano compliant mechanism; S12. Set the material elastic modulus, Poisson's ratio, thermal expansion coefficient, number of finite elements, initial value of element density, sensitivity filtering radius and scale parameter of the thermally - driven micro - nano compliant mechanism.

[0018] S2. Based on the modified couple stress and by introducing non - classical equivalent stress, establish the finite - element analysis model of the thermally - driven micro - nano compliant mechanism; Specifically, step S2 includes steps S21 to S22: S21. Based on the modified couple stress theory and the classical medium theory, describe the scale effect of the thermally - driven micro - nano compliant mechanism at the micro - scale; It can be understood that the modified couple stress theory is a high - order elastic theory derived from the principle of minimum potential energy. According to this theory, in a two - dimensional problem under the assumption of isotropic plane stress, the displacement field includes the element displacement vector and the element micro - rotation displacement vector , where is the element micro - rotation displacement vector, and , the components of the symmetric curvature tensor are . Correspondingly, the components of the Cauchy stress tensor are , and the components of the modified couple stress tensor are . In summary, both the stress components and strain components of the two-dimensional element consist of five components, and the stress-strain matrix considering couple stress is: ; ; wherein, is the stress matrix, are the stress component in the x-direction, the stress component in the y-direction, the shear stress component, the couple stress component in the x-direction, and the couple stress component in the y-direction respectively, is the strain matrix, are the strain component in the x-direction, the strain component in the y-direction, the shear strain component, the curvature component in the x-direction, and the curvature component in the y-direction respectively, and the superscript T represents the transpose symbol.

[0019] The stress-strain relationship is: ; wherein, is the stress matrix, is the elastic matrix, is the strain matrix.

[0020] In this embodiment, only for two-dimensional design problems, the micro-rotation angle is constrained to be equal to the macro-rotation angle, that is = , so the rotation can be calculated from the displacement as follows: ; wherein, is the micro-rotation displacement vector of the element, respectively represent the partial derivatives of the element displacement vector with respect to the independent variable , and the partial derivatives of the element displacement vector with respect to the independent variable .

[0021] Two components of the curvature are obtained: ; wherein, is the curvature component in the x-direction, is the curvature component in the y-direction, is the second-order partial derivative of the element displacement vector with respect to the independent variable , is the second-order partial derivative of the element displacement vector with respect to the independent variable and the independent variable . is the element displacement vector for the independent variable and the independent variable the second-order partial derivative of, is the element displacement vector for the independent variable the second-order partial derivative of.

[0022] S22, introduce the non-classical equivalent stress, and characterize the scale effect strength of the thermally driven micro-nano compliant mechanism with a scale parameter to obtain the finite element analysis model of the thermally driven micro-nano compliant mechanism; It can be understood that the strain-displacement relationship under the isotropic plane stress problem based on the modified couple stress theory is: ; ; In the formula, is the strain matrix, are the strain component in the x direction, the strain component in the y direction, the shear strain component, the curvature component in the x direction, and the curvature component in the y direction respectively, is the curvature matrix, are the two components of the element displacement vector respectively, is the element displacement vector, , is the element microscopic rotation displacement vector, is the partial derivative symbol.

[0023] The corresponding constitutive equation is: ; ; In the formula, is the stress matrix, are the stress component in the x direction, the stress component in the y direction, the shear stress component, the couple stress component in the x direction, and the couple stress component in the y direction respectively, is the strain matrix, are the strain component in the x direction, the strain component in the y direction, the shear strain component, the curvature component in the x direction, and the curvature component in the y direction respectively, is the curvature matrix, is the couple stress matrix, the superscript T represents the transpose symbol, G represents the shear modulus, given by and is the material elastic modulus, is the material Poisson's ratio.

[0024] It should be noted that an additional material parameter is introduced in the constitutive relationship , known as the material characteristic length parameter. This parameter is an important material parameter reflecting the size effect and does not exist in classical elasticity theory. In actual calculations, The value of is determined through experiments. The total constitutive matrix Consists of the classical elastic constitutive matrix And the couple stress constitutive matrix The relationship is: ; In the formula, Is the total constitutive matrix, Is the classical elastic constitutive matrix, Is the couple stress constitutive matrix.

[0025] S3, based on the penalty model, represents the relationship between the design conditions and the material property indicators, derives the equivalent nodal thermal load expression according to this relationship, and further solves the thermo-solid coupling finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism; Specifically, the step S3 includes steps S31 to S32: S31, using the improved solid isotropic material penalty model to represent the relationship between the material elastic modulus and the initial value of the element density in the material property indicators, and deriving the nodal load expression according to this relationship; It can be understood that the SIMP material interpolation model is used to describe the relationship between the material properties and the design variable x, and the expression is: ; In the formula, Represents the Elastic modulus of the th Element and the elastic modulus of the solid material The relationship function between them, and the specific expression is: , Represents the element density design variable, Represents the initial element density design variable, Represents the minimum element density design variable, Represents the penalty coefficient. In this embodiment, The values of are all 3; Thermal strain Will be generated when the temperature changes, and its expression is: ; In the formula, Represents the thermal strain, Represents the linear expansion coefficient of the material, Represents the initial temperature, Represents the steady-state temperature of the compliant mechanism, and the superscript Indicates the transpose symbol; When considering a uniform temperature change, a hypothetical temperature load applied to each node can be equivalent to the nodal thermal load, which is equivalent to a nodal force, and its expression is: ; In the formula, Represents the temperature load related to the element density, Represents the strain matrix, Represents the elastic matrix, Represents the design domain, Represents the thermal strain, Represents the thickness of the thermally actuated compliant mechanism.

[0026] The equivalent nodal thermal load of the element is expressed as: ; In the formula, Represents the equivalent nodal thermal load of the element, Represents the strain matrix, Represents the elastic matrix, Represents the linear expansion coefficient of the material, Represents the initial temperature, Represents the steady-state temperature of the compliant mechanism, Represents the elastic modulus, Represents the temperature difference between a certain moment and the initial moment, Represents the Poisson's ratio of the material, and the superscript T represents the transpose symbol.

[0027] S32. Solve the finite element equilibrium equation according to the nodal load expression, and perform finite element analysis on the structure of the thermally actuated micro-nano compliant mechanism based on the finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism; It can be understood that in this embodiment, in the structural field, the finite element equilibrium equation is: ;

[0028] In the formula, Represents the load column matrix, Represents the overall structural stiffness matrix, Represents the overall nodal displacement column matrix, Is the transformation matrix that converts the element stiffness matrix into the global stiffness matrix, Is the design domain, Represents the element design domain, Is the strain-displacement matrix of classical mechanics, Is the strain-displacement matrix of the couple stress theory, Is the element elastic matrix of classical theory, is the elastic matrix of the couple stress theory element, and the superscript represents the transpose symbol.

[0029] S4, with the maximization of the output displacement of the thermally actuated micro-nano compliant mechanism as the objective function and the volume of the thermally actuated micro-nano compliant mechanism as the constraint, a mathematical model for the topology optimization of the thermally actuated micro-nano compliant mechanism is established; In this embodiment, the expression of the mathematical model for the topology optimization of the thermally actuated micro-nano compliant mechanism is: ; In the formula, represents the output displacement of the mechanism, represents a constant, where , represents the number of elements, represents the design variable element density of the th element, , , respectively represent displacement vector one, displacement vector two, and displacement vector three, represents the overall stiffness matrix of the design domain, represents the equivalent nodal thermal load vector, represents the th element elastic modulus and the relationship function between the elastic modulus of the solid material , represents the temperature difference between a certain moment and the initial moment, represents the linear expansion coefficient of the material, represents the elastic modulus, represents the Poisson's ratio of the material, and the superscript represents the transpose symbol, is the transformation matrix for converting the element stiffness matrix into the global stiffness matrix, is the design domain, is the strain-displacement matrix of classical mechanics, is the strain-displacement matrix of the couple stress theory, is the classical theory element elastic matrix, is the couple stress theory element elastic matrix, is the constraint function, is the element volume, is the initial volume of the mechanism, is the mechanism volume constraint, represents the element design domain.

[0030] S5. Calculate the output displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally actuated micro-nano compliant mechanism according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism. Specifically, step S5 includes steps S51 to S52: S51. Calculate the output displacement of the thermally actuated micro-nano compliant mechanism according to the mutual strain energy of the mechanism, and calculate the structural volume of the thermally actuated micro-nano compliant mechanism through the element density to obtain the optimization objective and volume constraint. S52. Calculate the maximization of the output displacement of the objective function of the optimization objective and the sensitivity information of the volume constraint according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism. It can be understood that in this embodiment, in the structural thermal field of the compliant mechanism, the displacement field of the structure can be obtained by the following formula: ; In the formula, represents the thermal load array, represents the total stiffness matrix of the modified couple stress theory, represents the global nodal displacement array. Taking the derivative of both sides of the formula, we can get: ; represents the temperature load related to the element density. By substituting and taking the derivative, we can get: ; The adjoint matrix equation is: ; In the formula, represents the unit vector, represents the total stiffness matrix of the modified couple stress theory, represents the adjoint vector of the displacement, represents the elastic modulus of the solid material, represents the elastic modulus of the void material; Therefore, it can be deduced that: ; Therefore, the upper limit of displacement and the lower limit of displacement of the sensitivity of the design variable and can be obtained respectively; Finally, the sensitivity of the output displacement of the thermally actuated micro-nano compliant mechanism to the design variable can be obtained: ; In the formula, , Respectively represent the upper limit of displacement The sensitivity to the design variable, the lower limit of displacement The sensitivity to the design variable. From the upper limit of displacement And the lower limit of displacement The sensitivity information of the objective function can be obtained from the sensitivity.

[0031] The constraint, that is, the sensitivity of the volume fraction to the element density, is obtained as: ; In the formula, Represents the volume fraction of the element, Represents the element density, Represents the partial derivative symbol, Represents the volume constraint.

[0032] S6. Adopt the sensitivity filtering technology to correct the optimization objective function and the sensitivity information, and use the Heaviside mapping function to smooth the sensitivity information; Specifically, the step S6 includes steps S61 to S62: S61. Adopt the sensitivity filtering technology to correct the optimization objective function and the sensitivity information; S62. Use the Heaviside mapping function to smooth the sensitivity information, so that the element density concentrates towards both ends of the preset interval range to reduce the appearance of intermediate gray-scale elements in the topological configuration; It can be understood that the formula of the Heaviside mapping function is: ; In the formula, Represents the processed design variable, Represents the threshold parameter, Represents the parameter controlling the smoothness of the change, Represents the relative density of the material, Represents the hyperbolic tangent function symbol.

[0033] It should be explained that in this embodiment, the preset interval range is 0 - 1. By concentrating the element density towards both ends of 0 - 1, the appearance of intermediate gray-scale elements in the topological configuration can be reduced.

[0034] S7. Adopt the moving asymptote optimization algorithm to solve the optimization problem of the thermally driven micro-nano compliant mechanism, and judge whether the convergence condition of the moving asymptote optimization algorithm is satisfied. If so, output the optimal topological configuration of the thermally driven micro-nano compliant mechanism; Further, if the convergence condition of the moving asymptote optimization algorithm is not satisfied, the following steps are repeatedly executed: establish a finite element analysis model of the thermally actuated micro-nano compliant mechanism based on the modified couple stress and the introduction of non-classical equivalent stress; represent the relationship between the design conditions and the material property indexes based on the penalty model, derive the equivalent nodal thermal load expression according to this relationship, and further solve the thermo-solid coupled finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro-nano compliant mechanism; establish a mathematical model for the topology optimization of the thermally actuated micro-nano compliant mechanism with the maximization of the output displacement of the thermally actuated micro-nano compliant mechanism as the objective function and the volume of the thermally actuated micro-nano compliant mechanism as the constraint; calculate the sensitivity information of the output displacement of the optimization objective function and the constrained volume of the thermally actuated micro-nano compliant mechanism according to the mathematical model of the topology optimization of the thermally actuated micro-nano compliant mechanism; correct the optimization objective function and the sensitivity information by using the sensitivity filtering technique, and smooth the sensitivity information by using the Heaviside mapping function; solve the optimization problem of the thermally actuated micro-nano compliant mechanism by using the moving asymptote optimization algorithm, and judge whether the convergence condition of the moving asymptote optimization algorithm is satisfied until the optimal topology configuration of the thermally actuated micro-nano compliant mechanism is output.

[0035] To further verify the effectiveness of the topology optimization method for thermally actuated micro-nano compliant mechanisms considering the scale effect, a thermally actuated micro-nano compliant mechanism is taken as an example for explanation.

[0036] The design domain, boundary conditions, input end and output end of the thermally actuated micro-nano compliant mechanism are as Figure 2 shown. In the whole compliant mechanism, the upper, lower and left sides are all fixed, and the output displacement is at the midpoint on the right side. Since the mechanism is symmetric, only the lower half is taken for design analysis. Similarly, it is discretized into 20,000 planar quadrilateral elements for calculation. When the temperature rises, the left side of the mechanism deforms and squeezes, causing the structure at the output position to move to the right, thus achieving the effect of thermal actuation.

[0037] In this example, the size of the compliant mechanism is , the elastic modulus of the thermally actuated material is 100 GPa, the Poisson's ratio is , the coefficient of thermal expansion is , the volume is set to 0.15, the elastic modulus of the void phase material is . In the Heaviside mapping function of the thermal actuator, the number of steps for doubling the value of the iterative control parameter is 50 steps, the initial value is 1, the maximum value is 16, and the parameter ​The value is 0.5. To prevent the material from converging too quickly to both sides at the initial stage of iteration, the penalty coefficient is set with an initial value of 0.5, a maximum value of 3, and for every 30 steps of iteration, the penalty coefficient increases by 0.5. The iteration stop condition is set as when the total number of steps exceeds 500 steps, or the change in element density is less than 0.001.

[0038] Without considering the scale effect, the thermally actuated micro-nano compliant mechanism obtained by using the classical medium theory for topology optimization, as Figure 3 shown, the output displacement of the thermally actuated micro-nano compliant mechanism is 1.5684, and the volume constraint is 0.150.

[0039] Considering the scale effect, under the condition of setting the scale parameter , the thermally actuated micro-nano compliant mechanism obtained by using the modified couple stress theory for topology optimization, as Figure 4 shown, the output displacement of the thermally actuated micro-nano compliant mechanism is 1.6037, the volume constraint is 0.150, and the mechanism has an obvious scale effect.

[0040] In summary, for the thermally actuated micro-nano compliant mechanism topology optimization method considering the scale effect in the above embodiments of the present invention, based on the modified couple stress theory, a size-dependent non-classical equivalent stress is introduced to establish a finite element analysis model of the thermally actuated micro-nano compliant mechanism, and the structural displacement response of the thermally actuated micro-nano compliant mechanism is obtained by solving the thermo-solid coupling finite element equilibrium equation. The sensitivity information of the optimization objective function and constraints is calculated through the thermally actuated micro-nano compliant mechanism topology optimization model considering the scale effect, and then it is judged whether the convergence condition is satisfied through the moving asymptote algorithm, so as to be able to obtain the optimal topology configuration of the thermally actuated micro-nano compliant mechanism, and further be able to effectively show the scale effect of the thermally actuated micro-nano compliant mechanism.

[0041] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0042] The above-described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation to the scope of the patent for the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the patent for the present invention shall be subject to the appended claims.

Claims

1. A topology optimization method for thermally actuated micro-nano compliant mechanisms considering scale effect, characterized in that The method includes: defining the design conditions of the thermally actuated micro / nano compliant mechanism and setting the material property indexes of the thermally actuated micro / nano compliant mechanism; establishing a finite element analysis model of the thermally actuated micro / nano compliant mechanism based on the modified couple stress and introducing non-classical equivalent stress; representing the relationship between the design conditions and the material property indexes based on the penalty model, deriving an expression for the equivalent nodal thermal load according to the relationship, and further solving the thermo-solid coupling finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro / nano compliant mechanism; establishing a mathematical model for the topology optimization of the thermally actuated micro / nano compliant mechanism with the maximum output displacement of the thermally actuated micro / nano compliant mechanism as the objective function and the volume of the thermally actuated micro / nano compliant mechanism as the constraint; calculating the output end displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally actuated micro / nano compliant mechanism according to the mathematical model for the topology optimization of the thermally actuated micro / nano compliant mechanism; correcting the optimization objective function and the sensitivity information by using the sensitivity filtering technique and smoothing the sensitivity information by using the Heaviside mapping function; solving the optimization problem of the thermally actuated micro / nano compliant mechanism by using the moving asymptote optimization algorithm and judging whether the convergence condition of the moving asymptote optimization algorithm is satisfied. If so, output the optimal topological configuration of the thermally actuated micro / nano compliant mechanism.

2. The topology optimization method of a thermally driven micro-nano compliant mechanism considering the scale effect according to claim 1, wherein The steps of defining the design conditions of the thermally actuated micro / nano compliant mechanism and setting the material property indexes of the thermally actuated micro / nano compliant mechanism include: defining the design domain, boundary conditions and applied load action of the thermally actuated micro / nano compliant mechanism; setting the material elastic modulus, Poisson's ratio, thermal expansion coefficient, number of finite elements, initial value of element density, sensitivity filtering radius and scale parameter of the thermally actuated micro / nano compliant mechanism.

3. The topology optimization method of a thermally driven micro-nano compliant mechanism considering the scale effect according to claim 1, characterized in that, The steps of establishing a finite element analysis model of the thermally actuated micro / nano compliant mechanism based on the modified couple stress and introducing non-classical equivalent stress include: describing the scale effect of the thermally actuated micro / nano compliant mechanism at the microscale based on the modified couple stress theory and the classical medium theory; introducing non-classical equivalent stress and characterizing the strength of the scale effect of the thermally actuated micro / nano compliant mechanism with a scale parameter to obtain the finite element analysis model of the thermally actuated micro / nano compliant mechanism.

4. The topology optimization method of a thermally driven micro-nano compliant mechanism considering the scale effect according to claim 1, characterized in that, The steps of representing the relationship between the design conditions and the material property indexes based on the penalty model, deriving an expression for the equivalent nodal thermal load according to the relationship, and further solving the thermo-solid coupling finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro / nano compliant mechanism include: using an improved solid isotropic material penalty model to represent the relationship between the material elastic modulus and the initial value of element density in the material property indexes and deriving a nodal load expression according to the relationship; solving the finite element equilibrium equation according to the nodal load expression and performing finite element analysis on the structure of the thermally actuated micro / nano compliant mechanism based on the finite element equilibrium equation to obtain the structural displacement response of the thermally actuated micro / nano compliant mechanism.

5. The topology optimization method of a thermally driven micro-nano compliant mechanism considering the scale effect according to claim 1, characterized in that The expression of the mathematical model for the topology optimization of the thermally actuated micro / nano compliant mechanism is: ； In the formula, represents the output displacement of the mechanism, represents a constant, where , represents the number of elements, represents the th unit density of the design variable of the th unit, , respectively represent displacement vector one, displacement vector two, and displacement vector three, represents the overall stiffness matrix of the design domain, represents the equivalent nodal thermal load vector, represents the th unit elastic modulus and the relationship function between the elastic modulus of the solid material, represents the temperature difference between a certain moment and the initial moment, represents the linear expansion coefficient of the material, represents the elastic modulus, represents the Poisson's ratio of the material, and the superscript represents the transpose symbol, is the transformation matrix for converting the element stiffness matrix into the global stiffness matrix, is the design domain, is the strain-displacement matrix of classical mechanics, is the strain-displacement matrix of the couple stress theory, is the classical theory element elastic matrix, is the couple stress theory element elastic matrix, is the constraint function, is the unit volume, is the initial volume of the mechanism, is the mechanism volume constraint, represents the unit design domain.

6. The topology optimization method of a thermally driven micro-nano compliant mechanism considering the scale effect according to claim 1, characterized in that The steps of calculating the output - end displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally - driven micro - nano compliant mechanism according to the mathematical model of the topology optimization of the thermally - driven micro - nano compliant mechanism include: Calculating the output - end displacement of the thermally - driven micro - nano compliant mechanism according to the mutual strain energy of the mechanism, and calculating the structural volume of the thermally - driven micro - nano compliant mechanism through the element density to obtain the optimization objective and the volume constraint; Calculating the maximization of the output displacement of the objective function of the optimization objective and the sensitivity information of the volume constraint according to the mathematical model of the topology optimization of the thermally - driven micro - nano compliant mechanism.

7. The topology optimization method of the thermally driven micro-nano compliant mechanism considering the scale effect according to claim 1, characterized in that The steps of using the sensitivity filtering technology to correct the optimization objective function and the sensitivity information, and using the Heaviside mapping function to smooth the sensitivity information include: Using the sensitivity filtering technology to correct the optimization objective function and the sensitivity information; Using the Heaviside mapping function to smooth the sensitivity information, so that the element density concentrates at both ends of the preset interval range to reduce the appearance of intermediate - gray - level elements in the topology configuration.

8. The topology optimization method of a thermally-driven micro-nano compliant mechanism considering the scale effect according to claim 1, characterized in that After the step of judging whether the convergence condition of the moving asymptote optimization algorithm is satisfied, the method further includes: If the convergence condition of the moving asymptote optimization algorithm is not satisfied, then repeatedly execute: establishing a finite - element analysis model of the thermally - driven micro - nano compliant mechanism based on the modified couple stress and introducing non - classical equivalent stress; representing the relationship between the design conditions and the material property indexes based on the penalty model, deriving the equivalent nodal thermal load expression according to the relationship, and further solving the thermo - solid coupling finite - element balance equation to obtain the structural displacement response of the thermally - driven micro - nano compliant mechanism; taking the maximization of the output displacement of the thermally - driven micro - nano compliant mechanism as the objective function and taking the volume of the thermally - driven micro - nano compliant mechanism as the constraint to establish a mathematical model of the topology optimization of the thermally - driven micro - nano compliant mechanism; calculating the output - end displacement of the optimization objective function and the sensitivity information of the constrained volume of the thermally - driven micro - nano compliant mechanism according to the mathematical model of the topology optimization of the thermally - driven micro - nano compliant mechanism; using the sensitivity filtering technology to correct the optimization objective function and the sensitivity information, and using the Heaviside mapping function to smooth the sensitivity information; using the moving asymptote optimization algorithm to solve the optimization problem of the thermally - driven micro - nano compliant mechanism, and judging whether the convergence condition of the moving asymptote optimization algorithm is satisfied until the optimal topology configuration of the thermally - driven micro - nano compliant mechanism is output.

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