Topology Optimization Method for Compliant Mechanisms Based on Adaptive Volume Constraints

Abstract

This invention provides a topology optimization method for a compliant mechanism with specified compliance based on adaptive volume constraints. The method includes defining design conditions for the compliant mechanism and setting material property indices; obtaining the structural displacement response of the compliant mechanism under input load and virtual unit load; adaptively changing the volume constraint value of the mechanism based on the difference between the total compliance and the specified total compliance; establishing a mathematical model for topology optimization of the compliant mechanism with specified compliance based on adaptive volume constraints; calculating the optimization objective function and the sensitivity information of the constraints; correcting the sensitivity of the optimization objective and constraints; solving the topology optimization problem using the moving asymptote algorithm; and determining whether the convergence condition is met. If so, the optimal topology configuration of the compliant mechanism is output. This invention realizes the topology optimization design of a compliant mechanism based on adaptive volume constraints, and the obtained compliant mechanism has specified compliance performance.

Description

Technical Field

[0001] This invention relates to the field of compliant mechanism optimization design technology, and in particular to a topology optimization method for a specified compliance compliant mechanism based on adaptive volume constraints. Background Technology

[0002] Compliant mechanisms are a new type of assembly-free mechanism that uses flexible joints or hinges instead of the traditional motion hinges, employing large-deformation flexible elements rather than all rigid components to transmit or convert motion, force, or energy. Compared to traditional rigid mechanisms, compliant mechanisms overcome the drawbacks of high processing and assembly costs and wear of moving parts, offering advantages such as low manufacturing costs, assembly-free operation, high precision, and high efficiency. Currently, most compliant mechanisms are designed using topology optimization methods.

[0003] In existing technologies, traditional mechanism topology optimization mostly uses maximizing compliance as the objective function, optimizing a certain mechanism configuration under certain volume fraction constraints. Compared with traditional fixed volume constraint topology optimization, adaptive volume constraint methods can redistribute materials and, by introducing design methods that specify compliance, obtain more compliant mechanisms while satisfying the stiffness requirements. In most mechanism topology optimization designs that aim to maximize output displacement, it is rare to simultaneously ensure that both the input and output ends of the mechanism have sufficient stiffness. Summary of the Invention

[0004] Therefore, the purpose of this invention is to provide a topology optimization method for a specified compliance mechanism based on adaptive volume constraints, so as to overcome the shortcomings of the prior art.

[0005] This invention provides a topology optimization method for a specified compliance mechanism based on adaptive volume constraints, the method comprising:

[0006] Define the design conditions for the specified compliance mechanism and set the material property indexes for the specified compliance mechanism;

[0007] The relationship between the element elastic modulus and element design variables of the specified compliance mechanism is expressed based on the solid isotropic material penalty model. The finite element equilibrium equations are solved under input load and virtual unit load respectively to obtain the structural displacement response.

[0008] The total compliance of the specified compliance mechanism is constructed by weighting the input compliance and the output compliance, and the volume constraint value of the specified compliance mechanism is adaptively changed according to the difference between the total compliance and the specified compliance.

[0009] With the goal of maximizing the output displacement of the specified compliance mechanism, and with adaptive volume as the constraint, a mathematical model for topology optimization of the specified compliance mechanism is established based on the adaptive volume constraint.

[0010] The output displacement, volume, and total compliance of the specified compliance mechanism are calculated based on the topology optimization mathematical model of the specified compliance mechanism, and the optimization objective function and the sensitivity information of the constraints to the design variables are solved.

[0011] The optimization objective function and the sensitivity information are corrected using sensitivity filtering technology;

[0012] The optimization problem of the specified compliance mechanism is solved by the moving asymptotic optimization algorithm, and it is determined whether the convergence condition of the moving asymptotic optimization algorithm is met. If so, the optimal topology of the specified compliance mechanism is output.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: by solving the finite element equilibrium equations under input load and virtual unit load, the structural displacement response is obtained, and the total compliance of the mechanism is constructed by weighting the input compliance and output compliance. Then, the volume constraint value of the mechanism is adaptively changed according to the difference between the total compliance and the specified total compliance. The optimization objective function and the sensitivity information of the constraint are calculated according to the mathematical model of topology optimization of the specified compliance mechanism based on adaptive volume constraint. Then, the convergence condition is determined by the moving asymptotic algorithm, thereby obtaining the optimal specified compliance topology configuration, which can effectively improve the stiffness of the specified compliance mechanism.

[0014] Furthermore, the steps of defining the design conditions for the compliance mechanism and setting the material property indices for the compliance mechanism include:

[0015] Define the design domain, boundary conditions, and loads of the specified compliance mechanism;

[0016] The material elastic modulus, Poisson's ratio, number of finite elements, initial element density, sensitivity filtration radius, volume fraction, and specified compliance value of the specified compliance mechanism are set.

[0017] Furthermore, the steps of representing the relationship between the element elastic modulus and element design variables of the specified compliance mechanism based on the solid isotropic material penalty model, and solving the finite element equilibrium equations under input load and virtual unit load respectively to obtain the structural displacement response include:

[0018] An improved solid isotropic material penalty model is used to represent the relationship between the element elastic modulus and element design variables of the specified compliance mechanism, and the nodal load expression is derived based on the relationship.

[0019] The finite element equilibrium equations under input load and virtual unit load are solved based on the nodal load expression, and the structure of the specified compliance mechanism is analyzed by finite element analysis to obtain the structural displacement response of the specified compliance mechanism.

[0020] Furthermore, the step of constructing the total compliance value of the specified compliance mechanism by weighting the input compliance value and the output compliance value, and adaptively changing the volume constraint value of the specified compliance mechanism according to the difference between the total compliance value and the specified compliance value includes:

[0021] The strain energy of the specified compliance mechanism under actual load is defined as the real compliance value, and the strain energy under unit virtual load is defined as the virtual compliance value. The total compliance of the specified compliance mechanism is constructed by weighting the real compliance value and the virtual compliance value.

[0022] The structure of the specified compliance mechanism is modified based on the difference between the total compliance and the specified total compliance, so as to adaptively change the volume constraint value of the specified compliance mechanism.

[0023] Furthermore, the expression for the mathematical model of the topology optimization of the specified compliance mechanism is as follows:

[0024] ;

[0025] In the formula, Describe the objective function. Indicates the output displacement. Indicates the average flexibility of the mechanism. Indicates the first Unit density of each design variable Indicates the transpose symbol. Indicates the change factor. This represents the initial average compliance value of the mechanism. This represents the array of input loads applied at the mechanism's input point. This represents the unit virtual load array loaded at the output point. Indicates the unit number. To design variable cell density, The overall stiffness matrix of the specified compliance mechanism is... The displacement matrix of the specified compliance mechanism under input load. Let be the displacement matrix of the specified compliance mechanism under a unit virtual load at the output end. The total compliance value of the specified compliance mechanism. For the volume of the unit, The total number of units, The number of volume fractions that varies with the number of iterations. The specified compliance value is the output compliance value of the compliance mechanism. The input compliance value is the specified compliance value for the compliance mechanism.

[0026] Furthermore, the step of calculating the output displacement, volume, and total compliance of the specified compliance mechanism based on the topology optimization mathematical model of the specified compliance mechanism, and solving for the optimization objective function and the sensitivity information of the constraints to the design variables includes:

[0027] The output displacement and total compliance of the specified compliance mechanism are calculated based on the displacement field, and the structural volume of the specified compliance mechanism is calculated through the element density to obtain the optimization objective and constraints.

[0028] The objective function output displacement and the sensitivity information of the adaptive volume constraint are calculated based on the specified compliance mechanism topology optimization mathematical model.

[0029] Furthermore, after the step of determining whether the convergence condition of the moving asymptotic optimization algorithm is met, the method further includes:

[0030] If the convergence condition of the moving asymptotic optimization algorithm is not met, the design conditions for the defined compliance mechanism are repeatedly executed, and the material property indices of the defined compliance mechanism are set. The relationship between the element elastic modulus and element design variables of the defined compliance mechanism is represented based on a solid isotropic material penalty model, and the finite element equilibrium equations are solved under input load and virtual unit load respectively to obtain the structural displacement response. The total compliance of the defined compliance mechanism is constructed by weighting the input compliance and output compliance, and the volume constraint value of the defined compliance mechanism is adaptively changed according to the difference between the total compliance and the defined compliance. The optimization objective is to maximize the output displacement of the structure, and a mathematical model for topology optimization of the compliant mechanism with specified compliance is established based on the adaptive volume constraint. The output displacement, volume, and total compliance of the compliant mechanism are calculated according to the mathematical model, and the optimization objective function and the sensitivity information of the constraints to the design variables are solved. Sensitivity filtering technology is used to correct the optimization objective function and the sensitivity information. A moving asymptotic optimization algorithm is used to solve the optimization problem of the compliant mechanism with specified compliance, and the convergence condition of the moving asymptotic optimization algorithm is determined until the optimal topology configuration of the compliant mechanism with specified compliance is output. Attached Figure Description

[0031] Figure 1 This is a flowchart of the topology optimization method for a specified compliance mechanism based on adaptive volume constraints in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram illustrating the design domain, load, and boundary conditions of a compliance mechanism with specified flexibility in an embodiment of the present invention.

[0033] Figure 3 This is the topology optimization result of the specified compliance inverter in the embodiments of the present invention;

[0034] Figure 4 This is an iterative diagram of the objective function of the specified compliance inverter in an embodiment of the present invention.

[0035] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0036] Please see Figure 1 The figure shows a topology optimization method for a specified compliance mechanism based on adaptive volume constraints in an embodiment of the present invention. The method includes steps S1 to S7:

[0037] S1, define the design conditions for the specified compliance mechanism and set the material property index of the specified compliance mechanism;

[0038] Specifically, step S1 includes steps S11 to S12:

[0039] S11, define the design domain, boundary conditions, and loads of the specified compliance mechanism;

[0040] S12, set the material elastic modulus, Poisson's ratio, number of finite elements, initial value of element density, sensitivity filtration radius, volume fraction, and specified flexibility value of the specified flexibility compliance mechanism.

[0041] S2, based on the solid isotropic material penalty model, represents the relationship between the element elastic modulus and element design variables of the specified compliance mechanism, and solves the finite element equilibrium equations under input load and virtual unit load respectively to obtain the structural displacement response.

[0042] Specifically, step S2 includes steps S21 to S22:

[0043] S21, an improved solid isotropic material penalty model is used to represent the relationship between the element elastic modulus and element design variables of the specified compliance mechanism, and the nodal load expression is derived based on the relationship;

[0044] Understandably, the SIMP material interpolation model is used to describe the relationship between material properties and the design variable x, expressed as:

[0045] ;

[0046] In the formula, This represents the interpolated element elastic modulus. Represents the element density design variable, where, , Represents the minimum unit density design variable. This represents the penalty coefficient, in this embodiment, The value of is 3. This represents the initial unit density design variable.

[0047] S22, Solve the finite element equilibrium equations under the action of input load and virtual unit load according to the nodal load expression, and perform finite element analysis on the structure of the specified compliance mechanism to obtain the structural displacement response of the specified compliance mechanism;

[0048] It is understood that, in this embodiment, the displacement sequence of the compliance mechanism under input load is specified. The displacement array of a compliant mechanism under a unit virtual load at the output end and the specified compliance mechanism The expression is:

[0049] ;

[0050] ;

[0051] In the formula, To define the overall stiffness matrix of a compliant mechanism, To define the displacement matrix of a compliant mechanism under input load, To define the displacement array of a compliant mechanism under a unit virtual load at the output end, Indicates the actual load. A virtual payload array for each unit.

[0052] Specify the overall stiffness matrix of a compliant mechanism It can be represented by the following expression:

[0053]

[0054] In the formula, To define the overall stiffness matrix of a compliant mechanism, To design variable cell density, Indicates the penalty coefficient. The element stiffness matrix, For spring stiffness, For unit numbering, The total number of units;

[0055] Simultaneously, the compliance of the unit, the output compliance value of the specified compliance mechanism, and the input compliance value of the specified compliance mechanism can be expressed in discrete form, as follows:

[0056] ;

[0057] ;

[0058] ;

[0059] In the formula, , , These represent the compliance of the unit, the output compliance value of the specified compliance mechanism, and the input compliance value of the specified compliance mechanism, respectively. To define the displacement matrix of a compliant mechanism under input load, To define the displacement array of a compliant mechanism under a unit virtual load at the output end, To define the overall stiffness matrix of a compliant mechanism, This is the displacement array of the element under actual load. It is the transpose symbol. To design variable cell density.

[0060] S3, construct the total compliance of the specified compliance mechanism by weighting the input compliance and the output compliance, and adaptively change the volume constraint value of the specified compliance mechanism according to the difference between the total compliance and the specified compliance.

[0061] Specifically, step S3 includes steps S31 to S32:

[0062] S31, the strain energy of the specified compliance mechanism under actual load is defined as the real compliance value and the strain energy under unit virtual load is defined as the virtual compliance value. The total compliance of the specified compliance mechanism is constructed by weighting the real compliance value and the virtual compliance value.

[0063] It is understandable that the expressions for the output compliance value and the input compliance value of the specified compliance mechanism are:

[0064] ;

[0065] ;

[0066] In the formula, , These represent the output compliance value and the input compliance value of the specified compliance mechanism, respectively. To define the displacement matrix of a compliant mechanism under input load, To define the displacement array of a compliant mechanism under a unit virtual load at the output end, To define the overall stiffness matrix of a compliant mechanism, It is the transpose symbol. To design variable cell density;

[0067] The virtual total compliance value is defined as the sum of the virtual compliance value and the real compliance value of a compliance mechanism, expressed as:

[0068] ;

[0069] In the formula, This is a virtual total compliance value. This is the virtual compliance value. This is the actual softness value. To design variable cell density, These are the weighting coefficients.

[0070] In this embodiment, the magnitudes of the virtual compliance value and the actual compliance value are affected by the spring and material properties, and both have the same magnitude. If the value is 1, then:

[0071] .

[0072] S32, Based on the difference between the total compliance and the specified total compliance, the structure of the specified compliance mechanism is changed to adaptively change the volume constraint value of the specified compliance mechanism;

[0073] It is understandable that the total compliance value of a specified compliance mechanism is taken as a certain value and denoted as... The volume is changed by the difference between the total compliance value during the process and the specified total compliance value. If the total compliance value of the mechanism is greater than the specified total compliance value, then:

[0074] ;

[0075] If the overall compliance value of the mechanism is less than the specified overall compliance value, then:

[0076] ;

[0077] In the formula, Indicates the number of iterations. This represents the number of volume fractions that change with the number of iterations. The overall compliance value of the mechanism. This specifies the total compliance value of a compliance mechanism.

[0078] S4, with the maximization of the output displacement of the specified compliance mechanism as the optimization objective, and with the adaptive volume as the constraint, establish a topology optimization mathematical model of the specified compliance mechanism based on the adaptive volume constraint;

[0079] In this embodiment, the expression for the mathematical model of the topology optimization of the specified compliance mechanism is:

[0080] ;

[0081] In the formula, Describe the objective function. Indicates the output displacement. Indicates the average flexibility of the mechanism. Indicates the first Unit density of each design variable Indicates the transpose symbol. Indicates the change factor. This represents the initial average compliance value of the mechanism. This represents the array of input loads applied at the mechanism's input point. This represents the unit virtual load array loaded at the output point. Indicates the unit number. To design variable cell density, The overall stiffness matrix of the specified compliance mechanism is... The displacement matrix of the specified compliance mechanism under input load. Let be the displacement matrix of the specified compliance mechanism under a unit virtual load at the output end. The total compliance value of the specified compliance mechanism. For the volume of the unit, The total number of units, The number of volume fractions that varies with the number of iterations. The specified compliance value is the output compliance value of the compliance mechanism. The input compliance value is the specified compliance value for the compliance mechanism.

[0082] S5. Calculate the output displacement, volume, and total compliance of the specified compliance mechanism according to the specified compliance mechanism topology optimization mathematical model, and solve for the optimization objective function and the sensitivity information of the constraints to the design variables.

[0083] Specifically, step S5 includes steps S51 to S52:

[0084] S51, calculate the output displacement and total compliance of the specified compliance mechanism based on the displacement field, and calculate the structural volume of the specified compliance mechanism through the element density to obtain the optimization target and constraints;

[0085] S52, calculate the objective function output displacement and the sensitivity information of the adaptive volume constraint of the optimization target according to the specified compliance mechanism topology optimization mathematical model;

[0086] It is understandable that in this embodiment, due to the displacement of the output terminal... Magnitude and mutual strain energy The magnitudes of the two forces are numerically equal in absolute value, and the first derivative of the mutual strain energy is relatively easy to solve. Therefore, the mutual strain energy can be used to replace the displacement as the objective function, expressed as:

[0087] ;

[0088] ;

[0089] Differentiating the objective function, we have:

[0090] ;

[0091] Furthermore, the derivative of the output displacement with respect to the design variables is:

[0092] ;

[0093] From the above equation and the previously derived formula, we can obtain:

[0094] ;

[0095] For the global stiffness matrix Differentiation yields:

[0096] ;

[0097] From the above equation and the previously derived formula, we obtain the sensitivity of the objective function of the specified compliance mechanism to the design variables:

[0098] ;

[0099] in, For softness, For design variables, namely element density, As a penalty factor, it is usually set to 3. The element stiffness matrix, It is the transpose symbol. The displacement array of the element under virtual load. This is the displacement array of the element under actual load.

[0100] The sensitivity of adaptive volume constraints to design variables is consistent in principle and the sensitivity of constant volume constraints are expressed in the same form. It can be directly derived from the volume fractions with respect to design variables. Therefore, the first derivative of the structural volume with respect to design variables is:

[0101] ;

[0102] In the formula, For the volume of the mechanism, For design variables, namely element density, For the volume of the unit, This is the sign for a partial derivative.

[0103] S6, employ sensitivity filtering technology to correct the optimization objective function and the sensitivity information;

[0104] It is understandable that sensitivity filtering technology is used to correct the optimization objective function and sensitivity information in order to avoid instability in the chessboard values ​​and grid-dependent values.

[0105] S7. The moving progressive optimization algorithm is used to solve the optimization problem of the specified compliance mechanism, and it is determined whether the convergence condition of the moving progressive optimization algorithm is met. If so, the optimal topology of the specified compliance mechanism is output.

[0106] It should be noted that if the convergence condition of the moving asymptotic optimization algorithm is not met, the design conditions for the defined compliance mechanism are repeatedly executed, and the material property indices of the defined compliance mechanism are set; the relationship between the element elastic modulus and element design variables of the defined compliance mechanism is represented based on the solid isotropic material penalty model, and the finite element equilibrium equations are solved under input load and virtual unit load respectively to obtain the structural displacement response; the total compliance of the defined compliance mechanism is constructed by weighting the input compliance and output compliance, and the volume constraint value of the defined compliance mechanism is adaptively changed according to the difference between the total compliance and the defined compliance; the defined compliance is then used to further refine the design conditions. The optimization objective is to maximize the output displacement of the compliant mechanism. A mathematical model for topology optimization of the compliant mechanism based on adaptive volume constraints is established. The output displacement, volume, and total compliance of the compliant mechanism are calculated according to the mathematical model, and the optimization objective function and the sensitivity information of the constraints to the design variables are solved. Sensitivity filtering technology is used to correct the optimization objective function and the sensitivity information. The optimization problem of the compliant mechanism is solved using a moving asymptotic optimization algorithm, and the convergence condition of the moving asymptotic optimization algorithm is determined until the optimal topology configuration of the compliant mechanism is output.

[0107] To further verify the effectiveness of the topology optimization method for a specified compliance mechanism based on adaptive volume constraints in this invention, a specified compliance inverter is used as an example for explanation.

[0108] Specify the design domain, boundary conditions, and input / output terminals of the compliant mechanism. Figure 2 As shown, the upper and lower ends on the left side of the design domain are fixed and connected to other structures, and external loads... The design is applied at the midpoint on the left side of the mechanism. Since the mechanism is symmetrical, only half of it is taken for design analysis. Similarly, it is discretized into 40,000 planar quadrilateral elements for design.

[0109] In this example, the dimensions of the compliant reverser... for The thickness of the mechanism for The upper and lower ends on the left side of the design domain are fixed and connected to other structures, and external loads... Applied at the midpoint of the left side of the mechanism, with a size of The output point is at the midpoint of the right end. The input spring of the design domain is... The spring stiffness is The spring at the output end is The spring stiffness is This is used to simulate the stiffness of components in external contact. The iteration stopping condition is set when the total number of iterations exceeds 500, or when the change in element density between two adjacent iterations is less than 0.001.

[0110] Inverter topology optimization configurations incorporating adaptive volume constraints with specified flexibility, such as... Figure 3 As shown. By Figure 3 It can be seen that in the inverter configuration of the adaptive volume constraint method with specified flexibility, there is no obvious hinge phenomenon. The distribution of solid material shifts from a large accumulation in the rigid part to the more compliant part. This redistribution of material allows the inverter's mutual strain energy to have better stiffness under the specified value. In the iterative process of optimizing the displacement at the output end of the objective function, it also changes from small to large, tending to stabilize and gradually converge after 150 steps. Figure 4 As shown.

[0111] In summary, the adaptive volume constraint-based topology optimization method for compliant mechanisms in the above embodiments of the present invention obtains the structural displacement response by solving the finite element equilibrium equations under input load and virtual unit load, and constructs the total compliance of the mechanism by weighting the input compliance and output compliance. Then, it adaptively changes the volume constraint value of the mechanism based on the difference between the total compliance and the specified total compliance. By calculating the optimization objective function and the constraint sensitivity information according to the mathematical model of topology optimization for compliant mechanisms based on adaptive volume constraints, and then determining whether the convergence condition is met through the moving asymptotic algorithm, the optimal compliant topology configuration with specified compliance can be obtained, which can effectively improve the performance of compliant mechanisms under stiffness constraints.

[0112] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0113] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A topology optimization method for a specified compliance mechanism based on adaptive volume constraints, characterized in that, The method includes: Define the design conditions for the specified compliance mechanism and set the material property indexes for the specified compliance mechanism; The relationship between the element elastic modulus and element design variables of the specified compliance mechanism is expressed based on the solid isotropic material penalty model. The finite element equilibrium equations are solved under input load and virtual unit load respectively to obtain the structural displacement response. The total compliance of the specified compliance mechanism is constructed by weighting the input compliance and the output compliance, and the volume constraint value of the specified compliance mechanism is adaptively changed according to the difference between the total compliance and the specified compliance. With maximizing the output displacement of the specified compliance mechanism as the optimization objective, and with adaptive volume as the constraint, a mathematical model for topology optimization of the specified compliance mechanism is established. The expression of the mathematical model for topology optimization of the specified compliance mechanism is as follows: ； In the formula, Describe the objective function. Indicates the output displacement. Indicates the average flexibility of the mechanism. Indicates the first Unit density of each design variable Indicates the transpose symbol. Indicates the change factor. This represents the initial average compliance value of the mechanism. This represents the array of input loads applied at the mechanism's input point. This represents the unit virtual load array loaded at the output point. Indicates the unit number. To design variable cell density, The overall stiffness matrix of the specified compliance mechanism is... The displacement matrix of the specified compliance mechanism under input load. Let be the displacement matrix of the specified compliance mechanism under a unit virtual load at the output end. The total compliance value of the specified compliance mechanism. For the volume of the unit, The total number of units, The number of volume fractions that varies with the number of iterations. The specified compliance value is the output compliance value of the compliance mechanism. The input compliance value for the specified compliance mechanism; The output displacement, volume, and total compliance of the specified compliance mechanism are calculated based on the topology optimization mathematical model of the specified compliance mechanism, and the optimization objective function and the sensitivity information of the constraints to the design variables are solved. The optimization objective function and the sensitivity information are corrected using sensitivity filtering technology; The optimization problem of the specified compliance mechanism is solved by the moving asymptotic optimization algorithm, and it is determined whether the convergence condition of the moving asymptotic optimization algorithm is met. If so, the optimal topology of the specified compliance mechanism is output.

2. The topology optimization method for a specified compliance mechanism based on adaptive volume constraints according to claim 1, characterized in that, The steps of defining the design conditions for the compliance mechanism and setting the material property indices for the compliance mechanism include: Define the design domain, boundary conditions, and loads of the specified compliance mechanism; The material elastic modulus, Poisson's ratio, number of finite elements, initial element density, sensitivity filtration radius, volume fraction, and specified compliance value of the specified compliance mechanism are set.

3. The topology optimization method for a specified compliance mechanism based on adaptive volume constraints according to claim 1, characterized in that, The steps of using a solid isotropic material penalty model to represent the relationship between the element elastic modulus and element design variables of the specified compliance mechanism, and solving the finite element equilibrium equations under input load and virtual unit load respectively to obtain the structural displacement response include: An improved solid isotropic material penalty model is used to represent the relationship between the element elastic modulus and element design variables of the specified compliance mechanism, and the nodal load expression is derived based on the relationship. The finite element equilibrium equations under input load and virtual unit load are solved based on the nodal load expression, and the structure of the specified compliance mechanism is analyzed by finite element analysis to obtain the structural displacement response of the specified compliance mechanism.

4. The topology optimization method for a specified compliance mechanism based on adaptive volume constraints according to claim 1, characterized in that, The step of constructing the total compliance value of the specified compliance mechanism by weighting the input compliance value and the output compliance value, and adaptively changing the volume constraint value of the specified compliance mechanism according to the difference between the total compliance value and the specified compliance value includes: The strain energy of the specified compliance mechanism under actual load is defined as the real compliance value, and the strain energy under unit virtual load is defined as the virtual compliance value. The total compliance of the specified compliance mechanism is constructed by weighting the real compliance value and the virtual compliance value. The structure of the specified compliance mechanism is modified based on the difference between the total compliance and the specified total compliance, so as to adaptively change the volume constraint value of the specified compliance mechanism.

5. The topology optimization method for a specified compliance mechanism based on adaptive volume constraints according to claim 1, characterized in that, The steps of calculating the output displacement, volume, and total compliance of the specified compliance mechanism based on the specified compliance mechanism topology optimization mathematical model, and solving for the optimization objective function and the sensitivity information of constraints to design variables include: The output displacement and total compliance of the specified compliance mechanism are calculated based on the displacement field, and the structural volume of the specified compliance mechanism is calculated through the element density to obtain the optimization objective and constraints. The objective function output displacement and the sensitivity information of the adaptive volume constraint are calculated based on the specified compliance mechanism topology optimization mathematical model.

6. The topology optimization method for a specified compliance mechanism based on adaptive volume constraints according to claim 1, characterized in that, After the step of determining whether the convergence condition of the moving asymptotic optimization algorithm is met, the method further includes: If the convergence condition of the moving asymptotic optimization algorithm is not met, the design conditions for the defined compliance mechanism are repeatedly executed, and the material property indices of the defined compliance mechanism are set. The relationship between the element elastic modulus and element design variables of the defined compliance mechanism is represented based on a solid isotropic material penalty model, and the finite element equilibrium equations are solved under input load and virtual unit load respectively to obtain the structural displacement response. The total compliance of the defined compliance mechanism is constructed by weighting the input compliance and output compliance, and the volume constraint value of the defined compliance mechanism is adaptively changed according to the difference between the total compliance and the defined compliance. The optimization objective is to maximize the output displacement of the structure, and a mathematical model for topology optimization of the compliant mechanism with specified compliance is established based on the adaptive volume constraint. The output displacement, volume, and total compliance of the compliant mechanism are calculated according to the mathematical model, and the optimization objective function and the sensitivity information of the constraints to the design variables are solved. Sensitivity filtering technology is used to correct the optimization objective function and the sensitivity information. A moving asymptotic optimization algorithm is used to solve the optimization problem of the compliant mechanism with specified compliance, and the convergence condition of the moving asymptotic optimization algorithm is determined until the optimal topology configuration of the compliant mechanism with specified compliance is output.

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