A method for topology optimization of ribbed cylinder for spinning-additive hybrid manufacturing

Abstract

The application discloses a kind of topological optimization methods for spinning-additive composite manufacturing of ribbed cylinder, it is related to structural design field, including: definition design area and non-design area, set the physical property parameter of material;Initialization design variable;Introduce size constraint method, calculate the background physical density of rib, to meet the spinning manufacturing size requirement;Design variable is mapped as the spinning and additive design variable of rib;Carry out statics analysis and linear buckling analysis, obtain each order linear buckling factor and buckling mode;The design response of each cylinder structure is calculated, and sensitivity is analyzed;Solve topological optimization model, obtain design variable and skin thickness;Post-processing is carried out to optimization result, and the cylinder structure after optimization is established.The application can be used for the high inner rib cylinder design of spinning-additive composite manufacturing, give full play to design freedom, reasonably distribute rib layout, rib spinning and additive forming part, obtain the thin-walled ribbed cylinder structure of lightweight, high bearing performance.

Description

Technical Field

[0001] The present invention relates to the field of structural design, and in particular to a topology optimization method for a ribbed cylinder for spinning-additive composite manufacturing. Background Art

[0002] The structural performance of ribbed thin-walled cylinders is affected by design parameters such as skin thickness, rib layout, and rib height. Optimizing these parameters can significantly improve their mechanical properties and lightweighting. Existing designs for ribbed thin-walled cylinders often feature uniform, regular layouts such as orthogonal, oblique, orthogonal, or equilateral triangles. This design method, which pre-defines the rib layout, significantly limits the structural design space, resulting in large design margins and insufficient lightweighting. Topology optimization, on the other hand, is a structural design method driven by functional requirements and simulation. It determines the availability of material point by point, maximizing structural performance within given constraints. Combining topology optimization technology with thin-walled cylinder structural design can avoid the design capability limitations imposed by pre-determining the rib layout, exploring as many novel rib configurations as possible within the design space, and ultimately resulting in a lightweight ribbed thin-walled cylinder structure with excellent mechanical properties.

[0003] Spinning is a manufacturing process in which a hollow cylinder is fixed on the die of a spinning machine. When the cylinder rotates with the spindle of the machine tool, a rotating wheel is used to pressurize the cylinder material to produce local plastic deformation. Figure 2 As shown. This process has the advantages of small forming load, high processing precision, and high material utilization rate. It can be used not only for the processing of smooth-walled cylindrical components, but also for the integrated forming and manufacturing of thin-walled cylindrical parts with internal ribs, meeting the lightweight manufacturing needs of high-performance components on aerospace equipment. Compared with the traditional forming method of forging cylinder blank + milling, the use of spinning manufacturing process to process the cylinder can avoid the waste of a large amount of material being removed, long-term machining leading to low production efficiency, metal streamlines being cut off to reduce component strength, and residual stress rebalancing caused by machining leading to poor shape accuracy. However, due to the limitations of the spinning process, the rib forming height is limited. On the basis of the spinning cylinder, through the additive manufacturing process (such as Figure 3 The high-rib or local boss structure can be formed by breaking through the limitation of the forming capability of the spinning process and obtaining a high-rib thin-walled cylindrical structure that can be manufactured by spinning-additive composite.

[0004] Therefore, technicians in this field are committed to developing a topology optimization method for ribbed cylinders for spinning-additive composite manufacturing. Summary of the Invention

[0005] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is that the existing design method of reinforced cylinder based on engineering experience pre-determines the reinforcement layout, which has the problems of limited design space and insufficient lightweightness.

[0006] To achieve the above objectives, the present invention provides a topology optimization method for a ribbed cylinder for spinning-additive composite manufacturing. The method optimizes the topology design of a ribbed thin-walled cylinder for spinning-additive composite manufacturing. The method comprises the following steps:

[0007] S101: For the ribbed thin-walled cylinder to be designed, define a design area and a non-design area, and set material physical parameters;

[0008] S103: Initializing design variables, wherein the design variables include a design variable indirectly indicating the presence or absence of rib material and a design variable indicating the design height of the rib;

[0009] S105: introducing a size constraint method to calculate the background physical density of the ribs so that the ribs meet the size requirements of spinning manufacturing;

[0010] S107: Mapping the background physical density design variable and the rib height design variable into the rib spinning design variable and the additive design variable;

[0011] S109: Perform static analysis and linear buckling analysis on the reinforced thin-walled cylinder structure to obtain the linear buckling factors and buckling modes of each order;

[0012] S111: Calculate the design responses of a reinforced thin-walled cylindrical structure and analyze the sensitivity of each design response to the design variables.

[0013] S113: Solve the topology optimization model through an iterative optimization algorithm to obtain updated design variables and skin thickness;

[0014] S115: Post-processing the optimization results, and establishing an optimized structure of the ribbed thin-walled cylinder based on the post-processing results.

[0015] Furthermore, in step S101, when defining the design area and the non-design area, the area of ​​the ribbed thin-walled cylinder is discretized using a finite element mesh, and the area where the skin is located is defined as the skin design domain, the area to be reinforced is defined as the rib design domain, and the upper and lower end frames are defined as the rib non-design domain.

[0016] Furthermore, in step S103, when initializing the design variable that indirectly indicates the presence or absence of rib material, the following rules are followed:

[0017] If the background element i belongs to a non-design domain that must have ribs, the component of the design variable of the element is initialized to 1;

[0018] If the background element i belongs to a non-design domain where reinforcement arrangement is not allowed, the components of the design variables of the element are initialized to 0 and remain unchanged in subsequent optimization iterations;

[0019] The rib design variables in the rest of the design domain are between 0 and 1.

[0020] Furthermore, in step S103, when initializing the design variable representing the rib design height, the design variable is normalized so that the design variable is between 0 and 1, and the design variable is set to the ratio of the rib height to the total height of the radial unit.

[0021] Furthermore, in step S105, the design variable indirectly indicating the presence or absence of a unit rib is converted into a background physical density directly indicating the presence or absence of the unit rib through density filtering and projection methods. The background physical density naturally meets the requirements of spinning manufacturing for the minimum size, minimum spacing, and maximum size of the rib in terms of distribution mathematics, and the background physical density is converted into the contour rib physical density of the corresponding unit on the cylinder. The contour rib physical density and the background physical density satisfy a linear mapping relationship:

[0022]

[0023] in, is the physical density of the equal-height reinforcement of a unit on the cylinder, is the background physical density representing the presence or absence of reinforcement in a unit, L is the mapping matrix, and m and n are the number of units.

[0024] Furthermore, in step S107, a parametric design model of a spinning-additive cylinder is constructed based on the maximum spinning height representation model, and the portion of the rib design variable field in the design model where the rib height is greater than the maximum spinning height is manufactured using an additive process;

[0025] The rib spinning design variables are:

[0026]

[0027] The rib additive design variables are:

[0028] ρ a =max(ρ-ρ s ,0);

[0029] in,

[0030]

[0031] In the above formula, is the maximum rib height, ρ is the rib physical density field, physical density of the constant-height rib of a certain unit on the cylinder, unit density of the cylinder structure, denotes a set of units with a distance not exceeding d / 2 from unit e, d is a distance parameter, x i , x e are coordinates of unit i and unit e, tanh is the hyperbolic tangent function, β is a projection parameter steepness, which controls the clarity of the grid boundary, η ij is a projection threshold value, which is equal to the normalized coordinate value of the jth unit in the rib height direction corresponding to the ith background grid, Ω is the rib design domain.

[0032] Further, in the step S109, in the statics analysis, the following statics equation is used:

[0033] KU = F;

[0034] In the linear buckling analysis, the following finite element simulation formula is used:

[0035]

[0036] where K is the elastic stiffness matrix of the cylinder structure, U is the node displacement vector, F is the load vector, G is the geometric stiffness matrix, which is related to the node displacement vector U, λ i (i = 1, 2, …, k) is each linear buckling factor, is the corresponding buckling mode, and k is the number of buckling modes.

[0037] Further, in the step S111, when analyzing the sensitivity of each design response to the design variable p, the chain rule is used to calculate the sensitivity of each design response to the design variable p, and the chain rule is:

[0038]

[0039] where μ is a design variable representing the presence or absence of a rib, h is a design variable representing the design height of the rib, i, j, and k are unit numbers, and n is the number of units.

[0040] Further, in the step S113, the topology optimization model to be solved is:

[0041]

[0042] where μ is a design variable representing the presence or absence of a rib, h is a design variable representing the design height of the rib, T add is the skin thickness, V is the total volume of the cylinder, λ1 is the first-order buckling factor, and λ * is the expected value of the first-order buckling factor.

[0043] Furthermore, in step S115, when post-processing the optimization result, if the value of the background physical variable indicating whether the unit i has a structure is greater than a preset threshold, the background physical variable is set to 1, otherwise it is set to 0;

[0044] The optimized skin thickness is: t = t0 + T add , y0 is the initial thickness of the skin.

[0045] In a preferred embodiment of the present invention, compared with the prior art, the present invention has the following beneficial technical effects:

[0046] 1. This invention introduces a background density mapping method to obtain rib characteristics, establishes a linear buckling simulation model for the cylinder and buckling constraints, achieves buckling stability control, and combines it with an optimization algorithm to achieve lightweight improvement. The cylinder structure designed by the proposed method can achieve a lightweight rib layout design for thin-walled cylinders with ribs while ensuring buckling stability, avoiding the problem of large design margins in traditional methods.

[0047] 2. The present invention introduces a dimensional constraint method based on the characteristics of the spinning process to control the maximum spinning height of the rib, which can meet the rib height requirements during spinning manufacturing, thereby avoiding problems such as difficulty in manufacturing the spinning mold and insufficient rib filling.

[0048] 3. According to the maximum spinning height, the present invention represents the ribs as spinning and additive parts, expresses the mechanical properties of the two parts respectively, and establishes a parametric expression model of the geometry and mechanical properties of the cylinder, which can meet the constraints of the spinning process, while giving full play to the advantages of spinning-additive manufacturing, expanding the design optimization space, and designing and manufacturing a lighter, better-performing high-internal-rib cylinder structure.

[0049] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a cylinder topology optimization method according to an embodiment of the present invention;

[0051] Figure 2 It is a schematic diagram of the spinning process of a thin-walled cylinder with ribs in the prior art;

[0052] Figure 3 Schematic diagram of the high internal reinforcement additive manufacturing process in the prior art;

[0053] Figure 4 Schematic diagram of the design domain and non-design domain of an embodiment of the present invention;

[0054] Figure 5 Schematic diagram of a parametric expression model of a high-inner-rib cylinder according to an embodiment of the present invention;

[0055] Figure 6 Schematic diagram of a method for generating cylindrical rib features according to an embodiment of the present invention;

[0056] Figure 7 is a function of mapping the rib height variable to the discretized unit height in an embodiment of the present invention;

[0057] Figure 8 A flowchart of a method optimization process according to an embodiment of the present invention;

[0058] Figure 9 This is the post-processing result of the optimization model according to the embodiment of the present invention;

[0059] Figure 10 This is the solution result of the optimization model of the embodiment of the present invention and the corresponding optimized cylinder structure.

[0060] The descriptions of the numbers in the figure are as follows:

[0061] 1- mandrel, 2- sheet, 3- rotating wheel, 4- reinforced area, 5- non-reinforced area. DETAILED DESCRIPTION

[0062] The following describes several preferred embodiments of the present invention with reference to the accompanying drawings to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0063] In the drawings, components with identical structures are denoted by the same reference numerals, and components with similar structures or functions are denoted by similar reference numerals. The size and thickness of each component shown in the drawings are arbitrary and are not limited by the present invention. For clarity, the thickness of components in some places in the drawings is appropriately exaggerated.

[0064] like Figure 1 As shown, the present invention proposes a topology optimization method for ribbed cylinders for spinning-additive composite manufacturing, which can be used for the lightweight design of high-internal-ribbed cylinders manufactured by spinning-additive composite manufacturing. Compared with the traditional casting-machining production of ribbed cylinders, spinning-additive composite manufacturing has the advantages of lower material removal rate and higher processing efficiency; compared with the processing method of welding ribs on the skin, it reduces welds and improves structural reliability. Specifically, the topology optimization method for ribbed cylinders for spinning-additive composite manufacturing proposed in an embodiment of the present invention includes the following steps:

[0065] S1: For the ribbed thin-walled cylinder to be designed, define the design area and non-design area, and set the material physical properties.

[0066] For the thin-walled reinforced cylindrical structure to be designed, the design and non-design regions are defined using a finite element mesh. The skin region is defined as the skin design domain, the region to be reinforced is defined as the rib design domain, and the upper and lower end frames are defined as the rib non-design domain. Material properties are set, including Young's modulus and Poisson's ratio.

[0067] S2: Initialize the design variables, which include the design variables that indirectly indicate whether there is rib material and the design variables that indicate the rib design height.

[0068] When initializing the design variables that indirectly represent the presence or absence of rib material, follow the following rules:

[0069] 1) If the background element i belongs to the non-design domain where ribs are required, the components of the element’s design variables are initialized to 1;

[0070] 2) If the background element i belongs to the non-design domain where reinforcement is not allowed, the components of the element's design variables are initialized to 0 and remain unchanged in subsequent optimization iterations;

[0071] 3) The rib design variables in the remaining design domains are between 0 and 1.

[0072] When initializing the design variable representing the rib design height, the design variable is normalized so that the design variable is between 0 and 1, and the design variable is set to the ratio of the rib height to the total height of the radial unit.

[0073] S3: Introduce the size constraint method to calculate the background physical density of the ribs so that the ribs meet the size requirements of spinning manufacturing.

[0074] Through density filtering and projection methods, the design variables that indirectly indicate the presence or absence of ribs in a certain unit are converted into background physical density that directly indicates the presence or absence of ribs in the unit. The background physical density naturally meets the requirements of spinning manufacturing for the minimum size, minimum spacing, and maximum size of ribs in terms of distribution mathematics. The background physical density is also converted into the physical density of the contour ribs of the corresponding unit on the cylinder. The contour rib physical density and the background physical density satisfy a linear mapping relationship:

[0075]

[0076] in, is the physical density of the equal-height reinforcement of a unit on the cylinder, is the background physical density representing the presence or absence of a certain unit reinforcement, L is the mapping matrix, m, n are the number of units. If the density of the jth background unit is mapped to the i-th unit of the cylindrical structure, then L ij =1, otherwise 0.

[0077] S4: Map the background physical density design variables and rib height design variables into the rib spinning design variables and additive design variables.

[0078] Based on the maximum spinnable height representation model, a parametric design model for the spinning-additive cylinder was constructed. Parts of the rib design variable field in the design model with a rib height greater than the maximum spinnable height were manufactured using additive manufacturing.

[0079] The design variables for rib spinning are:

[0080]

[0081] The rib additive design variables are:

[0082] ρ a =max(ρ-ρ s ,0);

[0083] in,

[0084]

[0085] In the above formula, is the maximum rib height, ρ is the rib physical density field, is the physical density of the equal-height reinforcement of a unit on the cylinder, is the unit density of the cylindrical structure, Represents a set of units whose distance from unit e does not exceed d / 2, where d is the distance parameter and x i , x e are the coordinates of unit i and unit e, tanh is the hyperbolic tangent function, β is the projection parameter steepness, which controls the clarity of the grid boundary, and η ij is the projection threshold, which is equal to the normalized coordinate value of the jth element corresponding to the i-th background grid in the rib height direction, and Ω is the rib design domain.

[0086] S5: Perform static analysis and linear buckling analysis on the reinforced thin-walled cylinder structure to obtain the linear buckling factors and buckling modes of each order.

[0087] In static analysis, the following static equations are used:

[0088] KU=F;

[0089] In the linear buckling analysis, the following finite element simulation formula is used:

[0090]

[0091] Among them, K is the elastic stiffness matrix of the cylindrical structure, U is the node displacement vector, F is the load vector, G is the geometric stiffness matrix, which is related to the node displacement vector U, λi (i=1,2,…,k) are the linear buckling factors, is the corresponding buckling mode, and k is the number of buckling modes.

[0092] S6: Calculate the various design responses of the reinforced thin-walled cylindrical structure and analyze the sensitivity of each design response to the design variables.

[0093] When analyzing the sensitivity of each design response to the design variable ρ, the chain rule is used to calculate the sensitivity of each design response to the design variable ρ. The chain rule is:

[0094]

[0095] Among them, μ is the design variable indicating whether there is rib material, h is the design variable indicating the design height of the rib, i, j, k are the unit numbers, and n is the number of units.

[0096] S7: Solve the topology optimization model through an iterative optimization algorithm to obtain updated design variables and skin thickness.

[0097] The solved topology optimization model is:

[0098]

[0099] Among them, μ is the design variable indicating whether there is rib material, h is the design variable indicating the rib design height, T add is the skin thickness, V is the total volume of the cylinder, λ1 is the first-order buckling factor, λ * is the expected value of the first-order buckling factor.

[0100] S8: Post-process the optimization results and establish the optimized ribbed thin-walled cylinder structure based on the post-processing results.

[0101] When post-processing the optimization results, if the value of the background physical variable indicating whether unit i has a structure is greater than a preset threshold, the background physical variable is set to 1, otherwise it is set to 0;

[0102] The optimized skin thickness is: t = t0 + T add , t0 is the initial thickness of the skin.

[0103] Compared with the prior art, the topology optimization method for ribbed cylinders for spinning-additive composite manufacturing provided by the embodiments of the present invention has the following advantages:

[0104] 1. In view of the existing design method of reinforced cylinder based on engineering experience, the rib layout is formulated in advance, which has the problems of limited design space and insufficient lightweighting. The present invention proposes a topological optimization method for the rib layout of reinforced thin-walled cylinder, which obtains an innovative rib layout design that is different from the traditional uniform layout, and realizes the optimization of the mechanical properties and lightweighting of the cylinder to the greatest extent. On the basis of the traditional topological optimization model, the present invention introduces the background density mapping method to obtain the rib characteristics, establishes the linear buckling simulation model and buckling constraints of the cylinder, realizes buckling stability control, and combines the optimization algorithm to achieve lightweighting improvement. The cylinder structure designed by the method proposed in the present invention can realize the lightweight rib layout design of reinforced thin-walled cylinder as much as possible under the condition of ensuring buckling stability, avoiding the problem of large design margin of traditional methods.

[0105] 2. In response to the lack of a process constraint modeling method for the height of the spun ribs in existing topology optimization models, the present invention proposes a method for constraining the maximum spun rib height in spinning manufacturing, establishing a parametric design model and performance expression model for spun-additive cylinders. Based on the traditional topology optimization model and the characteristics of the spinning process, the present invention introduces a dimensional constraint method to control the maximum spun rib height. The cylinder structure designed by the proposed method can meet the rib height requirements of spinning manufacturing, thus avoiding problems such as the difficulty of manufacturing the spinning mold and insufficient rib filling.

[0106] 3. In view of the lack of parametric expression and performance modeling for spinning-additive process cylinders in existing topology optimization models, the present invention proposes a parametric model of ribbed cylinders and a mechanical property expression model for spinning-additive. Based on the traditional topology optimization model, the present invention represents the ribs as spinning and additive parts according to the maximum spinning height, expresses the mechanical properties of the two parts respectively, and establishes a parametric expression model of the geometry and mechanical properties of the cylinder. The cylinder structure designed by the method proposed in the present invention can meet the constraints of the spinning process, while giving full play to the manufacturing advantages of spinning-additive, expanding the design optimization space, and designing and manufacturing a lighter, better-performing high-internal-rib cylinder structure.

[0107] The present invention is described in detail below in conjunction with the preferred embodiments of the present invention.

[0108] like Figure 8 As shown, the collaborative topology optimization method for a ribbed thin-walled cylinder proposed in a preferred embodiment of the present invention includes the following steps:

[0109] Step 1: Given the design domain, non-design domain, and material properties.

[0110] like Figure 4 As shown in the figure, a high-ribbed cylindrical structure is designed using the method of the present invention. The area containing the cylinder to be designed is discretized using a finite element grid, and the area where the skin is located is defined (Figure 4 The outer gray area in the figure is the skin design domain Ω0, and the area to be reinforced ( Figure 4 The gray shaded area in the middle is the reinforcement design domain Ω, and the upper and lower end frames are the reinforcement non-design domain Ω1.

[0111] In this embodiment, the skin thickness t is also a design variable.

[0112] The dimensional parameters of the given cylindrical structure are D = 250 mm, H = 150 mm, T = 7.5 mm, the initial thickness of the skin is t0 = 2.5 mm, and the physical properties of the material are set as follows: Young's modulus E0 = 68000 MPa, Poisson's ratio v = 0.3.

[0113] Step 2: Initialize the design variables.

[0114] like Figure 5 As shown in the figure, the initialization indirectly indicates the presence or absence of rib material design variables μ=(μ1,μ2,…,μ n ), where n is the total number of background elements. In the initialization phase, if the background element i belongs to the non-design domain where ribs are required, the component μ in the design variable μ is set to i Initialized to 1; if the background element i belongs to the non-design domain where ribs are not allowed to be arranged, the component μ in the design variable μ is set to i Initialized to 0 and remain unchanged in subsequent optimization iterations; the rib design variables μ in the remaining design domain i Between 0 and 1.

[0115] Initialize the design variable h = (h1, h2, ..., h n ), h i A normalized variable designed for rib height, between 0 and 1, representing the ratio of rib height to the total height of the radial element.

[0116] In this embodiment, the number of radial units is 4 and the total height is 10 mm.

[0117] Step 3: Introduce the size constraint method to calculate the background physical density to meet the spinning manufacturing size requirements.

[0118] like Figure 6 As shown in the figure, by introducing size constraints through density filtering and projection methods, the design variable μ that indirectly indicates whether there is a rib at a certain location is converted into the background physical density that directly indicates whether there is a rib at a certain location. The distribution of the ribs mathematically naturally meets the requirements of spinning manufacturing for the minimum size, minimum spacing and maximum size of the ribs. Figure 7 As shown, the background physical density indicating whether there is a rib at a certain location can be Converted into the physical density of the corresponding unit on the cylinder The two satisfy the linear mapping relationship:

[0119]

[0120] Where L is the mapping matrix, m, n are the number of units. If the density of the jth background unit is mapped to the i-th unit of the cylinder structure, then L ij =1, otherwise 0.

[0121] To obtain the discrete representation of the rib height variable value, such as Figure 7 As shown, the smooth Heaviside function is used to obtain the physical variables of the rib height of the cylindrical structure through the height mapping method.

[0122]

[0123] Among them, tanh is the hyperbolic tangent function, β is the projection parameter steepness, which controls the clarity of the grid boundary, and η ij is the projection threshold, which is equal to the normalized coordinate value of the jth element corresponding to the i-th background grid in the rib height direction, and Ω is the rib design domain.

[0124] By mapping, if the normalized coordinate value η of the unit center in the rib height direction is ij Smaller than the design value of the normalized height of the reinforcement at that location Then the cell density Set to 1, otherwise set the cell density to 0.

[0125] The background density field variables are combined with the rib height design variables to finally obtain the rib physical density field with variable layout and variable rib height.

[0126] Step 4: Map the background density and rib height to the rib spinning and additive design variables.

[0127] A maximum spinning height characterization model is introduced. According to the aspect ratio limit of the rib forming limit in the spinning process, the theoretical value of the rib spinning height at any position is related to the width of the rib at that location. The model determines the amount of material that can flow into the rib filling area under the spinning process based on the rib layout within a certain range, and evaluates and calculates the maximum rib height.

[0128]

[0129] in, It represents the set of units whose distance from unit e does not exceed d / 2. In this example, d is 3.

[0130] When the rib height in the rib design variable field is greater than the maximum spinnable height, the raised part of the rib needs to be manufactured through additive manufacturing.

[0131] Increment T of combined cylinder thickness add , variable field for spinning rib design And the additive reinforcement design variable field ρ a =max(ρ-ρ s ,0), and obtain the parametric expression model of the spinning-additive high internal rib cylinder.

[0132] Step 5: Mechanical properties simulation.

[0133] Based on the SIMP formula, an interpolation model of the physical variable ρ, which directly represents the presence or absence of a unit structure, and the unit stiffness and stress is established. Static analysis and linear buckling analysis of the cylindrical structure are performed to obtain the linear buckling factors of various orders and their modes.

[0134] Among them, the interpolation models of the unit stiffness and stress of the spinning forming part are:

[0135]

[0136] in, and are the Young's modulus of unit e obtained by interpolation for stiffness and stress calculation; E min To avoid small values ​​introduced by matrix singularity, it is 0.1 MPa in this example; p is the penalty factor of the SIMP interpolation model, and p=5 in this embodiment.

[0137] In view of the performance difference between the additive part and the spinning part, the proportional factor α is introduced to describe the elastic modulus of the additive part material:

[0138]

[0139] In this embodiment, α=0.9, which means that the performance of the additive part is slightly weaker than that of the spun part.

[0140] The cylinder is subjected to static analysis, where the load is applied according to the actual service conditions of the cylinder. Based on the static analysis KU=F, the finite element simulation formula for linear buckling analysis is:

[0141]

[0142] Among them, K is the elastic stiffness matrix of the cylindrical structure, U is the node displacement vector, F is the load vector, G is the geometric stiffness matrix, which is related to the node displacement vector U, λ i (i=1,2,…,k) are the linear buckling factors, is the corresponding buckling mode, and k is the number of buckling modes.

[0143] Step 6: Calculate each design response.

[0144] Calculate the various design responses of the cylindrical structure: first-order buckling factor λ1, total volume V, etc.

[0145] Step 7: Sensitivity analysis.

[0146] Calculate the sensitivity of each design response to the design variables.

[0147] The sensitivity of each design response to the design variable ρ can be expressed by the chain rule as:

[0148]

[0149] Step 8: Use optimization algorithm to solve the optimization model.

[0150] The topology optimization model is solved by iterative optimization algorithm to obtain updated design variables μ, h and skin thickness variable T add .

[0151] The topology optimization model solved in this embodiment is:

[0152]

[0153] Among them, λ * is the expected value of the first-order buckling factor, which is taken as 2.9 in this embodiment.

[0154] Step 9: Determine convergence.

[0155] Determine whether the method has converged. If all constraints are satisfied and the relative change of the objective function for 5 consecutive steps is less than 0.5%, go to step 10. Otherwise, go to step 3.

[0156] Step 10: Post-processing of results.

[0157] Post-process the optimization results, such as Figure 9 The background physical variable ρ, which indicates whether a unit has a structure, is post-processed. A threshold value (0.5 in this embodiment) is selected, and the elements in ρ that are greater than the threshold value are set to 1, and the elements in ρ that are not greater than the threshold value are set to 0.

[0158] Based on the post-processed ρ and skin thickness t=t0+T add Establish the corresponding optimized cylinder structure, such as Figure 10 As shown in the figure (the gray part is the spinning part, and the black part is the additive part), the first-order buckling factor of the design is 2.95, which meets the buckling stability constraint.

[0159] The present invention proposes a topology optimization method for ribbed cylinders for spinning-additive composite manufacturing, which can be used for the lightweight design of high-internal-ribbed cylinders manufactured by spinning-additive composite manufacturing. Compared with the traditional casting-machining production of ribbed cylinders, spinning-additive composite manufacturing has the advantages of lower material removal rate and higher processing efficiency. Compared with the processing method of welding ribs to the skin, the welds are reduced and the structural reliability is improved. The optimization method proposed in the present invention can give full play to the design freedom of the above-mentioned process, reasonably allocate the rib layout, the rib spinning forming part and the additive forming part, and obtain a lightweight, high-load-bearing thin-walled ribbed cylinder structure, which is applied to the optimization design of thin-walled load-bearing structures such as aerospace vehicles.

[0160] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A topology optimization method for a ribbed cylinder for spinning-additive composite manufacturing, characterized in that: The method designs and optimizes the topological structure of a ribbed thin-walled cylinder manufactured by spinning-additive composite manufacturing, and the method comprises the following steps: S101: For the ribbed thin-walled cylinder to be designed, define a design area and a non-design area, and set material physical parameters; S103: Initializing design variables, wherein the design variables include a design variable indirectly indicating the presence or absence of rib material and a design variable indicating the design height of the rib; S105: introducing a size constraint method to calculate the background physical density of the ribs so that the ribs meet the size requirements of spinning manufacturing; S107: Mapping the background physical density design variable and the rib height design variable into the rib spinning design variable and the additive design variable; S109: Perform static analysis and linear buckling analysis on the reinforced thin-walled cylinder structure to obtain the linear buckling factors and buckling modes of each order; S111: Calculate the design responses of a reinforced thin-walled cylindrical structure and analyze the sensitivity of each design response to the design variables. S113: Solve the topology optimization model through an iterative optimization algorithm to obtain updated design variables and skin thickness; S115: Post-processing the optimization results, and establishing an optimized structure of the ribbed thin-walled cylinder based on the post-processing results; in, In step S107, a parametric design model of a spinning-additive cylinder is constructed based on the maximum spinning height representation model, and the portion of the rib design variable field in the design model where the rib height is greater than the maximum spinning height is manufactured using an additive process; The rib spinning design variables are: ； The rib additive design variables are: ； in, ； ； ； ； In the above formula, is the maximum rib height, is the physical density field of the tendon, is the physical density of the equal-height reinforcement of a unit on the cylinder, is the unit density of the cylindrical structure, Representation and Unit No more than The unit collection, is the distance parameter, For unit and unit The coordinates of is the hyperbolic tangent function, is the projection parameter steepness, which controls the clarity of the grid boundary. is the projection threshold, which is equal to The background grid corresponds to the The normalized coordinate value of each element in the rib height direction, is the reinforcement design domain; In step S111, when analyzing the effects of each design response on the design variables When the sensitivity of each design response to the design variable is The sensitivity of , the chain rule is: in, is the design variable indicating whether there is rib material or not, is the design variable representing the design height of the rib, is the unit number, is the number of units; In step S113, the topology optimization model solved is: in, is the design variable indicating whether there is rib material or not, is the design variable representing the design height of the rib, is the skin thickness, is the total volume of the cylinder, is the first-order buckling factor, is the expected value of the first-order buckling factor.

2. The method according to claim 1, wherein In step S101, when defining the design area and the non-design area, the area of ​​the ribbed thin-walled cylinder is discretized using a finite element mesh, and the area where the skin is located is defined as the skin design domain, the area to be reinforced is defined as the rib design domain, and the upper and lower end frames are defined as the rib non-design domain.

3. The method according to claim 2, wherein In step S103, when initializing the design variable that indirectly indicates the presence or absence of rib material, the following rules are followed: If the background unit If it belongs to a non-design domain that must have ribs, the component of the design variable of the unit is initialized to 1; If the background unit If it belongs to a non-design domain where reinforcement arrangement is not allowed, the components of the design variables of the unit are initialized to 0 and remain unchanged in subsequent optimization iterations; The rib design variables in the rest of the design domain are between 0 and 1.

4. The method according to claim 3, wherein In step S103 , when initializing the design variable representing the rib design height, the design variable is normalized so that the design variable is between 0 and 1, and the design variable is set to the ratio of the rib height to the total height of the radial unit.

5. The method according to claim 4, wherein In step S105, the design variable indirectly indicating the presence or absence of a unit rib is converted into a background physical density directly indicating the presence or absence of the unit rib through density filtering and projection methods. The background physical density naturally meets the requirements of spinning manufacturing for the minimum size, minimum spacing, and maximum size of the rib in terms of distribution mathematics. The background physical density is also converted into the contour rib physical density of the corresponding unit on the cylinder. The contour rib physical density and the background physical density satisfy a linear mapping relationship: in, is the physical density of the equal-height reinforcement of a unit on the cylinder, To represent the background physical density of whether a certain unit has reinforcement bars, is the mapping matrix, is the number of units.

6. The method according to claim 5, wherein In step S109, in the statics analysis, the following statics equation is used: ； In the linear buckling analysis, the following finite element simulation formula is used: in, is the elastic stiffness matrix of the cylindrical structure, is the node displacement vector, is the load vector, is the geometric stiffness matrix, and the node displacement vector Related, are the linear buckling factors, is the corresponding buckling mode, is the number of buckling modes.

7. The method according to claim 6, wherein In step S115, when the optimization result is post-processed, if the unit If the value of the background physical variable with or without structure is greater than a preset threshold, the background physical variable is set to 1, otherwise it is set to 0; The optimized skin thickness is: , is the initial thickness of the skin.

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