Thin-walled structure topology optimization design method and device, system and storage medium

Abstract

The application discloses a thin-wall structure topology optimization design method and device, system and storage medium, and comprises the following steps: calculating the density of any unit in the design domain according to a structure topology optimization model; calculating a displacement vector according to the density of any unit in the design domain, a total stiffness matrix and an external load vector; calculating structure flexibility according to a unit stiffness matrix and the displacement vector; obtaining the sensitivity of a target function and a constraint function to a design variable according to the unit density and the structure flexibility; establishing a topology optimization model by taking the minimization of the structure flexibility as the target function, taking the welding point area as the constraint condition and taking the normalized height as the design variable; and updating and iterating the design variable by using the MMA algorithm according to the sensitivity of the target function and the constraint function to the design variable and the topology optimization model, so as to obtain an optimized structure. By adopting the technical scheme, the structure with excellent mechanical properties can be obtained under the premise of meeting the process constraint of superplastic forming technology.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of structural optimization design, and particularly relates to a thin-walled structure topology optimization design method and device, system and storage medium. BACKGROUND

[0002] With the rapid development of aerospace, automobile manufacturing, medical devices and high-end equipment manufacturing industry, lightweight design has become the core direction to improve product performance, reduce energy consumption and enhance competitiveness. Lightweight design not only reduces material consumption and manufacturing cost, but also significantly improves energy efficiency. However, traditional manufacturing processes face many challenges in preparing complex lightweight structures, and a large amount of material is wasted. Therefore, an advanced manufacturing technology that can balance high precision, high material utilization rate and complex geometric forming capability is urgently needed.

[0003] Superplastic forming is an advanced forming process based on the superplastic behavior of metals. Superplasticity refers to the abnormal high ductility of certain fine-grained metal materials at a specific temperature and extremely low strain rate, which enables the formation of complex thin-walled structures that cannot be achieved by traditional processes. Compared with traditional manufacturing processes, superplastic forming can achieve near-net shaping through single gas pressurization forming, with a material utilization rate of more than 90%. Currently, this technology has been widely used in aerospace, automotive and medical fields.

[0004] However, the existing superplastic forming technology still has some limitations. The structures prepared must meet the process constraints of this technology. Therefore, in lightweight design, how to consider the process constraints is a key factor to ensure the manufacturability and forming quality of the structure, but there is currently no lightweight design scheme considering the process constraints of superplastic forming. SUMMARY

[0005] The technical problem to be solved by the application is to provide a thin-walled structure topology optimization design method and device, system and storage medium, which can obtain a structure with excellent mechanical properties under the premise of meeting the process constraints of superplastic forming technology.

[0006] To achieve the above-mentioned purpose, the application adopts the following technical solution:

[0007] A thin-walled structure topology optimization design method, comprising:

[0008] Constructing a structure topology optimization model oriented to superplastic forming technology;

[0009] Calculating the density of any element in the design domain according to the structure topology optimization model;

[0010] Calculating the displacement vector according to the density of any element in the design domain, the overall stiffness matrix and the external load vector;

[0011] According to the unit stiffness matrix and the displacement vector, the structural flexibility is calculated;

[0012] According to the unit density and the structural flexibility, the sensitivity of the design variable to the objective function and the constraint function is obtained;

[0013] A topology optimization model is established by taking the minimum structural flexibility as the objective function, taking the weld point area as the constraint condition, and taking the normalized height as the design variable.

[0014] According to the sensitivity of the design variable to the objective function and the constraint function and the topology optimization model, the design variable is updated and iterated by using the MMA algorithm to obtain the optimized structure.

[0015] The application also provides a thin-walled structure topology optimization design device, comprising:

[0016] The first processing module is used to construct a structure topology optimization model facing the superplastic forming technology.

[0017] The second processing module is used to calculate the density of any unit in the design domain according to the structure topology optimization model.

[0018] The third processing module is used to calculate the displacement vector according to the density of any unit in the design domain, the overall stiffness matrix and the external load vector.

[0019] The fourth processing module is used to calculate the structural flexibility according to the unit stiffness matrix and the displacement vector.

[0020] The fifth processing module is used to obtain the sensitivity of the design variable to the objective function and the constraint function according to the unit density and the structural flexibility.

[0021] The sixth processing module is used to establish a topology optimization model by taking the minimum structural flexibility as the objective function, taking the weld point area as the constraint condition, and taking the normalized height as the design variable.

[0022] The seventh processing module is used to obtain the optimized structure by updating and iterating the design variable by using the MMA algorithm according to the sensitivity of the design variable to the objective function and the constraint function and the topology optimization model.

[0023] The application also provides a thin-walled structure topology optimization design system, comprising a memory and a processor, wherein the memory stores a computer program run by the processor, and the computer program executes the thin-walled structure topology optimization design method when run by the processor.

[0024] The application also provides a storage medium, wherein the storage medium stores a computer program, and the computer program executes the thin-walled structure topology optimization design method when run.

[0025] The present application firstly establishes a thin-walled structure topology description method meeting the superplastic forming process constraints based on the Heaviside function, and determines the design variables and establishes the corresponding mathematical optimization formula based on the same; the sensitivities of the objective function and the constraint function to the design variables are derived based on the constructed optimization formula, which is the basis of the gradient optimization algorithm; the MMA gradient optimization algorithm is used for step-by-step iteration, and finally the structure with high mechanical properties which meets the superplastic forming process constraints (including volume constraint and weld area constraint) can be prepared. BRIEF DESCRIPTION OF DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only a part of the embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0027] Figure 1 The flow chart of the thin-walled structure topology optimization design method of the embodiments of the present application;

[0028] Figure 2 The optimization model and boundary conditions;

[0029] Figure 3 The design variable structure diagram;

[0030] Figure 4 Different values of the Heaviside function;

[0031] Figure 5 The stiffened thin-walled structure;

[0032] Figure 6 The superplastic forming thin-walled structure; wherein (a) w is the superplastic forming optimization result, and (b) is the cross-sectional view of the optimization result. DETAILED DESCRIPTION

[0033] The technical solutions of the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0034] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail with reference to the drawings and specific embodiments.

[0035] Embodiment 1:

[0036] As Figure 1 shown, the embodiment of the present application provides a thin-walled structure topology optimization design method, comprising:

[0037] Step 1: Construct a structure topology optimization model oriented to superplastic forming technology, the domain of which is a cuboid, and define the boundary conditions as: the degrees of freedom of the four corner points on the lower surface are completely fixed in three directions, and a vertical downward load is applied at the center of the upper surface. In order to improve the optimization stability, the elements near the load and constraint nodes are selected as the non-design domain, and the remaining part is selected as the design domain.

[0038] Further, a cuboid domain with a size of 1.28m×1.28m×0.64m is established, as Figure 2 shown, the selected regular hexahedral element domain is subjected to finite element meshing, the element size is 0.02m, the number of mesh elements is 64*64*32, the thicknesses of the superplastic forming deformable blank and the fixed substrate blank are both set to 0.08m, and the design variable is the height of the deformable blank neutral surface from the structure bottom surface , The number of elements in the plane within the domain.

[0039] Step 2: As Figure 3 shown, the normalized height of the center of any element within the domain is defined as , wherein is the actual height of the element center, is the total height of the domain, is the normalized height of the deformable blank neutral surface.

[0040] According to the design variable, the density of any element within the design domain can be obtained , and the relationship between the two is:

[0041] (1.1)

[0042] wherein, is the thickness of the superplastic forming deformable blank, is the Heaviside function used for continuous, and its expression is

[0043] (1.2)

[0044] wherein, the parameter determines the smoothness of the Heaviside function, the larger the value, the closer the function value is to 0-1 distribution, as Figure 4 shown. Through numerical testing, the initial value of can be defined as 1, and increased by 1 every 20 steps.

[0045] Step 3: Calculate the element stiffness matrix Assemble the global stiffness matrix using the SIMP method commonly used in the field of topology optimization Apply typical simply supported plate load boundary conditions to obtain the external load vector F Finally, the displacement vector U can be obtained according to equation (1.3),

[0046] (1.3)

[0047] Step 4: According to the element stiffness matrix and the displacement vector U obtained by solving, the objective function, i.e. the structural flexibility c, can be calculated,

[0048] (1.4)

[0049] Step 5: Superplastic forming process requires the structure to meet the local connectivity requirement, which can make the material bulge along the predetermined path during the forming process, forming a lightweight high-strength hollow or rib plate integrated structure. In order to make the designed structure meet the above process requirements, the weld point area constraint is constructed, that is,

[0050] (1.5)

[0051] where, is the total number of elements in the deformable blank that are in contact with the base plate blank, is the element volume, is the required weld point area proportion of the contact surface, is the total volume of the elements above the contact surface, is the element density in the deformable blank that is in contact with the base plate blank.

[0052] Step 6: According to (1.1), the derivative of the element density with respect to the design variable is obtained:

[0053] (1.6)

[0054] where, is the vertical height.

[0055] According to formula (1.4), the sensitivity of the objective function flexibility c to the element density is obtained:

[0056] (1.7)

[0057] According to the chain rule, the sensitivity of the objective function to the design variable is obtained:

[0058] (1.8)

[0059] The sensitivity of the constraint function to the design variable can be obtained at the same time:

[0060] ;

[0061] Step 7: The final topology optimization expression is established, taking the structural flexibility c as the objective function, taking the welding point area as the constraint condition, and taking the normalized height as the design variable The topology optimization model is established as follows:

[0062] (1.9)

[0063] Step 8: According to the sensitivity of the design variable to the objective function and the constraint function and the topology optimization model calculated in step 6, the design variable is updated and iterated by using the MMA algorithm, and finally the optimized structure is obtained, and the three-dimensional model is shown in Figure 5 and Figure 6 .

[0064] It can be seen from Figure 5 and Figure 6 and the final objective function value that the flexibility of the superplastic forming thin-walled structure obtained by the post-optimization is 9.3642, and the flexibility of the stiffened thin-walled structure obtained by the optimization is 12.778, compared with the thin-walled structure prepared by the superplastic forming process under the same material consumption, the stiffness is greater, as shown in Table 1.

[0065] Table 1

[0066]

[0067] Example 2:

[0068] The embodiment of the application also provides a thin-walled structure topology optimization design device, comprising:

[0069] The first processing module is used for constructing a structure topology optimization model facing the superplastic forming technology;

[0070] The second processing module is used for calculating the density of any unit in the design domain according to the structure topology optimization model;

[0071] The third processing module is used for calculating the displacement vector according to the density of any unit in the design domain, the overall stiffness matrix and the external load vector;

[0072] The fourth processing module is used for calculating the structural flexibility according to the unit stiffness matrix and the displacement vector;

[0073] The fifth processing module is used for obtaining the sensitivity of the design variable to the objective function and the constraint function according to the unit density and the structural flexibility;

[0074] The sixth processing module is used to establish a topology optimization model with a structural flexibility as an objective function, a solder area as a constraint condition, and a normalized height as a design variable;

[0075] The seventh processing module is used to update and iterate the design variable by using the MMA algorithm according to the sensitivity of the design variable to the objective function and the constraint function and the topology optimization model, so as to obtain an optimized structure.

[0076] Embodiment 3:

[0077] The embodiment of the present application also provides a thin-walled structure topology optimization design system, comprising a memory and a processor, the memory stores a computer program run by the processor, and the computer program executes the thin-walled structure topology optimization design method when run by the processor.

[0078] Embodiment 4:

[0079] The embodiment of the present application also provides a storage medium, which stores a computer program, and the computer program executes the thin-walled structure topology optimization design method when run.

[0080] The above-described embodiments are only descriptions of the preferred modes of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those skilled in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. A thin-walled structure topology optimization design method, characterized by, The method comprises the following steps: constructing a structural topology optimization model for superplastic forming technology; calculating the density of any unit in the design domain according to the structural topology optimization model; calculating a displacement vector according to the density of any unit in the design domain, the global stiffness matrix and the external load vector; calculating the structural flexibility according to the unit stiffness matrix and the displacement vector; obtaining the sensitivity of the target function and the constraint function to the design variable according to the unit density and the structural flexibility; establishing a topology optimization model by taking the minimum structural flexibility as the target function, taking the welding point area as the constraint condition and taking the normalized height as the design variable; updating and iterating the design variable by using the MMA algorithm according to the sensitivity of the target function and the constraint function to the design variable and the topology optimization model, and obtaining the optimized structure; the constraint g of the welding point area, i.e. ； wherein, is the total number of cells in the deformable blank in contact with the substrate blank, is the cell volume, is the proportion of the contact surface that is required to be the pad area, is the total volume of cells in the layer above the contact surface, is the cell density in the deformable blank in contact with the substrate blank; Cell density Sensitivity to design variables: ； wherein, is the vertical direction height; is the normalized height of the center of any unit within the domain; Objective function compliance c sensitivity to cell density of the cell density: ； wherein, is the unit stiffness matrix; the sensitivity of the target function to the design variable is obtained according to the chain rule: ； the sensitivity of the constraint function to the design variable is also obtained: ； Taking the minimum structural compliance c as the objective function, taking the weld point area as the constraint condition, and taking the design variable as The topology optimization model is established as follows: ； where c is the minimization structure flexibility, F is the external load vector ， U is the displacement vector.

2. A thin-walled structure topology optimization design device that implements the thin-walled structure topology optimization design method according to claim 1, characterized by The method comprises the following steps: a first processing module is configured to construct a structural topology optimization model for superplastic forming technology; a second processing module is configured to calculate the density of any unit in the design domain according to the structural topology optimization model; a third processing module is configured to calculate a displacement vector according to the density of any unit in the design domain, the global stiffness matrix and the external load vector; a fourth processing module is configured to calculate the structural flexibility according to the unit stiffness matrix and the displacement vector; a fifth processing module is configured to obtain the sensitivity of the target function and the constraint function to the design variable according to the unit density and the structural flexibility; a sixth processing module is configured to establish a topology optimization model by taking the minimum structural flexibility as the target function, taking the welding point area as the constraint condition and taking the normalized height as the design variable; a seventh processing module is configured to update and iterate the design variable by using the MMA algorithm according to the sensitivity of the target function and the constraint function to the design variable and the topology optimization model, and obtain the optimized structure.

3. A thin-walled structure topology optimization design system characterized by, The method comprises the following steps: a memory and a processor, wherein the memory stores a computer program which is run by the processor, and the computer program performs the thin-walled structure topology optimization design method according to claim 1 when being run by the processor.

4. A storage medium, characterized by The storage medium stores a computer program which performs the thin-walled structure topology optimization design method according to claim 1 when being run.

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