Reliability Topology Optimization Method for Multiphase Material Compliant Mechanisms Considering Stress Constraints

Abstract

This invention provides a reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints. The method includes defining design conditions for the multiphase material compliant mechanism; calculating the element stiffness and stress of the multiphase material compliant mechanism; using the K-S function to aggregate the stress constraints of each phase material into a global constraint, with the optimization objective being minimizing the total material volume fraction, and using stress constraint reliability, output displacement, and the volume fraction of each phase material as constraint conditions; constructing a function based on stress constraints; establishing a two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on a separable stress interpolation model; using the moving asymptote method to update design variables and find the most likely failure point; and determining whether the iteration satisfies the convergence condition. If so, a topology configuration of the multiphase material compliant mechanism that meets the stress constraint reliability requirements is obtained. This invention results in a multiphase material compliant mechanism with better 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 multiphase material compliant mechanisms that considers stress constraints. Background Technology

[0002] Compliant mechanisms rely on the elastic deformation of flexible components to transmit motion, conduct force, and convert energy. Compared to traditional rigid connection mechanisms, compliant mechanisms offer several significant advantages: they eliminate the need for rotating pairs, fundamentally reducing friction; they have a low space occupancy rate, effectively saving space resources; they enable integrated machining, simplifying manufacturing processes; and they offer high precision, meeting the requirements of high-precision operations. Based on these advantages, compliant mechanisms have found widespread application in fields such as micro-nano manipulation, precision machining, and microelectromechanical systems (MEMS).

[0003] In current technologies, traditional structural topology optimization design typically uses single-phase materials. However, the performance requirements for structures in practical engineering applications are becoming increasingly stringent. To address this issue, using multiphase materials for topology optimization design can yield structures with better overall performance. To meet the strength requirements of the mechanism, it is necessary to consider the maximum stress constraint in the topology optimization design of multiphase material compliant mechanisms. Traditional multiphase material structural topology optimization designs are mostly performed under deterministic conditions, neglecting the impact of uncertainties on mechanism performance. Therefore, it is necessary to study stress-constrained reliability topology optimization methods for multiphase material compliant mechanisms that consider stress constraints. Summary of the Invention

[0004] Based on this, the purpose of this invention is to provide a reliability topology optimization method for multiphase material 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 multiphase material compliant mechanisms considering stress constraints, the method comprising:

[0006] Define the design conditions for compliant mechanisms;

[0007] The element stiffness and stress of the compliant mechanism are calculated using a separable stress interpolation model.

[0008] The KS aggregation function is used to aggregate the von Mises equivalent stress of each phase material of the compliant mechanism into a global constraint, and the function function is constructed by the aggregation function constraint.

[0009] An interval model is used to quantify the load uncertainty, and a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model is established.

[0010] Taking the minimization of the volume of the compliant mechanism as the objective function, and considering stress constraint reliability, output displacement, and the first... The volume fraction of the multiphase material is used as a constraint, and the optimization objective is to minimize the total volume fraction of the multiphase material. A function is constructed with stress constraints, and a function metric is used to evaluate reliability. A two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on the separable stress interpolation model is established.

[0011] Sensitivity analysis was performed based on the bilayer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model.

[0012] The design variables are updated using the moving progressive algorithm, and it is determined whether the iteration meets the convergence condition. If so, the compliant mechanism topology that meets the stress constraint reliability requirements is obtained.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: the element stiffness and stress of the multiphase material compliant mechanism are calculated using a separable stress interpolation model; the stress constraints of each phase material are aggregated into a global constraint using the KS function; the optimization objective is to minimize the total volume fraction of the material; the constraints are the reliability of the stress constraint, the output displacement, and the volume fraction of each phase material; a function is constructed using the stress constraint; the reliability is evaluated using the function metric method; a two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism considering stress constraints is established; and by updating the design variables and judging whether the iteration meets the convergence condition, the optimal topology configuration of the compliant mechanism can be obtained, and the compliant mechanism has better stress constraint reliability.

[0014] Furthermore, the design conditions include the design domain, constraint boundary conditions, load magnitude, initial values ​​of design variables, elastic modulus of the material, Poisson's ratio of the material, virtual spring stiffness at the input end, virtual spring stiffness at the output end, allowable output displacement value, minimum filter radius, reliability index, median of uncertain load, and deviation.

[0015] Furthermore, the step of calculating the element stiffness and stress of the compliant mechanism using a separable stress interpolation model includes:

[0016] The relationship between element interpolation stiffness and element density, as well as the relationship between element stress and element density, in the design conditions are described using a separable stress interpolation model.

[0017] Furthermore, the step of using the KS aggregation function to aggregate the von Mises equivalent stress of each phase material of the compliant mechanism into a global constraint, and constructing the function function with the aggregation function constraint, includes:

[0018] The signed von Mises equivalent stress is calculated based on the random response, and the stress of each phase material is aggregated using the KS function to obtain the aggregated stress constraint. The aggregated stress constraint is then corrected using a correction parameter.

[0019] The stress constraint limit state function of the compliant mechanism is constructed based on the cohesive stress constraint.

[0020] Furthermore, the steps of quantifying load uncertainty using an interval model and establishing a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model include:

[0021] The uncertainty of the load is quantified using an interval model;

[0022] The reliability assessment was performed using the functional metric method, and a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model was established.

[0023] Furthermore, the expression for the reliability bilayer cyclic topology optimization model of the multiphase material compliant mechanism based on the separable stress interpolation model is as follows:

[0024] ;

[0025] In the formula, Represents the element density matrix. , , , These respectively represent the material density corresponding to the first term of the first unit, and the density of the first term of the second unit. N The first unit corresponds to the first item of material density, and the first unit corresponds to the first item of material density. M Item material density, the first unit corresponds to the first M Material density, For the optimized structural volume, This represents the number of elements after discretizing the entire structural design domain. Indicates the first e The unit corresponds to the first j Material density, Represents the volume that fills the material unit. For the overall stiffness matrix, For the payload array, For displacement arrays, For the mechanism to output displacement, For the allowed output displacement value, For the first Permissible volume fractions of phase materials M Indicates the quantity of material phases; For permissible reliability index limits; For interval nonprobabilistic reliability index under maximum stress constraint, For the limit state function, Represents the uncertainty parameter. This represents the lower bound of the unit density.

[0026] Furthermore, the step of performing sensitivity analysis based on the multiphase material compliant mechanism reliability bilayer cyclic topology optimization model based on the separable stress interpolation model includes:

[0027] Based on the aforementioned bilayer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model, the chain method is used to calculate the sensitivity of the stress reliability constraint of the target compliant mechanism to the element density, and the sensitivity of the limit state function to the interval uncertain parameters is calculated.

[0028] Furthermore, after the step of determining whether the iteration satisfies the convergence condition, the method further includes:

[0029] If the iteration does not meet the convergence condition, the design conditions for the compliant mechanism are repeatedly defined; the element stiffness and stress of the compliant mechanism are calculated using a separable stress interpolation model; the von Mises equivalent stress of each phase material of the compliant mechanism is aggregated into a global constraint using the KS aggregation function, and the function is constructed using the aggregation function constraint; the load uncertainty is quantified using an interval model, and a two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on the separable stress interpolation model is established; the volume minimization of the compliant mechanism is taken as the objective function, and the stress constraint reliability, output displacement, and the first The volume fraction of multiphase materials is used as a constraint, and the optimization objective is to minimize the total volume fraction of multiphase materials. A function is constructed using stress constraints, and a function metric is used for reliability assessment. A two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model is established. Sensitivity analysis is performed based on the two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model. The moving asymptotic algorithm is used to update design variables and find the most likely failure point, and it is determined whether the iteration meets the convergence condition until the iteration meets the convergence condition. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1This is a flowchart of a reliability topology optimization design method for a multiphase material compliant mechanism considering stress constraints in an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram showing the design domain, boundary conditions, and load application of the clamping mechanism in an embodiment of the present invention.

[0033] Figure 3 This is the deterministic topology optimization result of the multiphase material compliant gripper in the embodiments of the present invention;

[0034] Figure 4 Von Mises stress cloud diagram for deterministic topology optimization of the multiphase material compliant gripper in this embodiment of the invention;

[0035] Figure 5 This is the topological configuration of the flexible gripper in the embodiment of the present invention;

[0036] Figure 6 This is a Von Mises stress cloud diagram of the flexible clamp of the flexible clamp in an embodiment of the present invention.

[0037] The embodiments of the present invention will be further described below with reference to the accompanying drawings. Detailed Implementation

[0038] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0039] Please see Figure 1 The figure shows a reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints in an embodiment of the present invention. The method includes steps S1 to S7:

[0040] S1 defines the design conditions for the compliant mechanism;

[0041] It should be noted that, in this embodiment, the design conditions include the design domain, constraint boundary conditions, load magnitude, initial values ​​of design variables, elastic modulus of the material, Poisson's ratio of the material, virtual spring stiffness at the input end, virtual spring stiffness at the output end, allowable output displacement value, minimum filter radius, reliability index, median and deviation of uncertain loads.

[0042] S2, Calculate the element stiffness and stress of the compliant mechanism using a separable stress interpolation model;

[0043] Specifically, step S2 includes step S21:

[0044] S21, The relationship between element interpolation stiffness and element density, as well as the relationship between element stress and element density, in the design conditions are described using a separable stress interpolation model.

[0045] In this embodiment, the expression for the material property interpolation model based on the separable stress interpolation model is:

[0046] ;

[0047] In the formula, It is a unit Material properties, Indicates the number of phases of the material. The unit corresponding to the first The material density of the phase, This represents the material density of the j-th phase corresponding to the unit cell. , They represent the first Phase penalty factor, the first Phase penalty factor, Indicates the first Material properties of phase materials It is a multiplication operator;

[0048] Based on the material property interpolation model of the separable stress interpolation model, the separable stiffness interpolation model for multiphase materials can be derived, expressed as:

[0049] ;

[0050] In the formula, For unit interpolation stiffness, For unit The corresponding number Stiffness matrix of phase material, for , For unit Full of the first Stiffness matrix of phase material, Represents the density of each material in element e, where, , This represents the transpose of the local strain-displacement matrix. Represents the local strain-displacement matrix. Indicates the volume of the unit. It is the first Elastic matrix of phase material:

[0051] ;

[0052] In the formula, It is the first Young's modulus of phase material It is the first Poisson's ratio of the phase material.

[0053] To avoid stress singularity problems, for any element For the first Unit stress of phase material Perform relaxation treatment

[0054] ;

[0055] In the formula, For element stresses that have not undergone stress relaxation, Indicates the first e The unit corresponds to the first i Material density, The strain-displacement matrix, For unit The nodal displacement vector, The stress relaxation factor is 0.5.

[0056] unit Corresponding to the The equivalent von Mises stress of a phase material can be expressed as

[0057]

[0058] In the formula, For element stresses that have not undergone stress relaxation, and These are represented as principal stresses in two directions. For shear stress, This is an auxiliary matrix.

[0059] Similarly, for unit Corresponding to the Equivalent Von Mises stress of phase materials Perform relaxation treatment

[0060]

[0061] In the formula, For elements that have not undergone stress relaxation Corresponding to the The equivalent Von Mises stress of the phase material, Indicates the first e The unit corresponds to the first i Material density, This is the stress relaxation factor.

[0062] S3, the KS aggregation function is used to aggregate the von Mises equivalent stress of each phase material of the compliant mechanism into a global constraint, and the function function is constructed by the aggregation function constraint;

[0063] Specifically, step S3 includes steps S31 to S32:

[0064] S31, calculate the signed von Mises equivalent stress based on the random response, and use the KS function to aggregate the stress of each phase material to obtain the aggregated stress constraint, and use the correction parameter to correct the aggregated stress constraint;

[0065] S32, Construct the stress constraint limit state function of the compliant mechanism based on the cohesive stress constraint;

[0066] It needs to be explained that the von Mises equivalent stress of each phase material is aggregated using the Kieisselmeier-Steinhauser aggregation function, and the expression is as follows;

[0067] ;

[0068] In the formula, The constraint function represents the material strength constraint condition used in multi-material optimization. The polymerization constant, For the first The global maximum Mises stress of the phase material For the first The stress limit of the phase material, then Indicates the stress limit of the first phase material. Indicates the stress limit of the second phase material;

[0069] In Kieisselmeier-Steinhauser aggregation functions, typically The larger the value, the closer the aggregation result is to the expected value. and The maximum value in, but The larger the value, the greater the impact on the stability of the algorithm. Therefore, here... The value is set to 8. Since the KS aggregation function has a certain error, this defect is compensated for by adjusting the parameters. Make corrections:

[0070] ;

[0071] In the formula, This represents the modified constraint function, where the modification parameter is... It changes with each iteration step, the 1st... The expression for the correction parameter in the next iteration is:

[0072] ;

[0073] In the formula, This represents the change in the exponential form of the correction parameter with each iteration step. This represents the Mises stress of the first type of material. This represents the Mises stress of the second material; due to the maximum value function Since the algorithm is not differentiable and the moving asymptote algorithm is a gradient-based optimization algorithm, the Kieisselmeier-Steinhauser aggregation function is used to approximate the maximum Mises stress. Simultaneously, correction parameters are used. Make corrections:

[0074] ;

[0075] No. n Step correction parameters The expression is:

[0076] ;

[0077] Combining them, we can obtain:

[0078] ;

[0079] in, The number of elements after discretizing the entire structural design domain. Represents the polymerization constant. Indicates the first i The approximate maximum stress of this material This represents the approximate maximum stress of the first type of material. This represents the approximate maximum stress of the second material. Indicates the first n Step correction parameters .

[0080] S4. The interval model is used to quantify the load uncertainty and a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanism based on separable stress interpolation model is established.

[0081] Specifically, step S4 includes steps S41 to S42:

[0082] S41, uses an interval model to quantify load uncertainty;

[0083] In interval models, uncertain variables are represented by interval variables that include upper and lower bounds. If For a certain interval variable, For interval variables If the interval is , then we have:

[0084] ;

[0085] In the formula, For interval The lower bound, For interval The upper bound; let In the formula, For interval variables The median, For interval variables The deviation;

[0086] interval vector It can also be transformed into a standardized interval model;

[0087] ;

[0088] In the formula, It is called a standardized interval vector.

[0089] S42, the functional metric method is used for reliability assessment, and a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model is established.

[0090] It is worth noting that the reliability optimization problem using the functional metric method can be written as:

[0091] ;

[0092] in, The material density represents the overall objective function. Index representing the constraint condition. This indicates the total number of constraints. It is a function. It can be obtained by solving in the following way:

[0093] ;

[0094] in, For those concerned with performance values, The point of interest can be obtained by solving the following problem:

[0095] ;

[0096] In the formula, Indicates the first i Transpose of the uncertainty of a design variable Indicates the first i Uncertainty of a design variable Indicates the acceptable reliability index. This indicates the total number of design variables.

[0097] S5, with minimizing the volume of the compliant mechanism as the objective function, and considering stress constraint reliability, output displacement, and the first... The volume fraction of the multiphase material is used as a constraint, and the optimization objective is to minimize the total volume fraction of the multiphase material. A function is constructed with stress constraints, and a function metric is used to evaluate reliability. A two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on the separable stress interpolation model is established.

[0098] In this embodiment, the expression for the reliability bilayer cyclic topology optimization model of the multiphase material compliant mechanism based on the separable stress interpolation model is as follows:

[0099] ;

[0100] In the formula, Represents the element density matrix. , , , These respectively represent the material density corresponding to the first term of the first unit, and the density of the first term of the second unit. N The first unit corresponds to the first item of material density, and the first unit corresponds to the first item of material density. M Item material density, the first unit corresponds to the first M Material density, For the optimized structural volume, This represents the number of elements after discretizing the entire structural design domain. Indicates the first e The unit corresponds to the first j Material density, Represents the volume that fills the material unit. For the overall stiffness matrix, For the payload array, For displacement arrays, For the mechanism to output displacement, For the allowed output displacement value, For the first Permissible volume fractions of phase materials M Indicates the quantity of material phases; For permissible reliability index limits; For interval nonprobabilistic reliability index under maximum stress constraint, For the limit state function, Represents the uncertainty parameter. This represents the lower bound of the unit density.

[0101] S6. Sensitivity analysis is performed based on the bilayer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model.

[0102] Specifically, step S6 includes step S61:

[0103] S61, based on the multiphase material compliant mechanism reliability double-layer cyclic topology optimization model based on the separable stress interpolation model, the sensitivity of the stress reliability constraint of the target compliant mechanism to the element density is calculated using the chain method, and the sensitivity of the limit state function to the interval uncertain parameters is calculated.

[0104] It is understandable that the chain method is used to calculate the sensitivity of the stress reliability constraint of the compliant mechanism; the sensitivity of the stress reliability constraint to the design variables is:

[0105] ;

[0106] In the formula, Indicates the partial derivative sign. Representation unit density, Indicates the correction parameter. Represents the polymerization constant. Indicates the first The stress limit of the phase material, where G represents the limit state function;

[0107] The sensitivity of polymer stress to design variables is:

[0108] ;

[0109] in:

[0110] ;

[0111] The derivatives of the Mises stress with respect to the stress components for each phase material are:

[0112] ;

[0113] In the formula, Indicates the first i The von Mises stress of the material in the e-th element, Indicates the first i The material in the first e In each unit x Stress components in the direction, Indicates the first i The material in the first e In each unit y Stress components in the direction;

[0114] The derivatives of the element stresses of each phase material with respect to the design variables are:

[0115] ;

[0116] In the formula, The stress relaxation factor is... Indicates the first e In the unit at the , i The density of the phase material, Indicates the first e Displacement array of elements, Represents the elasticity matrix. Represents the strain-displacement matrix;

[0117] The derivatives of the element displacements of each phase material with respect to the design variables are:

[0118] ;

[0119] Introducing the adjoint vector To satisfy the following adjoint equation:

[0120] ;

[0121] In the formula, Represents the adjoint vector. Indicates the first e The unit corresponds to the first k Phase material unit density;

[0122] The auxiliary matrix is ​​expressed as follows:

[0123] ;

[0124] The sensitivity of polymer stress to design variables can be expressed as:

[0125] ;

[0126] Through the limit state function, the stress reliability constraint on the standardized interval vector can be obtained. The derivative is

[0127] ;

[0128] Polymer stress versus standardized interval vector The sensitivity is

[0129] ;

[0130] The element stress versus the normalized interval vector of each phase material The sensitivity is:

[0131] .

[0132] S7. Update the design variables using the moving progressive algorithm and determine whether the iteration meets the convergence condition. If so, the compliant mechanism topology that meets the stress constraint reliability requirements is obtained.

[0133] It is worth noting that if the iteration does not meet the convergence condition, the design conditions for the compliant mechanism are repeatedly defined; the element stiffness and stress of the compliant mechanism are calculated using a separable stress interpolation model; the von Mises equivalent stress of each phase material of the compliant mechanism is aggregated into a global constraint using the KS aggregation function, and the function is constructed using the aggregation function constraint; the load uncertainty is quantified using an interval model, and a two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on the separable stress interpolation model is established; the volume minimization of the compliant mechanism is taken as the objective function, and the stress constraint reliability, output displacement, and the first Using the volume fraction of multiphase materials as a constraint and minimizing the total volume fraction of multiphase materials as the optimization objective, a function is constructed with stress constraints. Reliability is assessed using a function metric method, and a two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on the separable stress interpolation model is established. Sensitivity analysis is performed based on this model. A moving asymptotic algorithm is used to update design variables and find the most likely failure point, and the iteration is repeated until convergence is achieved. This yields a compliant mechanism topology configuration that meets strength and reliability requirements.

[0134] To further verify the effectiveness of the reliability topology optimization design method for multiphase material compliant mechanisms that considers stress constraints, this embodiment uses a flexible gripper as an example to explain the invention.

[0135] The design domain, boundary conditions, and loads of the clamping mechanism are as follows: Figure 2 As shown, the clamp design domain has dimensions of 80μm × 80μm. Fixed constraints are added at the upper left and lower left corners of the design domain. The output end is the right-side clamping part, and a load is applied at the midpoint of the left side. Since the design domain is symmetrical, only the lower half of the 20,000 planar quadrilateral elements are used for design analysis.

[0136] In a deterministic topology optimization mathematical model, the applied load F =1, permissible output displacement limit The allowable stress limit of material one The allowable stress limit for material 2 The permissible volume fraction limit for material 2 With the optimization objective of minimizing the total volume fraction of materials, and with the output displacement, KS aggregation function, and the volume fraction of material two as constraints, the topology optimization results are as follows: Figure 3 and Figure 4 As shown, Figure 3 These are the results of deterministic topology optimization. The red part represents Material 1, and the dark blue part represents Material 2. Figure 4 It is a stress cloud diagram.

[0137] In the mathematical model of stress-constrained topology optimization for the reliability of compliant mechanisms, the uncertain variable load F median Uncertain variable loading F deviation . Figure 5 and Figure 6 for Topological configuration and von Mises stress contour plot of the flexible gripper. Comparison. Figure 3 and Figure 5 It can be seen that, compared to the deterministic topology optimization configuration, the reliability topology optimization configuration retains more material and has thicker members to enhance its resistance to the influence of external uncertainties. In the deterministic topology optimization results, material two with a higher elastic modulus is used at the boundary fixing points of the gripper, the load input points, and the points where the gripper interacts with the gripped object. The skeleton of the gripper is mostly made of material one with a relatively lower elastic modulus, and the stress distribution cloud diagram shows a uniform stress distribution, with the maximum stress mainly occurring at the connection points of the configuration and at the junctions of different materials.

[0138] In summary, the stress-constrained multiphase material compliant mechanism reliability topology optimization method in the above embodiments of the present invention uses a separable stress interpolation model to calculate the element stiffness and stress of the multiphase material compliant mechanism, uses the KS function to aggregate the stress constraints of each phase material into a global constraint, takes minimizing the total volume fraction of materials as the optimization objective, and uses stress constraint reliability, output displacement, and volume fraction of each phase material as constraint conditions. A function is constructed based on stress constraints, and a function metric is used for reliability assessment. A two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism considering stress constraints is established. By updating the design variables and judging whether the iteration meets the convergence condition, the optimal compliant mechanism topology configuration can be obtained, and the compliant mechanism has better stress constraint reliability.

[0139] 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.

[0140] 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 method for reliability topology optimization of compliant mechanisms in multiphase materials considering stress constraints, characterized in that, The method includes: Define the design conditions for compliant mechanisms; The element stiffness and stress of the compliant mechanism are calculated using a separable stress interpolation model. The KS aggregation function is used to aggregate the von Mises equivalent stress of each phase material of the compliant mechanism into a global constraint, and the function function is constructed by the aggregation function constraint. An interval model is used to quantify the load uncertainty, and a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model is established. A function of minimizing the volume of the compliant mechanism is taken as an objective function, a stress-constrained reliability, an output displacement and a first A function of minimizing the volume of the multi-phase material is taken as an optimization objective, a stress constraint is used to construct a function, a function measurement method is used for reliability evaluation, and a multi-phase material compliant mechanism reliability double-layer circulation topology optimization model based on the separable stress interpolation model is established, and an expression of the multi-phase material compliant mechanism reliability double-layer circulation topology optimization model based on the separable stress interpolation model is: ； In the formula, Represents the element density matrix. , , , These respectively represent the material density corresponding to the first term of the first unit, and the density of the first term of the second unit. N The first unit corresponds to the first item of material density, and the first unit corresponds to the first item of material density. M Item material density, the first N The unit corresponds to the first M Material density, For the optimized structural volume, This represents the number of elements after discretizing the entire structural design domain. Indicates the first e The unit corresponds to the first j Material density, Represents the volume that fills the material unit. For the overall stiffness matrix, For the payload array, For displacement arrays, To output displacement for the mechanism, For the allowed output displacement value, For the first Permissible volume fractions of phase materials M Indicates the quantity of material phases; For permissible reliability index limits; For interval nonprobabilistic reliability index under maximum stress constraint, Let be the limit state function. Represents the uncertainty parameter. This represents the lower bound of the cell density; Sensitivity analysis was performed based on the bilayer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model. The design variables are updated using the moving progressive algorithm, and it is determined whether the iteration meets the convergence condition. If so, the compliant mechanism topology that meets the stress constraint reliability requirements is obtained.

2. The reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints according to claim 1, characterized in that, The design conditions include the design domain, constraint boundary conditions, load magnitude, initial values ​​of design variables, elastic modulus of the material, Poisson's ratio of the material, virtual spring stiffness at the input end, virtual spring stiffness at the output end, allowable output displacement value, minimum filter radius, reliability index, median of uncertain load, and deviation.

3. The reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints according to claim 1, characterized in that, The steps for calculating the element stiffness and stress of the compliant mechanism using a separable stress interpolation model include: The relationship between element interpolation stiffness and element density, as well as the relationship between element stress and element density, in the design conditions are described using a separable stress interpolation model.

4. The reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints according to claim 1, characterized in that, The step of using the KS aggregation function to aggregate the von Mises equivalent stress of each phase material of the compliant mechanism into a global constraint, and constructing the function function with the aggregation function constraint, includes: The signed von Mises equivalent stress is calculated based on the random response, and the stress of each phase material is aggregated using the KS function to obtain the aggregated stress constraint. The aggregated stress constraint is then corrected using a correction parameter. The stress constraint limit state function of the compliant mechanism is constructed based on the cohesive stress constraint.

5. The reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints according to claim 1, characterized in that, The steps of quantifying load uncertainty using an interval model and establishing a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model include: The uncertainty of the load is quantified using an interval model; The reliability assessment was performed using the functional metric method, and a two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on a separable stress interpolation model was established.

6. The reliability topology optimization method for multiphase material compliant mechanisms considering stress constraints according to claim 1, characterized in that, The steps for sensitivity analysis based on the bilayer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model include: Based on the aforementioned bilayer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model, the chain method is used to calculate the sensitivity of the stress reliability constraint of the target compliant mechanism to the element density, and the sensitivity of the limit state function to the interval uncertain parameters is calculated.

7. The reliability topology optimization method for multiphase material compliant mechanisms 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 compliant mechanism are repeatedly defined; the element stiffness and stress of the compliant mechanism are calculated using a separable stress interpolation model; the von Mises equivalent stress of each phase material of the compliant mechanism is aggregated into a global constraint using the KS aggregation function, and the function is constructed using the aggregation function constraint; the load uncertainty is quantified using an interval model, and a two-layer cyclic topology optimization model for the reliability of the multiphase material compliant mechanism based on the separable stress interpolation model is established; the volume minimization of the compliant mechanism is taken as the objective function, and the stress constraint reliability, output displacement, and the first The volume fraction of multiphase materials is used as a constraint, and the optimization objective is to minimize the total volume fraction of multiphase materials. A function is constructed using stress constraints, and a function metric is used for reliability assessment. A two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model is established. Sensitivity analysis is performed based on the two-layer cyclic topology optimization model for the reliability of multiphase material compliant mechanisms based on the separable stress interpolation model. The moving asymptotic algorithm is used to update design variables and find failure points, and it is determined whether the iteration meets the convergence condition until the iteration meets the convergence condition.

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