Ribbed cylinder topological optimization method for spinning-additive composite manufacturing

Abstract

The invention discloses a spinning-additive composite manufacturing oriented ribbed barrel topological optimization method, which relates to the field of structural design, and comprises the following steps: defining a design area and a non-design area, and setting physical property parameters of materials; initializing a design variable; a size constraint method is introduced, and the background physical density of the ribs is calculated to meet the spinning manufacturing size requirement; mapping the design variables into spinning and additive design variables of the ribs; statics analysis and linear buckling analysis are conducted, and linear buckling factors and buckling modes of all orders are obtained; calculating each design response of the cylinder structure, and analyzing the sensitivity; solving the topological optimization model to obtain a design variable and a skin thickness; and carrying out post-processing on an optimization result, and establishing an optimized cylinder structure. The method can be used for high-inner-rib barrel design of spinning-additive composite manufacturing, the design freedom degree is fully exerted, rib layout, rib spinning and additive forming parts are reasonably distributed, and a thin-wall ribbed barrel structure which is light in weight and high in bearing performance is obtained.

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 including skin thickness, rib layout, and rib height. By optimizing the above parameters, its mechanical properties and lightweight degree can be significantly improved. Existing ribbed thin-walled cylinder designs are mostly uniform and regular layouts such as upright orthogonal, oblique orthogonal, or equilateral triangles. This design method of pre-specifying the rib layout greatly limits the structural design space, and there are problems such as large design margins and insufficient lightweight. Topological optimization is a structural design method based on functional requirements and driven by simulation. It can determine the presence or absence of materials point by point and maximize the structural performance within given constraints. The design method that combines topological optimization technology with thin-walled cylinder structure design can avoid the design capacity limitations brought about by pre-specifying the rib layout, and explore the novel rib configurations in the design space as much as possible, thereby obtaining 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. While the cylinder rotates with the spindle of the machine tool, a spinning 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 accuracy, and high material utilization rate. It can not only be used 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 in aerospace equipment. Compared with the traditional forming method of forging cylinder blank + milling, the use of spinning manufacturing technology to process the cylinder can avoid the waste of a large amount of material being removed, long-term machining resulting in low production efficiency, the cutting of metal streamlines resulting in reduced component strength, and the rebalancing of residual stress caused by machining resulting in poor appearance accuracy. However, due to the limitations of the spinning process, the rib forming height is limited. On the basis of the spun cylinder, through additive manufacturing processes (such as Figure 3 The high-rib or local boss structure forming can be achieved by breaking through the limitation of the forming capacity of the spinning process and obtaining a high-rib thin-walled cylinder structure that can be manufactured by spinning-additive composite manufacturing.

[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 ribbed cylinder design method based on engineering experience predetermines the rib layout, has the problems of limited design space and insufficient lightweight.

[0006] To achieve the above object, the present invention provides a topology optimization method for a ribbed cylinder for spinning-additive composite manufacturing, wherein the method optimizes the topology structure of a ribbed thin-walled cylinder for spinning-additive composite manufacturing, and 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 property 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 rib design height;

[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 linear buckling factors and buckling modes of each order;

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

[0013] S113: Solving 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 the 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, 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 indirectly indicating 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 component of the design variable of the element is initialized to 0 and remains 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 certain 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 the minimum size, minimum spacing and maximum size of the ribs in spinning manufacturing in terms of distribution mathematics, and the background physical density is 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:

[0022]

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

[0024] Furthermore, in the step S107, a spinning-additive cylinder parametric design model is constructed based on the maximum spinnable height characterization model, and the portion of the rib design variable field in the design model where the rib height is greater than the maximum spinnable height is manufactured by 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, is the physical density of the equal-height ribs of a unit on the cylinder, is the unit density of the cylinder structure, represents the 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 unit corresponding to the ith background grid in the rib height direction, and Ω is the rib design domain.

[0032] Furthermore, in 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] Among them, 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) are the linear buckling factors, is the corresponding buckling mode, and k is the number of buckling modes.

[0037] Furthermore, in step S111, 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, and the chain rule is:

[0038]

[0039] 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.

[0040] Furthermore, in step S113, the topology optimization model solved is:

[0041]

[0042] 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.

[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. The present invention introduces a background density mapping method to obtain rib features, establishes a cylinder linear buckling simulation model and buckling constraints, realizes buckling stability control, and combines an optimization algorithm to achieve lightweight improvement. The cylinder structure designed by the method proposed in the present invention can achieve a lightweight rib layout design of a thin-walled cylinder with ribs as much as possible while ensuring buckling stability, avoiding the problem of large design margins in traditional methods;

[0047] 2. The present invention introduces a size constraint method according to the characteristics of the spinning process to control the maximum spinning height of the rib, which can meet the requirements for the rib height during spinning manufacturing, thereby avoiding the problems of difficult manufacturing of 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 model parametric expression 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 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 ribbed thin-walled cylinder in the prior art;

[0052] Figure 3 It is a schematic diagram of the high internal rib additive manufacturing process in the prior art;

[0053] Figure 4 A schematic diagram of a design domain and a non-design domain according to 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 It is a schematic diagram of a method for generating cylinder rib features according to an embodiment of the present invention;

[0056] Figure 7 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] Fig. 9 The post-processing result of the optimization model of the embodiment of the present invention;

[0059] Fig.10 It 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 symbols in the figure are as follows:

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

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

[0063] In the drawings, components with the same structure are indicated by the same numerical reference numerals, and components with similar structures or functions are indicated by similar numerical reference numerals. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is appropriately exaggerated in some places in the drawings.

[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 skin welding ribs, 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 properties.

[0066] For the ribbed thin-walled cylinder structure to be designed, when defining the design area and non-design area, the finite element mesh is used to discretize the area of ​​the ribbed thin-walled cylinder, and the area where the skin is located is defined as the skin design domain, the area to be reinforced is the rib design domain, and the upper and lower end frames are the rib non-design domain. The material physical properties are set including Young's modulus and Poisson's ratio.

[0067] S2: Initialize the design variables, which include the design variables indirectly indicating the presence or absence of rib material and the design variables indicating the design height of the rib.

[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 ribs are not allowed to be arranged, 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 design height of the rib, 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 a unit rib are converted into background physical density that directly indicates the presence or absence of the unit rib. The background physical density naturally meets the requirements of the minimum size, minimum spacing and maximum size of the ribs in spinning manufacturing in terms of distribution mathematics, and the background physical density is converted into the physical density of the ribs of the corresponding unit on the cylinder. The physical density of the ribs of the corresponding unit on the cylinder satisfies the linear mapping relationship with the background physical density:

[0075]

[0076] in, is the physical density of the equal-height ribs of a unit on the cylinder, is the background physical density indicating whether a certain unit has ribs or not, 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.

[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 characterization model, a parametric design model of a spinning-additive cylinder is constructed. The part of the rib design variable field in the design model with a rib height greater than the maximum spinnable height is manufactured through 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 ribs of a unit on the cylinder, is the unit density of the cylinder structure, represents the 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 unit corresponding to the ith 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 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, 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 cylinder 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: The topology optimization model is solved by 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 ribbed cylinder topology optimization method for spinning-additive composite manufacturing provided by the embodiment of the present invention has the following advantages:

[0104] 1. In view of the existing ribbed cylinder design method based on engineering experience, the rib layout is pre-determined, which has the problems of limited design space and insufficient lightweight. The rib layout topology optimization method of the ribbed thin-walled cylinder proposed in the present invention obtains an innovative rib layout design that is different from the traditional uniform layout, and optimizes the mechanical properties and lightweight 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 a cylinder linear buckling simulation model and buckling constraints, realizes buckling stability control, and combines the optimization algorithm to achieve lightweight improvement. The cylinder structure designed by the method proposed in the present invention can realize the lightweight rib layout design of the ribbed thin-walled cylinder as much as possible under the condition of ensuring buckling stability, avoiding the problem of large design margin of the traditional method.

[0105] 2. In view of the lack of process constraint modeling method for the height of the cylinder spinning ribs in the existing topology optimization model, the present invention proposes a maximum spinnable rib height constraint for spinning manufacturing, and establishes a parametric design model and performance expression model for the spinning-additive cylinder. Based on the traditional topology optimization model, the present invention introduces a dimensional constraint method according to the characteristics of the spinning process to control the maximum spinnable height of the ribs. The cylinder structure designed by the method proposed in the present invention can meet the requirements for the rib height during spinning manufacturing, so as to avoid the problems of difficult manufacturing of 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 model parametric expression 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 to a greater extent, expanding the design optimization space, and designing and manufacturing a lighter, higher-performance high-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 of a ribbed thin-walled cylinder proposed in a preferred embodiment of the present invention comprises the following steps:

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

[0110] like Figure 4 As shown, the method of the present invention is used to design a high-ribbed cylinder structure. 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 rib design domain Ω, and the upper and lower end frames are the rib non-design domain Ω1.

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

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

[0113] Step 2: Initialize the design variables.

[0114] like Figure 5 As shown in the figure, the initialization of the design variable μ=(μ1,μ2,…,μ n ), where n is the total number of background elements. In the initialization stage, if the background element i belongs to the non-design domain where ribs are required, the component μ in the design variable μ is 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 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 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 size requirements of spinning production.

[0118] like Figure 6 As shown in the figure, by introducing the size constraint through density filtering and projection method, the design variable μ indirectly indicating the presence or absence of ribs at a certain location is transformed into the background physical density directly indicating the presence or absence of ribs 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 the presence or absence of ribs 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 and 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 in the figure, the smooth Heaviside function is used to obtain the rib height physical variable of the cylinder 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 unit corresponding to the ith background grid in the rib height direction, and Ω is the rib design domain.

[0124] Through mapping, if the normalized coordinate value η of a unit center in the rib height direction ij Smaller than the normalized height design value of the rib at that location Then the unit 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] The maximum spinning height characterization model is introduced. According to the limitation of the aspect ratio of the rib forming limit in the spinning process, the theoretical value of the spinning height of the rib 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 according to 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 portion of the rib needs to be manufactured through additive manufacturing.

[0131] Combined cylinder thickness increment T add , Variable field of 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. Statics analysis and linear buckling analysis of the cylinder structure are carried out 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 spinning part.

[0140] The cylinder is subjected to static analysis, where the load is applied according to the actual service condition 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 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) 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 various design responses of the cylindrical structure: first-order buckling factor λ1, total volume V, etc.

[0145] Step 7: Sensitivity analysis.

[0146] Compute 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 the 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 it 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 Fig. 9 The background physical variable ρ indicating whether a unit has a structure is post-processed, a threshold value (the value is 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 Fig.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 on 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 preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined 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 property 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 rib design height; 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 linear buckling factors and buckling modes of each order; S111: Calculate the design responses of the reinforced thin-walled cylinder structure and analyze the sensitivity of each design response to the design variables; S113: Solving 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.

2. The method according to claim 1, characterized in that 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, 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, characterized in that 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 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; If the background element i belongs to a non-design domain where reinforcement arrangement is not allowed, the component of the design variable of the element is initialized to 0 and remains 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, characterized in that 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, characterized in that In step S105, the design variable indirectly indicating the presence or absence of a certain 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 the minimum size, minimum spacing and maximum size of the ribs in spinning manufacturing in terms of distribution mathematics, and the background physical density is 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: in, is the physical density of the equal-height ribs of a unit on the cylinder, is the background physical density representing the presence or absence of ribs in a unit, L is the mapping matrix, and m and n are the number of units.

6. The method according to claim 5, characterized in that In the step S107, a parametric design model of a spinning-additive cylinder is constructed based on the maximum spinnable height characterization model, and the portion of the rib design variable field in the design model where the rib height is greater than the maximum spinnable height is manufactured by an additive process; The rib spinning design variables are: The rib additive design variables are: r a =max(ρ-ρ s ,0); in, In the above formula, is the maximum rib height, ρ is the rib physical density field, is the physical density of the equal-height ribs of a unit on the cylinder, is the unit density of the cylinder structure, represents the 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 unit corresponding to the ith background grid in the rib height direction, and Ω is the rib design domain.

7. The method according to claim 6, characterized in that In the step S109, in the statics analysis, the following statics equation is used: KU=F; In the linear buckling analysis, the following finite element simulation formula is used: Among them, 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) are the linear buckling factors, is the corresponding buckling mode, and k is the number of buckling modes.

8. The method according to claim 7, characterized in that In step S111, 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, and the chain rule is: 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.

9. The method according to claim 8, characterized in that In step S113, the topology optimization model solved is: findμ,h,T add min V s.t.λ1≥λ * KU=F 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.

10. The method according to claim 9, characterized in that In the step S115, when the optimization result is post-processed, 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; The optimized skin thickness is: t = t0 + T add , t0 is the initial thickness of the skin.

Images