An Isogeometric Topology Optimization Design Method and Application Considering Stress Constraints

Abstract

The present invention belongs to the technical field related to structural topology optimization design, and discloses an isogeometric topology optimization design method and application considering stress constraints, including the following steps: (1) An improved stress vanishing constraint function is used to replace the stress constraint condition in the isogeometric topology optimization design model of the structure to be optimized, so as to obtain an improved topology optimization design model; (2) The augmented Lagrangian function method is used to construct an approximate model of the improved topology optimization design model, and the sensitivity information of the approximate model is deduced and calculated; (3) Based on the sensitivity information, the unconstrained MMA algorithm is used to realize the iterative update of the design variables of the approximate model. After every N l times of design variable updates, the Lagrange multiplier is updated once based on the KKT condition until the optimization design result of the approximate model converges, and then the current approximate model is used for the isogeometric topology optimization design of the structure. The present invention realizes the high-efficiency and high-precision control of the stress states of each local region of the structure.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural topology optimization design, and more specifically, relates to an isogeometric topology optimization design method and application considering stress constraints. Background Technique

[0002] As an efficient structural optimization design tool, topology optimization technology has important applications in many fields such as aerospace, marine vessels, and vehicle engineering, and is also a current research hotspot in academia. However, most of the current research work on topology optimization technology focuses on the stiffness characteristics of structures because the structural stiffness design problem has advantages such as easy numerical implementation and stable convergence. In actual engineering, in addition to considering the stiffness of the structure, the strength characteristics of the structure are more important because structural strength is a prerequisite for ensuring the normal performance of the structure. The index characterizing structural strength is the structural stress state, so it is necessary to study a topology optimization design method based on stress.

[0003] Topology optimization design based on stress is divided into two categories, namely stress minimization design and stress constraint design, among which stress constraint design is more in line with the conventional mode of engineering design and is also more challenging. Compared with topology optimization design based on stiffness, there are the following three major difficulties in stress-related design problems:

[0004] 1. Singularity phenomenon: The singularity phenomenon refers to that the global optimal solution of the optimization problem is located in a degenerate subspace with non-smooth transition within the feasible region. Conventional optimization algorithms cannot search for such a degenerate subspace, resulting in difficulty in obtaining the global optimal solution of the optimization problem.

[0005] 2. Local characteristics of stress: The structural stress state is a field function related to the spatial coordinates of any point within the structure, and the stress state distribution will change with the change of the structural material distribution. Therefore, controlling the maximum stress level of the structure requires setting stress constraints at any point within the structure, which will cause a large number of constraint conditions in the optimization problem, resulting in difficulty in calculating and solving the optimization problem.

[0006] 3. Highly nonlinear behavior of stress: The stress state at any point within the structure is highly related to the material distribution and local geometric characteristics around that point, and the relationship between the two has a nonlinear characteristic. Therefore, the structural stress level is very sensitive to the change of the structure topology, and the highly nonlinear behavior of stress will cause difficulty in the stable convergence of the optimization process. Summary of the Invention

[0007] In view of the above deficiencies or improvement requirements of the prior art, the present invention provides an isogeometric topology optimization design method and application considering stress constraints, which transforms the original optimization model into an unconstrained optimization model by using the augmented Lagrangian function, realizes the high-efficiency and high-precision control of the stress state of each local region of the structure, and effectively solves the problem of structural topology optimization design including stress constraints.

[0008] To achieve the above object, according to one aspect of the present invention, an isogeometric topology optimization design method considering stress constraints is provided, and the method mainly includes the following steps:

[0009] (1) Replace the stress constraint condition in the isogeometric topology optimization design model of the structure to be optimized with an improved stress vanishing constraint function to obtain an improved topology optimization design model; the improved stress vanishing constraint function is:

[0010]

[0011] where m E,a (ρ) is the Young's modulus at the evaluation point a; represents the von Mises stress at the evaluation point a, and σ lim is the stress constraint value, N v refers to the total number of stress evaluation points;

[0012] (2) Use the augmented Lagrangian function method to construct an approximate model of the improved topology optimization design model, and then deduce and calculate the sensitivity information of the approximate model;

[0013] (3) Based on the obtained sensitivity information, use the unconstrained MMA algorithm to realize the iterative update of the design variables of the approximate model. After every N l times of design variable updates, update the Lagrange multiplier once based on the KKT conditions until the optimization design result of the approximate model converges, and then use the current approximate model for the isogeometric topology optimization design of the structure; where N l >1.

[0014] Further, before step (1), there is also a step of constructing an isogeometric topology optimization design model of the structure to be optimized with the minimum material usage as the objective and the von Mises stress at the structural evaluation point as the constraint.

[0015] Further, the corresponding relationship between the optimization design variable ρ and the structural density field m V (ρ) and the Young's modulus field m E (ρ) is:

[0016] ρ = [ρ 1，1 ...ρ i，j …ρ n，m ​

[0017]

[0018] m E (ρ) = E min +(E0 - E min )[m V (ρ)] p

[0019] Where i and j represent the control point numbers along the parametric coordinates ξ and η directions, and ρ i，j represents the design variable corresponding to the i-th and j-th control points, represents the NURBS basis function corresponding to the i-th and j-th control points, and r and q respectively refer to the orders of the basis functions along the ξ and η directions; refers to the design variable after threshold projection processing, and n and m respectively represent the total number of control points along the ξ and η directions; E0 refers to the Young's modulus of the solid material, and E min is the set minimum Young's modulus; p is a penalty coefficient greater than 1, set to 3.5.

[0020] Furthermore, the expression of the isogeometric topology optimization design model is:

[0021]

[0022] In the formula, K is the structural stiffness matrix, U is the control point displacement vector, and F is the external load; represents the von Mises stress at the evaluation point a, and σ lim is the stress constraint value, and N c refers to the total number of stress evaluation points.

[0023] Furthermore, the expression of the improved topology optimization design model is:

[0024]

[0025] Furthermore, the expression of the approximate model is:

[0026]

[0027] Where s is the slack variable, λ a and μ are both Lagrange multipliers, and h a (ρ) is the stress constraint after introducing the slack variable; ρ is the optimization design variable; m V (ρ) is the structural density field; s a is the slack variable.

[0028] Furthermore,

[0029] h a (ρ) = g a (ρ) + Sa

[0030] Lagrange multiplier λ a The update criteria for λ and μ are as follows:

[0031] μ k+l = αμ k , where α > 1

[0032]

[0033] where k represents the iteration number of the Lagrange multiplier, and α is the set update coefficient.

[0034] The present invention provides an isogeometric topology optimization design device, which includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the isogeometric topology optimization design method considering stress constraints as described above.

[0035] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the isogeometric topology optimization design method considering stress constraints as described above.

[0036] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the isogeometric topology optimization design method and application considering stress constraints provided by the present invention mainly have the following beneficial effects:

[0037] 1. By using an improved stress vanishing constraint function expression to replace the stress constraint condition, the present invention can effectively improve the convergence speed of the topology optimization design result, so that the maximum von Mises stress of the structure quickly drops to near the stress constraint value in the initial stage of optimization iteration.

[0038] 2. The augmented Lagrangian multiplier method adopted by the present invention not only solves the calculation difficulties caused by a large number of stress constraint conditions in the optimization model, but also realizes local stress constraint control, and this control strategy can accurately constrain the maximum stress level of the structure.

[0039] 3. The method provided by the present invention can achieve the design of structural lightweighting or other optimization goals while ensuring that the maximum von Mises stress of the structure meets the stress constraint conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a schematic flow chart of the isogeometric topology optimization design method considering stress constraints provided by the present invention;

[0041] Figure 2In (a) and (b), they are respectively the design domain and boundary condition settings of the typical example "L-shaped beam" in the field of stress optimization and the stress distribution nephogram of the L-shaped beam structure;

[0042] Figure 3 In (a) and (b), they are respectively the topological structure obtained by the compliance minimization design including volume constraints and the stress distribution nephogram corresponding to this topological structure;

[0043] Figure 4 In (a) and (b), they are respectively the topological structure obtained by the volume minimization design considering stress constraints and the stress distribution nephogram corresponding to it;

[0044] Figure 5 are the convergence curves of the maximum von Mises stress and volume fraction of the structure. Detailed implementation manner

[0045] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to 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 used 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.

[0046] Please refer to Figure 1 , the present invention provides an isogeometric topology optimization design method considering stress constraints, and the method mainly includes the following steps:

[0047] Step 1, construct an isogeometric topology optimization design model of the structure to be optimized with the minimum material usage as the objective and the von Mises stress at the structure evaluation points as the constraint.

[0048] Specifically, based on the isogeometric analysis model of the structure to be optimized, establish the corresponding relationship between the optimization design variable ρ and the structure density field m V (ρ) and the Young's modulus field m E (ρ), and then construct an isogeometric topology optimization design model with the minimum material usage as the objective and the VonMises stress at the structure evaluation points as the constraint.

[0049] In this embodiment, before establishing the isogeometric topology optimization design model, first introduce the corresponding relationship between the design variable ρ and the structure density field m V (ρ) and the Young's modulus field m E (ρ) based on the isogeometric analysis model:

[0050] ρ = [ρ 1，1 …ρi ，j …ρ n，m (1)

[0051]

[0052] m E (ρ) = E min +(E0 - E min )[m y (ρ)] p (3)

[0053] where i, j represent the control point numbers along the parametric coordinates ξ and η directions, and ρ i,j represents the design variable corresponding to the i, j control points, represents the NURBS basis function corresponding to the i, j control points, and r and q respectively refer to the orders of the basis functions along the ξ and η directions; refers to the design variable after threshold projection processing, and n and m respectively represent the total number of control points along the ξ and η directions; E0 refers to the Young's modulus of the solid material, and E min is the set minimum Young's modulus, the purpose of which is to avoid singularity of the stiffness matrix, and is set to 0.001 MPa in this implementation; p is a penalty coefficient greater than 1 and is set to 3.5.

[0054] is obtained from the smoothed design variable after threshold projection, and the projection expression is:

[0055]

[0056] where β is the projection curvature control parameter, the larger the β value, the greater the curvature of the projection function curve, η is the projection threshold, variables greater than η approach 1 after projection, and vice versa approach 0, and η is set to 0.5 in this implementation; is obtained from the smoothed design variable ρ i,j after smoothing, and its expression is:

[0057]

[0058] where, is the C 4 compactly supported radial basis function.

[0059] Based on equations (1)-(3), the isogeometric topology optimization design model can be established, and the corresponding mathematical expression is:

[0060]

[0061] where K is the structural stiffness matrix, U is the control point displacement vector, and F is the external load; represents the von Mises stress at the evaluation point a, and σ lim is the stress constraint value, and N cRefers to the total number of stress evaluation points.

[0062] Specifically, the von Mises stress at the evaluation point Can be expressed as:

[0063]

[0064] Where, σ a Is the stress vector at the evaluation point, V refers to the stress coefficient matrix. For plane stress problems, σ a And the expressions of V are shown in Eqs. (8) and (9) respectively:

[0065]

[0066]

[0067] Where, D0 represents the elastic matrix of the solid material, B a Represents the strain-displacement matrix at the evaluation point, Represents the control point displacement index matrix corresponding to the span element containing the evaluation point a.

[0068] Step 2, use the improved stress vanishing constraint function to swap the stress constraint conditions in the isogeometric topology optimization design model to obtain an improved topology optimization design model; the improved stress vanishing constraint function is:

[0069]

[0070] Where, m E,a (ρ) is the Young's modulus at the evaluation point a; Represents the von Mises stress at the evaluation point a, σ lim Is the stress constraint value, N c Refers to the total number of stress evaluation points.

[0071] In this embodiment, to improve the convergence speed of the optimization design result and improve the design efficiency, the stress constraint conditions in the optimization model described in Eq. (6) are improved. The improved stress constraint expression is:

[0072]

[0073] The improved stress constraint is multiplied by the Young's modulus value at the evaluation point to make it a vanishing constraint, avoiding singularity phenomena. At the same time, the original first-order constraint function is changed to a second-order constraint function. This strategy can increase the penalty for high-stress regions in the structure while ensuring the stability of the optimization process, making the structural stress level quickly approach the stress constraint value and improving the convergence speed of the optimization design. The expression of the improved topology optimization design model is:

[0074]

[0075] Step 3: Construct an approximate model of the improved topology optimization design model by using the augmented Lagrangian function method.

[0076] The expression of the approximate model of the improved topology optimization design model constructed by the augmented Lagrangian function method is:

[0077]

[0078] where s is a slack variable, λ a and μ are both Lagrange multipliers, h a (ρ) is the stress constraint after introducing the slack variable, and its specific expression is:

[0079] h a (ρ) = g a (ρ) + S a

[0080] The update criteria for the Lagrange multipliers λ a and μ are respectively:

[0081] μ k+1 = αμ k , α > 1

[0082]

[0083] where k represents the iteration number of the Lagrange multiplier, and α is the set update coefficient.

[0084] In this embodiment, the optimization design model shown in formula (11) contains N c stress evaluation points. In this embodiment, the stress evaluation points are set as the Gaussian integration points of each span unit. Therefore, N c is equal to the total number of Gaussian integration points, which makes the above optimization design model contain too many stress constraint conditions and is prone to cause difficulties in solving. For this reason, this embodiment uses the augmented Lagrangian function method to construct an approximate model of the above optimization design model and integrates the stress constraint conditions into the objective function. Specifically, first introduce a slack variable s a :

[0085] s a ≥ 0, a = 1, 2,..., N c (12)

[0086] Let

[0087] h a (ρ) = g a (ρ) + s a = 0 (13)

[0088] Introduce the Lagrange multiplier λ a and μ to construct the penalty function P(ρ)

[0089]

[0090] Based on the penalty function P(ρ) and the objective function, construct the Lagrangian function L(ρ) to obtain:

[0091] L(ρ) = ∫ Ω m V (ρ)dΩ + P(ρ) (15)

[0092] The expression for establishing the approximate problem model is:

[0093]

[0094] Before solving the above approximate problem, the slack variables can be eliminated by solving the penalty term sub-problem shown in Equation (17):

[0095]

[0096] The solution of the above penalty term sub-problem is:

[0097]

[0098] Substitute Equation (18) into the expression (16) of the approximate problem model to eliminate the slack variable s a .

[0099] Step 4: Derive and calculate the sensitivity information of the approximate model.

[0100] As can be seen from Equation (16), the sensitivity information to be solved is the first derivative of the Lagrangian function L(ρ) with respect to the design variable, that is:

[0101]

[0102] Among them, from Equations (2)(4)(5), it can be obtained that:

[0103]

[0104] From Equation (15), it can be obtained that:

[0105]

[0106] Among them, the total volume of the structure can be expressed by the Gaussian integration method as:

[0107]

[0108] In Equation (22), and They are the Jacobian matrices of the two inverse mappings from the relative space to the physical space, ω a is the Gaussian integration weight coefficient, so:

[0109]

[0110] It can be seen from Equation (14) that

[0111]

[0112] It can be seen from Equation (18) that when h a (ρ) takes at this time, the above formula is 0. When h a (ρ) takes g a (ρ), there is:

[0113]

[0114] It can be obtained from Equations (7) and (8):

[0115]

[0116] It can be obtained by the adjoint method:

[0117]

[0118] Among them, the global stiffness matrix K can also be expressed by the Gaussian integration method as:

[0119]

[0120] Therefore, it can be obtained from the above formula:

[0121]

[0122] Step 5: Based on the obtained sensitivity information, use the unconstrained MMA algorithm to realize the iterative update of the design variables of the approximate model. After every N l times of design variable updates, update the Lagrange multipliers once based on the KKT conditions until the optimization design result of the approximate model converges. Furthermore, use the current approximate model for the isogeometric topology optimization design of the structure.

[0123] In this embodiment, the approximate model shown in Equation (16) has integrated all stress constraint conditions into the objective function. Therefore, in this embodiment, based on the sensitivity information of the objective function of the approximate model, the unconstrained MMA algorithm is used to realize the iterative update of the design variables. This update algorithm is suitable for solving optimization design problems with strong nonlinearity such as stress constraints, and can further improve the solution efficiency of the optimization problem, and ensure the stability of the optimization process to a certain extent.

[0124] The optimal design result obtained by solving the approximate optimization model is an approximate solution to the original optimization problem model in Equation (11). To obtain the exact solution to the original optimization problem, it is necessary to continuously update the Lagrange multipliers based on the KKT conditions during the optimization iteration process, so that the approximate optimization model gradually approaches the original optimization problem model until a stable and convergent optimal design result is obtained. The update criteria for the Lagrange multipliers λ a and μ are as follows:

[0125]

[0126] where k represents the iteration number of the Lagrange multipliers. To ensure the stability of the optimization process, the update frequency of the Lagrange multipliers should be less than that of the design variables, and it is usually set to update the Lagrange multipliers once every N l (N l >1) times of design variable updates. In this embodiment, N l =5. α is the set update coefficient, and the larger the α value, the faster the convergence speed of the design result, but the worse the algorithm stability. Therefore, the α value needs to be set by experience. In this embodiment, the α value is set to 1.1.

[0127] To prove the effectiveness of the present invention, the following uses a specific example to verify the present invention.

[0128] As shown in (a) of Figure 2 , the design domain and boundary condition settings of the typical example "L"-shaped beam optimization in the stress optimization field are shown. The upper boundary of the "L"-shaped beam is completely constrained, and a uniform load with a resultant force F = 1N acts on a line segment with a length of 0.06L at the upper part of its right boundary, where L = 1. Figure 2 As shown in (b) of Figure 3 , it is the stress distribution nephogram of the "L"-shaped beam structure. There is an obvious stress concentration phenomenon at its inner corner, and the maximum von Mises stress is as high as 187.3 MPa. In this example, the orders r and q of the NURBS basis functions selected are both 2, the "L"-shaped beam is divided into 9800 span elements, with a total of 10296 control points, the Young's modulus of the material is 1 MPa, and the Poisson's ratio is 0.25. Figure 3 As shown in (a) of

[0129] , it is the topological structure obtained by the compliance minimization design including volume constraints, where the volume constraint is set to 30%. Figure 3 As shown in (b) of

[0129] , it is the stress distribution nephogram corresponding to this topological structure. As can be seen from the figure, the compliance optimization design cannot reduce the stress level of the structure, and there is still a stress concentration phenomenon at the inner corner of the "L"-shaped beam, and the maximum von Mises stress reaches 293.2 MPa.

[0129] Next, the isogeometric topology optimization design method considering stress constraints constructed in this embodiment is used to optimize the design of the "L"-shaped beam. The von Mises stress constraint value is set to 70 MPa, and other optimization control parameters are kept consistent with the foregoing content. Figure 4 (a) in Figure 4 shows the topology structure obtained from the volume minimization design considering stress constraints. Figure 4 (b) in Figure 4 is the corresponding stress distribution nephogram. As can be seen from Figure 4 (a) in Figure 4 , the topology structure obtained by the method of this embodiment completely removes the material at the inner corner of the "L"-shaped beam, making it a rounded chamfer, avoiding the stress concentration phenomenon. The maximum von Mises stress value of the structure is 70.0 MPa, which is accurately controlled at the stress constraint value. At the same time, the structure volume ratio is 30.4%, and the weight is reduced by about 70% compared with the initial "L"-shaped beam, realizing the lightweight design of the structure. Figure 5 The convergence curves of the maximum von Mises stress and volume fraction of the structure are given, which are the ratio of the maximum von Mises stress of the structure to the stress constraint value and the structure volume fraction respectively. It can be seen that the convergence is stable throughout the optimization process. The maximum stress level of the structure rapidly drops to near the stress constraint value in the initial stage of the optimization process, and there is no obvious mutation phenomenon in the later iterations.

[0130] The present invention also provides an isogeometric topology optimization design device, which includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the isogeometric topology optimization design method considering stress constraints as described above.

[0131] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the isogeometric topology optimization design method considering stress constraints as described above.

[0132] In summary, the isogeometric topology optimization design method considering stress constraints constructed by the present invention can rapidly reduce the structural stress level by adopting an improved stress vanishing constraint function, improving the optimization design efficiency. At the same time, the present invention uses the augmented Lagrangian function method to eliminate a large number of stress constraints in the original optimization model, avoiding the difficulty of solving, and finally obtaining the numerical solution of the original optimization model by continuously updating the Lagrange multiplier. In addition, the stable convergence of the optimization design is realized by adopting the unconstrained MMA algorithm with good stability and reasonably setting the optimization process control parameters.

[0133] It is easy for those skilled in the art to understand 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 replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An isogeometric topology optimization design method considering stress constraints, characterized in that, The method includes the following steps: (1) Replace the stress constraint condition in the isogeometric topology optimization design model of the structure to be optimized with an improved stress disappearance constraint function to obtain an improved topology optimization design model; the improved stress disappearance constraint function is: Among them, m E,a (ρ) is the Young's modulus at the evaluation point a; represents the von Mises stress at the evaluation point a, and σ lim is the stress constraint value, and N c refers to the total number of stress evaluation points; (2) Use the augmented Lagrangian function method to construct an approximate model of the improved topology optimization design model, and then deduce and calculate the sensitivity information of the approximate model; (3) Implement iterative update of the design variables of the approximate model using the unconstrained MMA algorithm based on the obtained sensitivity information. After every N l times of design variable update, update the Lagrange multiplier once based on the KKT conditions until the optimization design result of the approximate model converges, and then perform isogeometric topology optimization design of the structure using the current approximate model; where N l > 1; The expression of the approximate model is: where s is the slack variable, λ a and μ are both Lagrange multipliers, h a (ρ) is the stress constraint after introducing the slack variable; ρ is the optimization design variable; m V (ρ) is the structural density field; s a is the slack variable.

2. The isogeometric topology optimization design method considering stress constraints as described in claim 1, wherein: Before step (1), there is also a step of constructing an isogeometric topology optimization design model of the structure to be optimized with the minimum material usage as the goal and the von Mises stress at the structural evaluation point as the constraint.

3. The isogeometric topology optimization design method considering stress constraints according to claim 2, characterized in that: Optimize the correspondence between the design variable ρ and the structural density field m V (ρ) and the Young's modulus field m E (ρ) is as follows: ρ = [ρ 1,1 … ρ i,j … ρ n,m ​ m E (ρ) = E min + (E0 - E min )[m V (ρ)] p where, i and j represent the control point numbers in the directions of the parametric coordinates ξ and η, and ρ i,j represents the design variable corresponding to the control points numbered i and j, represents the NURBS basis function corresponding to the control points numbered i and j, and r and q respectively refer to the orders of the basis functions in the directions of ξ and η; refers to the design variable after threshold projection processing, and n and m respectively represent the total numbers of control points in the directions of ξ and η; E0 refers to the Young's modulus of the solid material, and E min is the set minimum Young's modulus; p is a penalty coefficient greater than 1, set to 3.

5.

4. The isogeometric topology optimization design method considering stress constraints according to claim 3, characterized in that: The expression of the isogeometric topology optimization design model is: where K is the structural stiffness matrix, U is the control point displacement vector, and F is the external load; represents the von Mises stress at the evaluation point a, and σ lim is the stress constraint value, N c refers to the total number of stress evaluation points.

5. The isogeometric topology optimization design method considering stress constraints according to claim 4, characterized in that: The expression of the improved topology optimization design model is:

6. The isogeometric topology optimization design method considering stress constraints according to claim 1, wherein: h a (ρ) = g a (ρ) + s a Lagrange multipliers λ a and the update rules for μ are respectively as follows: μ k+1 = αμ k , α > 1 where k represents the number of iterations of the Lagrange multiplier, and α is a set update coefficient.

7. An isogeometric topology optimization design device, characterized in that: The device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the isogeometric topology optimization design method considering stress constraints according to any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, and when the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the isogeometric topology optimization design method considering stress constraints according to any one of claims 1-6.

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