Topological optimization design method of multi-material piezoelectric actuator

Abstract

The invention belongs to the technical field of structural topological optimization, and particularly discloses a topological optimization design method of a multi-material piezoelectric actuator, which comprises the following steps: taking a density field and an electrode direction of the piezoelectric actuator as design variables, and taking maximized output displacement obtained by an output displacement node of the piezoelectric actuator as a target function; constructing a topological optimization design model of the piezoelectric actuator by adopting structural volume constraint and manufacturing constraint; solving the topological optimization design model: during each iteration, solving a target function value and updating a design variable, then adopting a three-field topological optimization method, only filtering a density field, and then carrying out next iteration; and finishing iteration to obtain the piezoelectric actuator configuration. By controlling the geometrical shape of the structure, the material distribution is more uniform, the manufacturability and practicability of the mechanism are improved, and the application potential of the piezoelectric actuator in the engineering field is widened.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural topology optimization, and more specifically, relates to a topology optimization design method for a multi-material piezoelectric actuator. Background Art

[0002] A compliant mechanism is a type of mechanical structure that realizes force, motion, and energy transfer through the deformation of an elastomer, and has broad applications in fields such as robotics and micro-nano manufacturing. Different from traditional rigid-body mechanisms, part or all of the motion of a compliant mechanism comes from the flexure of compliant elements, and it has disadvantages such as poor accuracy and stress concentration. Piezoelectric materials have attracted the attention of many scholars due to their characteristics such as fast response speed, high deformation accuracy, small mass, and good electro-mechanical coupling effect. The compliant mechanism of piezoelectric materials is a piezoelectric actuator, which makes full use of the high-precision driving characteristics of piezoelectric materials.

[0003] Regarding the topology optimization design of piezoelectric actuators, relevant technical personnel in this field have conducted some research. For example, the paper "Luo, Z., Gao, W., & Song, C. (2010). Design of multi-phase piezoelectric actuators. Journal of Intelligent Material Systems and Structures, 21(18), 1851-1865." proposed a design method for multi-phase materials, in which the main material acts as a flexible amplifier to amplify the driving stroke of the piezoelectric material, and the maximum displacement design problem is transformed into a numerical process of iteratively distributing multiple materials in the design domain until both the main structure and the piezoelectric material element are optimized. The paper "Homayouni-Amlashi, A., et al. (2021). 2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters. Structural and Multidisciplinary Optimization, 63(2), 983-1014." proposed two independent topology optimization design methods for the driving and energy harvesting of piezoelectric materials. Taking the maximum output displacement at a specific point as the objective function, the structural density distribution and the electrode direction distribution are optimized simultaneously.

[0004] However, it is well known that piezoelectric materials are very fragile and prone to cracking or breaking during manufacturing and use, especially when the stiffness of the virtual spring interacting with the mechanism is small. Therefore, it is very important to reasonably design the geometric shape of the structure and avoid fine, non-uniform, and material distributions that may cause stress concentration. The layout of the positive and negative electrode materials has a significant impact on the driving effect. By optimizing the distribution of the positive and negative electrode materials, the output performance of the piezoelectric actuator can be effectively improved. So far, there is a lack of design methods for piezoelectric actuators considering manufacturing constraints and multi-materials, which greatly limits the design and application of piezoelectric actuators. How to break the traditional empirical design and construct a topology optimization design method for piezoelectric actuators that includes manufacturing constraints and optimizes the layout of positive and negative electrode materials is an urgent problem to be solved. Summary of the Invention

[0005] In view of the above defects or improvement requirements of the prior art, the present invention provides a topology optimization design method for a multi-material piezoelectric actuator, aiming to realize the reasonable distribution of the positive and negative electrode materials in the structure of the piezoelectric actuator and give full play to the driving performance of the piezoelectric material.

[0006] To achieve the above object, according to the first aspect of the present invention, a topology optimization design method for a multi-material piezoelectric actuator is proposed, including the following steps:

[0007] Taking the density field and electrode direction of the piezoelectric actuator as design variables, taking the maximization of the output displacement of the output displacement nodes of the piezoelectric actuator as the objective function, and using the structural volume constraint and manufacturing constraint to construct a topology optimization design model of the piezoelectric actuator;

[0008] Solving the topology optimization design model: In each iteration, solve the objective function value and update the design variables, and then use the three-field topology optimization method. After only filtering the density field, perform the next iteration; when the iteration ends, obtain the configuration of the piezoelectric actuator.

[0009] As a further preference, the topology optimization design model is specifically:

[0010] find x i , P i (i = 1, 2, 3,..., n)

[0011]

[0012] m s ≤ ε

[0013] m v ≤ ≤

[0014] 0 ≤ x i ≤ 1

[0015] 0 ≤ P i ≤ 1

[0016] where x i is the density of the i-th unit; P i is the polarization variable of the i-th unit; n is the total number of units, J is the output displacement, L is a vector with a value of 1 at the output node and 0 elsewhere; are the mechanical stiffness matrix, piezoelectric matrix, external mechanical force, displacement vector, and electric potential, respectively; m1 is the volume constraint function of the actuator, V m is the target overall volume fraction, v i is the volume of the i-th unit; m s and m v are the manufacturing constraint functions for the solid phase and void phase of the actuator, respectively, used to achieve the minimum size control of the solid phase and void phase; ε is the numerical error compensation amount.

[0017] As a further preference, the manufacturing constraint function is specifically:

[0018] Define the inflection point regions Ω1 and Ω2, and construct the indicator functions to represent the solid phase and void phase of the structure respectively:

[0019]

[0020] where s and v represent the solid phase and void phase respectively, N s and N v are the indicator functions of the solid phase and void phase respectively; c is the parameter controlling the decay rate of N s and N v , x, are the design field, filtering field, and physical field respectively, is the gradient of the filtering field;

[0021] Based on the indicator functions, construct the manufacturing constraints to achieve the size control of the solid phase and void phase:

[0022]

[0023] where are the indicator function of the solid phase of the i-th unit, the indicator function of the void phase, and the indicator function of the void phase respectively, and η1 and η2 are the thresholds of the inflection point regions Ω1 and Ω2 respectively.

[0024] As a further preference, during each iteration, solve the objective function value and update the design variables, specifically:

[0025] Based on the global finite element equation of the piezoelectric actuator perform finite element analysis to obtain the objective function value;

[0026] After obtaining the objective function value, the sensitivities of the objective function and the constraint function with respect to the design variables are solved respectively, and then the design variables are updated using the moving asymptote algorithm.

[0027] As a further optimization, the mechanical stiffness matrix is calculated based on the PEMAP-P piezoelectric material interpolation model and the piezoelectric matrix

[0028] As a further optimization, the PEMAP-P piezoelectric material interpolation model is expressed as:

[0029]

[0030] where is the normalized element mechanical stiffness matrix, is the normalized element piezoelectric matrix; E min and e min represent the minimum values of the mechanical stiffness matrix and the force-electric coupling matrix respectively, and E0 and e0 represent the maximum values of the mechanical stiffness matrix and the force-electric coupling matrix respectively; x is the density, and P is the polarization variable; p uu and p uφ and p P are the penalty coefficients of the mechanical stiffness matrix, the force-electric coupling matrix, and the polarization value respectively.

[0031] As a further optimization, the adjoint method is used to solve the sensitivity of the objective function with respect to the design variables;

[0032] The sensitivities of the constraint function with respect to the design variables include: the sensitivity of the constraint function with respect to the polarization variable is 0; the sensitivity of the volume constraint with respect to the density is 1, and the local gradient derivative method is used to solve the sensitivity of the manufacturing constraint with respect to the density.

[0033] As a further optimization, the convergence condition of the moving asymptote algorithm is:

[0034] max(|x k -x k-1 |, |P k -P k-1 |) ≤ change

[0035] where k is the current iteration step number, x k and x k-1 are the density ratios at the kth and (k - 1)th times respectively, P k and P k-1 are the polarization variables at the kth and (k - 1)th times respectively, and change is the convergence accuracy of the design variables.

[0036] According to the second aspect of the present invention, a topology optimization design system for a multi-material piezoelectric actuator is provided, including a processor configured to execute the topology optimization design method of the above multi-material piezoelectric actuator.

[0037] According to the third aspect of the present invention, a multi-material piezoelectric actuator is provided, which is designed by using the topology optimization design method of the above multi-material piezoelectric actuator.

[0038] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the following technical advantages are mainly presented:

[0039] 1. The present invention constructs a topology optimization model for the piezoelectric actuator, incorporating both the element density and the element polarization direction into the scope of optimization variables, enabling precise control of the distribution of the positive and negative voltage materials, thereby fully exploiting the driving potential of the piezoelectric material. This optimization method significantly improves the overall actuation performance of the actuator.

[0040] 2. The present invention introduces manufacturing constraints into the topology optimization design method of the piezoelectric actuator, specifically by constraining the optimized geometric shape, promoting a more uniform material distribution, avoiding overly sharp and fine features, thereby significantly improving the manufacturability and practicality of the mechanism. This improvement effectively alleviates problems such as uneven material distribution and stress concentration, further expanding the application potential of the piezoelectric actuator in the engineering field.

[0041] 3. The present invention adopts a density filtering and three-field topology optimization scheme, which can effectively avoid the common checkerboard phenomenon in the structural optimization process, making the structural boundary clearer and more definite; a piezoelectric material interpolation model with penalty and polarization is introduced, which is an interpolation model for the optimization design of piezoelectric materials, aiming to improve the optimization efficiency. At the same time, the method used in the present invention can achieve the minimum size control of the structure without additional finite element analysis, significantly improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of the topology optimization design method for the multi-material piezoelectric actuator according to the embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of the initial design domain and boundary conditions of the piezoelectric actuator constructed according to the embodiment of the present invention, where (a) and (b) correspond to the gripper and the displacement reverser respectively;

[0044] Figure 3 is a schematic diagram of the topology configuration obtained by optimization without applying manufacturing constraints according to the embodiment of the present invention, where (a) and (b) correspond to the gripper and the displacement reverser respectively;

[0045] Figure 4Schematic diagram of the topological configuration optimized when manufacturing constraints are imposed on the embodiments of the present invention, where (a) and (b) correspond to the gripper and the displacement reverser respectively;

[0046] Figure 5 Under the manufacturing constraints imposed on the embodiments of the present invention, the distribution of the positive and negative electrode materials in the optimization results is shown. Among them, (a) and (b) correspond to the positive and negative electrode material distribution diagrams of the gripper, and (c) and (d) correspond to the positive and negative electrode material distribution diagrams of the displacement reverser;

[0047] Figure 6 Iterative curve of the output displacement and volume fraction of the embodiments of the present invention, where (a) and (b) correspond to the gripper and the displacement reverser respectively. Detailed implementation manners

[0048] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0049] A topological optimization design method for a multi-material piezoelectric actuator provided by an embodiment of the present invention, as Figure 1 shown, includes the following steps:

[0050] S1. Construct a topological optimization design model for the piezoelectric actuator, including:

[0051] (1) Perform overall definitions, defining the geometric dimensions of the piezoelectric plate, the number of mesh divisions, boundary conditions, the volume fraction of the piezoelectric material, the virtual spring stiffness at the output end of the actuator, the voltage value applied to the piezoelectric material, etc.

[0052] (2) Construct the global finite element equation of the piezoelectric actuator to calculate the displacements of each node of the element (specifically, bilinear quadrilateral element).

[0053] Specifically, ignoring the damping effect, the coupled global finite element equation of the piezoelectric actuator can be written as: K uu U + K uφ Φ = F, where F is the external mechanical force;

[0054] The mechanical stiffness matrix K uu and the piezoelectric matrix K uφ in the above equation have a huge difference in values, which may lead to numerical instability. Therefore, by decomposing the maximum value of each element matrix for normalization, after normalization, the global finite element equation can be written as:

[0055] (3) Construct the PEMAP-P piezoelectric material interpolation model, and relate the material properties of the element to its density through a power-law interpolation function. This material interpolation model is used to characterize the mapping relationship between the mechanical stiffness matrix of the element on the finite element mesh and the piezoelectric coupling matrix and the density field.

[0056] Specifically, the formula of the PEMAP-P piezoelectric material interpolation model:

[0057]

[0058] Where is the normalized element mechanical stiffness matrix, is the normalized element piezoelectric matrix; E min , e min are used to define the minimum values of the stiffness matrix and the force-electric coupling matrix, and E0, e0 are used to define the maximum values of the relevant matrices; x is the density ratio of each element, that is, the pseudo-density with a value between 0 and 1; P is the polarization variable, whose value is also between 0 and 1, determining the polarization direction to obtain the positive and negative materials, 0 for the negative electrode, and 1 for the positive electrode; p uu , p uφ and p P are the penalty coefficients of the stiffness matrix, the coupling matrix, and the polarization value respectively.

[0059] (4) Taking the density field and electrode direction of the piezoelectric actuator as design variables, the material volume fraction and size control of the structure as constraint conditions, and the maximized output displacement obtained by the output displacement nodes of the piezoelectric actuator as the objective function, establish a topology optimization design model of the multi-material piezoelectric actuator considering manufacturing constraints.

[0060] Furthermore, the design of the size control constraint conditions includes:

[0061] The three-field topology optimization scheme defines the design field x, the filtering field and the physical field Define the inflection point regions Ω1, Ω2, and the two indicator functions of the solid phase and the void phase of the structure are expressed as:

[0062]

[0063] Where s and v represent the solid phase and the void phase respectively. When , c is the parameter for controlling the attenuation rate of N s and N v .

[0064] Construct the following two manufacturing constraints to achieve the minimum size control of the solid phase and the void phase respectively:

[0065]

[0066] where n is the total number of elements in the discretized set N e By satisfying these two constraints, the value of the filtered field will be greater than the threshold η1 at the inflection point region Ω1 and less than the threshold η2 at the region Ω2.

[0067] Specifically, the topological optimization design model expression of the multi-material piezoelectric actuator considering manufacturing constraints is:

[0068] find x i ,P i (i = 1, 2, 3,..., n)

[0069]

[0070] m s ≤ε

[0071] m v ≤ε

[0072] 0 ≤ x i ≤ 1

[0073] 0 ≤ P i ≤ 1

[0074] where J is the output displacement, L is a vector with a value of 1 at the output nodes and 0 elsewhere, is the normalized displacement vector. Define the final volume constraint of the actuator, V m is the target total volume fraction, v i is the volume of each element, n is the total number of elements, and N e = [1, 2, 3,..., n] is the discretized set. In addition, geometric constraints are added, m s and m v are the geometric constraints of the solid phase and the void phase of the actuator respectively, and ε is a decimal number used to compensate for numerical errors.

[0075] S2. Solve the topological optimization design model until convergence to obtain the piezoelectric actuator structure. Each iteration includes:

[0076] (1) Based on the PEMAP-P piezoelectric material interpolation model, obtain the mapping relationship between material properties and density. According to the normalized global finite element equation of the piezoelectric actuator, obtain the nodal displacements through finite element analysis and determine the objective function value.

[0077] (2) Use the adjoint method and the local gradient differentiation rule to solve the sensitivities of the objective function and the constraint functions.

[0078] Specifically, use the adjoint method to solve the sensitivity of the objective function with respect to the design variables. Introduce the global adjoint vector Λ, and the adjoint equation is: The sensitivity of the objective function with respect to the density design variable \(x\) i is: The sensitivity of the objective function with respect to the polarization direction design variable \(P\) i is: where the sensitivities of the stiffness matrix and the coupling matrix with respect to the design variables are:

[0079]

[0080] The sensitivity of the constraint function: The volume constraint \(m_1\) with respect to the design variable \(P\) i is 0, and with respect to the design variable \(x\) i is 1. The manufacturing constraints \(m\) s and \(m\) v with respect to the design variable \(P\) i are 0, and with respect to the design variable \(x\) i the sensitivity is solved using the local gradient differentiation method.

[0081] Where, Since the sensitivity of the solid phase indicator function \(N\) s with respect to \(x\) i is:

[0082]

[0083] Therefore, the sensitivity of \(m\) s with respect to \(x\) i is:

[0084]

[0085] Similarly, the sensitivity of the void phase indicator function \(N\) v with respect to \(x\) i is:

[0086]

[0087] The sensitivity of \(m\) v with respect to \(x\) i is:

[0088]

[0089] (3) Based on the sensitivities of the objective function and the constraint function, use the moving asymptote algorithm to update the design variables. After filtering and projection, judge whether the convergence condition is satisfied. If satisfied, stop the iteration; if not, perform the next iteration.

[0090] Furthermore, after updating the design variables using the moving asymptote algorithm, a three-field topology optimization scheme is adopted, where only the density of the structure is filtered and the polarity is not filtered. That is, through the three-field topology optimization method, the original density field is converted into three fields: the pseudo-density field, the filtering field, and the physical field to filter and project the density.

[0091] Specifically, the convergence condition of the moving asymptote algorithm is:

[0092] max(|x k -x k-k |, |P k -P k-1 |) ≤ change

[0093] where k is the current iteration step and change is the convergence accuracy of the design variables.

[0094] The following are specific embodiments:

[0095] Taking the gripper and the displacement reverser as examples, Figure 2 The initial design domain of the piezoelectric actuator is shown. Among them, (a) represents the gripper, the design domain size L is 0.01 m, symmetric up and down, the left end is the fixed boundary, the virtual spring acts on the rightmost end of the gripper notch, and the spring stiffness is 0.01 after normalization, representing the output displacement at the rightmost end of the gripper notch, that is, the objective function; (b) represents the displacement reverser, the left end is the fixed boundary, symmetric up and down, the virtual spring acts on the midpoint of the right end of the structure, and the spring stiffness is 0.005 after normalization, representing the output displacement at the midpoint of the right end, that is, the objective function. The allowable volume fraction of both examples is, and only the upper half is taken for optimization, discretized into 150×75 plane four-node elements. The piezoelectric material is PZT4.

[0096] Figure 3 The optimized topological configuration of the mechanism without applying manufacturing constraints is shown. Among them, (a) represents the gripper and (b) represents the displacement reverser. Figure 4 The optimized topological configuration of the mechanism with manufacturing constraints applied is shown. Among them, (a) represents the gripper and (b) represents the displacement reverser. Through comparative analysis, it can be seen that this design method can effectively control the minimum size of the structure, make the material distribution more uniform, and significantly improve the manufacturability and practicality of the mechanism. Figure 5 The distribution of the positive and negative electrode materials in the optimization results under the condition of applying manufacturing constraints is shown. Among them, (a) and (b) correspond to the positive and negative electrode material distribution diagrams of the gripper, and (c) and (d) correspond to the positive and negative electrode material distribution diagrams of the displacement reverser, indicating that by reasonably distributing the positive and negative polarities of the voltage, the driving potential of the piezoelectric material can be fully exploited. Figure 6The output displacement and volume fraction iteration curves of topology optimization are shown, where (a) and (b) correspond to the gripper and the displacement reverser respectively. It can be seen that although applying manufacturing constraints can make the material distribution more uniform, this method will have a certain impact on the maximization of the objective function.

[0097] In summary, the present invention constructs a topology optimization model for a multi-material piezoelectric actuator. The PEMAP-P piezoelectric material interpolation model is adopted to relate the material properties of the elements to their densities. Manufacturing constraints are introduced to achieve the minimum size control of the solid phase and the void phase, and a topology optimization design model for a multi-material piezoelectric actuator considering manufacturing constraints is established. The adjoint method and the local gradient derivative rule are used to solve the sensitivities of the objective function and the constraint function. The moving asymptote algorithm is used to update the design variables to obtain the final topology optimization result. Compared with the traditional method, the present invention takes both the density and the polarization direction as optimization variables, and can fully exploit the driving potential of piezoelectric materials by precisely controlling the distribution of the positive and negative electrode materials. The stress distribution of the high-degree-of-freedom structure and the electrode layout are comprehensively considered, and the reasonable distribution of materials and the optimal design of the structure are realized through the topology optimization method. The present invention controls the geometric shape of the structure, promotes the more uniform distribution of materials, avoids overly sharp and fine features, significantly improves the manufacturability and practicality of the mechanism, further expands the application potential of piezoelectric actuators in the engineering field, not only improves the performance and reliability of piezoelectric actuators, but also reduces their design complexity.

[0098] It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A topology optimization design method for a multi-material piezoelectric actuator, characterized in that: The steps include: The density field and electrode direction of the piezoelectric actuator are used as design variables, the output displacement of the piezoelectric actuator output displacement node is used as the objective function, and the structural volume constraint and manufacturing constraint are adopted to construct a topology optimization design model of the piezoelectric actuator. The topology optimization design model is solved: in each iteration, the objective function value is solved and the design variables are updated, and then the three-field topology optimization method is used to filter only the density field before the next iteration; the piezoelectric actuator configuration is obtained at the end of the iteration.

2. The topology optimization design method of a multi-material piezoelectric actuator according to claim 1, characterized in that: The topology optimization design model is specifically: find x i ,P i (i=1,2,3,...,n) m s ≤ε m v ≤ε 0≤x i ≤1 0≤P i ≤1 Among them, x i is the density of the ith unit; P i is the polarization variable of the i-th unit; n is the total number of units, J is the output displacement, and L is a vector whose value is 1 at the output node and 0 at the rest; are the mechanical stiffness matrix, piezoelectric matrix, external mechanical force, displacement vector, and electric potential respectively; m1 is the actuator volume constraint function, V m is the target overall score, v i is the volume of the i-th unit; m s and m are the manufacturing constraint functions of the solid phase and the void phase of the actuator, respectively, which are used to achieve the minimum size control of the solid phase and the void phase; ε is the numerical error compensation.

3. The topology optimization design method of a multi-material piezoelectric actuator according to claim 2, characterized in that: The manufacturing constraint function is as follows: Define the inflection point regions Ω1 and Ω2, and construct indicator functions to represent the solid phase and empty phase of the structure respectively: Among them, s and v represent the solid phase and the empty phase respectively, N s 、N v are the indicator functions of the solid phase and the empty phase respectively; c is the control N s and N v The decay rate parameter, x, They are design field, filter field and physical field respectively. is the gradient of the filter field; Based on the indicator function, the manufacturing constraints are constructed to achieve the size control of the solid phase and the void phase: in, are the solid phase indicator function, empty phase indicator function and empty phase indicator function of the ith unit respectively. η1 and η2 are the thresholds of the inflection point regions Ω1 and Ω2 respectively.

4. The topology optimization design method of a multi-material piezoelectric actuator according to claim 2, characterized in that: At each iteration, the objective function value is solved and the design variables are updated, specifically: Global finite element equations based on piezoelectric actuators Conduct finite element analysis to obtain the objective function value; After obtaining the objective function value, the sensitivity of the objective function and constraint function to the design variables are solved respectively, and then the design variables are updated using the moving asymptote algorithm.

5. The topology optimization design method of a multi-material piezoelectric actuator according to claim 4, characterized in that: Calculation of mechanical stiffness matrix based on PEMAP-P piezoelectric material interpolation model and piezoelectric matrix 6. The topology optimization design method of a multi-material piezoelectric actuator according to claim 5, characterized in that: PEMAP-P Piezoelectric Material Interpolation Model It is expressed as: in, is the normalized element mechanical stiffness matrix, is the normalized unit piezoelectric matrix; E min 、e min They represent the minimum values ​​of the mechanical stiffness matrix and the electromechanical coupling matrix, respectively. E0 and e0 represent the maximum values ​​of the mechanical stiffness matrix and the electromechanical coupling matrix, respectively. x is the density, P is the polarization variable, and p uu 、p uφ 、p P They are the penalty coefficients of mechanical stiffness matrix, electromechanical coupling matrix, and polarization value.

7. The topology optimization design method of a multi-material piezoelectric actuator according to claim 4, characterized in that: Adjoint method is used to solve the sensitivity of objective function to design variables; The sensitivity of the constraint function to the design variables includes: the sensitivity of the constraint function to the polarization variable is 0; The sensitivity of volume constraint to density is 1, and the local gradient derivation method is used to solve the sensitivity of manufacturing constraint to density.

8. The topology optimization design method of a multi-material piezoelectric actuator according to claim 4, characterized in that: The convergence condition of the moving asymptote algorithm is: max(|x k -x k-1 |,|P k -P k-1 |)≤change Among them, k is the current iteration number, x k 、x k-1 are the density ratios of the kth and k-1th times, P k , P k-1 are the k-th and k-1-th polarization variables respectively, and change is the convergence accuracy of the design variables.

9. A topology optimization design system for a multi-material piezoelectric actuator, characterized in that: It comprises a processor, wherein the processor is used to execute the topology optimization design method of the multi-material piezoelectric actuator as described in any one of claims 1 to 8.

10. A multi-material piezoelectric actuator, characterized in that: The multi-material piezoelectric actuator is designed using the topology optimization design method according to any one of claims 1 to 8.

Images