Mobile deformable component optimization method introducing topological variables

Abstract

The invention belongs to the technical field related to structural topological optimization, and discloses a method for optimizing a mobile deformable component by introducing topological variables. The method comprises the following steps that for a given design domain, design variables of all assemblies in the design domain are constructed, and the design variables comprise geometric variables and topological variables; constructing a topology description function containing a topology variable of each component by using the design variable of each component, and constructing a topology description function of an integral structure formed by connecting all the components by using the topology description functions of all the components; constructing an optimization model which takes the minimum flexibility value of the overall structure as a target and takes a design variable as an optimization object under the available volume constraint and the topological variable constraint; and initializing the design variable of each component, solving the optimization model and obtaining the optimal design variable of each component so as to realize the optimization of the structure. According to the invention, the optimization efficiency is improved, and the problem of assembly overlapping in the optimization structure is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural topology optimization, and more specifically, relates to a method for optimizing a movable deformable component by introducing topological variables. Background Art

[0002] In the field of structural optimization, topology optimization technology, which aims to find the best material layout in a given design domain, has now become an important part of the product innovation design platform. In particular, with the development of additive manufacturing technology, manufacturing-oriented topology optimization technology and its industrial applications have received widespread attention. At present, the most representative topology optimization methods include homogenization method, progressive structural optimization method, variable density method (such as SIMP), level set method, mobile deformable component (usually referred to as MMC) method, etc.

[0003] Compared with other optimization methods, the MMC method integrates shape, size, and topology optimization. The number of design variables is small and completely independent of the finite element analysis model (depending on the number of components in the design domain). It will not increase sharply due to the encryption of the finite element mesh, which greatly saves the calculation cost. Moreover, its materials are completely 0-1 distributed, there are no gray units, and the boundaries are clear, so it has developed rapidly in the past decade. In addition, we can easily extract the geometric size, position inclination and other information of the component, so this method can also be seamlessly connected with commercial software such as CAD.

[0004] However, the MMC method still has some problems. For example, there is a phenomenon of component overlap in the optimized structure, which brings inconvenience to the subsequent processing of the results. In addition, it is meaningless to optimize and analyze the hidden components during the optimization process, which is a waste of time. Therefore, a method is needed to avoid component overlap in the optimized structure. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a mobile deformable component optimization method that introduces topological variables to solve the problem of component overlap in the optimized structure.

[0006] To achieve the above object, according to one aspect of the present invention, a method for optimizing a mobile deformable component by introducing a topological variable is provided, the method comprising the following steps:

[0007] For a given design domain, construct design variables of each component in the design domain, the design variables include geometric variables and topological variables;

[0008] The topological description function of each component including the topological variables is constructed by using the design variables of each component, and the topological description function of all components is constructed by using the topological description functions of the overall structure formed by connecting all components, thereby obtaining the flexibility function of the overall structure;

[0009] An optimization model is constructed with the goal of minimizing the flexibility function value of the overall structure, the final value of the topological variable being either 0 or 1 as the constraint condition, and the design variable as the optimization object; the design variables of each component are initialized, and the optimization model is solved to obtain the optimal design variables of each component, so as to achieve component optimization.

[0010] Further preferably, the topology description function of the component including the topology variables is as follows:

[0011]

[0012] in

[0013]

[0014] Where (x, y) is the node coordinate, L i is the half length of the current component, θ i is the tilt angle of the current component, (x 0i ,y 0i ) is the center position coordinate of the current component; β i is the topological variable of the current component, q is the penalty for the topological variable, and f(x′) is the contour function of the component.

[0015] Further preferably, the flexibility function is as follows:

[0016]

[0017] Where (x, y) is the node coordinate, D is the summary of the design variables of all components in the design domain, and Ω D is the design domain, H = H(z) is the Heaviside function, φ s is the topological description function of the overall structure, Γ t is the Neumann boundary, f and t are respectively i , the body density at i=1,...,n and the surface traction at the Neumann boundary, and u is the displacement field.

[0018] Further preferably, the Heaviside function is as follows:

[0019]

[0020] where α is the void density to ensure the non-singularity of the global stiffness matrix; ∈ is a parameter that controls the magnitude of the regularization, and z is the independent variable.

[0021] Further preferably, the topological description function of the overall structure is as follows:

[0022] φ s(x, y) = max(φ1, ..., φ n )

[0023] where (x, y) are the node coordinates, n is the total number of components in the design domain, φ1, ..., φ n Represent the topological description functions of the 1st to nth components respectively.

[0024] Further preferably, the optimization model is as follows:

[0025] Find D=((D 1 ) T , ..., (D i ) T , ..., (D n ) T ) T , u(x, y)

[0026]

[0027] Where (x, y) is the node coordinate, n is the total number of components in the design domain, and D i is the design variable vector of the i-th component, D is the summary of the design variables of all components in the design domain, C is the flexibility, Ω D is the design domain, H = H(z) is the Heaviside function, φ s is the topological description function of the overall structure, Γ t and Γ u They are Neumann boundary and Dirichlet boundary respectively, and f and t are respectively in Ω i , the body force density at i = 1, ..., n and the surface traction at the Neumann boundary, u and v are the displacement field and the test function, respectively, ε is the second-order linear strain tensor, is the upper bound of the available volume of solid material, β i is the topological variable of the i-th component, μ is the upper bound of the topological variable constraint, is the admissible set of design variables, is the prescribed displacement on the Dirichlet boundary.

[0028] Further preferably, the optimization model is calculated using a pseudo material model finite element analysis method, wherein the Young's modulus E of the finite element mesh unit is e The calculation formula is as follows:

[0029]

[0030] Where E is the Young's modulus of the material, H is the Heaviside function, i = 1, ..., 4 is the value of the overall structural topology description function at the four nodes of unit e, that is, φ s .

[0031] Further preferably, when solving the optimization model, an optimization algorithm is used to update the design variables, wherein the updating of the design variables is achieved by calculating the sensitivity of the objective function and the constraint function and then combining the moving asymptote method.

[0032] Further preferably, the formula of the sensitivity of the objective function is as follows:

[0033]

[0034] Where C is the objective function, i.e., the structural flexibility, a is an arbitrary design variable; u is the displacement field, E is the Young's modulus of the material, NE represents the total number of units in the structure, and H = H(z) is the Heaviside function. i = 1, ..., 4 is the overall structural topology description function value at the four nodes of unit e (i.e. φ s ), k s For the corresponding Element stiffness matrix for i=1, ..., 4 and E=1.

[0035] The sensitivity of the constraint function is as follows:

[0036]

[0037]

[0038] Where V is the volume constraint function, a is an arbitrary design variable, NE is the total number of elements in the structure, H = H(z) is the Heaviside function, i = 1, ..., 4 is the value of the overall structural topology description function at the four nodes of unit e, that is, φ s ; g β is the topological variable constraint function, β i is the topological variable of the ith component.

[0039] Further preferably, the termination condition of the optimization iteration is as follows:

[0040] change=max{|D old -D new |}≤εorloop≥maxiter

[0041] Where change is the maximum absolute value of the difference between the last two consecutive iterations of the design variable, D old is the design variable value of the last iteration, D newis the design variable value of the current iteration, ε is the lower limit of change, loop is the current number of iterations, and maxiter is the upper limit of the number of iterations.

[0042] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0043] 1. The present invention introduces topological variables when constructing component design variables and introduces topological variables when constructing topological description functions. In the optimization process, redundant components will disappear as their topological variables gradually tend to zero, rather than being hidden in large components. This avoids optimization analysis of hidden components during the optimization process and improves optimization efficiency. At the same time, the final optimized structure is composed only of rigid components, avoiding component overlap.

[0044] 2. When constructing the optimization model, the present invention introduces topological variable constraints to avoid the existence of intermediate values ​​of topological variables and ensure that the topological variable values ​​of each component in the optimization result are either 0 or 1;

[0045] 3. The present invention adopts a pseudo material model to perform finite element analysis, and can obtain the Young's modulus of the unit according to the overall structural topological description function value of the four nodes of the unit, thereby improving the calculation efficiency;

[0046] 4. The Heaviside function used in the present invention is improved according to the modification of the component topology description function, so that its overall function graph is translated to the right by a unit length, which is adapted to the current component topology description model. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a mobile deformable component optimization method introducing topological variables constructed according to a preferred embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of geometrical variables of a component constructed according to a preferred embodiment of the present invention;

[0049] Figure 3 is a schematic diagram of the structure of an optimization model constructed according to a preferred embodiment of the present invention;

[0050] Figure 4 It is a schematic diagram of the structure of component initialization in the design domain constructed according to the preferred embodiment of the present invention;

[0051] Figure 5 It is the final result obtained by optimizing according to the traditional MMC method;

[0052] Figure 6 It is the final result obtained by optimizing the mobile deformable component optimization method that introduces topological variables constructed according to the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] like Figure 1 As shown, a mobile deformable component optimization method introducing topological variables comprises the following steps:

[0055] S1: Introducing topological variables in the classical mobile deformable component (MMC) method, the value of the topological variable varies between 0 and 1, the topological variable is 0, which means the component disappears, and the topological variable is 1, which means the component exists. The design variables constructed by the present invention include topological variables and geometric variables of components in the classical MMC method, the size, shape and position of the components are controlled by the geometric variables, and the existence of the components is controlled by the topological variables;

[0056] like Figure 2 As shown, a component with quadratic width variation is used, and each component is given a topological variable β i , at this time, for the i-th component in the design domain, its design variable is D i =(x 0i ,y 0i , L i , t 1i , t 2i , t 3i ,θ i , β i ) T , which includes two parts: geometric variables and topological variables.

[0057] S2: Use design variables to construct a topological description function for describing components. Use the topological description functions of all components to construct the topological description function of the overall structure through an operation similar to the Boolean union operation. Use the topological description function of the overall structure to construct a flexibility function.

[0058] (1) Constructing topological description functions for each component

[0059] In the classic MMC method, a topology description function (TDF) similar to the level set function is generally used to geometrically describe the component: for a component in the design domain, its internal TDF value is greater than 0, the edge TDF value is equal to 0, the external TDF value is less than 0, and a cut is made at height 0 to obtain the component outline.

[0060] Considering that after the topological variable is introduced, in order to make the components with topological variables equal to 0 disappear, the cutting surface can no longer be the 0-horizontal plane, so it is necessary to partially modify the TDF of the component: add 1 to the original TDF, and introduce the topological variable β i and penalty q. After modification, for any i-th component in the design domain, its TDF is defined as:

[0061]

[0062] in

[0063]

[0064] Where (x, y) represents the node coordinates, L i represents the half length of the current component, θ i Indicates the tilt angle of the current component, (x 0i ,y 0i ) represents the center position coordinates of the current component; β i represents the topological variable of the current component, q is the penalty for the topological variable, making it better driven to 0 or 1; f(x′) is the contour function of the component, which is defined as follows for components with quadratic width changes:

[0065]

[0066] Where, t 1i , t 2i , t 3i Respectively represent the half width of the left, right, and middle of the current component. At this time, for any i-th component in the design domain, its internal TDF value is greater than 1, its edge TDF value is equal to 1, and its external TDF value is less than 1, that is, there exists:

[0067]

[0068] Where (x, y) represents the node coordinates, Ω i represents the area occupied by the i-th component, Ω D Represents the design domain.

[0069] (2) Calculate the topological description function of the overall structure formed by all components

[0070] Then perform an operation similar to the Boolean operation to obtain the union of sets, and we have φ s (x, y) = max(φ1, ..., φ n ), where n is the total number of components in the design domain, thus obtaining the TDF of the overall structure:

[0071]

[0072] Where (x, y) represents the node coordinates, Ω s represents the area occupied by the overall structure, Ω D Indicates the design domain. At this time, when cutting is performed at height 1, the components with topological variables of 0 cannot be cut because their TDF becomes 0 and thus disappear.

[0073] (3) Constructing the flexibility function of the overall structure

[0074] The relationship of the flexibility function is as follows:

[0075]

[0076] Where (x, y) represents the node coordinates, D represents the summary of design variables of all components in the design domain, and Ω D represents the design domain, H = H(z) is the Heaviside function, φ s is the topological description function of the overall structure, Γ t represents the Neumann boundary, f and t are respectively i , the body density at i=1,...,n and the surface traction at the Neumann boundary, and u is the displacement field.

[0077] S3: Define the structural optimization problem: The design goal is to minimize the structural flexibility, and the design constraints include the volume constraint and topological variable constraint of the overall structure;

[0078] For topological variables β i Penalties are imposed to make it tend to 0 or 1 faster, so as to eliminate redundant components in the optimization process. However, from the optimization results, this penalty cannot guarantee the "black and white" of the components. i It may converge to an intermediate value between 0 and 1. Therefore, the topological variable constraint g is introduced in the optimization. β , to prevent β i Intermediate values ​​appear. The constraints are defined as follows:

[0079]

[0080] Where, the upper bound μ is a small positive number, n is the total number of components in the design domain, and β irepresents the topological variable of the i-th component. The continuation strategy is used to handle this constraint: the constraint first starts with a larger upper bound value, such as μ = 10; when the value of this constraint does not change much, that is, when the following formula is satisfied, the upper bound becomes a small positive number, such as μ = 0.01.

[0081]

[0082] Where tolerance δ g = 10%, k is the current iteration number, μ and δ g The specific value of can be adjusted according to the actual situation. Considering the flexibility minimization problem under the constraints of available volume and topological variables, the optimization model can be expressed as:

[0083] Find D=((D 1 ) T , ..., (D i ) T , ..., (D n ) T ) T , u((x, y))

[0084]

[0085] Where (x, y) is the node coordinate, n is the total number of components in the design domain, and D i is the design variable vector of the i-th component, D represents the summary of the design variables of all components in the design domain, C represents the flexibility, Ω D represents the design domain, H = H(z) is the Heaviside function, φ s is the topological description function of the overall structure, Γ t and Γ u represent the Neumann boundary and the Dirichlet boundary respectively, and f and t are respectively i , the body force density at i = 1, ..., n and the surface traction at the Neumann boundary, u and v are the displacement field and the surface traction at the Neumann boundary, respectively. of The corresponding test function on is the fourth-order isotropic elastic tensor of the material constituting the ith component, where E is Young's modulus, v is Poisson's ratio, and δ represent the fourth-order and second-order unit tensors respectively, is the Kronecker product, the symbol ε represents the second-order linear strain tensor, is the upper limit of the available volume of solid materials artificially defined, β i is the topological variable of the ith component, μ is the artificial upper limit of the topological variable constraint, is the admissible set of design variables, is the prescribed displacement on the Dirichlet boundary. To simplify the problem, we set

[0086] S4: Solving the Optimization Model

[0087] (1) The design domain is uniformly discretized using four-node bilinear rectangular elements. To improve computational efficiency, a pseudo material model is used for finite element analysis. In this embodiment, the design domain is meshed using finite elements. The number of rectangular mesh elements is 80×40, and the number of element nodes is 81×41.

[0088] like Figure 3 As shown, the present invention is explained by taking the optimization problem of minimizing the flexibility of a plane cantilever beam structure with a concentrated load as an example. In a given 2m×1m rectangular design domain Ω D The initialization structure is set up internally, the degrees of freedom in the left area are fixed, and a vertical downward concentrated force f=1N is applied at the midpoint of the right side. The design goal is to minimize the flexibility of the structure under the constraints of available solid materials.

[0089] As with most topology optimization methods, a four-node bilinear rectangular element is used to uniformly discretize the design domain. In order to improve computational efficiency, this study uses a pseudo material model for finite element analysis. Once the TDF values ​​of the four nodes of the element are known, the Young's modulus of the element can be interpolated as:

[0090]

[0091] Where E is the Young's modulus of the material, H = H(z) is the Heaviside function, i = 1, ..., 4 is the overall structural topology description function value at the four nodes of unit e (i.e. φ s ). For numerical implementation, as a common practice in the literature, the Heaviside function is often regularized to H ∈ (z):

[0092]

[0093] Among them, ∈ is a parameter that controls the regularization amplitude; α is a small positive number to ensure the non-singularity of the overall stiffness matrix. However, due to the modification of the component TDF in the previous article, the above Heaviside function also needs to be modified:

[0094]

[0095] Compared with the old Heaviside function, the new Heaviside function graph is shifted to the right by one unit length. The rationality of this change is that in the classic MMC method, the TDF value at the edge of the component is 0, and the TDF value interval corresponding to the edge transition zone is φ i ∈[-∈,∈]; In the improved method, the TDF value at the edge of the component is 1, and the TDF value range corresponding to the edge transition zone is

[0096] (2) calculating the sensitivity of the objective function to the design variables, calculating the sensitivity of the constraint function to the design variables, updating the design variables based on the above sensitivities, and solving the optimization design problem;

[0097] The objective function, constraint function, objective function sensitivity, and constraint function sensitivity are combined with the moving asymptote method to update the design variable D to obtain the updated design variable D new ; Using the updated design variable D new The updated TDF of each component is obtained to obtain the updated overall structure.

[0098] The objective function is the structural flexibility, and its sensitivity to any design variable a can be written as:

[0099]

[0100] Where K is the overall stiffness matrix of the structure, k s For the corresponding The element stiffness matrix with i = 1, ..., 4 and E = 1. Wherein, the symbol NE represents the total number of elements in the structure. can be easily calculated since φ s (x) is an explicit function of a. However, in the present invention, in order to enhance the versatility of the code, we use The finite difference quotient (i.e. ) to approximate Due to φ s (x) is an explicit function of a and is only finitely differencing at the cell level, so the computation Very fast. Numerical examples show that this method can handle the considered problem well.

[0101] In addition, we also have the sensitivity of the volume constraint function to any design variable a:

[0102]

[0103] Where NE represents the total number of units in the structure, H = H(z) is the Heaviside function, i = 1, ..., 4 represents the overall structural topology description function value (i.e. φ s ).

[0104] According to the topological variable constraint calculation formula, the sensitivity of the topological variable constraint function to the topological variable is:

[0105]

[0106] In the formula, β i is the topological variable of the ith component.

[0107] (3) When the updated structure meets the optimization termination condition, the optimization ends and an optimized structure that meets the requirements is obtained.

[0108] The optimization termination condition is set as:

[0109] change=max{|D old -D new |}≤εorloop≥maxiter

[0110] Where change is the maximum absolute value of the difference between the last two consecutive iterations of the design variable, D old represents the design variable value of the last iteration, D new represents the design variable value of the current iteration, ε represents the lower limit of the artificially specified change, loop represents the current number of iterations, and maxiter represents the upper limit of the artificially specified number of iterations. In this embodiment, ε is 0.25%, and maxiter is the upper limit of the number of iterations, which is 1000 here.

[0111] Initial design as Figure 4 As shown in FIG. 1 , 16 components are evenly distributed in the design domain. The cantilever beam optimization result obtained by the method provided by the present invention is as follows: Figure 6 As shown in the figure, after 155 iterations, the flexibility value is 74.461, and the optimized structure is composed of only 8 components. The computer takes 20.8172 seconds. In comparison, the cantilever beam optimization results obtained by the classic MMC method are shown in the figure. Figure 5 As shown, after 244 iterations, the flexibility value is 74.680, but the optimized structure contains 16 components and the computer takes 27.7380 seconds. Compared with the classical MMC method, the MMC method provided by the present invention, which introduces topological variables, improves the optimization efficiency while obtaining the optimal material distribution, so that the optimized structure is composed of only rigid components, there are no redundant components, and the phenomenon of component overlap in the optimization result is avoided.

[0112] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A mobile deformable component optimization method that introduces topological variables, characterized in that: The method comprises the following steps: For a given design domain, construct design variables of each component in the design domain, the design variables include geometric variables and topological variables; The topological description function of each component including the topological variables is constructed by using the design variables of each component, and the topological description function of all components is constructed by using the topological description functions of the overall structure formed by connecting all components, thereby obtaining the flexibility function of the overall structure; An optimization model is constructed with the goal of minimizing the flexibility function value of the overall structure, the final value of the topological variable being either 0 or 1 as the constraint condition, and the design variable as the optimization object; the design variables of each component are initialized, and the optimization model is solved to obtain the optimal design variables of each component, so as to achieve component optimization.

2. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 1, characterized in that: The topology description function of the component containing topology variables is as follows: in Where (x, y) is the node coordinate, L i is the half length of the current component, θ i is the tilt angle of the current component, (x 0i ,y 0i ) is the center position coordinate of the current component; β i is the topological variable of the current component, q is the penalty for the topological variable, and f(x′) is the contour function of the component.

3. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 1, characterized in that: The flexibility function is as follows: Where (x, y) is the node coordinate, D is the summary of the design variables of all components in the design domain, and Ω D is the design domain, H = H(z) is the Heaviside function, φ s is the topological description function of the overall structure, Γ t is the Neumann boundary, f and t are respectively i , the body density at i=1,...,n and the surface traction at the Neumann boundary, and u is the displacement field.

4. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 3, characterized in that: The Heaviside function is as follows: where α is the void density to ensure the non-singularity of the global stiffness matrix; ∈ is a parameter that controls the magnitude of the regularization, and z is the independent variable.

5. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 2 or 3, characterized in that: The topological description function of the overall structure is as follows: f s (x,y)=max(φ1,...,φ n ) where (x, y) are the node coordinates, n is the total number of components in the design domain, φ1, ..., φ n Represent the topological description functions of the 1st to nth components respectively.

6. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 1, characterized in that: The optimization model is as follows: Where (x, y) is the node coordinate, n is the total number of components in the design domain, and D i is the design variable vector of the i-th component, D is the summary of the design variables of all components in the design domain, C is the flexibility, Ω D is the design domain, H = H(z) is the Heaviside function, φ s is the topological description function of the overall structure, Γ t and Γ u They are Neumann boundary and Dirichlet boundary respectively, and f and t are respectively in Ω i , the body force density at i=1,...,n and the surface traction at the Neumann boundary, u and v are the displacement field and the test function, respectively, ε is the second-order linear strain tensor, is the upper bound of the available volume of solid material, β i is the topological variable of the i-th component, μ is the upper bound of the topological variable constraint, is the admissible set of design variables, is the prescribed displacement on the Dirichlet boundary.

7. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 6, characterized in that: The optimization model is calculated by using a pseudo material model finite element analysis method, in which the Young's modulus E of the finite element mesh unit is e The calculation formula is as follows: Where E is the Young's modulus of the material, H is the Heaviside function, is the value of the overall structural topology description function at the four nodes of unit e, that is, φ s .

8. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 1, characterized in that: When solving the optimization model, an optimization algorithm is used to update the design variables. The update of the design variables is achieved by calculating the sensitivity of the objective function and the constraint function and then combining the moving asymptote method.

9. A method for optimizing a mobile deformable component by introducing topological variables as claimed in claim 8, characterized in that: The formula for the sensitivity of the objective function is as follows: Where C is the objective function, i.e., the structural flexibility, a is an arbitrary design variable; u is the displacement field, E is the Young's modulus of the material, NE represents the total number of units in the structure, and H = H(z) is the Heaviside function. is the value of the overall structural topology description function at the four nodes of unit e (i.e. φ s ), k s For the corresponding and the element stiffness matrix with E=1. The sensitivity of the constraint function is as follows: Where V is the volume constraint function, a is an arbitrary design variable, NE is the total number of elements in the structure, H = H(z) is the Heaviside function, is the value of the overall structural topology description function at the four nodes of unit e, that is, φ s ; g β is the topological variable constraint function, β i is the topological variable of the ith component.

10. The method for optimizing a mobile deformable component by introducing topological variables according to claim 8, characterized in that: The termination conditions of the optimization iteration are as follows: change=max{|D old -D new |}≤εorloop≥maxiter Where change is the maximum absolute value of the difference between the last two consecutive iterations of the design variable, D old is the design variable value of the last iteration, D new is the design variable value of the current iteration, ε is the lower limit of change, loop is the current number of iterations, and maxiter is the upper limit of the number of iterations.

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