Layout optimization design and manufacturing method for discrete truss structures based on iterative cells

Abstract

The present invention relates to a layout optimization design and manufacturing method for a discrete truss structure based on a repetitive cell, and includes the steps of establishing a mathematical model for truss layout optimization, a direct solution based on the repetitive cell, a two-stage solution of first determining the cell layout, 3D printing manufacturing and integrated assembly. The beneficial effects of the present invention are as follows: additional constraints and variables for the characteristics of the repetitive cell are introduced, and a direct solution method based on the repetitive cell is provided, so that the optimization result of the truss layout has the characteristics of the repetitive cell; this direct solution method based on the repetitive cell can not only be used independently and directly, but also can provide a mathematical model for the two-stage solution of first determining the cell layout; when solving the problem of large scale, a two-stage solution is provided, which is to first solve the cell mode layout and then optimize the internal structure of the cell mode, making the load path of the structure clearer, and finally, under the condition of small impact on the volume of the optimized structure, the calculation efficiency is greatly improved.

Description

[Technical field]

[0001] The present invention belongs to the technical fields of structural engineering and additive manufacturing, and in particular to a layout optimization design and manufacturing method for discrete truss structures based on repetitive cells. [Background technology]

[0002] The increasingly complex engineering needs have led to a growing demand for the optimization design and 3D printing integrated assembly of complex truss structures. The topology optimization objects of structures include discrete structures and continuum structures, and the optimization of truss structures, which are widely used in practical engineering, belongs to the category of discrete structure topology optimization.

[0003] The layout optimization of a truss structure is a linear programming problem, and although the solution of conventional truss layout optimization algorithms can reach a numerical optimum, in actual manufacturing, due to the complexity of the structure, it is easy to encounter situations that are difficult to manufacture or even impossible to manufacture. In order to reduce the manufacturing cost, a common method is to add additional constraints such as classification of rod members, limiting the complexity of the structure, etc., to make the final result as easy to manufacture as possible, but the optimization solution becomes more complicated. The introduction of iterative cells is a reasonable and efficient solution to simplify the layout optimization problem.

[0004] In the continuum optimization process, optimization methods that introduce the concept of iterative cells are provided, mainly including the homogenization method and the small-scale integrated optimization method. The homogenization method equates microscopic cells to a macroscopically uniform medium, and the entire structure can be subjected to a macroscopically coarse-grained finite element analysis, but the homogenization method cannot control the connectivity between cells unless additional constraints are introduced. In the small-scale integrated optimization method, the price of optimizing the entire structure on a small scale is the high computational cost. Since the cells in architectural construction are generally discrete structures and have a limited size relative to the design domain, the above iterative cell algorithm for continuum optimization cannot be directly used to solve the layout optimization problem of truss structures.

[0005] In summary, it is very necessary to study the layout optimization design and manufacturing method of discrete truss structure based on repeating cells, and realize the layout optimization, 3D printing manufacturing and integrated assembly of complex truss structure. Summary of the Invention [Problem to be solved by the invention]

[0006] The present invention aims to overcome the shortcomings of the prior art and provide a layout optimization design and manufacturing method for a discrete truss structure based on iterative cells. [Means for solving the problem]

[0007] Such a structure layout optimization design and manufacturing method based on repetitive cells includes: S1, Establishment of a mathematical model for truss layout optimization: Firstly, determine the structural design domain, input the dimensions, loading conditions and boundary constraints, specify the cell mode and the complexity of the corresponding cell mode, use the grid discretization to process the design domain, connect any two nodes to establish the minimum connection basic structure, take the mechanical equilibrium equation as the constraint, take the minimization of the total volume of the rod members as the design objective, and establish a linear optimization model for truss layout optimization; S2, direct solution based on repeated cells: set a finite number of cell modes, perform cell division, ensure that all rod members belong to a certain cell mode, and there are no rod members that span across cell modes, and the cell layout of the same cell mode and the area of ​​the rod members at the corresponding positions are completely the same; for each rod member of the truss structure, use a binary variable to activate the cell mode, add repeated cell constraints to form nonlinear constraints, convert the nonlinear programming problem into a linear programming problem, and the repeated cells can be directly optimized and solved; S3, Two-step solution to first determine the cell layout: First, reduce the complexity of each cell mode, perform the first solution according to step S2, and then calculate the activated cell mode variable tc Then, according to the normal complexity of each cell mode, t c In step S2, the nonlinear constraint equation of the repetition cell of each rod member is substituted to convert it into a linear constraint, and a second solution is performed to obtain the optimization result. S4. 3D printing manufacturing and integrated assembly: This includes the steps of performing 3D modeling, slicing multiple types of repeating cells of the optimization result model to generate printing paths, performing 3D printing manufacturing, and performing integrated assembly between the repeating cells to manufacture the optimized structure.

[0008] Preferably, in step S1, an objective function corresponding to the design goal of minimizing the total volume of the rod members is expressed as follows: JPEG2025512638000002.jpg1951(1), The constraint formula is: JPEG2025512638000003.jpg4599(2), where l is the length vector of the rod member, a is the area vector of the rod member, B is the balance matrix, q is the internal force vector of the rod member, f is the nodal load vector, and σ c and σ t are the compressive strength vector and the tensile strength vector of the rod member, respectively, The three constraints in equation (2) respectively represent the force balance equation, the stress constraint of the rod member, and the non-negative constraint of the rod member area. The design variables are the area vector a of the rod member and the internal force vector q of the rod member, B and l are the constant matrix and constant vector generated based on the topology method of the rod member, respectively, and f, σ c and σ t is a constant determined by the actual working conditions.

[0009] Preferably, in step S1, if the balance matrix B of the minimum connected basic structure when optimizing the initial state cannot be solved, the member length threshold and grid density in the minimum connected basic structure are increased to form the minimum connected basic structure when optimizing the updated initial state, and the solution is repeated.

[0010] Preferably, in step S2, a binary variable is set for each rod member to activate a cell mode, and a cell constraint is repeatedly added to each rod member of the truss structure, i.e., the design domain is first filled with the cell mode, and then the nodes inside each cell mode are connected to the rod members two by two, and a cell structure is repeatedly constructed. In order to ensure that the areas of the rod members at the same position of the same type of cell mode are the same, when there are n types of cell modes in the structure, the following constraint is added to each rod member: JPEG2025512638000004.jpg14100(3) JPEG2025512638000005.jpg13164(4) In the formula, a i is the cross-sectional area of ​​the rod member, c is the number of the cell mode to which the rod member belongs, m is the position number of the rod member in the cell mode, and t c1 , t c2 , …, t cn is a binary variable of the cell mode activated by the cell mode to which the rod member belongs, the value being 1 or 0, where 1 indicates that the cell mode is activated and 0 indicates that the cell mode is deactivated; a m1 , a m2 , …, a mn is the possible cross-sectional area corresponding to the position of the rod member in the cell mode, and in equation (4), a m1 , a m2 , …, a mn and t c1 , t c2 , …, t cn are all variables, and two variables are multiplied together to form a nonlinear constraint.

[0011] Preferably, in step S2, the nonlinear constraints in equation (4) are converted to linear constraints using the large M method to obtain equation (5). JPEG2025512638000006.jpg32164(5) where M is a constant, each line of equation (5) represents a constraint on the rod member at that position of one cell mode, and a iWhen the cell mode to which t belongs activates the first cell mode, c1 =1, and the remainder is t cx =0, and in this case, the first line of the constraint (5) is a i =a m1 and other inequalities are relaxed, do not actually act, and a i When the cell mode to which t belongs activates the second cell mode, i.e., t c2 =1, and the remainder is t cx =0, and in this case, the second line of the constraint (5) is a i =a m2 and other inequalities are relaxed and do not act, and similarly, when a cell mode to which a rod member belongs activates a cell mode, the constraints of the corresponding row of the rod member become effective and the inequalities of the other rows are relaxed.

[0012] Preferably, step S3 specifically reduces the complexity of the cell mode first, i.e., reduces the number of nodes based on the normal cell mode structure, obtains a simplified cell mode structure, and performs a first solving process using the method of step S2, and reduces the cell mode variables t activated by each cell mode. c This corresponds to obtaining the layout of the cell mode that each rod member takes in the design domain, and then setting the complexity of the cell mode normally, regenerating the structure, and recalculating the t obtained in the first solution. c into equation (4), convert the optimization problem into a linear program, and solve it a second time directly.

[0013] Preferably, step S4 specifically extracts structural information of the repeating cell based on the optimization result, and the structural information includes the mode of the repeating cell, the position of the repeating cell, the connection of the repeating cell, and the cross-sectional dimensions of the rod member of the repeating cell; after the rod member assembly and node generation process of the repeating cell, a 3D solid model is established, and then multiple types of repeating cells of the solid model are respectively sliced ​​to generate printing paths, 3D printing manufacturing is performed, and then the repeating cells are connected and integrated assembly is performed to manufacture the optimized structure. Effect of the Invention

[0014] The beneficial effects of the present invention are as follows: 1) The layout optimization design and manufacturing method of discrete truss structure based on iterative cells provided by the present invention introduces additional constraints and variables for the characteristics of the iterative cells, and provides a direct solution method based on iterative cells, so that the optimization result of the truss layout has the characteristics of the iterative cells and is relatively easy to manufacture. This direct solution method based on iterative cells can not only be used independently and directly, but also provide a mathematical model for the two-stage solution to first determine the cell layout. 2) The layout optimization design and manufacturing method of the discrete truss structure based on the iterative cell provided by the present invention is based on the direct solution based on the iterative cell, and in response to the problem that the calculation time is too long when solving the problem of large scale, a two-stage solution is provided, which first solves the cell mode layout and then optimizes the internal structure of the cell mode, so that the load path of the structure is clearer, and the calculation efficiency is greatly improved under the condition that the impact on the volume of the finally optimized structure is small. 3) The layout optimization design and manufacturing method of the discrete truss structure based on the repeated cell provided by the present invention is based on the mathematical model for truss layout optimization, by setting a finite number of cell modes and adding repeated cell constraints, thereby realizing cell repeatability and structural regularity of the layout optimization result. The two-stage solution of first simplifying the cell complexity and then normalizing the cell complexity realizes a rapid and efficient solution based on the repeated cell layout optimization. Through 3D modeling, repeated cell model slicing, printing path generation and integrated assembly production, the 3D printing optimization design and integrated assembly manufacturing of the complex discrete truss optimization structure are realized. [Brief description of the drawings]

[0015] [Figure 1] 1 is a specific flowchart of the layout optimization design and manufacturing method of a discrete truss based on repeated cells of the present invention; [Figure 2a]A schematic diagram of a cell with complexity of 2x2. [Figure 2b] A schematic diagram of a cell with complexity of 3x3. [Figure 2c] A schematic diagram of a cell complexity of 4x4. [Diagram 3] FIG. 1 is a schematic diagram of a cantilever beam structure model. [Figure 4] FIG. 13 is a schematic diagram of a typical layout optimization result of step S1 of a cantilever beam structure. [Figure 5a] FIG. 13 is a schematic diagram of the layout optimization result of the direct solution of step S2 of the cantilever beam structure. [Figure 5b] These are four types of repeating cells when the complexity of the cell mode corresponding to the direct solution of step S2 of the cantilever beam structure is 4 × 4 and the number of cell modes is 4. [Figure 6a] This is the result of the first solution of the two-stage solution in step S3 when the complexity of the simplified cell mode of the cantilever beam structure is 2×2 and the complexity of the normal cell mode is 4×4. [Figure 6b] The corresponding second solution for the cantilever beam structure is shown. [Figure 7a] This is the result of the first solution of the two-stage solution in step S3 when the complexity of the simplified cell mode of the cantilever beam structure is 3×3 and the complexity of the normal cell mode is 4×4. [Figure 7b] The corresponding second solution for the cantilever beam structure is shown. [Figure 8a] This is the result of the second solution of the two-stage solution in step S3 when the complexity of the simplified cell mode of the cantilever beam structure is 3×3 and the complexity of the normal cell mode is 6×6. [Figure 8b] This is the result of the second solution of the two-stage solution in step S3 when the complexity of the simplified cell mode of the cantilever beam structure is 3×3 and the complexity of the normal cell mode is 8×8. [Figure 9] FIG. 1 is a schematic diagram of a frame-support structure model under horizontal wind load. [Figure 10a]This is a result of the second stage of the two-stage solution in step S3 when the number of repeating cell modes of the frame-support structure is 1. [Figure 10b] This is the solution result of the second stage of the two-stage solution in step S3 when the number of repeating cell modes of the frame-support structure is 4. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] The present invention will be further described below with reference to examples. The following examples are only for the purpose of helping the understanding of the present invention. However, those skilled in the art can make some improvements and modifications to the present invention without departing from the principle of the present invention, and these improvements and modifications are also included in the scope of the claims of the present invention.

[0017] Example 1 As an embodiment, as shown in FIG. 1, a layout optimization design and manufacturing method for a discrete truss structure based on repeating cells, in which additive manufacturing technology, i.e. 3D printing technology, realizes the generation of a structure by layer-by-layer accumulation of material, greatly expanding the flexibility of structural manufacturing, and can obtain good optimization results by optimizing the structural layout based on repeating cells, including the arrangement and combination of repeating cells, and further performs 3D printing and integrated assembly on a small number of repeating cells with some complex configurations to realize the integrated manufacturing of an optimized complex truss structure, specifically including steps S1 to S4. S1, Establish a mathematical model for truss layout optimization: Firstly, determine the structural design domain, input the constraints and parameters, establish the minimum connection basic structure, take the mechanical equilibrium equation as the constraint, take the minimization of the total volume of the rod members as the design goal, and establish a linear optimization model, which specifically includes steps S1.1 to S1.3. S1.1, Input of design conditions and parameters: Enter the dimensions of the design domain, the load operating conditions and boundary constraints, and specify the cell mode and the corresponding cell complexity. S1.2, Establishing a minimally connected basic structure: Process the design domain using a uniform grid discretization and connect any two nodes to form a minimally connected basic structure. S1.3. Establishing a mathematical model for layout optimization: The bottom layer of the optimization algorithm is a mathematical optimization problem. The mechanical equilibrium equation is the constraint, and the design goal is to minimize the total volume of the rod members. A linear optimization model for truss layout optimization is established. The objective function is JPEG2025512638000007.jpg2051(1), The constraint formula is: JPEG2025512638000008.jpg4299(2), where l is the length vector of the rod member, a is the area vector of the rod member, B is the balance matrix, q is the internal force vector of the rod member, f is the nodal load vector, and σ c and σ t are the compressive strength vector and the tensile strength vector of the rod member, respectively, The objective function formula (1) represents the optimization goal of minimizing the volume, and the constraint condition formula (2) represents the force balance equation, the stress constraint of the rod member, and the non-negative constraint of the area of ​​the rod member. The problem is a linear programming problem, and the design variables are the area vector a of the rod member and the internal force vector q of the rod member, B and l are a constant matrix and a constant vector generated according to the topology method of the rod member, respectively, and f, q c and q t is a constant determined by the actual working conditions.

[0018] In truss layout optimization, after the design domain is determined, a structure is determined in a certain way based on equation (1) and equation (2), and the necessary constants are calculated. In order to ensure that the results obtained by optimization can reach the theoretical optimum, the simplest way to determine the structure is to connect all nodes in the design domain two by two, include all possible rod members in the structure, and establish the minimum connection basic structure. The structure obtained by general truss layout optimization saves material and has reasonable loads, but the structure is often too complicated and difficult to manufacture.

[0019] If the balance matrix B of the minimum connection basic structure when optimizing the initial state cannot be solved, the member length threshold and grid density in the minimum connection basic structure are increased to form the minimum connection basic structure when optimizing the updated initial state, and the solution is repeated.

[0020] S2. Direct solution based on iterative cells: set a finite number of cell modes, perform cell division according to the cell modes, ensure that all rod members belong to a cell mode and there are no rod members that span cell modes, add iterative cell constraints to each rod member of the truss structure, and directly perform optimization solution, specifically including steps S2.1 to S2.3. S2.1, Setting a finite number of cell modes: Set a finite number of cell modes, so that all rod members belong to a certain cell mode, there are no rod members that span across cell modes, and the layout of the same kind of cell modes and the areas of the rod members at the corresponding positions are completely the same. The truss layout optimization based on the repetitive cells has two characteristics: first, all rod members belong to a certain cell mode, there are no rod members that span across cell modes, and second, all cells follow a finite number of cell modes, and the layout of the same kind of cell modes and the areas of the rod members at the corresponding positions are completely the same. To realize the repetitive cell structure, first fill the design domain with cells, and then connect the nodes inside each cell to rod members two by two, and the number of rod members included in the repetitive cell structure is greatly reduced compared with the truss optimization in step S1. S2.2, Adding Repeated Cell Constraints: Each rod member uses a binary variable that activates the cell mode, and a repeating cell constraint is added to each rod member of the truss structure. In order to ensure that the area of ​​rod elements at the same position of the same type of cell mode is the same, for example, when there are n types of cell modes in the structure, the following constraint is added to each rod element: JPEG2025512638000009.jpg1798(3) JPEG2025512638000010.jpg15164(4) In the formula, ai is the cross-sectional area of ​​the rod member, c is the number of the cell mode to which the rod member belongs, m is the position number of the rod member in the cell mode, and t c1 , t c2 , …, t cn is a binary variable of the cell mode activated by the cell mode to which the rod member belongs, the value being 1 or 0, where 1 indicates that the cell mode is activated and 0 indicates that the cell mode is deactivated; a m1 , a m2 , …, a mn is the possible cross-sectional area corresponding to the position of the rod member in the cell mode, and in equation (4), a m1 , a m2 , …, a mn and t c1 , t c2 , …, t cn are all variables, and multiplying two variables together forms a nonlinear constraint that is difficult to solve, so it must be converted to a linear problem so that it can be solved directly. S2.3. Direct solution based on iterative cells: Convert the nonlinear constraints to linear constraints using the large M algorithm, i.e., replace equation (4) with equation (5); JPEG2025512638000011.jpg33164(5) where M is a determined large constant, each line of equation (5) represents a constraint on the rod member at a given position of one cell mode, and a i When the cell mode to which t belongs activates the first cell mode, c1 =1, and the remainder is t cx =0, and in this case, the first line of the constraint (5) is a i =a m1 and other inequalities are relaxed, do not actually act, and a i When the cell mode to which t belongs activates the second cell mode, i.e., t c2 =1, and the remainder is t cx =0, and in this case, the second line of the constraint (5) is a i =a m2and other inequalities are relaxed and do not work, and so on. When the cell mode to which the rod member belongs activates a cell mode, only the constraint of the corresponding row of the rod member is enabled, and the inequalities of other rows are relaxed. Formula (5) can achieve the same effect as formula (4), and formula (5) is still a linear constraint, does not change the linear programming characteristics of the optimization problem, and is easy to solve. The iterative cell-based truss layout optimization is a linear programming problem with the objective function (1) and the constraints (2), (3), and (5).

[0021] Iterative cell-based truss layout optimization is a general continuous variable and t c This is a mixed integer programming problem that includes binary integer variables that exist due to the introduction of . This type of problem is solved directly by the commercial Gurobi solver, which is better suited to this type of problem, and the solver has a Python interface for easily calling the program.

[0022] S3, Two-step solution to first determine the cell layout: First, set a low level of cell mode complexity, perform the first solution using step S2, and activate the cell mode variable t c is obtained and substituted into equation (4), the constraint in equation (5) is discarded, converted to a linear constraint, and a second solution is performed, which specifically includes steps S3.1 to S3.2. S3.1, the first solution of simplified cell complexity: Due to the characteristics of the solution of mixed integer programming, as the design domain becomes larger, the number of cell modes becomes larger, and the complexity of the cell modes becomes higher, the method of step S2 may encounter the problem of the calculation time being too long during the calculation. In mixed integer programming, the number of integer variables and the number of continuous variables both affect the solution time, where the number of integer variables is determined by the number of cell modes and the number of cell modes, and these two parameters are determined by the specific problem and design requirements and cannot be freely modified, the number of continuous variables is determined by the number of rod members in the structure, and the number of rod members is determined by the number of repeated cells and the complexity of the cell modes, and the only variable that can be improved in the calculation process is the complexity of the cell modes. Therefore, the complexity of the cell modes is initially set to a low level, and the first solution is performed using step S2, which is a mixed integer linear programming problem, and the cell mode variables t activated by each cell mode are c get. As shown in Fig. 2a-c, the typical complexities are 2 × 2 cells, 3 × 3 cells, and 4 × 4 cells, respectively, and the complexities of the cell modes are n x ×n y represents the number of nodes included in the horizontal and vertical directions in the cell mode. The higher the complexity of the cell mode, the higher the structural freedom, and in theory, a better objective function value can be obtained. However, the higher the number of rod members included in the structure, the longer the solution time. First, set the complexity of the cell modes to a low level and perform a first run using the method in step S2. c This corresponds to obtaining the layout of the cell modes that each cell mode takes in the design domain. S3.2, Second solution of normal cell complexity: Next, set the cell mode complexity to normal cell mode, regenerate the structure, and use the t obtained in the first solution. c Substituting into equation (4), discarding the constraint in equation (5), t cSince is a constant vector already determined, equation (4) does not change the linear programming properties of the optimization problem, and at this time, there are no binary integer variables in the problem, that is, the second solution is not a mixed integer program, and the time required for calculation is much less than that of the first solution, and the time taken for the entire solution process can be almost negligible.

[0023] The time required for mixed integer programming is the determining factor of the overall optimization time. During the first solution of the refinement algorithm in step S3, the complexity of the cell mode is low and the number of continuous variables is small, so the calculation time can be significantly reduced compared with the first solution time in step S2. However, the first solution only actually determines the layout of multiple types of cell modes and does not show the internal structure of the specific cell modes, so it cannot be guaranteed that the result of the refinement algorithm in step S3 is completely consistent with the algorithm described in step S2. Generally, rod members with similar load levels in the load action use the same type of cell mode, but the number of cell modes and the complexity of the cell modes in the first solution may affect the result of the layout of the cell modes.

[0024] Increasing the number of cell modes is more beneficial to obtain a better structure than improving the complexity of the normal cell modes, but if conditions permit, the complexity of the simplified cell modes in the two-step solution should not be too low, otherwise the layout scheme of the cell modes may deviate from the optimum.

[0025] S4, 3D printing manufacturing and integrated assembly: 3D modeling is performed, multiple types of repeating cells of the solid model are sliced ​​to generate printing paths, 3D printing manufacturing is performed, and integrated assembly is performed between the repeating cells to manufacture an optimized structure. Specifically, the process includes steps S4.1 to S4.2. S4.1. 3D printing manufacturing of repeating cells: 3D modeling is performed by Rhino software, and multiple types of repeating cells of the solid model obtained by 3D modeling are sliced ​​by Cura software to generate printing paths. Structural information of the repeating cells is extracted according to the optimization results. The structural information includes the mode of the repeating cells, the position of the repeating cells, the connection of the repeating cells, and the cross-sectional dimensions of the rod members of the repeating cells. After the rod members of the repeating cells are assembled and the nodes are generated, a 3D solid model is established. Then, multiple types of repeating cells of the solid model are sliced ​​respectively to generate printing paths, and 3D printing manufacturing is performed. S4.2. Integrated assembly of repeating cells: The repeating cells are connected by welding, bolting, etc., and integrated assembly is performed to manufacture the optimized structure.

[0026] Example 2 As another embodiment, this embodiment shows that optimization design and manufacturing is performed for a cantilever beam problem by general layout optimization in step S1 of embodiment 1 and direct solution based on iterative cells in step S2.

[0027] As shown in Figure 3, the width of the design domain of the cantilever beam is 6, the height is 3, the height and width of the cell are both 1, the design domain has a total of 6 x 3 = 18 cells, a vertical downward unit load acts on the upper right corner of the design domain, and the horizontal and vertical degrees of freedom are constrained at the upper and lower nodes on the left side. All related quantities are dimensionless, the self-weight of the structure is ignored, and the allowable tensile stress and allowable compressive stress of the rod members are both σ c = σ t = 1. The initial values ​​of the design variables, the area vector a of the rod member and the internal force vector q of the rod member, are both set to 0. The calculations are performed on a workstation with an inteli7-12700K (3.61 GHz) CPU and 32 GB of memory.

[0028] In this embodiment, the structure obtained by the general layout optimization in step S1 saves material and has reasonable loads, but the structure is often too complicated to manufacture, and a schematic diagram of the optimization result is shown in Figure 4. In it, the light-colored rods represent tension, the dark-colored rods represent compression, the thickness of the rods represents the cross-sectional area, and if the area of ​​the rods is less than a threshold, they are not displayed, and the threshold is 1 / 1000 of the area of ​​the largest rod in the structure.

[0029] Based on this, in this embodiment, step S2 is continued, and based on the direct solution of the repeating cell, the cell complexity is set to 4×4, and the number of repeating cell modes is set to 4. A schematic diagram of the direct optimization result is shown in FIG. 5a, and a schematic diagram of the four types of repeating cell structures is shown in FIG. 5b. The volume of the directly solved structure is 32, and the solution time is 20498 s. The optimized structural force transmission path is similar to that of general layout optimization, but since there are no rod members spanning the cell modes, the difference in length of the rod members is not large, the number of rod members connected to the nodes is limited, and there are no nodes that are too complex. Compared with the general layout optimization result obtained in step S1, the difficulty of manufacturing the structure in step S2 is greatly reduced.

[0030] This embodiment illustrates the citation of some steps of the present invention in the layout optimization of a truss structure, and shows that the equation based on the iterative cell established in step S2 can be directly used to solve the optimization of the iterative cell, and good results can be obtained.

[0031] Example 3 As another example, according to the layout optimization design and manufacturing method of the discrete truss structure based on the repetitive cell provided in Example 1, for the same cantilever beam problem in Example 2, a two-stage solution is further carried out in step S3 by the direct solution method based on the repetitive cell in step S2.

[0032] The complexity of the normal cell mode is set to 4×4, the number of repeated cell modes is set to 4, and during the two-stage solution in step S3, the complexities of the simplified cells are set to 2×2 and 3×3, respectively.

[0033] In this embodiment, when the complexity of the simplified cell mode is 2×2 and the complexity of the normal cell mode is 4×4, a schematic diagram of the optimization result of the two-stage solution in step S3 is shown in FIG. 6, and when the complexity of the simplified cell mode is 3×3 and the complexity of the normal cell mode is 4×4, a schematic diagram of the optimization result of the two-stage solution in step S3 is shown in FIG. 7. The specific optimization results are as follows: JPEG2025512638000012.jpg96164

[0034] When the complexity of the simplified cell mode is 2×2: the volume of the structure directly solved in step S2 is 32, and the solution time is 20498 s, and the volumes of the structures solved in two stages in step S3 are 34,400 and 33,688, respectively. Compared with the direct solution, the volume increased by 5.28%, but the solution time was significantly reduced to 25 s, which is about 1 / 800 of the direct solution, and the computational efficiency was greatly improved.

[0035] When the complexity of the simplified cell mode is 3 × 3: the volumes of the structures solved in two steps in step S3 are 33 and 32, respectively, and the final volumes are consistent with the volumes solved directly, but the calculation time is 4241 s, which is about 1 / 5 of the direct solution, and the calculation efficiency is greatly improved.

[0036] In this embodiment, when the complexity of the simplified cell mode is 2x2, 3x3, there is a large difference in the structure layout and shape, and increasing the complexity of the simplified cell mode makes the cell layout result solved in the first stage closer to the ideal situation, and the final structure closer to the result solved directly, therefore, if conditions permit, ensuring the complexity of the simplified cell mode is beneficial to obtain a means closer to the optimal layout.

[0037] When the complexity of the simplified cell mode is 3x3: When the complexity of the normal cell mode is 6x6, 8x8, the second solution results of the two-stage solution in step S3 are shown in Figures 8a and 8b, respectively. Compared with the case where the complexity of the normal cell mode is 4x4, the overall layout of the structure is similar, but the internal details of the cell mode are more complex, and the final volumes of the corresponding structures are 31.486 and 31.530, respectively. Compared with the case where the complexity of the cell mode is 4x4, the difference is only about 1.5%, but the calculation time has increased rapidly.

[0038] This embodiment illustrates the quotation of some steps of the present invention in the layout optimization of a truss structure, and shows that the two-step solution in step S3 is carried out by the solving equation based on the iterative cell established in step S2, and good results can be obtained. The two-step solution of first solving the cell mode layout and then optimizing the internal structure of the cell mode makes the load path of the structure clearer, and the calculation efficiency is greatly improved under the condition that the impact on the volume of the finally optimized structure is small, which can be used for the problem of the calculation time being too long when solving large-scale problems.

[0039] Example 4 The optimization concept of the repeating cell used in the discrete structure of trusses is as follows: first, determine the structural design domain, set a finite number of cell modes, perform cell division, and finally the whole structure is composed of multiple complex configuration repeating cells, in this way, a small number of several cell modes can be mass-produced using 3D printing method, and simple integrated assembly can be performed. However, there is currently little research on the optimization of the repeating cell structure of trusses, and layout optimization is not included. Most of the current repeating cell structures use the same kind of cell modes in the same sub-design domain, that is, the number of repeating cell modes is set to 1, which is determined to some extent by the characteristics of the homogenization method, but the truss structure does not have such restrictions, and the cell mode selected by each rod member and its position are not necessarily related, so the layout of the final structure is more flexible. Therefore, the improved application of a rational and effective repeating cell algorithm is an important factor in the layout optimization of truss structures.

[0040] As another example, this example uses the layout optimization design and manufacturing method of the discrete truss structure based on the iterative cell provided in Example 1 to perform a two-stage solution of step S3 for the frame-support structure problem under horizontal wind load, and compares the difference in results due to different numbers of cell modes.

[0041] As shown in Figure 9, the design domain of the frame-support structure under the horizontal wind load has a width of 4 and a height of 12, the cell height is 2 and the width is 1, the design domain has a total of 6×3=18 cells, horizontal rightward unit loads act on both sides of the points at heights 4, 8 and 12, the horizontal and vertical degrees of freedom are constrained at the nodes at both ends of the bottom side, the complexity of the simplified cell mode is set to 2×2, the complexity of the normal cell mode is set to 6×6, and the number of repeated cell modes is set to 1 and 4, respectively.

[0042] In this embodiment, when the numbers of repeated cell modes are 1 and 4 respectively, the schematic diagram of the optimization result of the two-stage solution in step S3 is shown in FIG. JPEG2025512638000013.jpg74164

[0043] Two-stage solution of step S3: the number of repeated cell modes was 1, i.e., all cell modes had the same cell structure, the volumes of the structures solved in the first and second stages were 1082.47, the number of repeated cell modes was 4, i.e., there were four different cell structures, the volumes of the structures solved in the first and second stages were 300.43 and 295.33, respectively, and the solution time was 1852 s.

[0044] It can be seen from the above that after increasing the number of repeated cell modes, the structural volume becomes smaller, which is only about 30% of that when the number of repeated cell modes is 1, and the optimization effect is significant, which indicates that when the load is large, the advantage of material saving can be better exerted by appropriately increasing the number of repeated cell modes.

[0045] As can be seen from Examples 2, 3 and 4, the layout optimization design and manufacturing method of the discrete truss structure based on the repetitive cell provided by the present invention introduces additional constraints and variables for the characteristics of the repetitive cell, and the direct solution based on the provided repetitive cell makes the optimization result of the truss layout have the characteristics of the repetitive cell, so that the manufacturing is relatively easy. For the problem of the calculation time being too long when solving the problem of large scale, a two-step solution is carried out, which is to first solve the cell mode layout, and then optimize the internal structure of the cell mode, so that the load path of the structure is clearer, and finally, under the condition of small impact on the volume of the optimized structure, the calculation efficiency is greatly improved, thereby realizing the 3D printing optimization design and integrated assembly manufacturing of the complex discrete truss optimization structure. Through practical verification, the method of the present invention is effective.

Claims

1. An iterative cell-based structural layout optimization design and manufacturing method, comprising: S1, Establish a mathematical model for truss layout optimization: First, determine the structural design domain, input the dimensions, loading conditions and boundary constraints, specify the cell mode and the complexity of the corresponding cell mode, use lattice discretization to process the design domain, connect any two nodes to establish the minimum connection basic structure, take the mechanical equilibrium equation as the constraint, take the minimization of the total volume of the rod members as the design objective, and establish a linear optimization model for truss layout optimization; S2. Direct solution based on repeated cells: set a finite number of cell modes, perform cell division, ensure that all rod members belong to a cell mode and there are no rod members that span across cell modes, and ensure that the cell layouts of the same cell modes and the areas of the rod members at corresponding positions are completely the same; for each rod member of the truss structure, use a binary variable to activate the cell mode, add repeated cell constraints to form nonlinear constraints, and convert the nonlinear programming problem into a linear programming problem, so that the repeated cells can be directly optimized and solved; S3, Two-step solution to first determine the cell layout: First, reduce the complexity of each cell mode, perform the first solution according to step S2, and activate the cell mode variable t ｃ Then, according to the normal complexity of each cell mode, t ｃ In step S2, the nonlinear constraint equation of the repetition cell of each rod member is substituted to convert it into a linear constraint, and a second solution is performed to obtain an optimization result. S4. 3D printing manufacturing and integrated assembly: A structural layout optimization design and manufacturing method based on repeating cells, comprising the steps of: performing 3D modeling, slicing multiple types of repeating cells of the optimization result model to generate printing paths, performing 3D printing manufacturing, and performing integrated assembly between the repeating cells to manufacture an optimized structure.

2. In step S1, the objective function corresponding to the design goal of minimizing the total volume of the rod members is given by: (1) The constraint formula is: (2) In the formula, l is the length vector of the rod member, a is the area vector of the rod member, B is the balance matrix, q is the internal force vector of the rod member, f is the nodal load vector, and σ ｃ and σ ｔ are the compressive strength vector and the tensile strength vector of the rod member, respectively, The three constraints in equation (2) respectively represent the force balance equation, the stress constraint of the rod member, and the non-negative constraint of the area of ​​the rod member. The design variables are the area vector a of the rod member and the internal force vector q of the rod member, B and l are respectively a constant matrix and a constant vector generated based on the topology method of the rod member, and f, σ ｃ and σ ｔ 2. The method of claim 1, wherein: is a constant determined by actual working conditions.

3. The structural layout optimization design and manufacturing method based on the iterative cell according to claim 2, characterized in that in step S1, if the balance matrix B of the minimum-connected basic structure when optimizing the initial state cannot be solved, the member length threshold and grid density in the minimum-connected basic structure are increased to form the minimum-connected basic structure when optimizing the updated initial state, and the solution is re-solved.

4. In step S2, set a binary variable to activate a cell mode for each rod member, and add a repetitive cell constraint to each rod member of the truss structure, i.e., first fill the design domain with cell modes, connect the nodes inside each cell mode to rod members two by two, and configure the repetitive cells. In order to ensure that the areas of rod members at the same position of the same type of cell mode are the same, when there are n types of cell modes in the structure, add the following constraint to each rod member: （３） （４） In the formula, a ｉ is the cross-sectional area of ​​the rod member, c is the number of the cell mode to which the rod member belongs, m is the position number of the rod member in the cell mode, and t ｃ１ , t ｃ２ , …, t ｃｎ is a binary variable of the cell mode activated by the cell mode to which the rod member belongs, the value being 1 or 0, where 1 indicates that the cell mode is activated and 0 indicates that the cell mode is deactivated; a ｍ１ , a ｍ２ , ..., a ｍｎ is the possible cross-sectional area corresponding to the position of the rod member in the cell mode, and in equation (4), a ｍ１ , a ｍ２ , ..., a ｍｎ and t ｃ１ , t ｃ２ , …, t ｃｎ 2. The method of claim 1, wherein all of the variables are variables, and two variables are multiplied to form a nonlinear constraint.

5. In step S2, the nonlinear constraints in equation (4) are converted into linear constraints using the large M method to obtain equation (5), （５） where M is a constant, and each row of equation (5) represents a constraint on the rod member at that position of one cell mode, and a ｉ When the cell mode to which t belongs activates the first cell mode, ｃ１ = 1, and the remainder is t ｃｘ = 0, and in this case, the first line of the constraint equation (5) is a ｉ = a ｍ１ The other inequalities are relaxed and do not actually work, so a ｉ When the cell mode to which t belongs activates the second cell mode, i.e., t ｃ１ = 1, and the remainder is t ｃｘ = 0, and in this case, the second line of the constraint (5) is a ｉ = a ｍ２ The structural layout optimization design and manufacturing method based on repetitive cells as claimed in claim 4, characterized in that, when a cell mode to which a rod member belongs activates a cell mode, the constraints of the corresponding row of the rod member are activated and the inequality constraints of other rows are relaxed.

6. Step S3, specifically, first reduces the complexity of the cell mode, i.e., reduces the number of nodes based on the normal cell mode structure, obtains a simplified cell mode structure, and performs a first solving process using the method of step S2, and reduces the cell mode variable t activated by each cell mode. ｃ This corresponds to obtaining the layout of the cell mode that each rod member takes in the design domain, and then setting the complexity of the cell mode normally, regenerating the structure, and recalculating the t obtained in the first solution. ｃ The method for optimizing the structure layout and manufacturing process based on the iterative cell according to claim 4, characterized in that the optimization problem is converted into a linear program by substituting the above formula (4) into the formula (4), and the second solving is directly performed.

7. The structural layout optimization design and manufacturing method based on repeating cells as described in claim 1, characterized in that step S4 specifically comprises extracting structural information of the repeating cells based on the optimization result, the structural information including the mode of the repeating cells, the position of the repeating cells, the connection of the repeating cells, and the cross-sectional dimensions of the rod members of the repeating cells; after the rod member assembly and node generation process of the repeating cells, establishing a 3D solid model, then slicing multiple types of repeating cells of the solid model respectively to generate printing paths, performing 3D printing manufacturing, and then connecting the repeating cells and performing integrated assembly to manufacture the optimized structure.

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