Thermal drive compliant mechanism reliability topological optimization method considering stress constraint

Abstract

The invention provides a thermally driven compliant mechanism reliability topological optimization method considering stress constraint. The method comprises the steps of defining design conditions of a thermally driven compliant mechanism; describing the relationship between the unit elasticity modulus and the unit density in the design condition, and filtering the unit density by adopting a mapping filtering technology; structural thermosetting coupling finite element analysis is carried out, and stress constraints of all units are condensed into a global stress constraint; establishing a double-layer cyclic topological optimization model of the stress constraint reliability of the thermally driven compliant mechanism; solving the volume and output displacement of the optimization target compliant mechanism and the sensitivity of stress constraint to design variables; and searching a most probable failure point and updating a design variable by utilizing a moving asymptote method, judging whether iteration meets a convergence condition or not, and if so, obtaining a thermally driven compliant mechanism topological configuration meeting the stress constraint reliability. According to the invention, the obtained thermally driven compliant mechanism has better strength reliability.

Description

Technical Field

[0001] This invention relates to the technical field of compliant mechanism optimization design, and in particular to a reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints. Background Technology

[0002] Thermally driven compliant mechanisms utilize the elastic deformation of the material itself caused by temperature changes to generate the desired motion at the output end. Compared to other driving methods, thermally driven compliant mechanisms offer advantages such as the ability to generate larger output displacement and force, and easy compatibility with microelectromechanical systems (MEMS) manufacturing processes. Meeting strength requirements is the primary problem to be solved in the topology optimization design of thermally driven compliant mechanisms.

[0003] In existing technologies, the performance of thermally driven compliant mechanisms in practical engineering is easily affected by uncertainties such as material properties, geometric parameters, and load conditions. Therefore, it is necessary to consider the reliability topology optimization design of stress-constrained thermally driven compliant mechanisms to meet strength and reliability requirements. Summary of the Invention

[0004] Based on this, the purpose of this invention is to provide a reliability topology optimization method for thermally driven compliant mechanisms that considers stress constraints, so as to overcome the shortcomings of the prior art.

[0005] This invention provides a reliability topology optimization method for thermally driven compliant mechanisms considering stress constraints, the method comprising: Define the design conditions for thermally driven compliant mechanisms; An improved solid isotropic material penalty model is used to describe the relationship between the element elastic modulus and element density in the design conditions, and a mapping filtering technique is used to filter the element density. An interval model was used to quantify the load uncertainty caused by temperature changes, and a thermo-structure coupled finite element analysis of the structure was performed. The norm method integrates the stress constraints of all elements into a single global stress constraint. The optimization objective is to minimize the volume fraction of the thermally driven compliant mechanism. The constraints are stress-constrained reliability and output displacement. A function is constructed based on the stress constraints. The reliability is evaluated using the function metric method. A two-layer cyclic topology optimization model for the stress-constrained reliability of the thermally driven compliant mechanism is established. Based on the reliability of the stress constraint of the thermally driven compliant mechanism, a two-layer cyclic topology optimization model is used to solve the volume, output displacement, and sensitivity of the stress constraint to the design variables of the target compliant mechanism. Find the most likely failure point, substitute the most likely failure point into the outer finite element analysis, and calculate the sensitivity of the optimization objective and constraints to the design variables; The design variables are updated using the moving asymptote method, and it is determined whether the iteration satisfies the convergence condition. If so, the topology of the thermally driven compliant mechanism that satisfies the reliability of stress constraints is obtained.

[0006] Compared with the prior art, the beneficial effects of the present invention are: by describing the relationship between the unit elastic modulus and the unit density, and by establishing a non-probabilistic reliability topology optimization model based on the interval model and the functional energy method, and by establishing a thermally driven compliant mechanism double-layer cyclic topology optimization model considering stress constraint reliability by using stress reliability and output displacement as constraints, and by updating the design variables and judging whether the convergence condition is met, the optimal compliant mechanism topology configuration can be obtained, which meets the strength reliability requirements.

[0007] Furthermore, the design conditions include the design domain, constraint boundary conditions, setting initial values ​​of design variables, virtual spring stiffness at the output end, elastic modulus of the material, Poisson's ratio of the material, coefficient of thermal expansion, median and deviation of temperature load, and allowable reliability indicators.

[0008] Furthermore, the step of using an improved solid isotropic material penalty model to describe the relationship between the element elastic modulus and element density in the design conditions, and using a mapping filtering technique to filter the element density includes: An improved penalty model for solid isotropic materials is used to describe the interpolation relationship between the element elastic modulus and the element density; The cell density is corrected by combining sensitivity filtering and Heaviside mapping function to concentrate the filtered cell density towards the two ends of 0-1.

[0009] Furthermore, the interval model is used to quantify the load uncertainty caused by temperature changes, and a structural thermo-structure coupled finite element analysis is performed. The norm method involves the following steps to consolidate the stress constraints of all elements into a single global stress constraint: An interval model was used to quantify the uncertainty of temperature load, and the temperature load of each node was equivalent to nodal force. The thermo-mechanical coupling finite element analysis of the structure was then performed. Based on the calculated Von Mises stress of any element, a relaxation process is applied to the Von Mises stress of the element. The norm method agglomerates the stress constraints of all elements into a single global stress constraint, and then employs an adaptive constraint scaling method to further agglomerate the stress constraints. Norm stress is corrected.

[0010] Furthermore, the expression for the two-layer cyclic topology optimization model of the stress constraint reliability of the thermally driven compliant mechanism is as follows: ; In the formula, This represents the optimized volume. Indicates design variables, This represents the volume of a unit filled with material. Represents the overall stiffness matrix. Represents the global nodal displacement vector. Indicates the output displacement of the mechanism. Indicates the permissible output displacement limit. The interval nonprobabilistic reliability index representing stress constraints. This indicates the permissible reliability limit. The limit state function represents a variable that indicates uncertainty over an interval. This represents the design variables for each unit. Indicates the first Design variables for each unit, Indicates the number of units. This represents the equivalent nodal thermal load of the element. This represents the temperature difference from the initial time. This represents the lower bound of the design variable. Indicates the first Units.

[0011] Furthermore, the two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism includes an inner layer and an outer layer. The outer layer is a deterministic topology optimization based on the functional metric method, and the inner layer is a reliability analysis that finds the most likely failure point.

[0012] Furthermore, the steps of solving the volume, output displacement, and sensitivity of stress constraints to design variables of the target compliant mechanism using the two-layer cyclic topology optimization model based on the stress constraint reliability of the thermally driven compliant mechanism include: A two-layer cyclic topology optimization model based on the reliability of the stress constraint of the thermally driven compliant mechanism was used, and the chain method was employed to calculate the volume, output displacement, and sensitivity of the stress constraint to the design variables of the target compliant mechanism.

[0013] Furthermore, after the step of determining whether the iteration satisfies the convergence condition, the method further includes: If the iteration does not meet the convergence condition, the design conditions for the thermally driven compliant mechanism are repeatedly executed. An improved solid isotropic material penalty model is used to describe the relationship between the element elastic modulus and element density in the design conditions, and a mapping filtering technique is used to filter the element density. An interval model is used to quantify the load uncertainty caused by temperature changes, and a thermo-mechanical coupling finite element analysis of the structure is performed. The norm method is used to consolidate the stress constraints of all elements into a global stress constraint. The optimization objective is to minimize the volume fraction of the thermally driven compliant mechanism, with stress constraint reliability and output displacement as constraints. A function is constructed using the stress constraints, and a function metric is used for reliability assessment to establish a two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism. Based on this model, the volume, output displacement, and sensitivity of the stress constraints to design variables of the target compliant mechanism are solved. The most likely failure point is identified and substituted into the outer finite element analysis, and the sensitivity of the optimization objective and constraints to design variables is calculated. The moving asymptote method is used to update the design variables, and the convergence condition of the iteration is checked until the topology of the thermally driven compliant mechanism that satisfies the stress constraint reliability is obtained. Attached Figure Description

[0014] Figure 1 This is a flowchart of a reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints in an embodiment of the present invention. Figure 2 This is a schematic diagram showing the design domain, boundary conditions, and output of the thermal actuator mechanism in an embodiment of the present invention. Figure 3 This is a schematic diagram of the topological configuration of the heat driver in an embodiment of the present invention; Figure 4 This is a Von Mises stress cloud diagram of the compliant thermal actuator in an embodiment of the present invention; Figure 5 This is an iterative diagram of the topology optimization of the compliant thermal actuator in an embodiment of the present invention.

[0015] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0016] See also Figure 1 The figure shows a reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints in an embodiment of the present invention. The method includes steps S1 to S7: S1 defines the design conditions for a thermally driven compliant mechanism; It should be noted that, in this embodiment, the design conditions include the design domain, constraint boundary conditions, setting initial values ​​of design variables, virtual spring stiffness at the output end, elastic modulus of the material, Poisson's ratio of the material, coefficient of thermal expansion, median and deviation of temperature load, and allowable reliability indicators.

[0017] S2, an improved solid isotropic material penalty model is used to describe the relationship between the element elastic modulus and element density in the design conditions, and a mapping filtering technique is used to filter the element density; Specifically, step S2 includes steps S21 to S22: S21, an improved solid isotropic material penalty model is used to describe the interpolation relationship between the element elastic modulus and the element density; It is understood that, in this embodiment, the expression for the interpolation relationship between the element elastic modulus and the element density is: ; In the formula, Indicates the material in the interpolated element The elastic modulus, Representation unit Element density; This represents the elastic modulus of the solid material after interpolation. This represents a very small positive number used to eliminate the singularity problem of the stiffness matrix during finite element analysis; here, we take... , This is the penalty parameter, and its value is 3.

[0018] S22, the cell density is corrected by combining sensitivity filtering and Heaviside mapping function, so as to concentrate the filtered cell density towards the two ends of 0-1; Understandably, to obtain a clearer topology, a smooth Heaviside mapping function is used to correct the filtered cell density, thereby concentrating the cell density variable towards the 0 and 1 extremes. The expression for the mapping projection filter is:

[0019] In the formula, For the processed design variables, This is a threshold parameter with a value of 0.5. Parameters used to control the smoothness of changes.

[0020] S3 employs an interval model to quantify the load uncertainty caused by temperature changes, performs structural thermo-mechanical coupled finite element analysis, and uses... The norm method integrates the stress constraints of all elements into a single global stress constraint. Specifically, step S3 includes steps S31 to S32: S31 uses an interval model to quantify the uncertainty of temperature load, and converts the temperature load of each node into nodal force to perform structural thermo-mechanical coupling finite element analysis. It is understandable that elastic materials will experience thermal strain when the temperature changes, and its expression is: ; In the formula, It is the coefficient of linear expansion of the material. It is the initial temperature. It is the steady-state temperature of the compliant mechanism.

[0021] It is worth noting that in the interval model, the hypothetical temperature load on each node when the temperature changes can be equivalent to a nodal thermal load, which is equivalent to a nodal force. It can be represented as: ; In the formula, It is the strain matrix. It is the transpose of the strain matrix, with superscript. Represents transpose. It is an elasticity matrix. It is the unit equivalent nodal thermal load. This is the thickness of the thermally driven compliant mechanism. From the above equation, the equivalent nodal thermal load of the element can be obtained as: ; In the formula, It is the temperature difference from the initial moment. It is Poisson's ratio.

[0022] S32, based on the calculated Von Mises stress of any element, performs relaxation treatment on the Von Mises stress of the element, using... The norm method agglomerates the stress constraints of all elements into a single global stress constraint, and then employs an adaptive constraint scaling method to further agglomerate the stress constraints. Normative stress is corrected; It is understandable that the element is solved according to the finite element theory. stress vector Based on the distortion energy theory, the Von Mises stress of any element can be expressed as:

[0023] ; In the formula, Representation unit Von Mises stress, Representation unit The stress vector, This represents the transpose of the stress vector. This is the transformation matrix used to calculate the Von Mises stress. , as well as These are the three components of the element stress vector; The Von Mises stress of the element is relaxed, and the expression is as follows: ; In the formula, The relaxation stress of the element; This is the relaxation factor, which is set to 0.5 here.

[0024] To overcome the limitations of stress constraint, the following approach is adopted: The norm method consolidates the stress constraints of all elements into a single global stress constraint. Normative stress It can be represented as: ; in, for The parameters of the norm method This represents the number of units.

[0025] An adaptive constraint scaling method is used to correct the P-norm stress, thus addressing the problem of nonlinearity in the optimization results caused by the P-norm stress. The expression is as follows: ; In the formula, For maximum stress, For adaptive constraint scaling factor, Stress is in the P-norm. When the number of iterations Adaptive scaling factor It can be represented as: ; In the formula, As a control parameter, it is set to 0.5 in this invention. Indicates the number of iteration steps. The adaptive scaling factor, express Maximum stress during iteration step express P-norm stress during the iteration step; S4. With minimizing the volume fraction of the thermally driven compliant mechanism as the optimization objective, stress constraint reliability and output displacement as constraints, a function is constructed with stress constraints, and a reliability assessment is performed using the function metric method to establish a two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism. In this embodiment, the expression for the two-layer cyclic topology optimization model of the stress constraint reliability of the thermally driven compliant mechanism is: ; In the formula, This represents the optimized volume. Indicates design variables, This represents the volume of a unit filled with material. Represents the overall stiffness matrix. Represents the global nodal displacement vector. Indicates the output displacement of the mechanism. Indicates the permissible output displacement limit. The interval nonprobabilistic reliability index representing stress constraints. This indicates the permissible reliability limit. The limit state function represents a variable that indicates uncertainty over an interval. This represents the design variables for each unit. Indicates the first Design variables for each unit, Indicates the number of units. This represents the equivalent nodal thermal load of the element. This represents the temperature difference from the initial time. This represents the lower bound of the design variable. Indicates the first Units.

[0026] It should be noted that the two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism includes an inner layer and an outer layer. The outer layer is a deterministic topology optimization based on the functional metric method, and the inner layer is a reliability analysis that finds the most likely failure point.

[0027] S5. Based on the two-layer cyclic topology optimization model of the stress constraint reliability of the thermally driven compliant mechanism, the volume, output displacement and the sensitivity of stress constraint to design variables of the target compliant mechanism are solved. Specifically, step S5 includes step S51: S51, a two-layer cyclic topology optimization model based on the stress constraint reliability of the thermally driven compliant mechanism is used, and the chain method is employed to calculate the volume, output displacement, and sensitivity of the stress constraint to the design variables of the target compliant mechanism. Understandably, the sensitivity of the output displacement and stress reliability constraints of the compliant mechanism to design variables is calculated using the chain method. The sensitivity of the output displacement constraint to design variables is as follows: ; In the formula, Indicates the partial derivative sign. Representation unit density, It is the adjoint vector. It is the adjoint matrix. It is the global nodal displacement vector. Temperature load related to element density, The output displacement of the mechanism is represented by the adjoint vector, which can take any value and satisfies the equation. The above formula can be rewritten as: ; For temperature loads related to element density, their sensitivity to design variables is: ; In the formula, It is the coefficient of linear expansion of the material. It is the thickness of the heat-driven compliance mechanism. It is the temperature difference from the initial moment. It is Poisson's ratio. yes The parameters of the norm method, combined with the above equation, yield the sensitivity of the output displacement to the design variable as follows: ; The sensitivity of stress reliability constraints to design variables is: ; In the formula, Representation unit Corrected equivalent stress Let P-norm stress be represented. Solving for each term on the right side yields: ; Von Mises stress The sensitivity to element stress components is: ; Element stress vector The sensitivity to design variables is: ; In the formula, Represents the elasticity matrix. Represents the strain-displacement matrix; By using the limit state function, the stress reliability constraint on the standardized interval vector can be obtained. The sensitivity is: ; Solving for the terms on the right side of the above equation, we get: .

[0028] S6. Find the most likely failure point, substitute the most likely failure point into the outer finite element analysis of the two-layer cyclic topology optimization model of the stress constraint reliability of the thermally driven compliant mechanism, and calculate the sensitivity of the optimization objective and constraint conditions to the design variables. S7. Update the design variables using the moving asymptote method and determine whether the iteration satisfies the convergence condition. If so, the topology of the thermally driven compliant mechanism that satisfies the reliability of stress constraints is obtained. Furthermore, if the iteration does not meet the convergence condition, the design conditions for the thermally driven compliant mechanism are repeatedly executed; an improved solid isotropic material penalty model is used to describe the relationship between the element elastic modulus and element density in the design conditions, and a mapping filtering technique is used to filter the element density; an interval model is used to quantify the load uncertainty caused by temperature changes, and a thermo-mechanical coupling finite element analysis of the structure is performed, and... The norm method is used to consolidate the stress constraints of all elements into a global stress constraint. The optimization objective is to minimize the volume fraction of the thermally driven compliant mechanism, with stress constraint reliability and output displacement as constraints. A function is constructed using the stress constraints, and a function metric is used for reliability assessment to establish a two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism. Based on this model, the volume, output displacement, and sensitivity of the stress constraints to design variables of the target compliant mechanism are solved. The most likely failure point is identified and substituted into the outer finite element analysis, and the sensitivity of the optimization objective and constraints to design variables is calculated. The moving asymptote method is used to update the design variables, and the convergence condition of the iteration is checked until the topology of the thermally driven compliant mechanism that satisfies the stress constraint reliability is obtained.

[0029] It should be explained that the outer loop is a deterministic topology optimization based on the function metric method, which uses the moving asymptotic optimization algorithm to update the design variables; the inner loop is a reliability analysis, which uses the moving asymptotic optimization algorithm to find the most likely failure point; it determines whether the convergence condition of the optimization algorithm is met, and if so, it obtains the topology configuration of the thermally driven compliant mechanism that satisfies stress constraint reliability.

[0030] To further verify the effectiveness of the reliability topology optimization method for thermally driven compliant mechanisms that considers stress constraints, this embodiment uses a thermal actuator as an example to explain the invention.

[0031] The design domain and boundary conditions of the heat driver are as follows: Figure 2 As shown, its upper, lower, and left boundaries are all fixed, the output displacement is at the midpoint on the right side, and the design domain size of the thermal actuator is... Output spring stiffness Because the design domain of this mechanism is vertically symmetrical, to improve computational efficiency, half of the design domain is used for calculation. This half is discretized into 20,000 planar quadrilateral elements. When the temperature rises, the left side of the mechanism deforms and compresses, causing the output position structure to move to the right, thus achieving a thermally driven effect. In the numerical example, the elastic modulus of the thermally driven material... Poisson's ratio The initial unit design variable is set to 1, and the coefficient of thermal expansion is... Elastic modulus of air-phase materials Set a uniform temperature field temperature load median temperature difference Temperature difference Minimum filtration radius The objective function is the volume fraction of the thermally driven compliant mechanism, with output displacement and global maximum stress as constraints, and their limits are as follows: and .

[0032] Figure 3 , Figure 4 and Figure 5 These figures represent the deterministic topology optimization configuration, Von Mises stress distribution diagram, and optimization iteration diagram of the thermally driven compliant mechanism obtained by considering stress constraints using a reliability topology optimization design method when the reliability index is 1.5. Figure 3 and Figure 4 It can be seen that the thermally driven compliant mechanism obtained by the reliability topology optimization design method considering stress constraints can meet the reliability requirements under stress constraints.

[0033] In summary, the stress-constrained thermally driven compliant mechanism reliability topology optimization method in the above embodiments of the present invention describes the relationship between the element elastic modulus and element density, performs finite element analysis on the thermally driven compliant mechanism through multi-physics coupling, quantifies the load uncertainty caused by temperature changes through interval models, transforms the deterministic topology optimization problem into a reliability topology optimization problem using the functional metric method, establishes a two-layer cyclic topology optimization model for the stress-constrained reliability of the thermally driven compliant mechanism through stress-constrained reliability and output displacement, and obtains the optimal topology configuration of the thermally driven compliant mechanism by updating design variables and judging whether the iteration meets the convergence condition, thereby enabling the thermally driven compliant mechanism to have better stress-constrained reliability.

[0034] 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.

[0035] 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 reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints, characterized in that, The method comprises: Define the design conditions for thermally driven compliant mechanisms; An improved solid isotropic material penalty model is used to describe the relationship between the element elastic modulus and element density in the design conditions, and a mapping filtering technique is used to filter the element density. An interval model was used to quantify the load uncertainty caused by temperature changes, and a thermo-structure coupled finite element analysis of the structure was performed. The norm method integrates the stress constraints of all elements into a single global stress constraint. The optimization objective is to minimize the volume fraction of the thermally driven compliant mechanism. The constraints are stress-constrained reliability and output displacement. A function is constructed based on the stress constraints. The reliability is evaluated using the function metric method. A two-layer cyclic topology optimization model for the stress-constrained reliability of the thermally driven compliant mechanism is established. Based on the reliability of the stress constraint of the thermally driven compliant mechanism, a two-layer cyclic topology optimization model is used to solve the volume, output displacement, and sensitivity of the stress constraint to the design variables of the target compliant mechanism. Find the most likely failure point, substitute the most likely failure point into the outer finite element analysis of the two-layer cyclic topology optimization model of the stress constraint reliability of the thermally driven compliant mechanism, and calculate the sensitivity of the optimization objective and constraint conditions to the design variables. The design variables are updated using the moving asymptote method, and it is determined whether the iteration satisfies the convergence condition. If so, the topology of the thermally driven compliant mechanism that satisfies the reliability of stress constraints is obtained.

2. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, The design conditions include the design domain, constraint boundary conditions, setting initial values ​​of design variables, virtual spring stiffness at the output end, elastic modulus of the material, Poisson's ratio of the material, coefficient of thermal expansion, median and deviation of temperature load, and allowable reliability indicators.

3. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, The steps of using an improved solid isotropic material penalty model to describe the relationship between the element elastic modulus and element density in the design conditions, and using mapping filtering technology to filter the element density, include: An improved penalty model for solid isotropic materials is used to describe the interpolation relationship between the element elastic modulus and the element density; The cell density is corrected by combining sensitivity filtering and Heaviside mapping function to concentrate the filtered cell density towards the two ends of 0-1.

4. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, The interval model is used to quantify the load uncertainty caused by temperature changes, and a thermo-structure coupled finite element analysis of the structure is performed. The norm method involves the following steps to consolidate the stress constraints of all elements into a single global stress constraint: An interval model was used to quantify the uncertainty of temperature load, and the temperature load of each node was equivalent to nodal force. The thermo-mechanical coupling finite element analysis of the structure was then performed. Based on the calculated Von Mises stress of any element, a relaxation process is applied to the Von Mises stress of the element. The norm method agglomerates the stress constraints of all elements into a single global stress constraint, and then employs an adaptive constraint scaling method to further agglomerate the stress constraints. Norm stress is corrected.

5. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, The expression for the two-layer cyclic topology optimization model of the stress constraint reliability of the thermally driven compliant mechanism is as follows: ； Where, This represents the optimized volume. Indicates design variables, This represents the volume of a unit filled with material. Represents the overall stiffness matrix. Represents the global nodal displacement vector. Indicates the output displacement of the mechanism. Indicates the permissible output displacement limit. The interval nonprobabilistic reliability index representing stress constraints. This indicates the permissible reliability limit. The limit state function represents a variable that indicates uncertainty over an interval. This represents the design variables for each unit. Indicates the first Design variables for each unit, Indicates the number of units. This represents the equivalent nodal thermal load of the element. This represents the temperature difference from the initial time. This represents the lower bound of the design variable. Indicates the first Units.

6. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, The two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism includes an inner layer and an outer layer. The outer layer is a deterministic topology optimization based on the function metric method, and the inner layer is a reliability analysis that finds the most likely failure point.

7. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, The steps of solving the volume, output displacement, and sensitivity of stress constraints to design variables of the target compliant mechanism using the two-layer cyclic topology optimization model based on the stress constraint reliability of the thermally driven compliant mechanism include: A two-layer cyclic topology optimization model based on the reliability of the stress constraint of the thermally driven compliant mechanism was used, and the chain method was employed to calculate the volume, output displacement, and sensitivity of the stress constraint to the design variables of the target compliant mechanism.

8. The reliability topology optimization method for a thermally driven compliant mechanism considering stress constraints according to claim 1, characterized in that, After the step of determining whether the iteration satisfies the convergence condition, the method further includes: If the iteration does not meet the convergence condition, the design conditions for the thermally driven compliant mechanism are repeatedly executed. An improved solid isotropic material penalty model is used to describe the relationship between the element elastic modulus and element density in the design conditions, and a mapping filtering technique is used to filter the element density. An interval model is used to quantify the load uncertainty caused by temperature changes, and a thermo-mechanical coupling finite element analysis of the structure is performed. The norm method is used to consolidate the stress constraints of all elements into a global stress constraint. The optimization objective is to minimize the volume fraction of the thermally driven compliant mechanism, with stress constraint reliability and output displacement as constraints. A function is constructed using the stress constraints, and a function metric is used for reliability assessment to establish a two-layer cyclic topology optimization model for the stress constraint reliability of the thermally driven compliant mechanism. Based on this model, the volume, output displacement, and sensitivity of the stress constraints to design variables of the target compliant mechanism are solved. The most likely failure point is identified and substituted into the outer finite element analysis, and the sensitivity of the optimization objective and constraints to design variables is calculated. The moving asymptote method is used to update the design variables, and the convergence condition of the iteration is checked until the topology of the thermally driven compliant mechanism that satisfies the stress constraint reliability is obtained.

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