Layout Optimization Design and Manufacturing Method of Discrete Truss Structure Based on Repeating 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 particularly relates to a layout optimization design and manufacturing method for a discrete truss structure based on repetitive cells.

Background Art

[0002] Due to the increasingly complex engineering needs, the demand for the optimization design of complex truss structures and 3D printing integrated assembly is increasing. The topology optimization targets of structures include discrete structures and continuum structures. The optimization of truss-like structures widely used in actual engineering belongs to the category of topology optimization of discrete structures.

[0003] The layout optimization of a truss structure is a linear programming problem. Although the solution of the conventional truss layout optimization algorithm can reach the numerically optimal one, in actual manufacturing, due to the complexity of the structure, it is likely to occur that it is 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 the classification of rod members and the limitation of the structural complexity to make the final result as easy to manufacture as possible, but the optimization solution becomes more complex. The introduction of repetitive cells is a reasonable and efficient solution for simplifying the layout optimization problem.

[0004] In the optimization process of a continuum, an optimization method introducing the concept of repetitive cells is provided, mainly including the Homogenization Method and the small-scale integration optimization method. The homogenization method equates microscopic cells to a macroscopically uniform medium and can perform finite element analysis with the whole structure macroscopically coarsened. However, without introducing additional constraints, the homogenization method cannot control the connectivity between cells. In the small-scale integration optimization method, as the cost of integrating and optimizing the whole structure on a small scale, the calculation cost becomes high. Cells in construction projects are generally discrete structures, and since the size is limited for the design area, the above repetitive cell algorithms for continuum optimization cannot be directly used to solve the layout optimization problem of truss structures.

[0005] To summarize, it is very necessary to study the layout optimization design and manufacturing method of a discrete truss structure based on repetitive cells and to realize the layout optimization, 3D printing manufacturing, and integrated assembly of the repetitive cells of a complex truss structure.

Summary of the Invention

Problems to be Solved by the Invention

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

Means for Solving the Problems

[0007] Such a layout optimization design and manufacturing method for a structure based on repetitive cells is as follows: S1. Establishment of a mathematical model for truss layout optimization: First, determine the structural design area, input dimensions, load working conditions, and boundary constraints, specify the cell mode and the complexity of the corresponding cell mode, process the design area using lattice discretization, connect any two nodes to establish a minimum connection basic structure, use the mechanical equilibrium equation as a constraint condition, and minimize the total volume of rod members as the design goal to establish a linear optimization model for truss layout optimization. S2. Direct solution based on repetitive 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 spanning cell modes, and ensure that the cell layout of the same type of cell mode and the area of the rod members at the corresponding positions are exactly the same. For each rod member of the truss structure, use a binary variable to activate the cell mode, add repetitive cell constraints to form non-linear constraints, convert the non-linear programming problem into a linear programming problem, and directly optimize and solve the repetitive cells. S3. Two-stage solution for first determining the cell layout: First, reduce the complexity of each cell mode, perform the first solution according to step S2, and obtain the cell mode variable t activated corresponding to each cell mode.c Obtain \(t\), and then substitute \(t\) into the non - linear constraint equations of the repeating cells of each rod member in step S2 to convert them into linear constraints, perform the second solution, and obtain the optimization result. c S4, 3D printing manufacturing and integrated assembly: It includes steps of performing 3D modeling, slicing multiple types of repeating cells of the optimization result model respectively to generate a printing path, performing 3D printing manufacturing, and performing integrated assembly between the repeating cells to manufacture the optimized structure.

[0008] Preferably, in step S1, the objective function corresponding to taking the minimization of the total volume of the rod member as the design goal is JPEG0007715363000001.jpg1951(1), The expression of the constraint condition is JPEG0007715363000002.jpg4599(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, \(\sigma\) c and \(\sigma\) t are respectively the compression strength vector and the tensile strength vector of the rod member. The three constraint conditions of formula (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 respectively the constant matrix and the constant vector generated based on the topology method of the rod member. \(f\), \(\sigma\) c and \(\sigma\) t are constants determined by the actual working conditions.

[0009] Preferably, in step S1, when the balance matrix \(B\) of the minimum connection basic structure cannot be solved during the optimization of the initial state, increase the length threshold and grid density of the members in the minimum connection basic structure, form the minimum connection basic structure when optimizing the updated initial state, and perform re - solution. ​

[0010] Preferably, in step S2, a binary variable for activating the cell mode is set for each rod member, and cell constraints are repeatedly added to each rod member of the truss structure. That is, first, the design area is filled with the cell mode, and then the nodes inside each cell mode are connected to two rod members each to repeatedly form a cell structure. To ensure that the areas of the rod members at the same position in the same type of cell mode are the same, when there are n types of cell modes in the structure, the following constraints are added to each rod member: JPEG0007715363000003.jpg14 (3) JPEG0007715363000004.jpg13 (4) where 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, t c1 t c2 … t cn are the binary variables of the cell modes activated by the cell mode to which the rod member belongs, and the values are 1 or 0. 1 indicates activating the cell mode, and 0 indicates deactivating the cell mode. a m1 a m2 … a mn are the possible cross-sectional areas corresponding to the positions of the rod member in the cell mode. In Equation (4), a m1 a m2 … a mn and t c1 t c2 … t cn are all variables, and multiplying two variables forms a non-linear constraint.

[0011] Preferably, in step S2, the large M method is used to convert the non-linear constraint in Equation (4) into a linear constraint to obtain Equation (5). JPEG0007715363000005.jpg32 (5) where M is a constant, and each row of Equation (5) represents the constraint for the rod member at that position of one type of cell mode. a iWhen the cell mode to which it belongs activates the first type of cell mode, t c1 = 1, and the rest is t cx = 0. At this time, the first line equation of the constraint formula (5) becomes a i = a m1 and the other inequalities are relaxed and do not actually act. When the cell mode to which a i belongs activates the second type of cell mode, that is, t c2 = 1, and the rest is t cx = 0. At this time, the second line equation of the constraint formula (5) becomes a i = a m2 and the other inequalities are relaxed and do not act. Similarly, when the cell mode to which the rod member belongs activates a certain cell mode, the corresponding row constraint of the rod member becomes effective, and the constraints of the inequalities in other rows are relaxed.

[0012] Preferably, step S3 specifically first reduces the complexity of the cell mode, that is, reduces the number of nodes based on the normal cell mode structure to obtain a simplified cell mode structure, performs the first solution using the method of step S2, and obtains the cell mode variable t c activated by each cell mode, which corresponds to obtaining the layout of the cell mode taken by each rod member in the design area. Next, the complexity of the cell mode is set to normal, the structure is regenerated, and the t c obtained in the first solution is substituted into formula (4), the optimization problem is converted into a linear program, and the second solution is directly performed.

[0013] Preferably, step S4 specifically extracts the structural information of the repeating cell based on the optimization result. 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 members of the repeating cell. After the rod member assembly and node generation processing of the repeating cell, a 3D solid model is established. Next, a plurality of types of repeating cells of the solid model are sliced respectively to generate a printing path, and 3D printing manufacturing is performed. Next, the repeating cells are connected and integrated assembly is performed to manufacture the optimized structure.

Advantages of the Invention

[0014] The beneficial effects of the present invention are as follows. 1) 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, provides a direct solution method based on the repetitive cell, enables the optimization result of the truss layout to have the characteristics of the repetitive cell, and makes manufacturing relatively easy. This direct solution method based on the repetitive cell can not only be used independently directly, but also provide a mathematical model for the two-stage solution that first determines the cell layout. 2) The layout optimization design and manufacturing method of the discrete truss structure based on the repetitive cell provided by the present invention provides a two-stage solution of first solving the cell mode layout and then optimizing the internal structure of the cell mode for the problem that the calculation time is too long when solving the problem of large scale based on the direct solution based on the repetitive cell. The load path of the structure becomes clearer, and the calculation efficiency is greatly improved under the condition that the influence 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 repetitive cell provided by the present invention sets a finite number of cell modes based on the mathematical model for truss layout optimization and adds repetitive cell constraints to realize the cell repeatability and structural regularity of the layout optimization result. It realizes a fast and efficient solution based on the repetitive cell layout optimization compared with the two-stage solution of first simplifying the complexity of the cell and then normalizing the complexity of the cell. Through 3D modeling, repetitive cell model slicing, printing path generation and integrated assembly production, the 3D printing optimization design and integrated assembly manufacturing of complex discrete truss optimized structures are realized.

Brief Description of the Drawings

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Embodiments for Carrying Out the Invention

[0016] Hereinafter, the present invention will be further described with reference to embodiments. The following description of the embodiments is only for helping to understand the present invention. Those skilled in the art can make several 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] Embodiment 1 As an embodiment, as shown in FIG. 1, it is a layout optimization design and manufacturing method of a discrete truss structure based on repetitive cells. The additive manufacturing technology, which is a 3D printing technology, realizes the generation of a structure by the accumulation of each layer of materials, greatly expands the flexibility of structure manufacturing, and can obtain good optimization results through the optimization of the structure layout based on repetitive cells, including the arrangement and combination of repetitive cells. Furthermore, 3D printing and integrated assembly are performed on a small number of complex repetitive cells, and the integrated manufacturing of the optimized complex truss structure is realized. Specifically, it includes steps S1 to S4. S1. Establishment of a mathematical model for truss layout optimization: First, determine the structural design area, input the constraint conditions and parameters, establish the minimum connection basic structure, use the mechanical equilibrium equation as the constraint condition, and minimize the total volume of rod members as the design goal to establish a linear optimization model. Specifically, it includes steps S1.1 to S1.3. S1.1. Input of design conditions and parameters: Input the dimensions of the design area, load working conditions, and boundary constraints, and specify the cell mode and the complexity of the corresponding cells. S1.2. Establishment of the minimum connection basic structure: Process the design area using uniform grid discretization, and connect any two nodes to form the minimum connection basic structure. S1.3. Establishment of a mathematical model for layout optimization: The underlying layer of the optimization algorithm is a mathematical optimization problem. Taking the mechanical equilibrium equation as a constraint condition and minimizing the total volume of the rod members as the design goal, a linear optimization model for truss layout optimization is established. The objective function is JPEG0007715363000006.jpg2051(1), The formula for the constraint condition is JPEG0007715363000007.jpg4299(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, σ c and σ t are respectively the compression strength vector and the tensile strength vector of the rod member. The objective function formula (1) represents the optimization goal of minimizing the volume, and the constraint condition formula (2) represents the force equilibrium equation, the stress constraint of the rod member, and the non-negativity constraint of the rod member area. This problem is a linear programming problem. 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. f, q c and q t are constants determined by the actual working conditions.

[0018] After the design area is determined, for truss layout optimization, based on formulas (1) and (2), the structure is determined in a certain way, the necessary constants are calculated, and to ensure that the result obtained by optimization can reach the theoretically optimal one, the simplest way to determine the structure is to connect all the nodes in the design area in pairs, include all possible rod members in the structure, and establish a minimum connection basic structure. The structure obtained by general truss layout optimization saves materials and has a reasonable load, but its structure is often too complex to be manufactured.

[0019] When the balance matrix B of the minimum connection basic structure cannot be solved when optimizing the initial state, increase the length threshold of the members and the grid density in the minimum connection basic structure, form the minimum connection basic structure when optimizing the updated initial state, and perform re-solving.

[0020] S2. Direct solution based on repetitive cells: Set a finite number of cell modes, perform cell division according to the cell modes, ensure that all rod members belong to a certain cell mode and there are no rod members spanning cell modes, add repetitive 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 of a finite number of cell modes: Set a finite number of cell modes, ensure that all rod members belong to a certain cell mode, there are no rod members spanning cell modes, and make the layout of the same type of cell mode and the area of the rod members at the corresponding positions exactly the same. There are two characteristics in the truss layout optimization based on repetitive cells. The first is that all rod members belong to a certain cell mode and there are no rod members spanning cell modes. The second is that all cells follow a finite number of cell modes, and the layout of the same type of cell mode and the area of the rod members at the corresponding positions are exactly the same. To realize the repetitive cell structure, first fill the design area with cells, then connect the nodes inside each cell to two rod members each. The number of rod members included in the repetitive cell structure is significantly reduced compared to the truss optimization in step S1. S2.2. Addition of repetitive cell constraints: Each rod member uses a binary variable to activate the cell mode, and add repetitive cell constraints to each rod member of the truss structure. To ensure that the areas of the rod members at the same position of the same type of cell mode are the same, taking the case where there are n types of cell modes in the structure as an example, add the following constraints to each rod member. JPEG0007715363000008.jpg1798(3) JPEG0007715363000009.jpg15164(4) In the formula, ai is the cross-sectional area of the rod member, c is the cell mode number to which the rod member belongs, m is the position number in the cell mode of the rod member, t c1 , t c2 , …, t cn are binary variables of the cell modes activated by the cell mode to which the rod member belongs, the values are 1 or 0, 1 indicates activating the cell mode, 0 indicates deactivating the cell mode, a m1 , a m2 , …, a mn are the possible cross-sectional areas corresponding to the positions in the cell mode of the rod member. In Equation (4), a m1 , a m2 , …, a mn and t c1 , t c2 , …, t cn are all variables. Multiplying two variables forms a non-linear constraint, making it difficult to solve directly. Therefore, it is necessary to convert it into a linear problem so that it can be solved directly. S2.3, direct solution based on iterative cells: Use the big M method to convert non-linear constraints into linear constraints, that is, replace Equation (4) with Equation (5), JPEG0007715363000010.jpg33164(5) where M is a determined large constant. Each row of Equation (5) represents the constraint on the rod member at that position for one type of cell mode. When the cell mode to which a i belongs activates the first type of cell mode, t c1 = 1, and the rest are t cx = 0. At this time, the formula for the first row of the constraint Equation (5) becomes a i = a m1 , and the other inequalities are relaxed and do not actually act. When the cell mode to which a i belongs activates the second type of cell mode, that is, t c2 = 1, and the rest are t cx = 0. At this time, the formula for the second row of the constraint Equation (5) becomes a i = a m2It becomes such that other inequalities are relaxed and do not act. Similarly hereinafter, when activating a cell mode having a cell mode to which the rod member belongs, only the constraints of the corresponding row of the rod member become effective, and the constraints of the inequalities of other rows are relaxed. The same effect as Equation (4) can be achieved by Equation (5), and Equation (5) is still a linear constraint, without changing the linear programming characteristics of the optimization problem and being easy to solve. The truss layout optimization based on the repetitive cell is a linear programming problem with Equation (1) as the objective function and Equations (2), (3) and (5) as the constraints.

[0021] The truss layout optimization based on the repetitive cell is a mixed integer programming problem including general continuous variables and binary integer variables existing due to the introduction of t c This type of problem is directly solved by the gurobi commercial solver which is more proficient in this kind of problem, and the solver has an interface for Python for easily calling the program.

[0022] S3. Two-stage solution for first determining the cell layout: First, set the complexity of the low-level cell mode, perform the first solution using Step S2, obtain the activated cell mode variable t c Substitute it into Equation (4), discard the constraints of Equation (5), convert it into a linear constraint, and perform the second solution, specifically including Steps S3.1 to S3.2. S3.1. First solution for the complexity of the simplified cell: Due to the solution characteristics of the mixed-integer program, as the design area increases, the number of cell modes increases, or the complexity of the cell modes increases, there may be a problem that the calculation time is too long during the calculation in the method of step S2. In the mixed-integer program, both the number of integer variables and the number of continuous variables affect the solution time. Here, 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 specific problems 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 repeating cells and the complexity of the cell modes. The only variable that can be improved in the calculation process is the complexity of the cell modes. Therefore, first, set the complexity of the cell modes to a low level, perform the first solution using the method of step S2, which is a mixed-integer linear programming problem, and obtain the cell mode variable t c activated by each cell mode. As shown in FIGS. 2a to 2c, the general complexities are 2×2 cells, 3×3 cells, and 4×4 cells respectively, and the complexity n x ×n y of the cell mode represents the number of nodes included in the horizontal and vertical directions within the cell mode. The higher the complexity of the cell mode, the higher the degree of freedom of the structure, and theoretically, a better objective function value can be obtained. Correspondingly, the number of rod members included in the structure increases, and the solution time becomes longer. First, set the complexity of the cell modes to a low level, perform the first solution using the method of step S2, and obtain the cell mode variable t c activated by each cell mode, which is equivalent to obtaining the layout of the cell mode taken by each cell mode in the design area. S3.2. Second solution for the complexity of the normal cell: Next, set the complexity of the cell modes to the normal cell mode, regenerate the structure, substitute the t c obtained in the first solution into Equation (4), and discard the constraints of Equation (5). At this time, t cSince it is a constant vector that has already been determined, Equation (4) does not change the characteristics of the linear programming of the optimization problem. 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 occupied in the entire solution process can be almost ignored.

[0023] The time required for the mixed integer program is a decisive factor in the overall optimization time. When the first solution of the improved algorithm in step S3 is performed, the complexity of the cell mode is low and the number of continuous variables is small. Therefore, 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 specific cell modes. Therefore, it cannot be guaranteed that the results of the improved algorithm in step S3 are exactly the same as the algorithm described in step S2. Generally, rod members with similar load levels under load action use the same type of cell mode, but the number of cell modes and the complexity of the cell modes during the first solution may affect the results of the cell mode layout.

[0024] Increasing the number of cell modes is beneficial for obtaining an excellent structure rather than improving the complexity of normal cell modes. However, when conditions permit, the complexity of the simplified cell modes during two-stage solution should not be too low, otherwise, the cell mode layout method may deviate from the optimum.

[0025] S4, 3D printing manufacturing and integrated assembly: Perform 3D modeling, slice multiple types of repeating cells of the solid model respectively to generate a printing path, perform 3D printing manufacturing, perform integrated assembly between the repeating cells, and manufacture the optimized structure. Specifically, it includes steps S4.1~S4.2. S4.1, 3D printing manufacturing of repetitive cells: Perform 3D modeling using Rhino software, slice multiple types of repetitive cells of the solid model obtained from 3D modeling using Cura software to generate a printing path, extract the structural information of the repetitive cells according to the optimization result, where the structural information includes the mode of the repetitive cell, the position of the repetitive cell, the connection of the repetitive cell, and the cross-sectional dimensions of the rod member of the repetitive cell. After the rod member assembly and node generation process of the repetitive cell, establish a 3D solid model, then slice multiple types of repetitive cells of the solid model respectively to generate a printing path, and perform 3D printing manufacturing. S4.2, integrated assembly of repetitive cells: The repetitive cells are connected by welding, bolting, etc. to perform integrated assembly and manufacture an optimized structure.

[0026] Example 2 As another example, this example shows that, based on the general layout optimization in step S1 and the direct solution based on repetitive cells in step S2 of Example 1, an optimized design and manufacture are performed for the cantilever beam problem.

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

[0028] In this embodiment, the structure obtained by the general layout optimization in step S1 saves materials and has a reasonable load, but its structure is often too complex to be manufactured. The schematic diagram of the optimization result is shown in FIG. 4. Among them, the light-colored rod members represent tension, the dark-colored rods represent compression, the thickness of the rod members represents the size of the cross-sectional area, and if the area of the rod member is less than the threshold value, it is not displayed. The threshold value is set to 1 / 1000 of the area of the largest rod member in the structure.

[0029] Based on this, in this embodiment, step S2 is continuously implemented. Based on the direct solution of the repeating cell, the complexity of the cell is set to 4×4, the number of repeating cell modes is set to 4, the schematic diagram of the direct optimization result is shown in FIG. 5a, and the schematic diagrams of the four types of repeating cell structures are shown in FIG. 5b. The volume of the structure obtained by direct solution is 32, the solution time is 20498 s, and the optimized structure force transmission path is similar to the general layout optimization, but there is no rod member spanning cell modes, so the difference in the length of the rod members is not large, the number of rod members connected to the nodes is limited, there is no overly complex node, and compared with the general layout optimization result obtained in step S1, the manufacturing difficulty of the structure is significantly reduced in step S2.

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

[0031] Embodiment 3 As another embodiment, according to the layout optimization design and manufacturing method of the discrete truss structure based on the repeating cell provided in Embodiment 1, for the same simply supported beam problem in Embodiment 2, the two-stage solution in step S3 is further performed by the direct solution method based on the repeating cell in step S$.

[0032] Set the complexity of the normal cell mode to 4×4, set the number of repeated cell modes to 4, and when performing the two-stage solution in step S3, set the complexity of the simplified cells 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. 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. JPEG0007715363000011.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, the solution time is 20498 s. 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 shortened to 25 s, which is about 1 / 800 of the direct solution, and the calculation efficiency was greatly improved.

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

[0036] In this embodiment, when the complexity of the simplified cell mode is 2×2 and 3×3, there are significant differences in the structure layout and form. The improvement of 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 is closer to the result directly solved. Therefore, when conditions permit, ensuring the complexity of the simplified cell mode is beneficial for obtaining a means closer to the optimal layout.

[0037] When the complexity of the simplified cell mode is 3×3: When the complexity of the normal cell mode is 6×6 or 8×8, the second solution results obtained by the two-step solution in step S3 are shown in FIGS. 8a and 8b respectively. Compared with the case where the complexity of the normal cell mode is 4×4, the overall layout of the structure is similar, but the details inside 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 4×4, there is only a difference of about 1.5%, but the calculation time has increased rapidly.

[0038] This embodiment shows the citation of some steps of the present invention in the layout optimization of the truss structure. It shows that the two-step solution in step S3 is performed by the solution equation based on the repeated cell established in step S2, and it shows that good effects 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 influence on the volume of the finally optimized structure is small, and it can be used to solve the problem that the calculation time is 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 area, set a finite number of cell modes, perform cell division, and finally the overall structure is composed of multiple repeating cells with complex configurations. In this way, a small number of cell modes can be mass-produced using 3D printing methods and simple integrated assembly can be carried out. However, there is currently little research on the optimization of the repeating cell structure of trusses, and layout optimization is not included. Many of the current repeating cell structures use the same type of cell mode within the same sub-design area, 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. However, there is no such limitation for truss structures, and the cell mode and its position selected by each rod member are not necessarily related. Therefore, the layout of the final structure becomes more flexible. Therefore, the improved application of a reasonable and effective repeating cell algorithm is an important factor in the layout optimization of truss structures.

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

[0041] As shown in FIG. 9, the design area of the frame-support structure under the horizontal wind load has a width of 4, a height of 12, a cell height of 2, and a width of 1. The design area has a total of 6×3 = 18 cells. Horizontal rightward unit loads act on both sides of the locations with heights of 4, 8, and 12. The degrees of freedom in the horizontal and vertical directions are restricted 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 repeating cell modes is set to 1 and 4 respectively.

[0042] In this example, when the number of repeating cell modes is 1 and 4 respectively, the schematic diagrams of the optimization results of the two-step solution in step S3 are shown in FIG. 10, and the specific optimization results are as follows. JPEG0007715363000012.jpg74164

[0043] Two - stage solution in step S3: The number of repetitive cell modes is 1, that is, all cell modes have the same cell structure, and the volumes of the structures solved for the first and second times are 1082.47. The number of repetitive cell modes is 4, that is, there are four different cell structures, and the volumes of the structures solved for the first and second times are 300.43 and 295.33 respectively, and the solution time is 1852 s.

[0044] As can be seen from the above, after increasing the number of repetitive cell modes, the structural volume becomes smaller, only about 30% of the case where the number of repetitive cell modes is 1, and the optimization effect is remarkable. This indicates that when the load is large, by appropriately increasing the number of repetitive cell modes, the advantage of material saving can be more exerted.

[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 introduce additional constraints and variables on the characteristics of the repetitive cell. The direct solution based on the provided repetitive cell enables the optimization result of the truss layout to have the characteristics of the repetitive cell, making the manufacturing relatively easy. To solve the problem that the calculation time is too long when solving the problem of large scale, a two - stage solution is carried out, first solving the cell mode layout and then optimizing the internal structure of the cell mode. The load path of the structure becomes clearer, and under the condition that the influence on the volume of the finally optimized structure is small, the calculation efficiency is greatly improved, thereby realizing the 3D printing optimization design and integrated assembly manufacturing of complex discrete truss optimization structures. Practical verification shows that the method of the present invention is effective.

Claims

1. A method for optimizing the design and manufacturing of a structural layout based on repetitive cells, comprising: S1. Establishing a mathematical model for truss layout optimization: First, determine the structural design area, input dimensions, load working conditions, and boundary constraints, specify the cell mode and the complexity of the corresponding cell mode, process the design area using grid discretization, connect any two nodes to establish a minimum connection basic structure, use the mechanical equilibrium equation as a constraint condition, and minimize the total volume of rod members as the design goal to establish a linear optimization model for truss layout optimization; S2. Direct solution based on repetitive 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 spanning cell modes, and the cell layouts of the same type of cell mode and the areas of the rod members at the corresponding positions are exactly the same. For each rod member of the truss structure, use a binary variable to activate the cell mode, add repetitive cell constraints to form a non-linear constraint, convert the non-linear programming problem into a linear programming problem, and directly optimize and solve the repetitive cells; S3. Two-stage solution for initially determining the cell layout: First, reduce the complexity of each cell mode, perform the first solution according to step S2, and obtain the cell mode variable t ｃ activated corresponding to each cell mode. Next, according to the normal complexity of each cell mode, substitute t ｃ into the non-linear constraint equation of the repeated cells of each rod member in step S2 to convert it into a linear constraint, perform the second solution, and obtain the optimization result. S4. 3D printing manufacturing and integrated assembly: Perform 3D modeling, slice multiple types of repetitive cells of the optimization result model respectively to generate a printing path, perform 3D printing manufacturing, and perform integrated assembly between the repetitive cells to manufacture the optimized structure. A method for optimizing the design and manufacturing of a structural layout based on repetitive cells, characterized by including the above steps.

2. In step S1, the objective function corresponding to minimizing the total volume of rod members as the design goal is: (1), The formula for the constraint condition is: (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 \(\sigma\) ｃ and \(\sigma\) ｔ are the compressive strength vector and the tensile strength vector of the rod member, respectively, The three constraint conditions of Equation (2) respectively represent the force equilibrium 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 the constant vector generated based on the topology method of the rod member respectively, and f, σ ｃ and σ ｔ are constants determined by the actual working conditions. A structure layout optimization design and manufacturing method based on the repeated cell according to claim 1, characterized in that.

3. In step S1, when the balance matrix B of the minimum connection basic structure cannot be solved during the optimization of the initial state, increase the length threshold and grid density of the members in the minimum connection basic structure, form the minimum connection basic structure when optimizing the updated initial state, and re-solve. The method for optimizing the design and manufacturing of a structural layout based on repetitive cells according to claim 2, characterized by the above.

4. In step S2, a binary variable for activating the cell mode is set for each rod member, and cell constraints are repeatedly added to each rod member of the truss structure. That is, first, the design area is filled with the cell mode, two nodes inside each cell mode are connected to the rod member, and repeated cells are constructed. 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 constraints are added to each rod member. （３） （４） where a ｉ is the cross-sectional area of the rod member, c is the cell mode number to which the rod member belongs, m is the position number in the cell mode of the rod member, t ｃ１ , t ｃ２ , …, t ｃｎ are binary variables of the cell modes activated by the cell mode to which the rod member belongs, the values are 1 or 0, 1 indicates activating the cell mode, 0 indicates deactivating the cell mode, a ｍ１ , a ｍ２ , …, a ｍｎ are the possible cross-sectional areas corresponding to the positions in the cell mode of the rod member. In Equation (4), a ｍ１ , a ｍ２ , …, a ｍｎ and t ｃ１ , t ｃ２ , …, t ｃｎ are all variables, and the method for optimizing the design and manufacturing of a structure layout based on a repetitive cell according to claim 1, characterized in that two variables are multiplied to form a non-linear constraint.

5. In step S2, using the big M method, the non-linear constraint of Equation (4) is converted into a linear constraint to obtain Equation (5). （５） where M is a constant, each row of Equation (5) represents the constraint on the rod member at that position for one type of cell mode, and a ｉ When the cell mode to which it belongs activates the first type of cell mode, t ｃ１ = 1, and the rest is t ｃｘ = 0. At this time, the equation of the first row of the constraint equation (5) becomes a ｉ = a ｍ１ and the other inequalities are relaxed and do not actually act. When the cell mode to which a ｉ belongs activates the second type of cell mode, that is, t ｃ１ = 1, and the rest is t ｃｘ = 0. At this time, the equation of the second row of the constraint equation (5) becomes a ｉ = a ｍ２ and the other inequalities are relaxed and do not act. Similarly, when the cell mode to which the rod member belongs activates a certain cell mode, the constraint of the corresponding row of the rod member becomes effective, and the constraints of the inequalities of the other rows are relaxed. The structural layout optimization design and manufacturing method based on the repetitive cell according to claim 4, characterized in that.

6. Specifically, in step S3, first, the complexity of the cell mode is reduced, that is, the number of nodes is decreased based on the normal cell mode structure to obtain a simplified cell mode structure, and the first solution is performed using the method of step S2 to obtain the cell mode variable t activated by each cell mode ｃ which corresponds to obtaining the layout of the cell mode taken by each rod member in the design area. Next, the complexity of the cell mode is set to normal, the structure is regenerated, and t obtained in the first solution ｃ is substituted into formula (4), the optimization problem is converted into a linear programming problem, and the second solution is directly performed. The structure layout optimization design and manufacturing method based on the repeated cell according to claim 4, characterized in that

7. Step S4 specifically extracts the structural information of the repeated cells based on the optimization result. The structural information includes the mode of the repeated cells, the position of the repeated cells, the connection of the repeated cells, and the cross-sectional dimensions of the rod members of the repeated cells. After the rod member assembly and node generation process of the repeated cells, a 3D solid model is established. Next, multiple types of repeated cells of the solid model are sliced respectively to generate a printing path for 3D printing manufacturing. Then, the repeated cells are connected for integrated assembly to manufacture the optimized structure. The method for optimizing the design and manufacturing of the structure layout based on the repeated cells according to claim 1 is characterized by the above.

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