Meshless structure topological optimization method based on mobile boundary technology

Abstract

The invention provides a meshless structure topological optimization method based on a mobile boundary technology. The method relates to the technical field of structural topological optimization. The method comprises the following steps: combining a non-uniform rational B-spline with a global weak meshless method, describing a problem domain boundary by using a non-uniform rational B-spline curve, constructing a moving boundary meshless through a background grid differencing technology, and constructing a problem domain stiffness matrix; and carrying out structure topological optimization by taking the minimum structure flexibility as an objective function, taking the condition that the volume ratio is smaller than a set value as a constraint condition and taking the control point coordinates of the non-uniform rational B-spline as design variables. According to the method, the optimization efficiency and precision can be improved, the structure topology closer to the practical application is obtained, the application of complex constraint conditions is facilitated, and the engineering practical requirements are met.

Description

Technical Field

[0001] This application relates to the technical field of structural topology optimization, and particularly to a meshless structural topology optimization method based on the moving boundary technology. Background Art

[0002] In the field of structural topology optimization, the traditional finite element method has certain limitations when dealing with problems that require remeshing, such as large deformations, crack propagation, topology optimization, and adaptive analysis. The finite element method discretizes numerical problems by dividing a complex continuous geometric body into a finite number of elements and connecting them to form a mesh topology structure. Its calculation accuracy is greatly affected by the mesh quality. For complex 3D problems, it is difficult and costly to manually divide qualified finite element meshes. During topology optimization, it is difficult for finite element meshes to adaptively change to obtain high-quality hexahedral meshes, resulting in a decrease in calculation efficiency and accuracy. At the same time, existing structural topology optimization methods, such as the variable density method, have numerical problems such as checkerboards, gray-scale elements, mesh dependence, and local optimal solutions, and additional techniques need to be introduced to eliminate these unstable phenomena; although the level set method has clear optimization result boundaries, it has problems such as low solution efficiency and the need to continuously initialize the level set function. Summary of the Invention

[0003] This application provides a meshless structural topology optimization method based on the moving boundary technology, aiming to solve the problems of strong mesh dependence, low calculation efficiency, and unsatisfactory optimization results existing in existing structural topology optimization methods when dealing with complex problems, thereby improving the optimization efficiency and accuracy, obtaining a structural topology closer to actual applications, facilitating the imposition of complex constraint conditions, and meeting the actual needs of engineering.

[0004] In a first aspect, this application provides a meshless structural topology optimization method based on the moving boundary technology, including:

[0005] Combining non-uniform rational B-splines with the global weak form meshless method, using non-uniform rational B-spline curves to describe the problem domain boundary, constructing a moving boundary meshless through the background mesh subtraction technique, and constructing the stiffness matrix of the problem domain;

[0006] Taking the minimum structural compliance as the objective function, the volume ratio less than a set value as the constraint condition, and the control point coordinates of non-uniform rational B-splines as the design variables for structural topology optimization.

[0007] In a possible design, combining non-uniform rational B-splines with the global weak form meshless method, using non-uniform rational B-spline curves to describe the problem domain boundary, constructing a moving boundary meshless through the background mesh subtraction technique, and constructing the stiffness matrix of the problem domain, includes:

[0008] The boundary of the problem domain and the background grid are described by non-uniform rational B-spline curves, and the background grid is divided using mixed triangular elements;

[0009] For the problem of hole boundary change, by pre-dividing the background grid of the problem domain, describing the hole boundary with non-uniform rational B-spline curves, using the homotopy mapping method to quickly generate the background grid of the hole region, integrating the initial problem domain background grid and the hole region background grid respectively and then taking the difference set to construct the stiffness matrix of the problem domain.

[0010] In a possible design, taking the minimum structural compliance as the objective function, the volume ratio being less than a set value as the constraint condition, and the control point coordinates of the non-uniform rational B-spline as the design variables for structural topology optimization, including:

[0011] Initialize the design variables and the problem domain, and give the initial values of the moving step design variables corresponding to the variable boundary control points of the problem domain and the initial values of the additional design variables;

[0012] Construct the GCMMA solution form of the topology optimization problem, define the objective function as the minimum structural compliance, and the constraint functions of the objective function include volume constraint, boundary constraint, etc.;

[0013] Use the moving boundary meshless method to calculate and analyze the problem domain to obtain the objective function value, constraint function value, and corresponding sensitivity information;

[0014] Construct and solve the dual problem of the GCMMA sub-problem, judge whether a new hole is generated according to the topological sensitivity of the field nodes, and if a new hole is generated, increase the number of design variables;

[0015] Judge whether the topology optimization converges by comparing the objective function values of the previous and current generations. The result converges when the change rate before and after is less than the set value.

[0016] In a possible design, the problem domain is initialized in the following way:

[0017] Generate spherical holes at predetermined positions, arrange the control points evenly, and determine the initial coordinates of the control points;

[0018] Based on the non-uniform rational B-spline surface calculation program, generate the actual boundary of the spherical hole and calculate the volume sensitivity of each control point.

[0019] In a second aspect, the present application provides a meshless structural topology optimization device based on the moving boundary technology, and the device includes:

[0020] A stiffness matrix construction module, configured to combine non-uniform rational B-splines with the global weak form meshless method, use non-uniform rational B-spline curves to describe the boundary of the problem domain, construct a moving boundary meshless through the background grid difference technology, and construct the stiffness matrix of the problem domain;

[0021] A topology optimization module, configured to perform structural topology optimization with the minimum structural compliance as the objective function, the volume ratio less than a set value as the constraint condition, and the control point coordinates of non-uniform rational B-spline as the design variables.

[0022] In a possible design, the stiffness matrix construction module is further configured to:

[0023] Describe the boundary of the problem domain and the background mesh using non-uniform rational B-spline curves, and divide the background mesh using hybrid triangular elements;

[0024] For the problem of changing hole boundaries, by pre-dividing the background mesh of the problem domain, describing the hole boundaries using non-uniform rational B-spline curves, quickly generating the background mesh of the hole region using the homotopy mapping method, integrating the initial problem domain background mesh and the hole region background mesh respectively and then taking the difference set to construct the stiffness matrix of the problem domain.

[0025] In a possible design, the topology optimization module is further configured to:

[0026] Initialize the design variables and the problem domain, and give the initial values of the moving step design variables corresponding to the variable boundary control points of the problem domain and the initial values of the additional design variables;

[0027] Construct the GCMMA solution form of the topology optimization problem, define the objective function as the minimum structural compliance, and the constraint functions of the objective function include volume constraints, boundary constraints, etc.;

[0028] Use the moving boundary meshless method to perform computational analysis on the problem domain to obtain the objective function value, the constraint function value, and the corresponding sensitivity information;

[0029] Construct and solve the dual problem of the GCMMA sub-problem, judge whether to generate new holes according to the topological sensitivity of the field nodes, and if new holes are generated, increase the number of design variables;

[0030] Judge whether the topology optimization converges by comparing the objective function values of the previous and current generations. The result converges when the change rate before and after is less than the set value.

[0031] In a third aspect, an embodiment of the present application provides an electronic device, including: at least one processor and a memory; the memory stores computer-executable instructions; the at least one processor executes the computer-executable instructions stored in the memory, so that the at least one processor executes the meshless structural topology optimization method based on the moving boundary technology as described in the first aspect and various possible designs of the first aspect above.

[0032] Fourthly, an embodiment of the present application provides a computer-readable storage medium, in which computer-executable instructions are stored. When a processor executes the computer-executable instructions, the meshless structural topology optimization method based on the moving boundary technology described in the first aspect and various possible designs of the first aspect is implemented.

[0033] Fifthly, an embodiment of the present application provides a computer program product, including a computer program. When the computer program is executed by a processor, the meshless structural topology optimization method based on the moving boundary technology described in the first aspect and various possible designs of the first aspect is implemented.

[0034] The meshless structural topology optimization method based on the moving boundary technology provided by the present application has at least the following beneficial effects:

[0035] 1) High computational efficiency: Through the meshless method and the moving boundary technology, the problems of mesh generation and reconstruction in the traditional finite element method are avoided, and the computational efficiency is significantly improved;

[0036] 2) Strong adaptability: The moving boundary technology can adapt to the boundary movement problem and is applicable to the complex structure optimization of hypersonic vehicles;

[0037] 3) High accuracy: Through the globally convergent moving asymptote algorithm, the accuracy of the optimization result is ensured. Description of the Drawings

[0038] The drawings here are incorporated into the specification and form a part of the specification, showing the embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application.

[0039] Figure 1 It is a flowchart of a meshless structural topology optimization method based on the moving boundary technology provided by an embodiment of the present application;

[0040] Figure 2 It is a schematic diagram of the background grid difference principle provided by an embodiment of the present application;

[0041] Figure 3 It is a flowchart of the topology optimization of the moving boundary meshless method provided by an embodiment of the present application;

[0042] Figure 4 It is a schematic diagram of the geometric parameters of the rudder surface provided by an embodiment of the present application;

[0043] Figure 5 It is the optimization result of the variable density method after fairing provided by an embodiment of the present application;

[0044] Figure 6 It is a schematic diagram of the position of the center point of the topology optimization of the moving boundary meshless method provided by an embodiment of the present application;

[0045] Figure 7 This is the topology optimization result diagram of the moving boundary method provided by the embodiment of the present application;

[0046] Figure 8 This is the basic configuration diagram extracted from the optimization result provided by the embodiment of the present application;

[0047] Figure 9 This is the structural schematic diagram of a meshless structure topology optimization device based on the moving boundary technology provided by the embodiment of the present application.

[0048] Through the above-mentioned drawings, the specific embodiments of the present application have been shown, and there will be more detailed descriptions hereinafter. These drawings and textual descriptions are not intended to limit the scope of the concept of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by referring to specific embodiments. Detailed implementation manners

[0049] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all implementation manners consistent with the present application. On the contrary, they are merely examples of the devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0050] In the technical solution of the present application, the collection, storage, use, processing, transmission, provision, and disclosure of information such as financial data or user data comply with the provisions of relevant laws and regulations and do not violate public order and good customs.

[0051] It should be noted that in the embodiments of the present application, some industry-existing solutions such as certain software, components, models, etc. may be mentioned, and they should be considered exemplary. The purpose is only to illustrate the feasibility in the implementation of the technical solution of the present application, but it does not mean that the applicant has already or necessarily used this solution.

[0052] The following uses specific embodiments to describe in detail the technical solution of the present application and how the technical solution of the present application solves the above technical problems. These several specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below with reference to the drawings.

[0053] The embodiment of the present application provides a meshless structure topology optimization method based on the moving boundary technology, as Figure 1As shown in the figure, it is a flowchart of a meshless structural topology optimization method based on the moving boundary technology provided by an embodiment of the present application. The meshless structural topology optimization method based on the moving boundary technology includes the following steps S100 - S200.

[0054] S100: Combine non-uniform rational B-splines with the global weak-form meshless method. Use non-uniform rational B-spline curves to describe the problem domain boundary, construct a moving boundary meshless through the background mesh subtraction technique, and construct the stiffness matrix of the problem domain.

[0055] In this embodiment, the explanation of the global weak-form meshless method is as follows: The shape functions of the meshless method are based on the nodes in the local support domain and are independent of the mesh elements. Its solution accuracy is only closely related to the distribution and density of the nodes, thus avoiding the requirements for mesh quality. The global weak-form meshless method establishes the system equations of the problem through the global Galerkin weak form and the meshless shape functions.

[0056] In this embodiment, the method of combining non-uniform rational B-splines (NURBS) with the global weak-form meshless method is called the moving boundary meshless method. Specifically, use NURBS to describe the boundary and establish the moving boundary meshless method through the background mesh subtraction technique. Specifically, in the NURBS meshless method, use NURBS curves to describe the boundary of the problem domain and the background mesh, and use mixed triangular elements to divide the background mesh. For problems such as the change of hole boundaries, by pre-dividing the background mesh of the problem domain, using NURBS curves to describe the hole boundaries, using the homotopy mapping method to quickly generate the background mesh of the hole region, integrating the initial problem domain background mesh and the hole region background mesh respectively and then taking the difference set to efficiently construct the stiffness matrix of the problem domain.

[0057] Exemplarily, as Figure 2 shown, it is the schematic diagram of background mesh subtraction provided by an embodiment of the present application. Figure 2 In the figure, (a) represents the background mesh of the problem domain pre-divided based on isogeometric triangles, (b) represents the background mesh of the hole region divided based on the homotopy mapping method, (c) represents the equivalent problem domain corresponding to different hole regions, and the background mesh subtraction method is (a) - (b) = (c).

[0058] S200: Conduct structural topology optimization with the minimum structural compliance as the objective function, the volume ratio less than the set value as the constraint condition, and the control point coordinates of non-uniform rational B-splines as the design variables.

[0059] In this embodiment, step S200 is a topology optimization process that takes the control point coordinates of NURBS as variables and derives the derivatives of compliance and volume constraints with respect to the control point coordinates. The global convergence moving asymptote (GCMMA) optimization algorithm is combined for structural topology optimization. During the optimization process, the generation of new holes is judged based on topological sensitivity, and the interlacing of control points is avoided by restricting the moving direction and step size of the control points.

[0060] In an exemplary embodiment, as Figure 3 shown, it is the topology optimization flowchart of the moving boundary meshless method provided by the embodiment of the present application. The specific process of the moving boundary meshless method topology optimization can be as follows: First, initialize the design variables and the problem domain, and give the initial values of the moving step design variables corresponding to the variable boundary control points of the problem domain and the initial values of the additional design variables. Then construct the GCMMA solution form of the topology optimization problem, define the objective function as the minimum structural compliance, and the constraint functions include volume constraints and boundary constraints, etc. Next, use the moving boundary meshless method to calculate and analyze the problem domain to obtain the objective function value, constraint function value, and corresponding sensitivity information. Then construct and solve the dual problem of the GCMMA sub-problem, and judge whether to generate a new hole according to the topological sensitivity of the field nodes. If a new hole is generated, the number of design variables is increased. Finally, judge whether the topology optimization converges by comparing the objective function values of the previous and current generations. When the change rate before and after is less than the set value, the result converges.

[0061] Next, the embodiments of the present application will further illustrate the feasibility and progressiveness of the present application in combination with a specific case.

[0062] In the specific case provided by the present application, based on the geometric shape of the missile rudder surface, a structural finite element model is established. The geometric parameters of the rudder surface are as Figure 4 shown. The chord length at the root of the rudder surface is 740 mm, the chord length at the tip is 350 mm, the span is 265 mm, the leading edge sweep angle is 56°, and the maximum thickness of the rudder surface is d=(52 + 4×2) mm, where 4×2 mm represents the thickness of the upper and lower thermal protection layers and the heat insulation layer. First, optimize the model structure by the variable density method. In the moving boundary meshless method, the initial shape and the boundary of the optimization region do not change, and the optimization is the growth change process of internal holes. The internal holes are described by NURBS surfaces. In order to achieve uniform expansion of the holes, the initial shape of the holes is set as a sphere. First, evenly arrange control points on the surface of the sphere according to the parametric coordinates, and change the shape of the holes by calculating the moving step of the control points and calculating the new coordinates of the control points. The center position of the initial hole refers to the result of the topology optimization by the finite element method. After determining the center point coordinates, arrange control points around the center point and establish a spherical hole with an appropriate radius.

[0063] Please combine Figure 3 , the calculation process of this specific case is as follows:

[0064] Step 1. Initialize the problem domain: Calculate and store the initial stiffness matrix of the structure according to the requirements of the meshless method for reconstructing the stiffness matrix after generating holes.

[0065] Step 2. Initialize the design variables: Generate spherical holes at predetermined positions, uniformly arrange control points, and determine their initial coordinates. Call the NURBS surface calculation program to generate the actual boundary of the spherical holes. Calculate the volume sensitivity of each control point of the sphere. The processing results are as Figure 5 shown.

[0066] Step 3. Load calculation: Perform thermo-pneumatic elastic analysis on the new structure with added holes to update the optimized input load.

[0067] Step 4. Meshless method structural analysis with moving boundaries: Use the new flight load as the force boundary condition to calculate the deformation and compliance of the structure, and then obtain the shape sensitivity of the objective function.

[0068] Step 5. Combine the compliance sensitivity and volume sensitivity to determine the moving direction of all control points. The design variables are converted into the step lengths of each control point along the moving direction. Construct and solve the dual problem of GCMMA, and set the upper and lower limits of the design variables of the current sub-problem. Solve the dual problem to obtain the optimal moving step length and obtain the coordinates of the next generation of control points. The processing results are as Figure 6 shown.

[0069] Step 6. Topological optimization convergence judgment: Compare the structural compliance to determine whether the result converges or reaches the maximum number of iterations, and terminate the optimization process.

[0070] The final structural form of the rudder surface topological optimization is as Figure 7 shown. Based on the results of the topological optimization using the moving boundary meshless method, the structure tends to be an integral panel structure, retaining a relatively thick skin, with an internal honeycomb-like support structure. The support beams tend to be perpendicular to the ribs, which is beneficial to improving the structural stiffness. The basic configuration obtained according to the topological optimization results is as Figure 8 shown

[0071] This embodiment of the present application also provides a meshless structural topological optimization device based on the moving boundary technology, as Figure 9 shown. The meshless structural topological optimization device based on the moving boundary technology includes:

[0072] A stiffness matrix construction module 901, configured to combine non-uniform rational B-splines with the global weak form meshless method, use non-uniform rational B-spline curves to describe the problem domain boundary, construct a moving boundary meshless through the background grid difference technology, and construct the problem domain stiffness matrix;

[0073] The topology optimization module 902 is configured to perform structural topology optimization with minimum structural flexibility as the objective function, volume ratio less than a set value as the constraint condition, and control point coordinates of non-uniform rational B-spline as design variables.

[0074] In some embodiments, the stiffness matrix building module is further configured to:

[0075] The boundary and background mesh of the problem domain are described by using non-uniform rational B-spline curves, and the background mesh is divided by using hybrid triangle units.

[0076] For the problem of hole boundary changes, the problem domain background grid is pre-divided, the hole boundary is described by non-uniform rational B-spline curves, and the hole area background grid is quickly generated using the homotopy mapping method. The initial problem domain background grid and the hole area background grid are integrated respectively and the difference is calculated to construct the problem domain stiffness matrix.

[0077] In some embodiments, the topology optimization module is further configured to:

[0078] Initialize the design variables and problem domain, and give the initial values ​​of the moving step design variables and additional design variables corresponding to the variable boundary control points of the problem domain;

[0079] Constructing a GCMMA solution form for the topology optimization problem, defining the objective function as the minimum structural flexibility, and the constraint functions of the objective function include volume constraints and boundary constraints, etc.;

[0080] The moving boundary meshless method is used to calculate and analyze the problem domain to obtain the objective function value, constraint function value and corresponding sensitivity information;

[0081] Construct and solve the dual problem of the GCMMA subproblem, and determine whether to generate new holes based on the topological sensitivity of the field nodes. If new holes are generated, increase the number of design variables.

[0082] By comparing the objective function values ​​of the previous and next generations, it is judged whether the topology optimization has converged. The result converges when the rate of change between the previous and the next generations is less than the set value.

[0083] In some embodiments, the topology optimization module is further configured to initialize the problem domain in the following manner: generate a spherical hole according to a predetermined position, evenly arrange control points, and determine the initial coordinates of the control points; based on a non-uniform rational B-spline surface calculation program, generate the actual boundary of the spherical hole, and calculate the volume sensitivity of each control point.

[0084] An embodiment of the present application provides an electronic device, which may include: a processor and a memory, wherein the processor and the memory may communicate with each other; illustratively, the processor and the memory communicate with each other via a communication bus.

[0085] The processor executes the computer-executable instructions stored in the memory, enabling the processor to execute the solutions in the above embodiments. The processor can be a general-purpose processor, including a Central Processing Unit (CPU), a network processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0086] The communication bus can be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into an address bus, a data bus, a control bus, etc. The transceiver is used to implement communication between the database access device and other computers (such as clients, read-write libraries, and read-only libraries). The memory may include Random Access Memory (RAM), and may also include non-volatile memory.

[0087] The electronic device provided in the embodiments of the present application can be the terminal device in the above embodiments.

[0088] The embodiments of the present application also provide a computer-readable storage medium, in which computer instructions are stored. When the computer instructions run on a computer, the computer is enabled to execute the technical solutions of the meshless structural topology optimization method based on the moving boundary technology in the above embodiments.

[0089] The embodiments of the present application also provide a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium, and when at least one processor executes the computer program, the technical solutions of the meshless structural topology optimization method based on the moving boundary technology in the above embodiments can be implemented.

[0090] In several embodiments provided by the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections between each other can be indirect couplings or communication connections through some interfaces, devices or modules, and can be in electrical, mechanical or other forms.

[0091] The modules described as separate components may or may not be physically separated. The components shown as modules may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to implement the solution of this embodiment.

[0092] In addition, each functional module in various embodiments of the present application can be integrated in a processing unit, or each module can exist physically alone, or two or more modules can be integrated in one unit. The units formed by the above modules can be implemented in the form of hardware or in the form of a combination of hardware and software functional units.

[0093] The integrated modules implemented in the form of software functional modules can be stored in a computer-readable storage medium. The above software functional modules are stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods in various embodiments of the present application.

[0094] It should be understood that the above processor can be a Central Processing Unit (CPU for short), or other general-purpose processors, Digital Signal Processors (DSP for short), Application Specific Integrated Circuits (ASIC for short), etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in combination with the invention can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

[0095] The memory may include high-speed RAM memory and may also include non-volatile storage NVM, such as at least one disk memory, and can also be a USB flash drive, a mobile hard disk, a read-only memory, a magnetic disk or an optical disc, etc.

[0096] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0097] The above storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, a magnetic disk or an optical disc. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0098] An exemplary storage medium is coupled to the processor, enabling the processor to read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an Application Specific Integrated Circuits (ASIC). Of course, the processor and the storage medium can also exist as discrete components in an electronic control unit or a master control device.

[0099] Those of ordinary skill in the art can understand that all or part of the steps to implement the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps including the above method embodiments; and the foregoing storage medium includes: various media such as ROM, RAM, a magnetic disk or an optical disc that can store program codes.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A meshless structure topology optimization method based on moving boundary technology, characterized in that: The method comprises: The non-uniform rational B-spline is combined with the global weak meshless method, the boundary of the problem domain is described by the non-uniform rational B-spline curve, the moving boundary meshless method is constructed by the background grid difference technology, and the stiffness matrix of the problem domain is constructed; Structural topology optimization is carried out with the minimum structural flexibility as the objective function, the volume ratio less than the set value as the constraint condition, and the control point coordinates of the non-uniform rational B-spline as the design variables.

2. The meshless structure topology optimization method based on moving boundary technology according to claim 1 is characterized in that: The non-uniform rational B-spline is combined with the global weak meshless method, and the boundary of the problem domain is described by the non-uniform rational B-spline curve. The moving boundary meshless method is constructed by the background grid difference technology, and the problem domain stiffness matrix is ​​constructed, including: The boundary and background mesh of the problem domain are described by using non-uniform rational B-spline curves, and the background mesh is divided by using hybrid triangle units. For the problem of hole boundary changes, the problem domain background grid is pre-divided, the hole boundary is described by non-uniform rational B-spline curves, and the hole area background grid is quickly generated using the homotopy mapping method. The initial problem domain background grid and the hole area background grid are integrated respectively and the difference is calculated to construct the problem domain stiffness matrix.

3. The meshless structure topology optimization method based on moving boundary technology according to claim 1 is characterized in that: The structural topology optimization is carried out with the minimum structural flexibility as the objective function, the volume ratio less than the set value as the constraint condition, and the control point coordinates of the non-uniform rational B-spline as the design variables, including: Initialize the design variables and problem domain, and give the initial values ​​of the moving step design variables and additional design variables corresponding to the variable boundary control points of the problem domain; Constructing a GCMMA solution form for the topology optimization problem, defining the objective function as the minimum structural flexibility, and the constraint functions of the objective function include volume constraints and boundary constraints, etc.; The moving boundary meshless method is used to calculate and analyze the problem domain to obtain the objective function value, constraint function value and corresponding sensitivity information; Construct and solve the dual problem of the GCMMA subproblem, and determine whether to generate new holes based on the topological sensitivity of the field nodes. If new holes are generated, increase the number of design variables. By comparing the objective function values ​​of the previous and next generations, it is judged whether the topology optimization has converged. The result converges when the rate of change between the previous and the next generations is less than the set value.

4. The meshless structure topology optimization method based on moving boundary technology according to claim 1 is characterized in that: Initialize the problem domain as follows: Generate spherical holes according to the predetermined positions, evenly arrange the control points, and determine the initial coordinates of the control points; Based on the non-uniform rational B-spline surface calculation program, the actual boundary of the spherical hole is generated, and the volume sensitivity of each control point is calculated.

5. A meshless structure topology optimization device based on moving boundary technology, characterized in that: The device comprises: A stiffness matrix construction module is configured to combine non-uniform rational B-spline with global weak meshless method, use non-uniform rational B-spline curve to describe the boundary of the problem domain, construct the moving boundary meshless by background mesh difference technology, and construct the stiffness matrix of the problem domain; The topology optimization module is configured to perform structural topology optimization with the minimum structural flexibility as the objective function, the volume ratio being less than the set value as the constraint condition, and the control point coordinates of the non-uniform rational B-spline as the design variables.

6. The meshless structure topology optimization method based on moving boundary technology according to claim 5 is characterized in that: The stiffness matrix building block is further configured as: The boundary and background mesh of the problem domain are described by using non-uniform rational B-spline curves, and the background mesh is divided by using hybrid triangle units. For the problem of hole boundary changes, the problem domain background grid is pre-divided, the hole boundary is described by non-uniform rational B-spline curves, and the hole area background grid is quickly generated using the homotopy mapping method. The initial problem domain background grid and the hole area background grid are integrated respectively and the difference is calculated to construct the problem domain stiffness matrix.

7. The meshless structure topology optimization method based on moving boundary technology according to claim 5 is characterized in that: The topology optimization module is further configured to: Initialize the design variables and problem domain, and give the initial values ​​of the moving step design variables and additional design variables corresponding to the variable boundary control points of the problem domain; Constructing a GCMMA solution form for the topology optimization problem, defining the objective function as the minimum structural flexibility, and the constraint functions of the objective function include volume constraints and boundary constraints, etc.; The moving boundary meshless method is used to calculate and analyze the problem domain to obtain the objective function value, constraint function value and corresponding sensitivity information; Construct and solve the dual problem of the GCMMA subproblem, and determine whether to generate new holes based on the topological sensitivity of the field nodes. If new holes are generated, increase the number of design variables. By comparing the objective function values ​​of the previous and next generations, it is judged whether the topology optimization has converged. The result converges when the rate of change between the previous and the next generations is less than the set value.

8. An electronic device, characterized in that: include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory to implement the meshless structure topology optimization method based on the moving boundary technology as described in any one of claims 1 to 4.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the meshless structure topology optimization method based on the moving boundary technology as described in any one of claims 1 to 4.

10. A computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the method for meshless structure topology optimization based on moving boundary technology as claimed in any one of claims 1 to 4 is implemented.

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