Topological optimization design method and system for spherical pressure-resistant structure of deep-sea manned submersible vehicle

Abstract

The invention provides a topological optimization design method and system for a spherical pressure-resistant structure of a deep-sea manned submersible vehicle. The method comprises the steps that S1, a level set function is initialized, a spherical structure contour and a structure area are defined, and material parameters are determined; s2, constructing a topological optimization model which takes a structural shape as a design variable, takes volume minimization of a current material as an optimization target, and takes a K-S polymerization equation value of a buckling factor reciprocal of a first four-order characteristic value of the structure as an optimization constraint; s3, on the basis of the level set function, the spherical structure contour, the structure area and the material parameters, an updated level set function is obtained on the basis of the topological optimization model; and S3, repeatedly triggering the step S3 until the difference of the volume fractions obtained by two continuous iterative calculations is smaller than a preset value, obtaining a current level set function, and outputting the optimized spherical pressure-resistant structural form according to the current level set function.

Description

Technical Field

[0001] This invention relates to the field of spherical pressure-resistant structure design technology for deep-sea manned submersibles, specifically to a topology optimization design method and system for spherical pressure-resistant structures of deep-sea manned submersibles. Background Technology

[0002] As core equipment for deep-sea exploration and operations, the pressure-resistant structure of manned submersibles is crucial for ensuring the safety of personnel and equipment. Spherical structures, due to their superior mechanical properties under uniform deep-water pressure, have become the mainstream design choice for the pressure-resistant structures of deep-sea manned submersibles. However, traditional design methods rely heavily on engineering experience and homogeneous shell theory, making it difficult to achieve optimal matching of material distribution and structural performance under extreme weight constraints. Topology optimization, as an advanced and innovative design method, can intelligently seek the optimal material layout path under given design space, load, and constraints, providing a key technical means to overcome the bottlenecks of traditional design.

[0003] Patent document CN110217336B (application number: 201910625573.6) discloses a pressure-resistant structure for a deep-sea submersible, which is a composite structure. It includes an inner shell, an outer shell, a left flange, and a right flange. The inner shell is the main load-bearing structure, formed by winding the inner shell around the left and right flanges. The outer shell is made of rolled titanium alloy plate and welded longitudinally, tightly fitting the inner shell's annular ribs. The outer shell is then connected to the left and right flanges via annular welds at both ends. The inner shell uses a cylindrical structure with an outer annular rib, with the ribs evenly spaced. The specific spacing is optimized according to the minimum stress criterion for pressure-resistant structures under external pressure. The inner and outer shells are connected by butt-joint annular welds, which only bear tensile and compressive forces, resulting in a simple stress distribution. However, it does not consider optimizing the pressure-resistant structure for practical use with lightweight design as a goal.

[0004] Therefore, it is necessary to propose a topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible. This method applies topology optimization to the spherical pressure-resistant structure, achieving lightweight design while ensuring the ultimate load-bearing capacity meets requirements. This provides strong support for the optimized design of the spherical pressure-resistant structure of a deep-sea manned submersible. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a topology optimization design method and system for a spherical pressure-resistant structure of a deep-sea manned submersible.

[0006] A topology optimization design method for a spherical pressure-resistant structure of a deep-sea manned submersible, provided by the present invention, includes: Step S1: Initialize the level set function, define the spherical structure profile, structural region, and determine the material parameters; Step S2: Construct a topology optimization model with structural shape as the design variable, minimizing the volume of the current material as the optimization objective, and establishing the KS aggregation equation as the optimization constraint with the inverse of the buckling factor of the first four eigenvalues ​​of the structure. Step S3: Based on the level set function, spherical structure profile, structural region, and material parameters, obtain the updated level set function based on the topology optimization model; repeat step S3 until the difference between the volume fractions calculated in two consecutive iterations is less than the preset value, obtain the current level set function, and output the optimized spherical pressure-resistant structure form according to the current level set function.

[0007] Preferably, the topology optimization model in step S2 includes:

[0008] in, For the design domain, For the volume of the structure, For the displacement field of the structure, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, v This represents the virtual displacement of the structure. Represents the structural displacement field. This is the Neumann boundary, i.e., the boundary where the load is applied; KS polymerization equation For the first i The reciprocal of the first-order eigenvalue buckling factor. n It is 4. The parameters in the KS aggregation equation are used to make the result of KS aggregation approximate the reciprocal of the first-order buckling factor. ; This is a yield constraint.

[0009] Preferably, step S3 includes: Step S3.1: Under the current level set function and force, calculate the reciprocal of the buckling factor and the volume fraction of the first four eigenvalues ​​of the structure; Step S3.2: Calculate the shape derivative and Lagrange operator of the current objective function and optimization constraints. Solve the velocity field based on the calculation results and evolve a new level set function. Repeat steps S3.1 to S3.2 until the difference between the volume fractions calculated in two consecutive iterations is less than the preset value. Output the updated level set function. Step S3.3: Obtain the optimized spherical pressure-resistant structure form based on the updated level set function.

[0010] Preferably, the reciprocals of the buckling factors of the first four eigenvalues ​​of the structure in step S3.1 include:

[0011] in, For the design domain, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, , It is the mode after the structure undergoes eigenvalue buckling.

[0012] Preferably, step S3.2 includes: The evolution formula for the level set function based on the Hamilton-Jacobi equation is shown below:

[0013] in, , Given a set of known CSRBF radial basis functions, Representative at Always interpolation coefficients; For gradient operators; This is a regularization term used to control excessive differentiation of the internal structure during the optimization process; The velocity field controls the deformation of the structure during the optimization process; Velocity field obtained based on shape derivative theory The expression is as follows:

[0014] in, G The expression is as follows:

[0015] in, n It is 4. Represents the eigenvalue vector after regularization; the accompanying variable of the inverse of the eigenvalue buckling factor. It can be obtained from the following formula: where h These are the extreme points of the Lagrange function corresponding to the topology optimization model;

[0016] in, For Dirac functions, To augment the Lagrange operator;

[0017]

[0018] in, Values ​​greater than 5 These are the values ​​of the buckling constraint terms under the initial design. For fixed parameters, This is the current iteration step; For the iteration steps in which the Lagrange operator undergoes transformation, The value of the buckling constraint term in the current iteration step; It is calculated by the following formula: ; in, for During the optimization process, the increment changes. for The upper limit of the possible values.

[0019] Preferably, the method further includes: performing ultimate load-bearing capacity calculations on the obtained spherical pressure-resistant structure using finite element analysis software to verify the effectiveness of the lightweight topology optimization results.

[0020] A topology optimization design system for a spherical pressure-resistant structure of a deep-sea manned submersible, according to the present invention, includes: Module M1: Initializes the level set function, defines the spherical structure profile, structural regions, and determines material parameters; Module M2: Construct a topology optimization model with structural shape as the design variable, minimizing the volume of the current material as the optimization objective, and establishing KS aggregation equations with the inverse of the buckling factor of the first four eigenvalues ​​of the structure as optimization constraints. Module M3: Based on the level set function, spherical structure profile, structural region and material parameters, the updated level set function is obtained based on the topology optimization model; Module M3 is triggered repeatedly until the difference between the volume fractions calculated in two consecutive iterations is less than the preset value, the current level set function is obtained, and the optimized spherical pressure-resistant structure form is output according to the current level set function.

[0021] Preferably, the topology optimization model in module M2 includes:

[0022] in, For the design domain, For the volume of the structure, For the displacement field of the structure, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, v This represents the virtual displacement of the structure. Represents the structural displacement field. This is the Neumann boundary, i.e., the boundary where the load is applied; KS polymerization equation For the first i The reciprocal of the first-order eigenvalue buckling factor. n It is 4. The parameters in the KS aggregation equation are used to make the result of KS aggregation approximate the reciprocal of the first-order buckling factor. ; This is a yield constraint.

[0023] Preferably, the module M3 includes: Module M3.1: Under the current level set function and force, calculate the reciprocal of the buckling factor and the volume fraction of the first four eigenvalues ​​of the structure; Module M3.2: Calculates the shape derivative and Lagrange operator of the current objective function and optimization constraints, solves the velocity field based on the calculation results and evolves to obtain a new level set function, and repeatedly triggers modules M3.1 to M3.2 until the difference between the volume fractions calculated in two consecutive iterations is less than the preset value, and outputs the updated level set function; Module M3.3: Obtains the optimized spherical pressure-resistant structure form based on the updated level set function.

[0024] Preferably, the reciprocals of the buckling factors of the first four eigenvalues ​​of the structure in module M3.1 include:

[0025] in, For the design domain, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, , It is the mode after the structure undergoes eigenvalue buckling; The module M3.2 includes: The evolution formula for the level set function based on the Hamilton-Jacobi equation is shown below:

[0026] in, , Given a set of known CSRBF radial basis functions, Representative at Always interpolation coefficients; For gradient operators; This is a regularization term used to control excessive differentiation of the internal structure during the optimization process; The velocity field controls the deformation of the structure during the optimization process; Velocity field obtained based on shape derivative theory The expression is as follows:

[0027] in, G The expression is as follows:

[0028] in, n It is 4. Represents the eigenvalue vector after regularization; the accompanying variable of the inverse of the eigenvalue buckling factor. It can be obtained from the following formula: where h These are the extreme points of the Lagrange function corresponding to the topology optimization model;

[0029] in, For Dirac functions, To augment the Lagrange operator;

[0030]

[0031] in, Values ​​greater than 5 These are the values ​​of the buckling constraint terms under the initial design. For fixed parameters, This is the current iteration step; For the iteration steps in which the Lagrange operator undergoes transformation, The value of the buckling constraint term in the current iteration step; It is calculated by the following formula: ; in, for During the optimization process, the increment changes. for The upper limit of the possible values.

[0032] Compared with the prior art, the present invention has the following beneficial effects: 1. Based on the topology optimization method of parameterized level set, this invention realizes the accurate expression of the ring rib inward stabilization topology and the collaborative optimization of the pressure-resistant structure's shape and internal configuration, and realizes the lightweight design of the spherical pressure-resistant structure of the deep-sea manned submersible; 2. The method of this invention breaks through the limitations of traditional empirical design of spherical pressure-resistant structures for deep-sea manned submersibles, and obtains a spherical pressure-resistant structure design scheme with low sensitivity to geometric defects and meeting multiple requirements for strength and stability. Attached Figure Description

[0033] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 Flowchart of the topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible.

[0034] Figure 2 This is a schematic diagram of the design area and boundary conditions.

[0035] Figure 3 This is a schematic diagram of the topology optimization design results for a spherical pressure-resistant structure.

[0036] Figure 4 The graph shows the changes in the volume fraction during the optimization process of the spherical pressure-resistant structure.

[0037] Figure 5 This is a graph showing the variation of the load proportionality coefficient for a spherical pressure-resistant structure. Detailed Implementation

[0038] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0039] Example 1 According to the present invention, a topology optimization design method for a spherical pressure-resistant structure of a deep-sea manned submersible is provided, such as... Figure 1 As shown, the specific steps include the following: Step S1: Initialize the level set function; Specifically, step S1 includes: initializing the level set function, defining the spherical structure profile and structural region, and determining material parameters, algorithm parameters, and boundary conditions. A set of radial basis functions is input and interpolated onto the level set function to obtain the interpolation coefficients of the radial basis functions.

[0040] Step S2: Construct a topology optimization mathematical model; Specifically, step S2 includes: constructing a topology optimization model with structural shape as the design variable, minimizing material volume as the optimization objective, and establishing KS aggregation equations with the reciprocals of the buckling factors of the first four eigenvalues ​​of the structure as optimization constraints.

[0041] The structure, considering the KS aggregation equation with the reciprocals of the buckling factors of the first four eigenvalues ​​as constraints, has the following expression for the topology optimization model that minimizes the volume fraction:

[0042] In the formula, For the design domain, For the displacement field of the structure, For the pressure on the Neumann boundary, Represents the volume of the structure. The eigenvalue representing the reciprocal of the buckling factor of the structure. The parameters in the KS aggregation equation are used to make the result of KS aggregation approximate the reciprocal of the first-order buckling factor. . This is a yield constraint.

[0043] Step S3: Calculate the reciprocal of the eigenvalue buckling factor of the structure; Specifically, step S3 includes: calculating the reciprocals of the first four eigenvalue buckling factors of the structure under the current level set function and force. The reciprocals of the eigenvalue buckling factors of the structure. It can be obtained from the following formula: .

[0044] Step S4: Evolve the level set function; Specifically, step S4 includes: calculating the shape derivatives of the current objective function and the optimization constraints, as well as the Lagrange operator; solving the velocity field based on the calculation results and evolving a new level set function; and updating the interpolation coefficients before the radial basis function.

[0045] The evolution formula for the level set function based on the Hamilton-Jacobi equation is shown below:

[0046] In the formula, , Given a set of known CSRBF radial basis functions, Representative at Always The interpolation coefficients. This is a regularization term used to control excessive differentiation of the internal structure during the optimization process. The velocity field controls the deformation of the structure during the optimization process.

[0047] Furthermore, the velocity field is obtained based on the shape derivative theory. The expression is as follows:

[0048] In the formula, For Dirac functions, To augment the Lagrange operator, it can be calculated using the following formulas:

[0049]

[0050] In the formula, Values ​​greater than 5 These are the values ​​of the buckling constraint terms under the initial design. For fixed parameters, It is calculated by the following formula:

[0051] In the formula, for During the optimization process, the increment changes. for The upper limit of the possible values.

[0052] Step S5: Determine convergence; if not satisfied, return to S3; otherwise, terminate. Specifically, step S5 includes: determining convergence; if the convergence condition is met, outputting the lightweight topology optimization result; otherwise, returning to step S3.

[0053] Step S6: Perform ultimate load calculation to verify the effectiveness of the structure.

[0054] Specifically, step S6 includes: performing ultimate load calculations using finite element analysis software to verify the effectiveness of the optimized design.

[0055] This invention also provides a topology optimization design system for a spherical pressure-resistant structure of a deep-sea manned submersible. The topology optimization design system for the spherical pressure-resistant structure of a deep-sea manned submersible can be implemented by executing the process steps of the topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible. That is, those skilled in the art can understand the topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible as a preferred embodiment of the topology optimization design system for the spherical pressure-resistant structure of a deep-sea manned submersible.

[0056] Example 2 Example 2 is a preferred example of Example 1. In the design of spherical pressure-resistant structures, the structure is subjected to external hydrostatic pressure. This invention provides a three-dimensional calculation example of a pressure-resistant spherical structure under water pressure to illustrate the effectiveness of this method.

[0057] Step 1: Initialize the level set function. The design region and boundary conditions of the example are determined by... Figure 2As shown, the design region is a spherical shell with an outer diameter of 60 cm and a thickness of 2 cm. The structure is constrained at both ends, with the y and z directions fixed; it is also constrained at the top, with the x and z directions fixed. It is subjected to a hydrostatic pressure of 20 MPa. The design region is discretized into 180° segments using eight-node isoparametric spatial elements of unit length, width, and height. 120 A finite element mesh of size 5 was used. The structural material used in this example is titanium alloy with an elastic modulus of 114 GPa and a Poisson's ratio of 0.33. A set of CSRBF radial basis functions was used to interpolate the level set functions, thus obtaining the interpolation coefficients of the radial basis functions. CSRBF radial basis functions. The formula is

[0058] in, , For structural design area, The support radius of the radial basis functions. Refers to a sample point within the design area. It is a sufficiently small constant, and here it takes the value of .

[0059] Step 2: Construct a topology optimization model with structural shape as the design variable, minimizing material volume as the optimization objective, and establishing KS aggregation equations with the reciprocals of the buckling factors of the first four eigenvalues ​​of the structure as optimization constraints.

[0060] Furthermore, considering the KS aggregation equations of the reciprocals of the buckling factors of the first four eigenvalues ​​as constraints, the expression for the topology optimization model that minimizes the volume fraction is:

[0061] In the formula, For the design domain, For the displacement field of the structure, For the pressure on the Neumann boundary, Represents the volume of the structure. The eigenvalue representing the reciprocal of the buckling factor of the structure. The parameter in the KS aggregation equation is set to 100, so that the result of KS aggregation approaches the reciprocal of the first-order buckling factor. . As a yield constraint, it is set to 0.5.

[0062] Specifically, step S3 includes: calculating the reciprocals of the first four eigenvalue buckling factors of the structure under the current level set function and force. The reciprocals of the eigenvalue buckling factors of the structure. It can be obtained from the following formula:

[0063] Specifically, step S4 includes: calculating the shape derivatives of the current objective function and the optimization constraints, as well as the Lagrange operator; solving the velocity field based on the calculation results and evolving a new level set function; and updating the interpolation coefficients before the radial basis function.

[0064] The evolution formula for the level set function based on the Hamilton-Jacobi equation is shown below:

[0065] In the formula, , Given a set of known CSRBF radial basis functions, Representative at Always The interpolation coefficients. This is a regularization term used to control excessive differentiation of the internal structure during the optimization process. The velocity field controls the deformation of the structure during the optimization process.

[0066] Furthermore, the velocity field is obtained based on the shape derivative theory. The expression is as follows:

[0067] In the formula, For Dirac functions, To augment the Lagrange operator, it can be calculated using the following formulas:

[0068]

[0069] In the formula, The value is 5. These are the values ​​of the buckling constraint terms under the initial design. As a fixed parameter, it is set to 10. It is calculated by the following formula:

[0070] In the formula, for During the optimization process, the increment changes. for The upper limit of the possible values.

[0071] Specifically, step S5 includes: determining convergence; if the convergence condition is met, outputting the lightweight topology optimization result; otherwise, returning to S3.

[0072] Step S6: Use Abaqus to calculate the ultimate bearing capacity of the spherical pressure-resistant structure, with the load taken as 400 MPa. Figure 3 The optimal stability results for the spherical pressure shell structure are demonstrated. As can be seen from the results, the structure obtained by the method of this invention has smooth internal boundaries and can automatically generate ribs during the optimization process.

[0073] The volume fraction change curve of the structure during the lightweight optimization process is as follows: Figure 4 As shown in the figure. Because this invention uses the augmented Lagrange operator, the index, as shown in the figure, gradually stabilizes during oscillations until it converges. From Figure 4 The optimization process diagram shows that when the KS aggregation equation value is considered as a constraint based on the reciprocal of the buckling factor of the first four eigenvalues ​​of the structure, the volume fraction of the structure first increases and then stabilizes and converges, achieving the lightweight design objective that meets the requirements of strength and stability.

[0074] Finally, Abaqus was used to calculate the ultimate bearing capacity of the spherical pressure-resistant structure, with a load of 400 MPa. The resulting load proportioning factor diagram is shown below. Figure 5 As shown, the calculated ultimate bearing capacity of the spherical pressure-resistant structure obtained by the present invention is 20.8 MPa, which meets the design bearing requirements.

[0075] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0076] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A topology optimization design method for a spherical pressure-resistant structure of a deep-sea manned submersible, characterized in that, include: Step S1: Initialize the level set function, define the spherical structure profile, structural region, and determine the material parameters; Step S2: Construct a topology optimization model with structural shape as the design variable, minimizing the volume of the current material as the optimization objective, and establishing the KS aggregation equation as the optimization constraint with the inverse of the buckling factor of the first four eigenvalues ​​of the structure. Step S3: Based on the level set function, spherical structure profile, structural region, and material parameters, obtain the updated level set function using a topology optimization model; Repeat step S3 until the difference between the volume fractions calculated in two consecutive iterations is less than a preset value. Obtain the current level set function and output the optimized spherical pressure-resistant structure form based on the current level set function.

2. The topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 1, characterized in that, The topology optimization model in step S2 includes: in, For the design domain, For the volume of the structure, For the displacement field of the structure, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, v This represents the virtual displacement of the structure. Represents the structural displacement field. This is the Neumann boundary, i.e., the boundary where the load is applied; KS aggregation equation For the first i The reciprocal of the first-order eigenvalue buckling factor. n It is 4. The parameters in the KS aggregation equation are used to make the result of KS aggregation approximate the reciprocal of the first-order buckling factor. ; This is a yield constraint.

3. The topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 1, characterized in that, Step S3 includes: Step S3.1: Under the current level set function and force, calculate the reciprocal of the buckling factor and the volume fraction of the first four eigenvalues ​​of the structure; Step S3.2: Calculate the shape derivative and Lagrange operator of the current objective function and optimization constraints. Solve the velocity field based on the calculation results and evolve a new level set function. Repeat steps S3.1 to S3.2 until the difference between the volume fractions calculated in two consecutive iterations is less than the preset value. Output the updated level set function. Step S3.3: Obtain the optimized spherical pressure-resistant structure form based on the updated level set function.

4. The topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 3, characterized in that, The inverse of the buckling factor of the first four eigenvalues ​​of the structure in step S3.1 includes: in, For the design domain, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, , It is the mode after the structure undergoes eigenvalue buckling.

5. The topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 3, characterized in that, Step S3.2 includes: The evolution formula for the level set function based on the Hamilton-Jacobi equation is shown below: in, , Given a set of known CSRBF radial basis functions, Representative at Always interpolation coefficients; For gradient operators; This is a regularization term used to control excessive differentiation of the internal structure during the optimization process; The velocity field controls the deformation of the structure during the optimization process; Velocity field obtained based on shape derivative theory The expression is as follows: in, G The expression is as follows: in, n It is 4. Represents the eigenvalue vector after regularization; the accompanying variable of the inverse of the eigenvalue buckling factor. It can be obtained from the following formula: where h These are the extreme points of the Lagrange function corresponding to the topology optimization model; in, For Dirac functions, To augment the Lagrange operator; in, Values ​​greater than 5 These are the values ​​of the buckling constraint terms under the initial design. For fixed parameters, This is the current iteration step; For the iteration steps in which the Lagrange operator undergoes transformation, The value of the buckling constraint term in the current iteration step; It is calculated by the following formula: ； in, for During the optimization process, the increment changes. for The upper limit of the possible values.

6. The topology optimization design method for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 1, characterized in that, The method further includes: performing ultimate load-bearing capacity calculations on the obtained spherical pressure-resistant structure using finite element analysis software to verify the effectiveness of the lightweight topology optimization results.

7. A topology optimization design system for a spherical pressure-resistant structure of a deep-sea manned submersible, characterized in that, include: Module M1: Initializes the level set function, defines the spherical structure profile, structural regions, and determines material parameters; Module M2: Construct a topology optimization model with structural shape as the design variable, minimizing the volume of the current material as the optimization objective, and establishing KS aggregation equations with the inverse of the buckling factor of the first four eigenvalues ​​of the structure as optimization constraints. Module M3: Based on the level set function, spherical structure profile, structural region, and material parameters, the updated level set function is obtained based on the topology optimization model; Repeatedly trigger module M3 until the difference between the volume fractions calculated in two consecutive iterations is less than a preset value, obtain the current level set function, and output the optimized spherical pressure-resistant structure form based on the current level set function.

8. The topology optimization design system for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 7, characterized in that, The topology optimization model in module M2 includes: in, For the design domain, For the volume of the structure, For the displacement field of the structure, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, v This represents the virtual displacement of the structure. Represents the structural displacement field. This is the Neumann boundary, i.e., the boundary where the load is applied; KS aggregation equation For the first i The reciprocal of the first-order eigenvalue buckling factor. n It is 4. The parameters in the KS aggregation equation are used to make the result of KS aggregation approximate the reciprocal of the first-order buckling factor. ; This is a yield constraint.

9. The topology optimization design system for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 7, characterized in that, The module M3 includes: Module M3.1: Under the current level set function and force, calculate the reciprocal of the buckling factor and the volume fraction of the first four eigenvalues ​​of the structure; Module M3.2: Calculates the shape derivative and Lagrange operator of the current objective function and optimization constraints, solves the velocity field based on the calculation results and evolves to obtain a new level set function, and repeatedly triggers modules M3.1 to M3.2 until the difference between the volume fractions calculated in two consecutive iterations is less than the preset value, and outputs the updated level set function; Module M3.3: Obtains the optimized spherical pressure-resistant structure form based on the updated level set function.

10. The topology optimization design system for the spherical pressure-resistant structure of a deep-sea manned submersible according to claim 9, characterized in that, The inverse of the buckling factor of the first four eigenvalues ​​of the structure in module M3.1 includes: in, For the design domain, A This represents the elastic constitutive relation matrix corresponding to Hooke's law. e Represents the strain operator, u For structural displacement, , It is the mode after the structure undergoes eigenvalue buckling; The module M3.2 includes: The evolution formula for the level set function based on the Hamilton-Jacobi equation is shown below: in, , Given a set of known CSRBF radial basis functions, Representative at Always interpolation coefficients; For gradient operators; This is a regularization term used to control excessive differentiation of the internal structure during the optimization process; The velocity field controls the deformation of the structure during the optimization process; Velocity field obtained based on shape derivative theory The expression is as follows: in, G The expression is as follows: in, n It is 4. Represents the eigenvalue vector after regularization; the accompanying variable of the inverse of the eigenvalue buckling factor. It can be obtained from the following formula: where h These are the extreme points of the Lagrange function corresponding to the topology optimization model; in, For Dirac functions, To augment the Lagrange operator; in, Values ​​greater than 5 These are the values ​​of the buckling constraint terms under the initial design. For fixed parameters, This is the current iteration step; For the iteration steps in which the Lagrange operator undergoes transformation, The value of the buckling constraint term in the current iteration step; It is calculated by the following formula: ； in, for During the optimization process, the increment changes. for The upper limit of the possible values.

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