Adaptive volume constraint-based specified flexibility compliant mechanism topological optimization method

Abstract

The invention provides a specified flexibility compliant mechanism topological optimization method based on adaptive volume constraint, and the method comprises the steps: defining design conditions of a compliant mechanism, and setting material attribute indexes of the compliant mechanism; obtaining the structure displacement response of the compliant mechanism under the action of the input load and the virtual unit load; adaptively changing the volume constraint value of the mechanism according to the difference between the total flexibility and the specified total flexibility; establishing a specified flexibility compliant mechanism topological optimization mathematical model based on adaptive volume constraint; calculating and optimizing an objective function and constrained sensitivity information; correcting the sensitivity of the optimization target and the constraint; and solving a topological optimization problem by adopting a moving asymptote algorithm, judging whether a convergence condition is met or not, and if yes, outputting an optimal compliant mechanism topological configuration. According to the method, the topological optimization design of the compliant mechanism based on the adaptive volume constraint is realized, and the obtained compliant mechanism has specified flexibility performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of compliant mechanism optimization design, in particular to a prescribed flexibility compliant mechanism topology optimization method based on adaptive volume constraint. BACKGROUND

[0002] Compliant mechanism replaces traditional mechanism kinematic joint with its own flexible joint or hinge, and adopts large deformation flexible element instead of all rigid elements to transmit or convert motion, force or energy, which is a new type of assembly-free mechanism. Compared with traditional rigid mechanism, compliant mechanism overcomes the defects of traditional mechanism such as high processing and assembly cost, wear of kinematic pair, and has many advantages such as low manufacturing cost, assembly-free, precision, work efficiency, etc. At present, compliant mechanism is mostly designed by topology optimization method.

[0003] In the prior art, in the traditional mechanism topology optimization, the maximum flexibility is mostly taken as the objective function, and under the constraint of a certain volume fraction, a certain mechanism configuration is obtained. Compared with the traditional fixed volume constraint topology optimization, the method of adaptive volume constraint can redistribute the material, and by introducing the design method of prescribed compliance, the performance of the compliant mechanism is obtained under the premise of the stiffness of the compliant mechanism. In the case of most mechanism topology optimization design pursuing the maximum output displacement, the input end and the output end of the mechanism are rarely considered to have a certain stiffness. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a prescribed flexibility compliant mechanism topology optimization method based on adaptive volume constraint to solve the above problems in the prior art.

[0005] The present application provides a prescribed flexibility compliant mechanism topology optimization method based on adaptive volume constraint, which comprises: defining the design conditions of the prescribed flexibility compliant mechanism, and setting the material attribute index of the prescribed flexibility compliant mechanism; representing the relationship between the unit elastic modulus of the prescribed flexibility compliant mechanism and the unit design variable based on the solid isotropic material penalty model, and solving the finite element balance equation under the action of the input load and the virtual unit load respectively to obtain the structural displacement response; constructing the total flexibility of the prescribed flexibility compliant mechanism by weighting the input flexibility and the output flexibility, and adaptively changing the volume constraint value of the prescribed flexibility compliant mechanism according to the difference between the total flexibility and the prescribed flexibility; maximizing the output displacement of the prescribed flexibility compliant mechanism as the optimization objective, and establishing a mathematical model of the prescribed flexibility compliant mechanism topology optimization based on adaptive volume constraint by taking adaptive volume as the constraint; The output displacement, volume and total flexibility of the prescribed flexibility compliant mechanism are calculated according to the prescribed flexibility compliant mechanism topological optimization mathematical model, and the optimization objective function and the sensitivity information of the constraint to the design variable are solved; The optimization objective function and the sensitivity information are corrected by using the sensitivity filtering technology; The optimization problem of the prescribed flexibility compliant mechanism is solved by using the moving asymptotic optimization algorithm, and whether the convergence condition of the moving asymptotic optimization algorithm is met is judged, if yes, the optimal prescribed flexibility compliant mechanism topological configuration is output.

[0006] Compared with the prior art, the beneficial effects of the present application are that by solving the finite element balance equation under the action of the input load and the virtual unit load, the structural displacement response is obtained, and the total flexibility of the mechanism is constructed by the weighted sum of the input flexibility and the output flexibility, and then the volume constraint value of the mechanism is adaptively changed according to the difference between the total flexibility and the prescribed total flexibility, and then the optimization objective function and the sensitivity information of the constraint are calculated according to the prescribed flexibility compliant mechanism topological optimization mathematical model based on the adaptive volume constraint, and then whether the convergence condition is met is judged by using the moving asymptotic algorithm, so that the optimal prescribed flexibility compliant topological configuration can be obtained, and the stiffness of the prescribed flexibility compliant mechanism can be effectively improved.

[0007] Further, the step of defining the design conditions of the prescribed flexibility compliant mechanism and setting the material property indexes of the prescribed flexibility compliant mechanism comprises: The design domain, boundary conditions and load action of the prescribed flexibility compliant mechanism are defined; The material elastic modulus, Poisson's ratio, finite element number, initial value of element density, sensitivity filtering radius, volume fraction and prescribed flexibility value of the prescribed flexibility compliant mechanism are set.

[0008] Further, the step of representing the relationship between the element elastic modulus of the prescribed flexibility compliant mechanism and the element design variable based on the solid isotropic material penalty model, and solving the finite element balance equation under the action of the input load and the virtual unit load to obtain the structural displacement response comprises: The relationship between the element elastic modulus of the prescribed flexibility compliant mechanism and the element design variable is represented by using the improved solid isotropic material penalty model, and the node load expression is derived according to the relationship; The finite element balance equation under the action of the input load and the virtual unit load is solved according to the node load expression, and the finite element analysis of the structure of the prescribed flexibility compliant mechanism is carried out to obtain the structural displacement response of the prescribed flexibility compliant mechanism.

[0009] Further, the step of constructing the total compliance of the prescribed compliance mechanism by weighting the input compliance and the output compliance, and adaptively changing the volume constraint value of the prescribed compliance mechanism according to the difference between the total compliance and the prescribed compliance comprises: defining the strain energy of the prescribed compliance mechanism under the actual load as a real compliance value and the strain energy under the unit virtual load as a virtual compliance value, and constructing the total compliance of the prescribed compliance mechanism by weighting the real compliance value and the virtual compliance value; changing the structure of the prescribed compliance mechanism based on the difference between the total compliance and the prescribed total compliance, to adaptively change the volume constraint value of the prescribed compliance mechanism.

[0010] Further, the expression of the mathematical model of the topology optimization of the prescribed compliance mechanism is: ; In the formula, the target function is represented by f, the output displacement is represented by y, the average compliance of the mechanism is represented by K, the first design variable unit density is represented by ρ, the transposition symbol is represented by T, the change multiple is represented by α, the initial average compliance value of the mechanism is represented by K0, the input load array loaded at the input point of the mechanism is represented by F, the unit virtual load array loaded at the output point is represented by Q, the unit virtual load array loaded at the output point is represented by Q, the unit number is represented by e, the design variable unit density is represented by ρ, the overall stiffness matrix of the prescribed compliance mechanism is represented by K, the displacement array of the prescribed compliance mechanism under the input load is represented by y, the displacement array of the prescribed compliance mechanism under the unit virtual load at the output end is represented by y, the total compliance value of the prescribed compliance mechanism is represented by K, the volume of the unit is represented by V, the total number of units is represented by E, the volume fraction changing with the iteration step number is represented by α, the output compliance value of the prescribed compliance mechanism is represented by K, the input compliance value of the prescribed compliance mechanism is represented by K.

[0011] Further, the step of calculating the output displacement, volume and total compliance of the prescribed compliance compliant mechanism according to the prescribed compliance compliant mechanism topology optimization mathematical model, and solving the sensitivity information of the optimization objective function and the constraint to the design variable comprises: According to the displacement field, the output displacement and total compliance of the prescribed compliance compliant mechanism are calculated, and the structural volume of the prescribed compliance compliant mechanism is calculated by the unit density to obtain the optimization objective and constraint; According to the prescribed compliance compliant mechanism topology optimization mathematical model, the objective function output displacement of the optimization objective and the sensitivity information of the adaptive volume constraint are calculated.

[0012] Further, after the step of judging whether the moving asymptotic optimization algorithm convergence condition is met, the method further comprises: If the moving asymptotic optimization algorithm convergence condition is not met, the design condition of the prescribed compliance compliant mechanism is repeatedly defined, the material attribute index of the prescribed compliance compliant mechanism is set, the relationship between the unit elastic modulus of the prescribed compliance compliant mechanism and the unit design variable is represented based on the solid isotropic material with penalization model, the finite element balance equation is solved under the action of the input load and the virtual unit load respectively to obtain the structural displacement response, the total compliance of the prescribed compliance compliant mechanism is constructed by the weighted sum of the input compliance and the output compliance, and the volume constraint value of the prescribed compliance compliant mechanism is adaptively changed according to the difference between the total compliance and the prescribed compliance, the optimization objective of the maximum output displacement of the prescribed compliance compliant mechanism is taken, and the prescribed compliance compliant mechanism topology optimization mathematical model based on the adaptive volume constraint is established by taking the adaptive volume as the constraint, the output displacement, volume and total compliance of the prescribed compliance compliant mechanism are calculated according to the prescribed compliance compliant mechanism topology optimization mathematical model, and the sensitivity information of the optimization objective function and the constraint to the design variable is solved, the sensitivity filtering technology is used to correct the optimization objective function and the sensitivity information, the moving asymptotic optimization algorithm is used to solve the optimization problem of the prescribed compliance compliant mechanism, and whether the moving asymptotic optimization algorithm convergence condition is met is judged until the optimal prescribed compliance compliant mechanism topology configuration is output. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The flow chart of the prescribed compliance compliant mechanism topology optimization method based on adaptive volume constraint in the embodiment of the application; Figure 2 The schematic diagram of the design domain, load and boundary condition of the prescribed compliance compliant mechanism in the embodiment of the application; Figure 3 The prescribed compliance compliant mechanism design domain, load and boundary condition in the embodiment of the application; Figure 4Iteration diagram of a target function of a prescribed flexibility compliant reverse device in an embodiment of the present application.

[0014] The following detailed description will further illustrate the present application in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0015] Referring to Figure 1 , a prescribed flexibility compliant mechanism topology optimization method based on adaptive volume constraint in an embodiment of the present application is shown, which comprises steps S1 to S7: S1, defining design conditions of a prescribed flexibility compliant mechanism, and setting material attribute indexes of the prescribed flexibility compliant mechanism; Specifically, the step S1 comprises steps S11 to S12: S11, defining a design domain, boundary conditions and load actions of the prescribed flexibility compliant mechanism; S12, setting material elastic modulus, Poisson's ratio, finite element number, initial value of element density, sensitivity filtering radius, volume fraction and prescribed flexibility value of the prescribed flexibility compliant mechanism.

[0016] S2, representing a relationship between element elastic modulus of the prescribed flexibility compliant mechanism and element design variable based on a solid isotropic material penalization model, and respectively solving finite element balance equations under input load actions and virtual unit load actions to obtain structural displacement responses.

[0017] Specifically, the step S2 comprises steps S21 to S22: S21, representing a relationship between element elastic modulus of the prescribed flexibility compliant mechanism and element design variable by using an improved solid isotropic material penalization model, and deriving a node load expression according to the relationship; It can be understood that a SIMP material interpolation model is used to describe a relationship between material attributes and design variable x, and the expression is: ; In the expression, represents an interpolated element elastic modulus, represents an element density design variable, wherein, , represents a minimum element density design variable, represents a penalty coefficient, in the embodiment, the values of all of the, and are 3, represents an initial element density design variable.

[0018] S22, solving the finite element equilibrium equation under the action of the input load and the action of the virtual unit load according to the node load expression, and performing finite element analysis on the structure of the prescribed flexibility compliance mechanism to obtain the structural displacement response of the prescribed flexibility compliance mechanism; It can be understood that in the embodiment, the expression of the displacement column of the prescribed flexibility compliance mechanism under the action of the input load and the displacement column array of the prescribed flexibility compliance mechanism under the action of the unit virtual load at the output end is: ; ; In the formula, is the overall stiffness matrix of the prescribed flexibility compliance mechanism, is the displacement column array of the prescribed flexibility compliance mechanism under the action of the input load, is the displacement column array of the prescribed flexibility compliance mechanism under the action of the unit virtual load at the output end, denotes the actual load, is the unit virtual load column array.

[0019] The overall stiffness matrix of the prescribed flexibility compliance mechanism can be expressed by the following formula:

[0020] In the formula, is the overall stiffness matrix of the prescribed flexibility compliance mechanism, is the design variable unit density, denotes the penalty coefficient, is the unit stiffness matrix, is the spring stiffness, is the unit number, is the total number of units; Meanwhile, the flexibility of the unit, the output compliance value of the prescribed flexibility compliance mechanism, and the input compliance value of the prescribed flexibility compliance mechanism can be expressed in a discrete form, and the expression is: ; ; ; In the formula, , , respectively denote the flexibility of the unit, the output compliance value of the prescribed flexibility compliance mechanism, and the input compliance value of the prescribed flexibility compliance mechanism, is the displacement column array of the prescribed flexibility compliance mechanism under the action of the input load, a displacement array of the prescribed-compliance compliance mechanism under the action of a unit virtual load at the output end, a global stiffness matrix of the prescribed-compliance compliance mechanism, a displacement array of the element under an actual load, a transpose symbol, a design variable element density.

[0021] S3, constructing a total compliance of the prescribed-compliance compliance mechanism from a weighted sum of an input compliance and an output compliance, and adaptively changing a volume constraint value of the prescribed-compliance compliance mechanism according to a difference between the total compliance and the prescribed compliance; Specifically, the step S3 includes steps S31 to S32: S31, defining a real compliance value of the prescribed-compliance compliance mechanism under the action of an actual load and a virtual compliance value of the prescribed-compliance compliance mechanism under the action of a unit virtual load, and constructing a total compliance of the prescribed-compliance compliance mechanism from a weighted sum of the real compliance value and the virtual compliance value; It can be understood that expressions of the output compliance value of the prescribed-compliance compliance mechanism and the input compliance value of the prescribed-compliance compliance mechanism are: ; ; In the expressions, , respectively represent the output compliance value of the prescribed-compliance compliance mechanism and the input compliance value of the prescribed-compliance compliance mechanism, a displacement array of the prescribed-compliance compliance mechanism under the action of an input load, a displacement array of the prescribed-compliance compliance mechanism under the action of a unit virtual load at the output end, a global stiffness matrix of the prescribed-compliance compliance mechanism, a transpose symbol, a design variable element density; defining a virtual total compliance value as a sum of the virtual compliance value and the real compliance value of the prescribed-compliance compliance mechanism, and expressing as: ; In the expressions, is the virtual total compliance value, is the virtual compliance value, is the real compliance value, is the design variable element density, is a weight coefficient.

[0022] In the embodiment, the numerical magnitude of the virtual compliance value and the real compliance value is affected by spring and material properties, both of which have the same magnitude, and the virtual compliance value is taken as 1, so that: ​ .

[0023] S32, changing the structure of the prescribed-compliance compliant mechanism based on the difference between the total compliance and the prescribed total compliance to adaptively change the volume constraint value of the prescribed-compliance compliant mechanism; It can be understood that the total compliance value of the prescribed-compliance compliant mechanism is taken as a certain value, that is, The volume is changed by the difference between the total compliance value of the mechanism and the prescribed total compliance value. If the total compliance value of the mechanism is greater than the prescribed total compliance value, there is: ; If the total compliance value of the mechanism is less than the prescribed total compliance value, there is: ; In the formula, represents the number of iteration steps, represents the volume fraction that changes with the number of iteration steps, is the total compliance value of the mechanism, is the total compliance value of the prescribed-compliance compliant mechanism.

[0024] S4, establishing a prescribed-compliance compliant mechanism topology optimization mathematical model based on adaptive volume constraint with the maximum output displacement of the prescribed-compliance compliant mechanism as the optimization objective and adaptive volume as the constraint; In the embodiment, the expression of the prescribed-compliance compliant mechanism topology optimization mathematical model is: ; In the formula, represents the objective function, represents the output displacement, represents the average compliance of the mechanism, represents the unit density of the design variable, represents the transpose symbol, represents the change multiple, represents the initial average compliance value of the mechanism, represents the input load matrix loaded at the input point of the mechanism, represents the unit virtual load matrix loaded at the output point, represents the unit virtual load matrix loaded at the output point, represents the cell number, is the unit density of the design variable, is the global stiffness matrix of the prescribed-compliance compliant mechanism, is the displacement matrix of the prescribed-compliance compliant mechanism under the action of the input load, is the displacement matrix of the prescribed-compliance compliant mechanism under the action of the unit virtual load at the output end, a total compliance value of the prescribed-compliance compliant mechanism, a volume of a unit, a total number of units, a volume fraction varying with iteration steps, an output compliance value of the prescribed-compliance compliant mechanism, an input compliance value of the prescribed-compliance compliant mechanism.

[0025] S5, calculating an output displacement, a volume and a total compliance of the prescribed-compliance compliant mechanism according to the prescribed-compliance compliant mechanism topology optimization mathematical model, and solving an optimization objective function and sensitivity information of a constraint to a design variable; Specifically, the step S5 includes steps S51 to S52: S51, calculating an output displacement and a total compliance of the prescribed-compliance compliant mechanism according to a displacement field, and calculating a structural volume of the prescribed-compliance compliant mechanism by a unit density to obtain an optimization objective and a constraint; S52, calculating a target function output displacement of the optimization objective and sensitivity information of an adaptive volume constraint according to the prescribed-compliance compliant mechanism topology optimization mathematical model; It can be understood that, in the embodiment, because a size of the output end displacement is equal to a size of the mutual strain energy in a numerical absolute value, and a first derivative of the mutual strain energy is relatively easy to solve, the mutual strain energy can be used to replace the displacement to become the target function, and an expression is: ; ; Derivation of the target function has: ; In addition, derivation of the output displacement to the design variable has: ; From the above formula and the previous derivation formula, it can be obtained that: ; Derivation of the whole stiffness matrix can obtain: ; From the above formula and the previous derivation formula, the sensitivity of the prescribed-compliance compliant mechanism target function to the design variable is obtained: ; wherein, a compliance, a design variable, i.e., a unit density, 3 is a penalty factor, K is a unit stiffness matrix, T is a transpose symbol, Dv is a displacement column vector of the unit under virtual load, Dp is a displacement column vector of the unit under actual load.

[0026] The sensitivity of the adaptive volume constraint to the design variable is consistent in principle and the same in form as the sensitivity of the constant volume constraint. The first-order derivative of the structure volume to the design variable is obtained by directly deriving the volume fraction with respect to the design variable, that is, ; In the formula, V is the volume of the mechanism, ρ is the design variable, that is, the unit density, V is the volume of the unit, ∂V / ∂ρ is a partial derivative symbol.

[0027] S6, the sensitivity filtering technique is used to correct the optimization objective function and the sensitivity information; It can be understood that the sensitivity filtering technique is used to correct the optimization objective function and the sensitivity information, so as to avoid the instability phenomenon of the chessboard numerical value and the grid-dependent numerical value.

[0028] S7, a moving asymptotic optimization algorithm is used to solve the optimization problem of the specified flexibility compliant mechanism, and it is judged whether the convergence condition of the moving asymptotic optimization algorithm is met. If yes, the optimal specified flexibility compliant mechanism topology is output. It should be noted that if the moving asymptotic optimization algorithm convergence condition is not met, the design condition of defining the prescribed flexibility compliant mechanism is repeatedly executed, and the material attribute index of the prescribed flexibility compliant mechanism is set; the relationship between the unit elastic modulus of the prescribed flexibility compliant mechanism and the unit design variable is represented based on a solid isotropic material with penalization model, and the finite element balance equation is solved under the action of the input load and the virtual unit load respectively to obtain the structural displacement response; the total flexibility of the prescribed flexibility compliant mechanism is constructed by weighting the input flexibility and the output flexibility, and the volume constraint value of the prescribed flexibility compliant mechanism is adaptively changed according to the difference between the total flexibility and the prescribed flexibility; the optimization objective of maximizing the output displacement of the prescribed flexibility compliant mechanism is established, and the adaptive volume is constrained to establish a prescribed flexibility compliant mechanism topology optimization mathematical model based on adaptive volume constraint; the output displacement, volume and total flexibility of the prescribed flexibility compliant mechanism are calculated according to the prescribed flexibility compliant mechanism topology optimization mathematical model, and the sensitivity information of the design variable to the optimization objective function and the constraint is solved; the sensitivity filtering technology is used to correct the optimization objective function and the sensitivity information; the moving asymptotic optimization algorithm is used to solve the optimization problem of the prescribed flexibility compliant mechanism, and whether the moving asymptotic optimization algorithm convergence condition is met is judged until the optimal prescribed flexibility compliant mechanism topology configuration is output.

[0029] In order to further verify the effectiveness of the prescribed flexibility compliant mechanism topology optimization method based on adaptive volume constraint, a prescribed flexibility compliant reverser is taken as an example for explanation.

[0030] The design domain, boundary condition and input and output of the prescribed flexibility compliant mechanism are shown in Figure 2 The upper and lower ends of the left side of the design domain are fixed ends connected with other structures, and the external load is applied at the midpoint position of the left side of the mechanism. Since the mechanism is symmetrical, only the lower half is taken for design analysis, and the same is discretized into 40000 planar four-edge elements for design.

[0031] In this example, the size of the compliant reverser is , the thickness of the mechanism is , the upper and lower ends of the left side of the design domain are fixed ends connected with other structures, and the external load is applied at the midpoint position of the left side of the mechanism with a size of , and the output point is at the right end midpoint. The input spring of the design domain is , and the spring stiffness is . The output spring is , and the spring stiffness is , which is used to simulate the stiffness of the components with external contact. The iteration stop condition is set to when the total number of iteration steps exceeds 500 or the change in element density between two adjacent iteration steps is less than 0.001.

[0032] The topology optimization configuration of the inverter using the adaptive volume constraint method with prescribed flexibility is shown in the following example: Figure 3 As shown. Figure 3 It can be seen that there is no obvious hinge phenomenon in the inverter configuration of the adaptive volume constraint method with specified flexibility. The distribution of the solid material is transferred from a large amount of accumulation in the rigid part to the part with high flexibility. The redistribution of the material makes the mutual strain energy of the inverter have better stiffness under the specified value. In the iterative process of optimizing the displacement of the output end of the objective function, it also changes from small to large, and tends to be stable and gradually converges after 150 steps, as shown in Figure 4 shown.

[0033] In summary, the topology optimization method of a prescribed flexibility compliant mechanism based on adaptive volume constraints in the above-mentioned embodiment of the present invention obtains the structural displacement response by solving the finite element equilibrium equation under the action of input load and virtual unit load, and constructs the total flexibility of the mechanism by weighted sum of input flexibility and output flexibility, and then adaptively changes the volume constraint value of the mechanism according to the difference between the total flexibility and the prescribed total flexibility. By calculating the optimization objective function and the sensitivity information of the constraint according to the mathematical model of the topology optimization of the prescribed flexibility compliant mechanism based on adaptive volume constraints, and then judging whether the convergence conditions are met through the moving asymptotic algorithm, the optimal prescribed flexibility compliant topology configuration can be obtained, which can effectively improve the performance of the compliant mechanism under the stiffness constraint conditions.

[0034] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations 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 any one or more embodiments or examples.

[0035] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A topology optimization method for a compliant mechanism with prescribed flexibility based on adaptive volume constraints, characterized in that: The method comprises: Defining design conditions for a compliant mechanism with prescribed flexibility and setting material property indicators for the compliant mechanism with prescribed flexibility; The relationship between the unit elastic modulus and the unit design variable of the prescribed flexibility compliant mechanism is represented based on a solid isotropic material penalty model, and the finite element equilibrium equation is solved under the action of input load and virtual unit load to obtain the structural displacement response; constructing a total compliance of the prescribed compliance mechanism by weighted sum of input compliance and output compliance, and adaptively changing a volume constraint value of the prescribed compliance mechanism according to a difference between the total compliance and the prescribed compliance; Taking maximizing the output displacement of the prescribed flexibility compliant mechanism as an optimization goal and taking the adaptive volume as a constraint, a mathematical model for topology optimization of the prescribed flexibility compliant mechanism based on the adaptive volume constraint is established; Calculating the output displacement, volume, and total compliance of the specified compliance mechanism according to the specified compliance compliance mechanism topology optimization mathematical model, and solving the optimization objective function and the sensitivity information of the constraints to the design variables; Using sensitivity filtering technology to correct the optimization objective function and the sensitivity information; A moving progressive optimization algorithm is used to solve the optimization problem of the specified flexibility compliant mechanism, and it is determined whether the convergence condition of the moving progressive optimization algorithm is met. If so, the optimal topological configuration of the specified flexibility compliant mechanism is output.

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

3. The method for topology optimization of a compliant mechanism with prescribed flexibility based on adaptive volume constraints according to claim 1, characterized in that: The steps of representing the relationship between the unit elastic modulus and the unit design variables of the specified flexibility compliant mechanism based on the solid isotropic material penalty model, and solving the finite element equilibrium equation under the input load and the virtual unit load to obtain the structural displacement response include: An improved solid isotropic material penalty model is used to represent the relationship between the unit elastic modulus and the unit design variable of the prescribed flexibility compliant mechanism, and a node load expression is derived based on the relationship; The finite element equilibrium equation under the action of the input load and the virtual unit load is solved according to the node load expression, and the finite element analysis is performed on the structure of the prescribed flexibility compliant mechanism to obtain the structural displacement response of the prescribed flexibility compliant mechanism.

4. The method for topology optimization of a compliant mechanism with prescribed flexibility based on adaptive volume constraints according to claim 1, characterized in that: The steps of constructing the total flexibility of the prescribed flexibility compliance mechanism by weighting the input flexibility and the output flexibility, and adaptively changing the volume constraint value of the prescribed flexibility compliance mechanism according to the difference between the total flexibility and the prescribed flexibility include: defining the strain energy of the prescribed compliance mechanism under an actual load as a real compliance value and the strain energy under a unit virtual load as a virtual compliance value, and constructing the total compliance of the prescribed compliance mechanism by weighted sum of the real compliance value and the virtual compliance value; The structure of the prescribed compliance mechanism is changed based on the difference between the total compliance and the prescribed total compliance to adaptively change the volume constraint value of the prescribed compliance mechanism.

5. The method for topology optimization of a compliant mechanism with prescribed flexibility based on adaptive volume constraints according to claim 1, characterized in that: The expression of the mathematical model of topology optimization of the specified flexibility compliant mechanism is: ； Where, represents the objective function, represents the output displacement, represents the average flexibility of the mechanism, Indicates the design variable unit density, represents the transpose symbol, Indicates the multiple of change, represents the initial average flexibility value of the mechanism, represents the input load array applied at the input point of the mechanism, Represents the unit virtual load array loaded at the output point, Indicates the unit number, is the design variable unit density, is the global stiffness matrix of the prescribed flexibility compliant mechanism, is the displacement array of the compliant mechanism with specified flexibility under the input load, is the displacement array of the specified compliance mechanism under the unit virtual load at the output end, is the total compliance value of the specified compliance mechanism, is the volume of the unit, is the total number of units, is the volume fraction that changes with the number of iterations, is the output compliance value of the specified compliance mechanism, is the input compliance value of the specified compliance mechanism.

6. The method for topology optimization of a compliant mechanism with prescribed flexibility based on adaptive volume constraints according to claim 1, characterized in that: The step of calculating the output displacement, volume and total compliance of the specified compliance mechanism according to the specified compliance compliance mechanism topology optimization mathematical model, and solving the optimization objective function and the sensitivity information of the constraints to the design variables includes: Calculating the output displacement and total compliance of the specified compliance mechanism according to the displacement field, and calculating the structural volume of the specified compliance mechanism by unit density to obtain an optimization target and constraints; The objective function output displacement of the optimization target and the sensitivity information of the adaptive volume constraint are calculated according to the prescribed flexibility compliant mechanism topology optimization mathematical model.

7. The method for topology optimization of a compliant mechanism with prescribed flexibility based on adaptive volume constraints according to claim 1, characterized in that: After the step of determining whether the convergence condition of the moving progressive optimization algorithm is satisfied, the method further includes: If the convergence condition of the mobile progressive optimization algorithm is not met, the design conditions for defining the prescribed flexibility compliant mechanism are repeatedly executed, and the material property indicators of the prescribed flexibility compliant mechanism are set; the relationship between the unit elastic modulus and the unit design variables of the prescribed flexibility compliant mechanism is represented based on the solid isotropic material penalty model, and the finite element equilibrium equation is solved under the action of the input load and the virtual unit load respectively to obtain the structural displacement response; the total flexibility of the prescribed flexibility compliant mechanism is constructed by the weighted sum of the input flexibility and the output flexibility, and the volume constraint value of the prescribed flexibility compliant mechanism is adaptively changed according to the difference between the total flexibility and the prescribed flexibility; the prescribed flexibility compliant mechanism is used to adjust the volume constraint value of the prescribed flexibility compliant mechanism. The output displacement of the structure is maximized as the optimization goal, and a mathematical model of topology optimization of a prescribed flexibility compliant mechanism based on adaptive volume constraints is established with adaptive volume as the constraint; the output displacement, volume and total flexibility of the prescribed flexibility compliant mechanism are calculated according to the mathematical model of topology optimization of the prescribed flexibility compliant mechanism, and the optimization objective function and the sensitivity information of the constraints to the design variables are solved; the sensitivity filtering technology is used to correct the optimization objective function and the sensitivity information; the moving progressive optimization algorithm is used to solve the optimization problem of the prescribed flexibility compliant mechanism, and it is judged whether the convergence condition of the moving progressive optimization algorithm is met, until the optimal topology configuration of the prescribed flexibility compliant mechanism is output.

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